NAME¶

GETTING STARTED¶

First contact
The fundamental syntactic object is a form. A form is parsed and immediately executed by the interpreter. A form is generally constructed with a function name and a set of arguments. The process of executing a form is called the evaluation. The next example illustrates one of the simplest form which is supported by the engine. This form simply displays the message hello world.

Hello world
At the interpreter prompt, a form is constructed with the special object println. The unique argument is a string which is placed between double quotes.

(axi) println "Hello World"
Hello World

The interpreter can be invoked to enter one or several forms interactively. The form can also be placed in a text file and the interpreted called to execute it. The alsis the referred extension for a text file, but it can be anything. A simple session which executes the above file -- assuming the original file is called hello.als-- is shown below.

zsh> axi hello.als
Hello World

In interactive mode, the interpreter waits for a form. When a form is successfully constructed, it is then immediately executed by the engine. Upon completion, the interpreter prompt is displayed and the interpreter is ready to accept a new form. A session is terminated by typing ctrl-d. Another way to use the engine is to call the compiler client called axc, and then invoke the interpreter with the compiled file. The interpreter assumes the .axcextension for compiled file and will automatically figure out which file to execute when a file name is given without an extension.

zsh> axc hello.als
zsh> axi hello.axc
Hello World
zsh> axi hello
Hello World

The order of search is determined by a special system called the file resolver. Its behavior is described in a special chapter of this manual.

Interpreter command
The interpreter can be invoked with several options, a file to execute and some program arguments. The hoption prints the various interpreter options.

zsh> axi -h
usage: axi [options] [file] [arguments]
[h]           print this help message
[v]           print system version
[m]           enable the start module
[i   path]    add a resolver path
[e   mode]    force the encoding mode
[f assert]    enable assertion checks
[f nopath]    do not set initial path
[f noseed]    do not seed random engine
[f   seed]    seed random engine

The voption prints the interpreter version and operating system. The foption turns on or off some additional options like the assertion checking. The use of program arguments is illustrated later in this chapter. The ioption adds a path to the interpreter resolver. Several ioptions can be specified. The order of search is determined by the option order. As mentioned earlier, the use of the resolver combined with the librarianis described in a specific chapter. If the initial file name to execute contains a directory path, such path is added automatically to the interpreter resolver path unless the nopathoption is specified.

Interactive line editing
Line editing capabilities is provided when the interpreter is used interactively. Error messages are displayed in red if the terminal supports colors. Various accelerators are bound to the terminal as indicated in the table below.

The arrow are also bound to their usual functions. Note that when using the history, a multi-line command editing access is provided by the interpreter.

Command line arguments
The interpreter command line arguments are stored in a vector called argvwhich is part of the interpobject. A complete discussion about object and class is covered in the class object chapter. At this time, it is just necessary to note that a method is invoked by a name separated from the object symbol name with a semicolon. The example below illustrates the use of the vector argument.

# argv.als
# print the argument length and the first one
println "argument length: " (interp:argv:length)
println "first argument : " (interp:argv:get 0)
zsh> axi argv.als hello world
2
hello

Loading a source file
The interpreter object provides also the loadmethod to load a file. The argument must be a valid file path or an exception is raised. The loadmethod returns nil. When the file is loaded, the interpreter input, output and error streams are used. The load operation reads one form after another and executes them sequentially.

# load the source file demo.als
(axi) interp:load "demo.als"
# load the compiled file demo.axc
(axi) interp:load "demo.axc"
# load whatever is found
(axi) interp:load "demo"

The loadmethod operates with the help of the interpreter resolver. By default the source file extension is als. If the file has been compiled, the axcextension can be used instead. This force the interpreter to load the compiled version. If you are not sure, or do not care about which file is loaded, the extension can be omitted. Without extension, the compiled file is searched first. If it is not found the source file is searched and loaded.

The compiler
The client axcis the cross compiler. It generates a binary file that can be run across several platforms. The hoption prints the compiler options.

usage: axc [options] [files]
[h]            print this help message
[v]            print version information
[i] path       add a path to the resolver
[e  mode]      force the encoding mode

One or several files can be specified on the command line. The source file is searched with the help of the resolver. The resolver ioption can be used to add a path to the resolver.

Writing structure
The structure of file is a succession of valid syntactic objects separated by blank lines or comments. During the compilation or the execution process, each syntactic object is processed one after another in a single pass. Reserved keywords are an integral part of the writing systems. The association of symbols and literal constitutes a form. A form is the basic execution block in the writing system. When the form uses reserved keyword, it is customary to refer to it as a special form.

Character set and comments
The writing system operates with the standard Unicode character set. Comments starts with the character #. All characters are consumed until the end of line. Comments can be placed anywhere in the source file. Comments entered during an interactive session are discarded.

Native objects
The writing system operates mostly with objects. An object is created upon request or automatically by the engine when a native representation is required. To perform this task, several native objects, namely Booleanfor boolean objects, Integer, Relatiffor integer numbers, Realfor floating-point number, Byte, Characterand Stringfor character or string manipulation are built inside the engine. Most of the time, a native object is built implicitly from its lexical representation, but an explicit representation can also be used.

const boolean  true
const integer  1999
const relatif  1234567890R
const real     2000.0
const string   "afnix"
const char     'a'
trans symbol   "hello world"
trans symbol   2000

The constand transreserve keywords are used to declare a new symbol. A symbol is simply a binding between a name and an object. Almost any standard characters can be used to declare a symbol. The constreserved keyword creates a constant symboland returns the last evaluated object. As a consequence, nested constconstructs are possible like trans b (const a 1). The transreserved keyword declare a new transient symbol. When a symbol is marked transient, the object bound to the symbol can be changed while this is not possible with a constant symbol. Eventually, a symbol can be destroyed with the special form unref. It is worth to note that it is the symbol which is destroyed and not the object associated with it.

Stop and resume parsing
The parsing process is stopped in the presence of the ◀character (Unicode U+25C0). The parsing operation is resumed with the ▶character (Unicode U+25B6). Such mechanism is useful when dealing with multi line statements. This mechanism is also a good example of Unicode based control characters.

Forms
An implicit form is a single line command. When a command is becoming complex, the use of the standard form notation is more readable. The standard form uses the (and )characters to start and close a form. A form causes an evaluation. When a form is evaluated, each symbol in the form are evaluated to their corresponding internal object. Then the interpreter treats the first object of the form as the object to execute and the rest is the argument list for the calling object. The use of form inside a form is the standard way to perform recursive evaluation with complex expressions.

const three (+ 1 2)

This example defines a symbol which is initialized with the integer 3, that is the result of the computation (+ 1 2). The example shows also that a Polish notation is used for arithmetic. If fact, +is a built-in operator which causes the arguments to be summed (if possible). Evaluation can be nested as well as definition and assignation. When a form is evaluated, the result of the evaluation is made available to the calling form. If the result is obtained at the top level, the result is discarded.

const  b (trans a (+ 1 2))
assert a 3
assert b 3

This program illustrates the mechanic of the evaluation process. The evaluation is done recursively. The (+ 1 2)form is evaluated as 3 and the result transmitted to the form (trans a 3). This form not only creates the symbol aand binds to it the integer 3, but returns also 3 which is the result of the previous evaluation. Finally, the form (const b 3)is evaluated, that is, the symbol bis created and the result discarded. Internally, things are a little more complex, but the idea remains the same. This program illustrates also the usage of the assertkeyword.

Lambda expression
A lambda expressionis another name for a function. The term comes historically from Lisp to express the fact that a lambda expression is analog to the concept of expression found in the lambda calculus. There are various ways to create a lambda expression. A lambda expression is created with the transreserved keyword. A lambda expression takes 0 or more arguments and returns an object. A lambda expression is also an object by itself When a lambda expression is called, the arguments are evaluated from left to right. The function is then called and the object result is transmitted to the calling form. The use of transvs constis explain later. To illustrate the use of a lambda expression, the computation of an integer factorial is described in the next example.

# declare the factorial function
trans fact (n) (
  if (== n 1) 1 (* n (fact (- n 1))))
# compute factorial 5
println "factorial 5 = " (fact 5)

This example calls for several comments. First the transkeyword defines a new function object with one argument called n. The body of the function is defined with the ifspecial form and can be easily understood. The function is called in the next form when the printlnspecial form is executed. Note that here, the call to factproduces an integer object, which is converted automatically by the printlnkeyword.

Block form
The notation used in the factprogram is the standard form notation originating from Lisp and the Scheme dialect. There is also another notation called the block formnotation with the use of the {and }characters. A block form is a syntactic notation where each form in the block form is executed sequentially. The form can be either an implicit or a regular form. The factprocedure can be rewritten with the block notation as illustrated below.

# declare the factorial procedure
trans fact (n) {
  if (== n 1) 1 (* n (fact (- n 1)))
}
# compute factorial 5
println "factorial 5 = " (fact 5)

Another way to create a lambda expression is via the lambdaspecial form. Recall that a lambda expression is an object. So when such object is created, it can be bounded to a symbol. The factorial example could be rewritten with an explicit lambda call.

# declare the factorial procedure
const fact (lambda (n) (
    if (== n 1) 1 (* n (fact (- n 1)))))
# compute factorial 5
println "factorial 5 = " (fact 5)

Note that here, the symbol factis a constant symbol. The use of constis reserved for the creation of gamma expression.

Gamma expression
A lambda expression can somehow becomes very slow during the execution, since the symbol evaluation is done within a set of nested call to resolve the symbols. In other words, each recursive call to a function creates a new symbol set which is linked with its parent. When the recursion is becoming deep, so is the path to traverse from the lower set to the top one. There is also another mechanism called gamma expressionwhich binds only the function symbol set to the top level one. The rest remains the same. Using a gamma expression can speedup significantly the execution.

# declare the factorial procedure
const fact (n) (
  if (== n 1) 1 (* n (fact (- n 1))))
# compute factorial 5
println "factorial 5 = " (fact 5)

We will come back later to the concept of gamma expression. The use of the reserved keyword constto declare a gamma expression makes now sense. Since most function definitions are constant with one level, it was a design choice to implement this syntactic sugar. Note that gammais a reserved keyword and can be used to create a gamma expression object. On the other hand, note that the gamma expression mechanism does not work for instance method. We will illustrate this point later in this book.

Lambda generation
A lambda expression can be used to generate another lambda expression. In other word, a function can generate a function, an that capability is an essential ingredient of the functional programmingparadigm. The interesting part with lambda expression is the concept of closed variables. In the next example, looking at the lambda expression inside gen, notice that the argument to the gamma is xwhile nis marked in a form before the body of the gamma. This notation indicates that the gamma should retain the value of the argument nwhen the closure is created. In the literature, you might discover a similar mechanism referenced as a closure. A closure is simply a variable which is closed under a certain context. When a variable is reference in a context without any definition, such variable is called a free variable. We will see later more programs with closures. Note that it is the object created by the lambda or the gamma call which is called a closure.

# a gamma which creates a lambda
const gen (n) (
  lambda (x) (n) (+ x n))
# create a function which add 2 to its argument
const add-2 (gen 2)
# call add-2 with an argument and check
println "result = " (add-2 3)

In short, a lambda expression is a function with or without closed variables, which works with nested symbol sets also called namesets. A gamma expression is a function with or without closed variable which is bounded to the top level nameset. The reserved keyword transbinds a lambda expression. The reserved keyword constbinds a gamma expression. A gamma expression cannot be used as an instance method.

Multiple arguments binding
A lambda or gamma expression can be defined to work with extra arguments using the special argsbinding. During a lambda or gamma expression execution, the special symbol argsis defined with the extra arguments passed at the call. For example, a gamma expression with 0 formal argument and 2 actual arguments has argsdefined as a cons cell.

const proc-nilp (args) {
  trans result 0
  for (i) (args) (result:+= i)
  eval result
}
assert 3 (proc-nilp 1 2)
assert 7 (proc-nilp 1 2 4)

The symbol argscan also be defined with formal arguments. In that case, argsis defined as a cons cell with the remaining actual arguments.

# check with arguments
const proc-args (a b args) {
  trans result (+ a b)
  for (i) (args) (result:+= i)
  eval result
}
assert 3 (proc-args 1 2)
assert 7 (proc-args 1 2 4)

It is an error to specify formal arguments after args. Multiple argsformal definition are not allowed. The symbol argscan also be defined as a constant argument.

# check with arguments
const proc-args (a b (const args)) {
  trans result (+ a b)
  for (i) (args) (result:+= i)
  eval result
}
assert 7 (proc-args 1 2 4)

Nameset and bindings
A namesetis a container of bindings between a name and symbolic variable. We use the term symbolic variableto denote any binding between a name and an object. There are various ways to express such bindings. The most common one is called a symbol. Another type of binding is an argument. Despite the fact they are different, they share a set of common properties, like being settable. Another point to note is the nature of the nameset. As a matter of fact, there is various type of namesets. The top level nameset is called a global setand is designed to handle a large number of symbols. In a lambda or gamma expression, the nameset is called a local setand is designed to be fast with a small number of symbols. The moral of this little story is to think always in terms of namesets, no matter how it is implemented. All namesets support the concept of parent binding. When a nameset is created (typically during the execution of a lambda expression), this nameset is linked with its parent one. This means that a symbol look-up is done by traversing all nameset from the bottom to the top and stopping when one is found. In term of notation, the current namesetis referenced with the special symbol '.'. The parent namesetis referenced with the special symbol '..'. The top level namesetis referenced with the symbol '...'.

Symbol
A symbol is an object which defines a binding between a name and an object. When a symbol is evaluated, the evaluation process consists in returning the associated object. There are various ways to create or set a symbol, and the different reserved keywords account for the various nature of binding which has to be done depending on the current nameset state. One of the symbol property is to be constor not. When a symbol is marked as a constant, it cannot be modified. Note here that it is the symbol which is constant, not the object. A symbol can be created with the reserved keywords constor trans.

Creating a nameset
A nameset is an object which can be constructed directly by using the object construction notation. Once the object is created, it can be bounded to a symbol. Here is a nameset called examplein the top level nameset.

# create a new nameset called example
const example (nameset .)
# bind a symbol in this nameset
const example:hello "hello"
println example:hello

Qualified name
In the previous example, a symbol is referenced in a given nameset by using a qualified namesuch like example:hello. A qualified name defines a path to access a symbol. The use of a qualified name is a powerful notation to reference an object in reference to another object. For example, the qualified name .:hellorefers to the symbol helloin the current nameset. The qualified name ...:hellorefers to the symbol helloin the top level nameset. There are other use for qualified names, like method call with an instance.

Symbol binding
The transreserved keyword has been shown in all previous example. The reserved keyword transcreates or set a symbol in the current nameset. For example, the form trans a 1is evaluated as follow. First, a symbol named ais searched in the current nameset. At this stage, two situations can occur. If the symbol is found, it is set with the corresponding value. If the symbol is not found, it is created in the current nameset and set. The use of qualified name is also permitted -- and encouraged -- with trans. The exact nature of the symbol binding with a qualified name depends on the partial evaluation of the qualified name. For example, trans example:hello 1will set or create a symbol binding in reference to the exampleobject. If examplerefers to a nameset, the symbol is bound in this nameset. If exampleis a class, hellois bounded as a class symbol. In theory, there is no restriction to use transon any object. If the object does not have a symbol binding capability, an exception is raised. For example, if nis an integer object, the form trans n:i 1will fail. With 3 or 4 arguments, transdefines automatically a lambda expression. This notation is a syntactic sugar. The lambda expression is constructed from the argument list and bounded to the specified symbol. The rule used to set or define the symbol are the same as described above.

# create automatically a lambda expression
trans min (x y) (if (< x y) x y)

Constant binding
The constreserved keyword is similar to trans, except that it creates a constant symbol. Once the symbol is created, it cannot be changed. This constant property is hold by the symbol itself. When trying to set a constant symbol, an exception is raised. The reserved keyword constworks also with qualified names. The rules described previously are the same. When a partial evaluation is done, the partial object is called to perform a constant binding. If such capability does not exist, an exception is raised. With 3 or 4 arguments, constdefines automatically a gamma expression. Like transthe rule are the same except that the symbol is marked constant.

# create automatically a gamma expression
const max (x y) (if (> x y) x y)

Symbol unreferencing
The unrefreserved keyword removes a symbol reference in a given context. When the context is a nameset, the object associated with the symbol is detached from the symbol, eventually destroyed with the symbol removed from the nameset.

# create a symbol number
const x 1
# unreference it
unref x

Arguments
An expression argument is similar to a symbol, except that it is used only with function argument. The concept of binding between a name and an object is still the same, but with an argument, the object is not stored as part of the argument, but rather at another location which is the execution stack. An argument can also be constant. On the other hand, a single argument can have multiple bindings. Such situation is found during the same function call in two different threads. An argument list is part of the lambda or gamma expression declaration. If the argument is defined as a constant argument a sub form notation is used to defined this matter. For example, the maxgamma expression is given below.

# create a gamma expression with const argument
const max (gamma ((const x) (const y)) (if (> x y) x y))

A special symbols named argsis defined during a lambda or gamma expression evaluation with the remaining arguments passed at the time the call is made. The symbol can be either nilor bound to a list of objects.

const proc-args (a b) {
  trans result (+ a b)
  for (i) (args) (result:+= i)
  eval result
}
assert 3 (proc-args 1 2)
assert 7 (proc-args 1 2 4)

Special forms
Special forms provides are reserved keywords which are most of the time imperative statement, as part of the writing system. Special forms are an integral part of the writing system and interact directly with the interpreter. In most cases, a special forms returns the last evaluated object. Most of the special forms are control flow statements.

If special form
The ifreserved keyword takes two or three arguments. The first argument is the boolean condition to check. If the condition evaluates to truethe second argument is evaluated. The form return the result of such evaluation. If the condition evaluates to false, the third argument is evaluated or nil is returned if it does not exist. An interesting example which combines the ifreserved keyword and a deep recursion is the computation of the Fibonacci sequence.

const fibo (gamma (n) (
    if (< n 2) n (+ (fibo (- n 1)) (fibo (- n 2))))

While special form
The whilereserved keyword takes 2 or 3 arguments. With 2 arguments, the loop is constructed with a condition and a form. With 3 arguments, the first argument is an initial condition that is executed only once. When an argument acts as a loop condition, the condition evaluate to a boolean. The loop body is executed as long as the boolean condition is true. An interesting example related to integer arithmetic with a whileloop is the computation of the greatest common divisor or gcd.

const gcd (u v) {
  while (!= v 0) {
    trans r (u:mod v)
    u:= v
    v:= r
  }
  eval u
}

Note in this previous example the use of the symbol =. The qualified name u:=is in fact a method call. Here, the integer uis assigned with a value. In this case, the symbol is not changed. It is the object which is muted. In the presence of 3 arguments, the first argument is an initialization condition that is executed only once. In this mode, it is important to note that the loop introduce its own nameset. The loop condition can be used to initialize a local condition variable.

while (trans valid (is:valid-p)) (valid) {
  # do something
  # adjust condition
  valid:= (and (is:valid-p) (something-else))
}

Do special form
The doreserved keyword is similar to the whilereserved keyword, except that the loop condition is evaluated after the body execution. The syntax call is opposite to the while. The loop can accept either 2 or 3 arguments. With 2 arguments, the first argument is the loop body and the second argument is the exit loop condition. With 3 arguments, the first argument is the initial condition that is executed only once.

# count the number of digits in a string
const number-of-digits (s) {
  const len (s:length)
  trans index 0
  trans count 0
  do {
    trans c (s:get index)
    if (c:digit-p) (count:++)
  } (< (index:++) len)
  eval count
}

Loop special form
The loopreserved keyword is another form of loop. It take four arguments. The first is the initialize form. The second is the exit condition. The third is the step form and the fourth is the form to execute at each loop step. Unlike the whileand doloop, the loopspecial form creates its own nameset, since the initialize condition generally creates new symbol for the loop only.

# a simple loop from 0 to 10
loop (trans i 0) (< i 10) (i:++) (println i)

A loop can also be designed with a Counterobject. In this case, a counter is created with an initial and final count values. The counter step-pmethod can then be used to run the loop

# a counter from 0 to 10
trans cntr (Counter 10)
# a simple loop from 1 to 10
loop (cntr:step-p) (println cntr)

In this example, the counter prints from 1 to 10 since the counter is designed to operate from 0 to 9, and the printlnfunction is called after the step-ppredicate.

Switch special form
The switchreserved keyword is a condition selector. The first argument is the switch selector. The second argument is a list of various value which can be matched by the switch value. A special symbol called elsecan be used to match any value.

# return the primary color in a rgb
const get-primary-color (color value) (
  switch color (
    ("red"   (return (value:substr 0 2)))
    ("green" (return (value:substr 2 4)))
    ("blue"  (return (value:substr 4 6)))
  ))

Return special form
The returnreserved keyword indicates an exceptional condition in the flow of execution within a lambda or gamma expression. When a return is executed, the associated argument is returned and the execution terminates. If returnis used at the top level, the result is simply discarded.

# initialize a vector with a value
const vector-init (length value) {
  # treat nil vector first
  if (<= length 0) return (Vector)
  trans result (Vector)
  do (result:add value) (> (length:--) 0)
}

Eval and protect
The evalreserved keyword forces the evaluation of the object argument. The reserved keyword evalis typically used in a function body to return a particular symbol value. It can also be used to force the evaluation of a protected object. In many cases, evalis more efficient than return. The protectreserved keyword constructs an object without evaluating it. Typically when used with a form, protectreturn the form itself. It can also be used to prevent a symbol evaluation. When used with a symbol, the symbol object itself is returned.

const add (protect (+ 1 2))
(eval add)

Note that in the preceding example that the evaluation will return a lambda expression which is evaluated immediately and which return the integer 3.

Assert special form
The assertreserved keyword check for equality between the two arguments and abort the execution in case of failure. By default, the assertion checking is turn off, and can be activated with the command option f assert. Needless to say that assertis used for debugging purpose.

assert true   (> 2 0)
assert 0      (- 2 2)
assert "true" (String true)

Block special form
The blockreserved keyword executes a form in a new local set. The local set is destroyed at the completion of the execution. The blockreserved keyword returns the value of the last evaluated form. Since a new local set is created, any new symbol created in this nameset is destroyed at the completion of the execution. In other word, the blockreserved keyword allows the creation of a local scope.

trans a 1
block {
  assert    a 1
  trans     a (+ 1 1)
  assert    a 2
  assert ..:a 1
}
assert 1 a

Built-in objects
Several built-in objects and built-in operators for arithmetic and logical operations are also integrated in the writing system. The Integerand Realclasses are primarily used to manipulate numbers. The Booleanclass is used to for boolean operations. Other built-in objects include Characterand String. The exact usage of these objects is described in the next chapter.

Arithmetic operations
Support for the arithmetic operations is provided with the standard operator notation. Normally, these operators will tolerate various object type mixing and the returned value will generally be bound to an object that provides the minimum loss of information. Most of the operations are done with the +, -, *and /operators.

(+ 1 2)
(- 1)
(* 3 5.0)
(/ 4.0 2)

Logical operations
The Booleanclass is used to represent the boolean value trueand false. These last two symbols are built-in in the interpreter as constant symbols. There are also special forms like not, andand or. Their usage is self understandable.

not true
and true (== 1 0)
or (< -1 0) (> 1 0)

Predicates
A predicateis a function which returns a boolean object. There is always a built-in predicate associated with a built-in object. By convention, a predicate terminates with the sequence -p. The nil-ppredicate is a special predicate which returns true if the object is nil. The object-ppredicate is the negation of the nil-ppredicate.

For example, one can write a function which returns trueif the argument is a number, that is, an integer or a real number.

# return true if the argument is a number
const number-p (n) (
  or (integer-p n) (real-p n))

Special predicates for functional and symbolic programming are also built-in in the engine.

Finally, for each object, a predicate is also associated. For example, cons-pis the predicate for the Consobject and vector-pis the predicate for the Vectorobject. Another issue related to evaluation, is to decide whether or not an object can be evaluated. The predicate eval-pwhich is a special form is designed to answer this question. Furthermore, the eval-ppredicate is useful to decide whether or not a symbol is defined or if a qualified name can be evaluated.

assert true  (eval-p .)
assert false (eval-p an-unknown-symbol)

Class and instance
Classes and instances are the fundamental objects that provide support for the object oriented paradigm. A classis a nameset which can be bounded automatically when an instanceof that class is created. The class model is sloppy. Compared to other systems, there is no need to declare the data members for a particular class. Data members are created during the instance construction. An instance can also be created without any reference to a class. Methods can be bound to the class or the instance or both. An instance can also be muted during the execution process.

Class and members
A class is declared with the reserved keyword class. The resulting object acts like a nameset and it is possible to bind symbol to it.

# create a class object
const Circle (class)
const Circle:PI 3.1415926535
# access by qualified name
println Circle:PI

In the previous example, the symbol Circleis created as a class object. With the help of a qualified name, the symbol PIis created inside the class nameset. In this case, the symbol PIis invariant with respect to the instance object. A form can also be bound to the class nameset. In both cases, the symbol or the form is accessed with the help of a qualified name.

Instances
An instance of a class is created like any built-in object. If a method called presetis defined for that class, the method is used to initialize the instance.

# create a class
const Circle (class)
trans Circle:preset (r) {
  const this:radius (r:clone)
}
# create a radius 1 circle
const c (Circle 1)

This example calls for several comments. First the presetlambda expression is bound to the class. Since presetis a reserved name for the class object, the form is automatically executed at the instance construction. Second, note that the instance data member radiusis created by the lambda expression and another reserved keyword called thisis used to reference the instance object as it is customary with other programming systems.

Instance method
When a lambda expression is bound to the class or the instance, that lambda can be invoked as an instance method. When an instance method is invoked, the instance nameset is set as the parent nameset for that lambda. This is the main reason why a gamma expression cannot be used as an instance method. Therefore, the use of the reserved keyword thisis not recommended in a gamma expression, although it is perfectly acceptable to create a symbol with such name.

# create a perimeter method
trans Circle:perimeter nil (
  * (* 2.0 Circle:PI) this:radius)
# call the method with our circle
trans p (c:perimeter)

It must be clear that the perimetersymbol defines a method at the class level. It is perfectly acceptable to define a methods at the instance level. Such method is called a specialized method.

Miscellaneous features

Iteration
An iteration facility is provided for some objects known as iterable objects. The Cons, Listand Vectorare typical iterable objects. There are two ways to iterate with these objects. The first method uses the forreserved keyword. The second method uses an explicit iterator which can be constructed by the object.

# compute the scalar product of two vectors
const scalar-product (u v) {
  trans result 0
  for (x y) (u v) (result:+= (* x y))
  eval result
}

The forreserved keyword iterate on both object uand v. For each iteration, the symbol xand yare set with their respective object value. In the example above, the result is obtained by summing all intermediate products.

# test the scalar product function
const v1 (Vector 1 2 3)
const v2 (Vector 2 4 6)
(scalar-product v1 v2)

The iteration can be done explicitly by creating an iterator for each vectors and advancing steps by steps.

# scalar product with explicit iterators
const scalar-product (u v) {
  trans result 0
  trans u-it   (u:get-iterator)
  trans v-it   (v:get-iterator)
  while (u:valid-p) {
    trans x (u:get-object)
    trans y (v:get-object)
    result:+= (* x y)
    u:next
    v:next
  }
  eval result
}

In the example above, two iterators are constructed for both vectors uand v. The iteration is done in a whileloop by invoking the valid-ppredicate. The get-objectmethod returns the object value at the current iterator position.

Exception
An exceptionis an unexpected change in the execution flow. The exception model is based on a mechanism which throws the exception to be caught by a handler. The mechanism is also designed to be compatible with the native implementation. An exception is thrown with the special form throw. When an exception is thrown, the normal flow of execution is interrupted and an object used to carry the exception information is created. Such exception object is propagated backward in the call stack until an exception handler catch it.The special form tryexecutes a form and catch an exception if one has been thrown. With one argument, the form is executed and the result is the result of the form execution unless an exception is caught. If an exception is caught, the result is the exception object. If the exception is a native one, the result is nil.

try (+ 1 2)
try (throw)
try (throw "hello")
try (throw "hello" "world")
try (throw "hello" "world" "folks")

The exception mechanism is also designed to install an exception handler and eventually retrieve some information from the exception object. The reserved symbol whatcan be used to retrieve some exception information.

# protected factorial
const fact (n) {
  if (not (integer-p n)) 
  (throw "number-error" "invalid argument")
  if (== n 0) 1 (* n (fact (- n 1)))
}
# exception handler
const handler nil {
  errorln what:eid ',' what:reason
}
(try (fact 5)       handler)
(try (fact "hello") handler)

The special symbol whatstores the necessary information about the place that generated the exception. Most of the time, the qualified name what:reasonor what:aboutis used.The only difference is that what:aboutcontains the file name and line number associated with the reason that generated the exception.

Regular Expressions
A regular expression or regexis an object which is used to match certain text patterns. Regular expressions are built implicitly by the parser with the use of the [and ]characters. Special class of characters are defined with the help of the $character. For example, $dis the class of character digits as defined by the Unicode consortium. Different regular expression can be grouped by region to be matched as indicated in the example below.

if (== (const re [($d$d):($d$d)]) "12:31") {
  trans hr (re:get 0)
  trans mn (re:get 1)
}

In the previous example, a regular expression object is bound to the symbol re. The regexcontains two groups. The call to the operator ==returns trueif the regex matches the argument string. The getmethod can be used to retrieve the group by index.

Delayed evaluation
The special form delaycreates a special object called a promisewhich records the form to be later evaluated. The special form forcecauses a promise to be evaluated. Subsequent call with forcewill produce the same result.

trans   y 3
const   l ((lambda (x) (+ x y)) 1)
assert  4 (force l)
trans   y 0
assert  4 (force l)

Threads
The interpreter provides a powerful mechanism which allows the concurrent execution of forms and the synchronization of shared objects. The engine provides supports the creation and the synchronization of threads with a native object locking mechanism. During the execution, the interpreter wait until all threads are completed. A threads is created with the reserved keyword launch. In the presence of several threads, the interpreter manages automatically the shared objects and protect them against concurrent access.

# shared variable access
const var 0
const decr nil (while true (var:= (- var 1)))
const incr nil (while true (var:= (+ var 1)))
const prtv nil (while true (println "value = " var))
# start 3 threads 
launch (prtv)
launch (decr)
launch (incr)

Form synchronization
Although, the engine provides an automatic synchronization mechanism for reading or writing an object, it is sometimes necessary to control the execution flow. There are basically two techniques to do so. First, protect a form from being executed by several threads. Second, wait for one or several threads to complete their task before going to the next execution step. The reserved keyword synccan be used to synchronize a form. When a form, is synchronized, the engine guarantees that only one thread will execute this form.

const print-message (code mesg) (
  sync {
    errorln "error  : " code
    errorln "message: " mesg
  }
)

The previous example create a gamma expression which make sure that both the error code and error message are printed in one group, when several threads call it.

Thread completion
The other piece of synchronization is the thread completion indicator. The thread descriptor contains a method called waitwhich suspend the calling thread until the thread attached to the descriptor has been completed. If the thread is already completed, the method returns immediately.

# simple flag
const flag false
# simple shared tester
const ftest (bval) (flag:= bval)
# run the thread and wait
const thr (launch (ftest true))
thr:wait
assert true flag

This example is taken from the test suites. It checks that a boolean variable is set in a thread. Note the use of the waitmethod to make sure the thread has completed before checking for the flag value. It is also worth to note that waitis one of the method which guarantees that a thread result is valid. Another use of the waitmethod can be made with a vector of thread descriptors when one wants to wait until all of them have completed.

# shared vector of threads descriptors
const thr-group (Vector)
# wait until all threads in the group are finished
const wait-all nil (for (thr) (thr-group) (thr:wait))

Condition variable
A condition variableis another mechanism to synchronize several threads. A condition variable is modeled with the Condvarobject. At construction, the condition variable is initialized to false. A thread calling the waitmethod will block until the condition becomes true. The markmethod can be used by a thread to change the state of a condition variable and eventually awake some threads which are blocked on it. The use of condition variable is particularly recommended when one need to make sure a particular thread has been doing a particular task.

The interpreter object
The interpreter can also be seen as an object. As such, it provides several special symbols and forms. For example, the symbol argvis the argument vector. The symbol libraryis an interpreter method that loads a library. A complete description of the interpreter object is made in a special chapter of this book.

LITERALS¶

Integer number
The fundamental number representation is the Integer. The integer is a 64 bits signed 2's complement number. Even when running with a 32 bits machine, the 64 bits representation is used. If a larger representation is needed, the Relatifobject might be more appropriate. The Integerobject is a literal object that belongs to the number class.

Integer format
The default literal format for an integer is the decimal notation. The minus sign (without blank) indicates a negative number. Hexadecimal and binary notations can also be used with prefix 0xand 0b. The underscore character can be used to make the notation more readable.

const a  123
trans b -255
const h  0xff
const b  0b1111_1111

Integer number are constructed from the literal notation or by using an explicit integer instance. The Integerclass offers standard constructors. The default constructor creates an integer object and initialize it to 0. The other constructors take either an integer, a real number, a character or a string.

const a (Integer)
const b (Integer 2000)
const c (Integer "23")

When the hexadecimal or binary notation is used, care should be taken to avoid a negative integer. For example, 0x_8000_0000_0000_0000is the smallest negative number. This number exhibits also the strange property to be equal to its negation since with 2's complement, there is no positive representation.

Integer arithmetic
Standard arithmetic operators are available as built-in operators. The usual addition +, multiplication *and division /operate with two arguments. The subtraction -operates with one or two arguments.

+ 3 4
- 3 4
- 3
* 3 4
/ 4 2

As a built-in object, the Integerobject offers various methods for built-in arithmetic which directly operates on the object. The following example illustrates these methods.

trans i 0
i:++
i:--
i:+ 4
i:= 4
i:- 1
i:* 2
i:/ 2
i:+= 1
i:-= 1
i:*= 2
i:/= 2

As a side effect, these methods allows a const symbol to be modified. Since the methods operates on an object, they do not modify the state of the symbol. Such methods are called mutable methods.

const i 0
i:= 1

Integer comparison
The comparison operators works the same. The only difference is that they always return a Booleanresult. The comparison operators are namely equal ==, not equal !=, less than <, less equal <=, greater >and greater equal >=. These operators take two arguments.

== 0 1
!= 0 1

Like the arithmetic methods, the comparison operators are supported as object methods. These methods return a Booleanobject.

i:=  1
i:== 1
i:!= 0

Integer calculus
Armed with all these functions, it is possible to develop a battery of functions operating with numbers. As another example, we revisit the Fibonacci sequence as demonstrated in the introduction chapter. Such example was terribly slow, because of the double recursion. Another method suggested by Springer and Friedman uses two functions to perform the same job.

const fib-it (gamma (n acc1 acc2) (
    if (== n 1) acc2 (fib-it (- n 1) acc2 (+ acc1 acc2))))
const fiboi (gamma (n) (
    if (== n 0) 0 (fib-it n 0 1)))

This later example is by far much faster, since it uses only one recursion. Although, it is no the fastest way to write it, it is still an elegant way to write complex functions.

Other Integer methods
The Integerclass offers other convenient methods. The odd-pand even-pare predicates. The modtake one argument and returns the modulo between the calling integer and the argument. The absmethods returns the absolute value of the calling integer.

i:even-p
i:odd-p
i:mod 2
i:= -1
i:abs
i:to-string

The Integerobject is a literal objectand a number object. As a literal object, the to-stringand to-literalmethods are provided to obtain a string representation for the integer object. Although the to-stringmethod returns a string representation of the calling integer, the to-literalmethod returns a parsable string. Strictly speaking for an integer, there is no difference between a string representation and a literal representation. However, this is not true for other objects.

(axi) const i 0x123
(axi) println (i:to-string)
291
(axi) println (i:to-literal)
291

As a number object, the integer number can also be represented in hexadecimal format. The to-hexaand to-hexa-strignmethods are designed to obtained such representation. In the first form, the to-hexamethod return a literal hexadecimal string representation with the appropriate prefix while the second one does not.

(axi) const i 0x123
(axi) println (i:to-hexa)
0x123
(axi) println (i:to-hexa-string)
123

Relatif number
A relatifor big number is an integer with infinite precision. The Relatifclass is similar to the Integerclass except that it works with infinitely long number. The relatif notation uses a ror Rsuffix to express a relatif number versus an integer one. The Relatifobject is a literal object that belongs to the number class. The predicate associated with the Relatifobject is relatif-p.

const a  123R
trans b -255R
const c  0xffR
const d  0b1111_1111R
const e (Relatif)
const f (Relatif 2000)
const g (Relatif "23")

Relatif operations
Most of the Integerclass operations are supported by the Relatifobject. The only difference is that there is no limitation on the number size. This naturally comes with a computational price. An amazing example is to compute the biggest know prime Mersenne number. The world record exponent is 6972593. The number is therefore:

const i 1R
const m (- (i:shl 6972593) 1)

This number has 2098960 digits. You can use the printlnmethod if you wish, but you have been warned...

Real number
The realclass implements the representation for floating point number. The internal representation is machine dependent, and generally follows the double representation with 64 bits as specified by the IEEE 754-1985 standard for binary floating point arithmetic. All integer operations are supported for real numbers. The Realobject is a literal object that belongs to the number class.

Real format
The parser supports two types of literal representation for real number. The first representation is the dotted decimalnotation. The second notation is the scientific notation.

const a  123.0 # a positive real
const b -255.5 # a negative real
const c  2.0e3 # year 2000.0

Real number are constructed from the literal notation or by using an explicit real instance. The Realclass offers standard constructors. The default constructor creates a real number object and initialize it to 0.0. The other constructors takes either an integer, a real number, a character or a string.

Real arithmetic
The real arithmetic is similar to the integer one. When an integer is added to a real number, that number is automatically converted to a real. Ultimately, a pure integer operation might generate a real result.

+ 1999.0 1   # 2000.0  
+ 1999.0 1.0 # 2000.0
- 2000.0 1   # 1999.0  
- 2000.0 1.0 # 1999.0
* 1000 2.0   # 2000.0  
* 1000.0 2.0 # 2000.0
/ 2000.0 2   # 1000.0  
/ 2000.0 2.0 # 1000.0

Like the Integerobject, the Realobject has arithmetic built-in methods.

trans  r 0.0 # 0.0  
r:++       # 1.0 
r:--       # 0.0  
r:+ 4.0    # 4.0  
r:= 4.0    # 4.0  
r:- 1.0    # 3.0  
r:* 2.0    # 8.0  
r:/ 2.0    # 2.0  
r:+= 1.0   # 5.0  
r:-= 1.0   # 4.0  
r:*= 2.0   # 8.0  
r:/= 2.0   # 4.0

Real comparison
The comparison operators works as the integer one. As for the other operators, an implicit conversion between an integer to a real is done automatically.

== 2000 2000   # true
!= 2000 1999   # true

Comparison methods are also available for the Realobject. These methods take either an integer or a real as argument.

r:=  1.0 # 1.0
r:== 1.0 # true  
r:!= 0.0 # true

A complex example
One of the most interesting point with functional programming language is the ability to create complex function. For example let's assume we wish to compute the value at a point xof the Legendre polynomial of order n. One of the solution is to encode the function given its order. Another solution is to compute the function and then compute the value.

# legendre polynomial order 0 and 1
const lp-0 (gamma (x) 1)
const lp-1 (gamma (x) x)
# legendre polynomial of order n
const lp-n (gamma (n) (
    if (> n 1) {
      const lp-n-1 (lp-n (- n 1))
      const lp-n-2 (lp-n (- n 2))
      gamma (x) (n lp-n-1 lp-n-2) 
      (/ (- (* (* (- (* 2 n) 1) x) 
            (lp-n-1 x))
          (* (- n 1) (lp-n-2 x))) n)
    } (if (== n 1) lp-1 lp-0)
  ))
# generate order 2 polynomial
const lp-2 (lp-n 2)
# print lp-2 (2)
println "lp2 (2) = " (lp-2 2)

Note that the computation can be done either with integer or real numbers. With integers, you might get some strange results anyway, but it will work. Note also how the closed variable mechanism is used. The recursion capture each level of the polynomial until it is constructed. Note also that we have here a double recursion.

Other real methods
The real numbers are delivered with a battery of functions. These include the trigonometric functions, the logarithm and couple others. Hyperbolic functions like sinh, cosh, tanh, asinh, acoshand atanhare also supported. The square root sqrtmethod return the square root of the calling real. The floorand ceilingreturns respectively the floor and the ceiling of the calling real.

const r0 0.0       # 0.0
const r1 1.0       # 1.0
const r2 2.0       # 2.0
const rn -2.0      # -2.0
const rq (r2:sqrt) # 1.414213
const pi 3.1415926 # 3.141592
rq:floor           # 1.0
rq:ceiling         # 2.0
rn:abs             # 2.0
r1:log             # 0.0
r0:exp             # 1.0
r0:sin             # 0.0
r0:cos             # 1.0
r0:tan             # 0.0
r0:asin            # 0.0
pi:floor           # 3.0
pi:ceiling         # 4.0

Accuracy and formatting
Real numbers are not necessarily accurate, nor precise. The accuracy and precision are highly dependent on the hardware as well as the nature of the operation being performed. In any case, never assume that a real value is an exact one. Most of the time, a real comparison will fail, even if the numbers are very close together. When comparing real numbers, it is preferable to use the ?=operator. Such operator result is bounded by the internal precision representation and will generally return the desired value. The real precision is an interpreter value which is set with the set-absolute-precisionmethod while the get-absolute-precisionreturns the interpreter precision. There is also a set-relative-precisionand get-relative-precisionmethods used for the definition of relative precision. By default, the absolute precision is set to 0.00001 and the relative precision is set to 1.0E-8.

interp:set-absolute-precision 0.0001
const r 2.0
const s (r:sqrt) # 1.4142135
(s:?= 1.4142)    # true

Real number formatting is another story. The formatmethod takes a precision argumentwhich indicates the number of digits to print for the decimal part. Note that the format command might round the result as indicated in the example below.

const pi 3.1415926535
pi:format 3  # 3.142

If additional formatting is needed, the Stringfill-leftand fill-rightmethods can be used.

const pi  3.1415926535        # 3.1415926535
const val (pi:format 4)       # 3.1416
println (val:fill-left '0' 9) # 0003.1416

Number object
The Integer, Relatifand Realobjects are all derived from the Numberobject which is a Literalobject. As such, the predicate number-pis the right mechanism to test an object for a number. The class also provides the basic mechanism to format the number as a string. For integer and relatif, the hexadecimal representation can be obtained by the to-hexaand to-hexa-stringmethods. For integer and real numbers, the formatmethod adjusts the final representation with the precision argument as indicated before. It is worth to note that a formatted integer gets automatically converted into a real representation.

Character
The Characterobject is another built-in object. A character is internally represented by a quad by using a 31 bit representation as specified by the Unicode standard and ISO 10646.

Character format
The standard quote notation is used to represent a character. In that respect, there is hare a substantial difference with other functional language where the quote protect a form.

const LA01 'a' # the character a
const ND10 '0' # the digit 0

All characters from the Unicode codesetare supported by the AFNIX engine. The characters are constructed from the literal notation or by using an explicit character instance. The Characterclass offers standard constructors. The default constructor creates a null character. The other constructors take either an integer, a character or a string. The string can be either a single quoted character or the literal notation based on the U+notation in hexadecimal. For example, U+40is the @character while U+3A3is the sigma capital letter.

const nilc (Character)        # null character
const a    (Character 'a')    # a
const 0    (Character 48)     # 0
const mul  (Character "*")    # *
const div  (Character "U+40") # @

Character arithmetic
A character is like an integer, except that it operates in the range 0 to 0x7FFFFFFF. The character arithmetic is simpler compared to the integer one and no overflow or underflow checking is done. Note that the arithmetic operations take an integer as an argument.

+ 'a' 1 # 'b' 
- '9' 1 # '8'

Several Characterobject methods are also provided for arithmetic operations in a way similar to the Integerclass.

trans  c 'a' # 'a'
c:++         # 'b'
trans  c '9' # '9'  
c:--         # '8'
c:+ 1        # '9'
c:- 9        # '0'

Character comparison
Comparison operators are also working with the Characterobject. The standard operators are namely equal ==, not equal !=, less than <, less equal <=, greater >and greater equal >=. These operators take two arguments.

== 'a' 'b' # false  
!= '0' '1' # true

Other character methods
The Characterobject comes with additional methods. These are mostly conversion methods and predicates. The to-stringmethod returns a string representation of the calling character. The to-integermethod returns an integer representation the calling character. The predicates are alpha-p, digit-p, blank-p, eol-p, eos-pand nil-p.

const LA01 'a'  # 'a'
const ND10 '0'  # '0'
LA01:to-string  # "a"
LA01:to-integer # 97
LA01:alpha-p    # true
ND10:digit-p    # true

String
The Stringobject is one of the most important built-in object in the AFNIX engine. Internally, a string is a vector of Unicode characters. Because a string operates with Unicode characters, care should be taken when using composing characters.

String format
The standard double quote notation is used to represent literally a string. Standard escape sequences are also accepted to construct a string.

const hello "hello"

Any literal object can be used to construct a string. This means that integer, real, boolean or character objects are all valid to construct strings. The default constructor creates a null string. The string constructor can also takes a string.

const nils (String)      # ""
const one  (String 1)    # "1"
const a    (String 'a')  # "a"
const b    (String true) # "true"

String operations
The Stringobject provides numerous methods and operators. The most common ones are illustrated in the example below. The lengthmethods returns the total number of characters in the string object. It is worth to note that this number is not necessarily the number of printed characters since some characters might be combining charactersused, for example, as diacritics. The non-combining-lengthmethod might be more adapted to get the number of printable characters.

const h "hello"
h:length       # 5
h:get 0        # 'h'
h:== "world"   # false
h:!= "world"   # true
h:+= " world"  # "hello world"

The sub-leftand sub-rightmethods return a sub-string, given the position index. For sub-left, the index is the terminating index, while sub-rightis the starting index, counting from 0.

# example of sub-left method
const msg "hello world"
msg:sub-left  5 # "hello"
msg:sub-right 6 # "world"

The strip, strip-leftand strip-rightare methods used to strip blanks and tabs. The stripmethod combines both strip-leftand strip-right.

# example of strip method
const str " hello world "
println (str:strip) # "hello world"

The splitmethod returns a vector of strings by splitting the string according to a break sequence. By default, the break sequence is the blank, tab and newline characters. The break sequence can be one or more characters passed as one single argument to the method.

# example of split method
const str "hello:world"
const vec (str:split ":" # "hello" "world")
println (vec:length) # 2

The fill-leftand fill-rightmethods can be used to fill a string with a character up to a certain length. If the string is longer than the length, nothing happens.

# example of fill-left method
const pi  3.1415926535  # 3.1415926535
const val (pi:format 4) # 3.1416
val:fill-left '0' 9     # 0003.1416

Conversion methods
The case conversion methods are the standard to-upperand to-lowermethods. The method operates with the internal Unicode database. As a result, the conversion might change the string length. Other conversion methods related to the Unicode representation are also available. These are rather technical, but can be used to put the string in a normal form which might be suitable for comparison. Such conversion always uses the Unicode database normal form representation.

# example of case conversion
const str "hello world"
println (str:to-upper) # HELLO WORLD

String hash value
The hashidmethod is a method that computes the hash value of a string. The value depends on the target machine and will change between a 32 bits and a 64 bits machine. Example example 0203.alsillustrates the computation of a hash value for our favorite test string.

# test our favorite string
const hello "hello world"
hello:hashid # 1054055120

The algorithm used by the engine is shown as an example below. As a side note, it is recommended to print the shift amount in the program. One may notice, that the value remains bounded by 24. Since we are xoringthe final value, it does illustrate that the algorithm is design for a 32 bits machine. With a 64 bits machine the algorithm is slightly modified to use the extra space. This also means that the hashid value is not portable across platforms.

# compute string hashid
const hashid (s) {
  const len (s:length)
  trans cnt 0
  trans val 0
  trans sht 17
  do {
    # compute the hash value
    trans i (Integer (s:get cnt))
    val:= (val:xor (i:shl sht))
    # adjust shift index
    if (< (sht:-= 7) 0) (sht:+= 24)
  } (< (cnt:++) len)
  eval val
}

Regular expression
A regular expression or regexis a special literal object designed to describe a character string in a compact form with regular patterns. A regular expression provides a convenient way to perform pattern matching and filed extraction within a character string.

Regex syntax
A regular expression is defined with a special Regexobject. A regular expression can be built implicitly or explicitly with the use of the Regexobject. The regex syntax uses the [and ]characters as block delimiters. When used in a source file, the parser automatically recognizes a regex and built the object accordingly. The following example shows two equivalent methods for the same regex expression.

# syntax built-in regex
(== [$d+] 2000)         # true
# explicit built-in regex
(== (Regex "$d+") 2000) # true

In its first form, the [and ]characters are used as syntax delimiters. The lexical analyzer automatically recognizes this token as a regex and built the equivalent Regexobject. The second form is the explicit construction of the Regexobject. Note also that the [and ]characters are also used as regex block delimiters.

Regex characters and meta-characters
Any character, except the one used as operators can be used in a regex. The $character is used as a meta-character -- or control character -- to represent a particular set of characters. For example, [hello world]is a regex which match only the "hello world"string. The [$d+]regex matches one or more digits. The following meta characters are built-in in the regex engine.

The uppercase version is the complement of the corresponding lowercase character set. A character which follows a $character and that is not a meta character is treated as a normal character. For example $[is the [character. A quoted string can be used to define character matching which could otherwise be interpreted as control characters or operator. A quoted string also interprets standard escaped sequencesbut not meta characters.

(== [$d+]   2000) # true
(== ["$d+"] 2000) # false

Combining alphanumerical characters can generate surprising result when used with Unicode string. Combining alphanumeric characters are alphanumeric characters and non spacing combining mark as defined by the Unicode consortium. In practice, the combining marks are the diacritics used with regular letter, such like the accents found in the western languages. Because the writing system uses a canonical decomposition for representing the Unicode string, it turns out that the printed string is generally represented with more bytes, making the string length longer than it appears.

Regex character set
A character set is defined with the <and >characters. Any enclosed character defines a character set. Note that meta characters are also interpreted inside a character set. For example, <$d+->represents any digit or a plus or minus. If the first character is the ^character in the character set, the character set is complemented with regards to its definition.

Regex blocks and operators
The [and ]characters are the regex sub-expressions delimiters. When used at the top level of a regex definition, they can identify an implicit object. Their use at the top level for explicit construction is optional. The following example is strictly equivalent.

# simple real number check
const real-1 (Regex "$d*.$d+")
# another way with [] characters
const real-2 (Regex "[$d*.$d+]")

Sub-expressions can be nested -- that's their role -- and combined with operators. There is no limit in the nesting level.

# pair of digit testing
(== [$d$d[$d$d]+] 2000)  # true
(== [$d$d[$d$d]+] 20000) # false

The following unary operators can be used with single character, control characters and sub-expressions.

Alternation is an operator which work with a secondary expression. Care should be taken when writing the right sub-expression. For example the following regex [$d|hello]is equivalent to [[$d|h]ello]. In other word, the minimal first sub-expression is used when compiling the regex.

Grouping
Groups of sub-expressions are created with the (and )characters. When a group is matched, the resulting sub-string is placed on a stack and can be used later. In this respect, the regex engine can be used to extract sub-strings. The following example extracts the month, day and year from a particular date format: [($d$d):($d$d):($d$d$d$d)]. This regex assumes a date in the form mm:dd:yyyy.

if (== (const re [($d$d):($d$d)]) "12:31") {
  trans hr (re:get 0)
  trans mn (re:get 1)
}

Grouping is the mechanism to retrieve sub-strings when a match is successful. If the regex is bound to a symbol, the getmethod can be used to get the sub-string by index.

Regex object
Although a regex can be built implicitly, the Regexobject can also be used to build a new regex. The argument is a string which is compiled during the object construction. A Regexobject is a literal object. This means that the to-stringmethod is available and that a call to the printlnspecial form will work directly.

const   re (Regex "$d+")
println re           # $d+
println re:to-string # [$d+]

Regex operators
The ==and !=operators are the primary operators to perform a regex match. The ==operator returns trueif the regex matches the string argument from the beginning to the end of string. Such operator implies the begin and end of string anchoring. The <operator returns true if the regex matches the string or a sub-string or the string argument.

Regex methods
The primary regex method is the getmethod which returns by index the sub-string when a group has been matched. The lengthmethod returns the number of group match.

if (== (const re [($d$d):($d$d)]) "12:31") {
  re:length # 2
  re:get 0  # 12
  re:get 1  # 31
}

The matchmethod returns the first string which is matched by the regex.

const regex [$d+]
regex:match "Happy new year 2000" # 2000

The replacemethod any occurrence of the matching string with the string argument.

const regex [$d+]
regex:replace "Hello year 2000" "3000" # hello year 3000

Argument conversion
The use of the Regexoperators implies that the arguments are evaluated as literal object. For this reason, an implicit string conversion is made during such operator call. For example, passing the integer 12or the string "12"is strictly equivalent. Care should be taken when using this implicit conversion with real numbers.

CONTAINER OBJECTS¶

Cons object
Originally, a Consobject or cons cellhave been the fundamental object of the Lisp or Scheme machine. The cons cell is the building block for list and is similar in some respect to the cons cellfound in traditional functional programming language. A Consobject is a simple element used to build linked list. The cons cell holds an object and a pointer to the next cons cell. The cons cell object is called carand the next cons cell is called the cdr. This original Lisp notation is maintained here for the sake of tradition. Although a cons cell is the building block for single linked list, the cell itself is not a list object. When a list object is needed, the Listdouble linked list object might be more appropriate.

Cons cell constructors
The default constructor creates a cons cell those car is initialized to the nil object. The constructor can also take one or several objects.

const nil-cons (Cons)
const lst-cons (Cons 1 'a' "hello")

The constructor can take any kind of objects. When all objects have the same type, the result list is said to be homogeneous. If all objects do not have the same type, the result list is said to be heterogeneous. List can also be constructed directly by the parser. Since all internal forms are built with cons cell, the construction can be achieved by simply protectingthe form from being interpreted.

const blist (protect ((1) ((2) ((3)))))

Cons cell methods
A Consobject provides several methods to access the carand the cdrof a cons cell. Other methods allows access to a list by index.

const c (Cons "hello" "world")
c:length   # 2
c:get-car  # "hello"
c:get-cadr # "world"
c:get 0    # "hello"
c:get 1    # "world"

The set-carmethod set the car of the cons cell. The addmethod adds a new cons cell at the end of the cons list and set the car with the specified object.

List object
The Listobject provides the facility of a double-link list. The Listobject is another example of iterable object. The Listobject provides support for forward and backward iteration.

List construction
A list is constructed like a cons cell with zero or more arguments. Unlike the cons cell, the Listcan have a null size.

const nil-list (List)
const dbl-list (List 1 'a' "hello")

List methods
The Listobject methods are similar the Consobject. The addmethod adds an object at the end of the list. The insertmethod inserts an object at the beginning of the list.

const list (List "hello" "world")
list:length      # 2
list:get 0       # "hello"
list:get 1       # "world"
list:add "folks" # "hello" "world" "folks"

Vector object
The Vectorobject provides the facility of an index array of objects. The Vectorobject is another example of iterable object. The Vectorobject provides support for forward and backward iteration.

Vector construction
A vector is constructed like a cons cell or a list. The default constructor creates a vector with 0 objects.

const nil-vector (Vector)
const obj-vector (Vector 1 'a' "hello")

Vector methods
The Vectorobject methods are similar to the Listobject. The addmethod appends an object at the end of the vector. The setmethod set a vector position by index.

const vec (Vector "hello" "world")
vec:length          # 2
vec:get 0           # "hello"
vec:get 1           # "world"
vec:add "folks"     # "hello" "world" "folks"
vec:set 0 "bonjour" # "bonjour" "world" "folks"

Set object
The Setobject provides the facility of an object container. The Setobject is another example of iterable object. The Setobject provides support for forward iteration. One of the property of a set is that there is only one object representation per set. Adding two times the same object results in one object only.

Set construction
A set is constructed like a vector. The default constructor creates a set with 0 objects.

const nil-set (Set)
const obj-set (Set 1 'a' "hello")

Set methods
The Setobject methods are similar to the Vectorobject. The addmethod adds an object in the set. If the object is already in the set, the object is not added. The lengthmethod returns the number of elements in the set.

const set       (Set "hello" "world")
set:get-size    # 2
set:add "folks" # "hello" "world" "folks"

Iteration
When an object is iterable, it can be used with the reserved keyword for. The forkeyword iterates on one or several objects and binds associated symbols during each step of the iteration process. All iterable objects provides also the method get-iteratorwhich returns an iterator for a given object. The use of iterator is justified during backward iteration, since foronly perform forward iteration.

Function mapping
Given a function func, it is relatively easy to apply this function to all objects of an iterable object. The result is a list of successive calls with the function. Such function is called a mapping function and is generally called map.

const map (obj func) {
  trans result (Cons)
  for (car) (obj) (result:link (func car))
  eval result
}

The linkmethod differs from the addmethod in the sense that the object to append is set to the cons cell car if the car and cdr is nil.

Multiple iteration
Multiple iteration can be done with one call to for. The computation of a scalar product is a simple but illustrative example.

# compute the scalar product of two vectors
const scalar-product (u v) {
  trans result 0
  for (x y) (u v) (result:+= (* x y))
  eval result
}

Note that the function scalar-productdoes not make any assumption about the object to iterate. One could compute the scalar product between a vector a list for example.

const u (Vector 1 2 3)
const v (List   2 3 4)
scalar-product u v

Conversion of iterable objects
The use of an iterator is suitable for direct conversion between one object and another. The conversion to a vector can be simply defined as indicted below.

# convert an iterable object to a vector
const to-vector (obj) {
  trans result (Vector)
  for (i) (obj) (result:add i)
  eval result
}

Explicit iterator
An explicit iterator is constructed with the get-iteratormethod. At construction, the iterator is reset to the beginning position. The get-objectmethod returns the object at the current iterator position. The nextadvances the iterator to its next position. The valid-pmethod returns trueif the iterator is in a valid position. When the iterator supports backward operations, the prevmethod move the iterator to the previous position. Note that Consobjects do not support backward iteration. The beginmethod reset the iterator to the beginning. The endmethod moves the iterator the last position. This method is available only with backward iterator.

# reverse a list
const reverse-list (obj) {
  trans result (List)
  trans itlist (obj:get-iterator)
  itlist:end
  while (itlist:valid-p) {
    result:add (itlist:get-object))
  itlist:prev
}
eval result
}

Special Objects
The engine incorporates other container objects. To name a few, such objects are the Queue, Bitsetor Fifoobjects.

Queue object
A queueis a special object which acts as container with a fifo policy. When an object is placed in the queue, it remains there until it has been dequeued. The Fifoand Queueobjects are somehow similar, with the fundamental difference that the queue resize itself if needed.

# create a queue with objects
const q (Queue "hello" "world")
q:empty-p # false
q:length  # 2 
# dequeue some object
q:dequeue # hello
q:dequeue # world
q:empty-p # true

Bitset object
A bit setis a special container for bit. A bit set can be constructed with a specific size. When the bit set is constructed, each bit can be marked and tested by index. Initially, the bitset size is null.

# create a bit set by size
const bs (Bitset 8)
bitset-p bs # true
# check, mark and clear
assert false (bs:marked-p 0)
bs:mark 0
assert true  (bs:marked-p 0)
bs:clear 0
assert false (bs:marked-p 0)

CLASSES¶

Class object
A class objectis simply a nameset which can be replicated via a construction mechanism. A class is created with the special form class. The result is an object of type Classwhich supports various symbol binding operations.

Class declaration and bindings
A new class is an object created with the reserved keyword class. Such class is an object which can be bound to a symbol.

const Color (class)

Because a class acts like a nameset, it is possible to bind directly symbols with the qualified namenotation.

const Color (class)
const Color:RED-FACTOR   0.75
const Color:BLUE-FACTOR  0.75
const Color:GREEN-FACTOR 0.75

When a data is defined in the class nameset, it is common to refer it as a class data member. A class data member is invariant over the instance of that class. When the data member is declared with the constreserved keyword, the symbol binding is in the class nameset.

Class closure binding
A lambda or gamma expression can be define for a class. If the class do not reference an instance of that class, the resulting closure is called a class methodof that class. Class methods are invariant among the class instances. The standard declaration syntax for a lambda or gamma expression is still valid with a class.

const Color:get-primary-by-string (color value) {
  trans val "0x"
  val:+= (switch color (
      ("red"   (value:substr 1 3))
      ("green" (value:substr 3 5))
      ("blue"  (value:substr 5 7))
    ))
  Integer val
}

The invocation of a class method is done with the standard qualified namenotation.

Color:get-primary-by-string "red"   "#23c4e5"
Color:get-primary-by-string "green" "#23c4e5"
Color:get-primary-by-string "blue"  "#23c4e5"

Class symbol access
A class acts as a nameset and therefore provides the mechanism to evaluate any symbol with the qualified name notation.

const Color:RED-VALUE "#ff0000"
const Color:print-primary-colors (color) {
  println "red   color " (
    Color:get-primary-color "red"   color)
  println "green color " (
    Color:get-primary-color "green" color)
  println "blue  color " (
    Color:get-primary-color "blue"  color)
}
# print the color components for the red color
Color:print-primary-colors Color:RED-VALUE

Instance
An instanceof a class is an object which is constructed by a special class method called a constructor. If an instance constructor does not exist, the instance is said to have a default construction. An instance acts also as a nameset. The only difference with a class, is that a symbol resolution is done first in the instance nameset and then in the instance class. As a consequence, creating an instance is equivalent to define a default nameset hierarchy.

Instance construction
By default, a instance of the class is an object which defines an instance nameset. The simplest way to define an anonymous instance is to create it directly.

const i     ((class))
const Color (class)
const red   (Color)

The example above define an instance of an anonymous class. If a class object is bound to a symbol, such symbol can be used to create an instance of that class. When an instance is created, the special symbol named thisis defined in the instance nameset. This symbol is bounded to the instance object and can be used to reference in an anonymous way the instance itself.

Instance initialization
When an instance is created, the engine looks for a special lambda expression called preset. This lambda expression, if it exists, is executed after the default instance has been constructed. Such lambda expression is a method since it can refer to the thissymbol and bind some instance symbols. The arguments which are passed during the instance construction are passed to the presetmethod.

const Color (class)
trans Color:preset (red green blue) {
  const this:red   (Integer red)
  const this:green (Integer green)
  const this:blue  (Integer blue)
}
# create some default colors
const Color:RED   (Color 255   0   0)
const Color:GREEN (Color   0 255   0)
const Color:BLUE  (Color   0   0 255)
const Color:BLACK (Color   0   0   0)
const Color:WHITE (Color 255 255 255)

In the example above, each time a color is created, a new instance object is created. The constructor is invoked with the thissymbol bound to the newly created instance. Note that the qualified name this:reddefines a new symbol in the instance nameset. Such symbol is sometimes referred as an instance data member. Note as well that there is no ambiguity in resolving the symbol red. Once the symbol is created, it shadows the one defined as a constructor argument.

Instance symbol access
An instance acts as a nameset. It is therefore possible to bind locally to an instance a symbol. When a symbol needs to be evaluated, the instance nameset is searched first. If the symbol is not found, the class nameset is searched. When an instance symbol and a class symbol have the same name, the instance symbol is said to shadow the class symbol. The simple example below illustrates this property.

const c   (class)
const c:a 1
const i   (c)
const j   (c)
const i:a 2
# class symbol access
println   c:a
# shadow symbol access
println   i:a
# non shadow access
println   j:a

When the instance is created, the special symbol metais bound in the instance nameset with the instance class object. This symbol can therefore be used to access a shadow symbol.

const c   (class)
const i   (c)
const c:a 1
const i:a 2
println   i:a
println   i:meta:a

The symbol metamust be used carefully, especially inside an initialization since it might create an infinite recursion as shown below.

const c (class)
trans c:preset nil (const i (this:meta))
const i (c)

Instance method
When lambda expression is defined within the class or the instance nameset, that lambda expression is callable from the instance itself. If the lambda expression uses the thissymbol, that lambda is called an instance method since the symbol thisis defined in the instance nameset. If the instance method is defined in the class nameset, the instance method is said to be global, that is, callable by any instance of that class. If the method is defined in the instance nameset, that method is said to be localand is callable by the instance only. Due to the nature of the nameset parent binding, only lambda expression can be used. Gamma expressions will not work since the gamma nameset has always the top level nameset as its parent one.

const Color (class)
# class constructor
trans Color:preset (red green blue) {
  const this:red   (Integer red)
  const this:green (Integer green)
  const this:blue  (Integer blue)
}
const Color:RF 0.75
const Color:GF 0.75
const Color:BF 0.75
# this method returns a darker color
trans Color:darker nil {
  trans lr (Integer (max (this:red:*   Color:RF) 0))
  trans lg (Integer (max (this:green:* Color:GF) 0))
  trans lb (Integer (max (this:blue:*  Color:BF) 0))
  Color lr lg lb
}
# get a darker color than yellow
const yellow      (Color 255 255 0)
const dark-yellow (yellow:darker)

Instance operators
Any operator can be defined at the class or the instance level. Operators like ==or !=generally requires the ability to assert if the argument is of the same type of the instance. The global operator ==will return true if two classes are the same. With the use of the metasymbol, it is possible to assert such equality.

# this method checks that two colors are equals
trans Color:== (color) {
  if (== Color color:meta) {
    if (!= this:red   color:red)   (return false)    
    if (!= this:green color:green) (return false)    
    if (!= this:blue  color:blue)  (return false)
    eval true
  } false
}
# create a new yellow color
const  yellow (Color 255 255 0)
(yellow:== (Color 255 255 0)) # true

The global operator ==returns trueif both arguments are the same, even for classes. Method operators are left open to the user.

Complex number example
As a final example, a class simulating the behavior of a complex number is given hereafter. The interesting point to note is the use of the operators. As illustrated before, the class uses uses a default method method to initialize the data members.

# class declaration
const Complex (class)
# constructor
trans Complex:preset (re im) {
  trans this:re (Real re)
  trans this:im (Real im)
}

The constructor creates a complex object with the help of the real part and the imaginary part. Any object type which can be bound to a Realobject is acceptable.

# class mutators
trans Complex:set-re (x) (trans this:re (Real re))
trans Complex:set-im (x) (trans this:im (Real im))
# class accessors
trans Complex:get-re nil (Real this:re)
trans Complex:get-im nil (Real this:im)

The accessors and the mutators simply provides the interface to the complex number components and perform a cloning of the calling or returned objects.

# complex number module
trans Complex:module nil {
  trans result (Real (+ (* this:re this:re) 
      (* this:im this:im)))
  result:sqrt
}
# complex number formatting
trans Complex:format nil {
  trans result (String this:re)
  result:+= "+i" 
  result:+= (String this:im)
}

The moduleand formatare simple methods. Note the the complex number formatting is arbitrary here.

# complex predicate
const complex-p (c) (
  if (instance-p c) (== Complex c:meta) false)

The complex-ppredicate is the perfect illustration of the use of the metareserved symbol. However, it shall be noted that the meta-comparison is done if and only if the calling argument is an instance.

# operators
trans Complex:== (c) (
  if (complex-p c) (and (this:re:== c:re) 
    (this:im:== c:im)) (
    if (number-p c)  (and (this:re:== c) 
      (this:im:zero-p)) false))
trans Complex:= (c) {
  if (complex-p c) {
    this:re:= (Real c:re)
    this:im:= (Real c:im)
    return this
  }
  this:re:= (Real c)
  this:im:= 0.0
  return this
}
trans Complex:+ (c) {
  trans result (Complex this:re this:im)
  if (complex-p c) {
    result:re:+= c:re
    result:im:+= c:im
    return result
  }
  result:re:+= (Real c)
  eval result
}

The operators are a little tedious to write. The comparison can be done with a complex number or a built-in number object. The assignation operator creates a copy for both the real and imaginary part. The summation operator is given here for illustration purpose.

Inheritance
Inheritance is the mechanism by which a class or an instance inherits methods and data member access from a parent object. The class model is based on a single inheritance model. When an instance object defines a parent object, such object is called a super instance. The instance which has a super instance is called a derived instance. The main utilization of inheritance is the ability to reuse methods for that super instance.

Derivation construction
A derived object is generally defined within the presetmethod of that instance by setting the superdata member. The superreserved keyword is set to nil at the instance construction. The good news is that any object can be defined as a super instance, including built-in object.

const c (class)
const c:preset nil {
  trans this:super 0
}

In the example above, an instance of class cis constructed. The super instance is with an integer object. As a consequence, the instance is derived from the Integerinstance. Another consequence of this scheme is that derived instance do not have to be built from the same base class.

Derived symbol access
When an instance is derived from another one, any symbol which belongs to the super instance can be access with the use of the superdata member. If the super class can evaluate a symbol, that symbol is resolved automatically by the derived instance.

const c       (class)
const i       (c)
trans i:a     1
const j       (c)
trans j:super i
println j:a

When a symbol is evaluated, a set of search rules is applied. The engine gives the priority to the class nameset vs the super instance. As a consequence, a class data member might shadow a super instance data member. The rule associated with a symbol evaluation can be summarized as follow.

Instance re-parenting
The ability to set dynamically the parent instance make the object model an ideal candidate to support instance re-parenting. In this model, a change in the parent instance is automatically reflected at the instance method call.

const c (class)
const i (c)
trans i:super 0
println (i:to-string) # 0
trans i:super "hello world"
println (i:to-string) # hello world

In this example, the instance is originally set with an Integerinstance parent. Then the instance is re-parentedwith a Stringinstance parent. The call to the to-stringmethod illustrates this behavior.

Instance re-binding
The ability to set dynamically the instance class is another powerful feature of the class model. In this approach, the instance meta class can be changed dynamically with the mutemethod. Furthermore, it is also possible to create initially an instance without any class binding, which is later muted.

# create a point class
const  point (class)
# point class
trans point:preset (x y) {
  trans this:x x
  trans this:y y
}
# create an empty instance
const p (Instance)
# bind the point class
p:mute point 1 2

In this example, when the instance is muted, the presetmethod is called automatically with the extra arguments.

Instance inference
The ability to instantiate dynamically inferred instance is offered by the instance model. An instance bis said to be inferred by the instance awhen the instance ais the super instance of the instance b. The instance inference is obtained by binding the infersymbol to a class. When an instance of that class is created, the inferred instance is also created.

# base class A
const A  (class)
# inferred class B
const B  (class)
const A:infer B
# create an instance from A
const  x (A)
assert B (x:meta)
assert A (x:super:meta)

In this example, when the instance is created, the inferred instance is also created and returned by the instantiation process. The presetmethod is only called for the inferred instance if possible or the base instance if there is no inferring class. Because the base presetpreset method is not called automatically, the inferred method is responsible to do such call.

trans B:preset (x y) {
  trans this:xb x
  trans this:yb y
  if (== A this:super:meta) (this:super:preset x y)
}

Because the class can mute from one call to another and also the inferred class, the presetmethod call must be used after a discrimination of the meta class has been made as indicated by the above example.

Instance deference
In the process of creating instances, one might have a generic class with a method that attempts to access a data member which is bound to another class. The concept of class deferenceis exactly designed for this purpose. With the help of reserved keyword defer, a class with virtual data member accessors can be bound to a base class as indicated in the example below.

# create the base and defer class
const bc (class)
const dc (class)
# bind the base preset method
trans bc:preset nil (const this:y 2)
# bind the defer accessor to the base data member
trans dc:get-y nil (eval this:y)
# bind the defer class in the base class
const bc:defer dc
# create an instance from the base class
const i (bc)
# access to the base member with the defer method
assert 2 (i:get-y)

It is worth to note that the class deference is made at the class level. When an instance of the base class is created, all methods associated with the deferentclass are visible from the base class, thus making the deferentclass a virtual interface to the base class.

ADVANCED CONCEPTS¶

Exception
An exceptionis an unexpected change in the execution flow. The exception model is based on a mechanism which throws the exception to be caught by a handler. The mechanism is also designed to be compatible with the native "C++" implementation.

Throwing an exception
An exception is thrown with the reserved keyword throw. When an exception is thrown, the normal flow of execution is interrupted and an object used to carry the exception information is created. Such exception object is propagated backward in the call stack until an exception handler catch it.

if (not (number-p n)) 
(throw "type-error" "invalid object found" n)

The example above is the general form to throw an exception. The first argument is the the exception id. The second argument is the exception reason. The third argument is the exception object. The exception id and reason are always a string. The exception object can be any object which is carried by the exception. The reserved keyword throwaccepts 0 or more arguments.

throw              
throw "type-error" 
throw "type-error" "invalid argument"

With 0 argument, the exception is thrown with the exception id set to "user-exception". With one argument, the argument is the exception id. With 2 arguments, the exception id and reason are set. Within a try block, an exception can be thrown again by using the exception object represented with the whatsymbol.

try {
  ...
} {
  println "exception caught and re-thrown"
  throw what
}

Exception handler
The special form tryexecutes a form and catch an exception if one has been thrown. With one argument, the form is executed and the result is the result of the form execution unless an exception is caught. If an exception is caught, the result is the exception object. If the exception is a native one, the result is nil.

try (+ 1 2)
try (throw)
try (throw "hello")
try (throw "hello" "world")
try (throw "hello" "world" "folks")

In its second form, the tryreserved keyword can accept a second form which is executed when an exception is caught. When an exception is caught, a new nameset is created and the special symbol whatis bounded with the exception object. In such environment, the exception can be evaluated.

try (throw "hello")              
(eval what:eid)
try (throw "hello" "world")      
(eval what:reason)
try (throw "hello" "world" 2000) 
(eval what:object)

Exceptions are useful to notify abruptly that something went wrong. With an untyped language, it is also a convenient mechanism to abort an expression call if some arguments do not match the expected types.

# protected factorial
const fact (n) {
  if (not (integer-p n)) 
  (throw "number-error" "invalid argument in fact")
  if (== n 0) 1 (* n (fact (- n 1)))
}
try (fact 5) 0
try (fact "hello") 0

Nameset
A nameset is created with the reserved keyword nameset. Without argument, the namesetreserved keyword creates a nameset without setting its parent. With one argument, a nameset is created and the parent set with the argument.

const nset (nameset)
const nset (nameset ...)

Default namesets
When a nameset is created, the symbol .is automatically created and bound to the newly created nameset. If a parent nameset exists, the symbol ..is also automatically created. The use of the current nameset is a useful notation to resolve a particular name given a hierarchy of namesets.

trans a 1 # 1
block {
  trans   a (+ a 1) # 2
  println ..:a 1    # 1
}
println a           # 1

Nameset and inheritance
When a nameset is set as the super object of an instance, some interesting results are obtained. Because symbols are resolved in the nameset hierarchy, there is no limitation to use a nameset to simulate a kind of multiple inheritance. The following example illustrates this point.

const   cls (class)
const   ins (cls)
const   ins:super (nameset)
const   ins:super:value 2000
const   ins:super:hello "hello world "
println ins:hello ins:value # hello world 2000

Delayed Evaluation
The engine provides a mechanism called delayed evaluation. Such mechanism permits the encapsulation of a form to be evaluated inside an object called a promise.

Creating a promise
The reserved keyword delaycreates a promise. When the promise is created, the associated object is not evaluated. This means that the promise evaluates to itself.

const a (delay (+ 1 2))
promise-p a # true

The previous example creates a promise and store the argument form. The form is not yet evaluated. As a consequence, the symbol aevaluates to the promise object.

Forcing a promise
The reserved keyword forcethe evaluation of a promise. Once the promise has been forced, any further call will produce the same result. Note also that, at this stage, the promise evaluates to the evaluated form.

trans   y 3
const   l ((lambda (x) (+ x y)) 1)
assert  4 (force l)
trans   y 0
assert  4 (force l)

Enumeration
Enumeration, that is, named constant bound to an object, can be declared with the reserved keyword enum. The enumeration is built with a list of literal and evaluated as is.

const  e    (enum E1 E2 E3)
assert true (enum-p e)

The complete enumeration evaluates to an Enumobject. Once built, enumeration item evaluates by literal and returns an Itemobject.

assert true   (item-p e:E1)
assert "Item" (e:E1:repr)

Items are comparable objects. Only items can be compared. For a given item, the source enumeration can be obtained with the get-enummethod.

# check for item equality
const i1 e:E1
const i2 e:E2
assert true  (i1:== i1)
assert false (== i1 i2)
# get back the enumeration
assert true (enum-p (i1:get-enum))

Logger
The Loggerclass is a message logger that stores messages in a buffer with a level. The default level is the level 0. A negative level generally indicates a warning or an error message but this is just a convention which is not enforced by the class. A high level generally indicates a less important message. The messages are stored in a circular buffer. When the logger is full, a new message replace the oldest one. By default, the logger is initialized with a 256 messages capacity that can be re-sized.

const log    (Logger)
assert true  (logger-p log)

When a message is added, the message is stored with a time-stamp and a level. The time-stamp is used later to format a message. The lengthmethod returns the number of logged messages. The get-messagemethod returns a message by index. Because the system operates with a circular buffer, the get-messagemethod manages the indexes in such way that the old messages are accessible with the oldest index. For example, even after a buffer circulation, the index 0 will point to the oldest message. The get-message-levelreturns the message level and the get-message-timereturns the message posted time.

const mesg (log:get-message 0)

In term of usage, the logger facility can be conveniently used with other derived classes. The standard i/o module provides several classes that permits to manage logging operations in a convenient way.

Interpreter
The interpreter is by itself a special object with specialized methods which do not have equivalent using the standard notation. The interpreter is always referred with the special symbol interp. The following table is a summary of the symbols and methods bound to the interpreter.

Arguments vector
The interp:argvqualified name evaluates to a vector of strings. Each argument is stored in the vector during the interpreter initialization.

zsh> axi hello world
(axi) println (interp:argv:length) # 2
(axi) println (interp:argv:get 0)  # hello

Interpreter version
Several symbols can be used to track the interpreter version and the operating system. The full version is bound to the interp:versionqualified name. The full version is composed of the major, minorand patchnumber. The operating system name is bound to the qualified name interp:os-name. The operating system type is bound to the interp:os-type.

println "major number   : " interp:major-version
println "minor number   : " interp:minor-version
println "patch number   : " interp:patch-version
println "version number : " interp:version
println "system name    : " interp:os-name
println "system type    : " interp:os-type
println "official uri   : " interp:afnix-uri

Method load
The interp:loadmethod loads and execute a file. The interpreter interactive command session is suspended during the execution of the file. In case of error or if an exception is raised, the file execution is terminated. The process used to load a file is governed by the file resolver. Without extension, a compiled file is searched first and if not found a source file is searched.

Method library
The interp:librarymethod loads and initializes a library. The interpreter maintains a list of opened library. Multiple execution of this method for the same library does nothing. The method returns the library object.

interp:library "afnix-sys"
println "random number: " (afnix:sys:get-random)

Method dup
The interpreter can be duplicated with the help of the dupmethod. Without argument, a clone of the current interpreter is made and a terminal object is attached to it. When used in conjunction with the rollmethod, this approach permits to create an interactive interpreter. The dupmethod also accepts a terminal object.

# duplicate the interpreter
const si (interp:dup)
# change the primary prompt
si:set-primary-prompt "(si)"

Method roll
The interpreter loop can be run with the roll. The loop operates by reading the interpreter input stream. If the interpreter has been cloned with the help of the dupmethod, this method provides a convenient way to operate in interactive mode. The method is not called loopbecause it is a reserved keyword and starting a loop is like having the ball rolling.

# duplicate the interpreter
const si (interp:dup)
# loop with this interpreter
si:roll

Method wait
The interpreter can wait for all normal threads to complete. When invoked, the interpreter monitors all normal threads and wait unil the terminate normally. This is a standard synchronization method in a multithreaded environment.

# create a thread
launch f
# wait for completion
interp:wait

Librarian object
A librarian fileis a special file that acts as a containers for various files. A librarian file is created with the axl-- cross librarian --utility. Once a librarian file is created, it can be added to the interpreter resolver. The file access is later performed automatically by name with the standard interpreter loadmethod.

Creating a librarian
The axlutility is the preferred way to create a librarian. Given a set of files, axlcombines them into a single one.

zsh: axl -h
usage: axl [options] [files]
[h]      print this help message
[v]      print version information
[c]      create a new librarian
[x]      extract from the librarian
[s]      get file names from the librarian
[t]      report librarian contents
[f] lib  set the librarian file name

The coption creates a new librarian. The librarian file name is specified with the foption.

zsh: axl -c -f librarian.axl file-1.als file-2.als

The previous command combines file-1.alsand file-2.alsinto a single file called librarian.axl. Note that any file can be included in a librarian.

Using the librarian
Once a librarian is created, the interpreter -ioption can be used to specify it. The -ioption accepts either a directory name or a librarian file. Once the librarian has been opened, the interpreter loadmethod can be used as usual.

zsh> axi -i librarian.axl
(axi) interp:load "file-1.als"
(axi) interp:load "file-2.als"

The librarian acts like a file archive. The interpreter file resolver takes care to extract the file from the librarian when the loadmethod is invoked.

Librarian contents
The axlutility provides the -tand -soptions to look at the librarian contents. The -soption returns all file name in the librarian. The -toption returns a one line description for each file in the librarian.

zsh: axl -t -f librarian.axl
--------       1234 file-1.als
--------       5678 file-2.als

The one line report contains the file flags, the file size and the file name. The file flags are not used at this time. One possible use in the future is for example, an auto-load bitor any other useful things.

Librarian extraction
The -xoption permits to extract file from the librarian. Without any file argument, all files are extracted. With some file arguments, only those specified files are extracted.

zsh: axl -x -f librarian.axl
zsh: axl -x -f librarian.axl file-1.als

Librarian object
The Librarianobject can be used as a convenient way to create a collection of files or to extract some of them.

Output librarian
The Librarianobject is a standard object. Its predicate is librarian-p. Without argument, a librarian is created in output mode. With a string argument, the librarian is opened in input mode, with the file name argument. The output mode is used to create a new librarian by adding file into it. The input mode is created to read file from the librarian.

# create a new librarian
const lbr (Librarian)
# add a file into it
lbr:add "file-1.als"
# write it
lbr:write "librarian.axl"

The addmethod adds a new file into the librarian. The writemethod the full librarian as a single file those name is writemethod argument.

Input librarian
With an argument, the librarian object is created in input mode. Once created, file can be read or extracted. The lengthmethod -- which also work with an output librarian -- returns the number of files in the librarian. The exists-ppredicate returns true if the file name argument exists in the librarian. The get-namesmethod returns a vector of file names in this librarian. The extractmethod returns an input stream object for the specific file name.

# open a librarian for reading
const lbr (Librarian "librarian.axl")
# get the number of files
println (lbr:length)
# extract the first file
const is (lbr:extract "file-1.als")
# is is an input stream - dump each line
while (is:valid-p) (println (is:readln))

Most of the time, the librarian object is used to extract file dynamically. Because a librarian is mapped into the memory at the right offset, there is no worry to use big librarian, even for a small file. Note that any type of file can be used, text or binaries.

File resolver
The file resolveris a special object used by the interpreter to resolve file path based on the search path. The resolver uses a mixed list of directories and librarian files in its search path. When a file path needs to be resolved, the search path is scanned until a matched is found. Because the librarian resolution is integrated inside the resolver, there is no need to worry about file extraction. That process is done automatically. The resolver can also be used to perform any kind of file path resolution.

Resolver object
The resolver object is created without argument. The addmethod adds a directory path or a librarian file to the resolver. The validmethod checks for the existence of a file. The lookupmethod returns an input stream object associated with the object.

# create a new resolver
const rslv (Resolver)
assert true (resolver-p rslv)
# add the local directory on the search path
rslv:add "."
# check if file test.als exists
# if this is ok - print its  contents
if (rslv:valid-p "test.als") {
  const is (rslv:lookup "test.als")
  while (is:valid-p) (println (is:readln))
}

Thread operations
The interpreter is a multi-threaded engine with a native implementation of objects locking. A thread is started with the reserved keyword launch. The execution is completed when all threads have terminated. This means that the master thread (i.e the first thread) is suspended until all other threads have completed their execution.

Starting a thread
A thread is started with the reserved keyword launch. The form to execute in a thread is the argument. The simplest thread to execute is the nilthread.

launch (nil)

There exists an alternate mechanism to start a thread with the reserved keyword launchand a thread object. Such mechanism is used when using deferred thread object creation or a thread generator object known as a thread set.

Thread object and result
When a thread terminate, the thread object holds the result of the last executed form. The thread object is returned by the launchcommand. The thread-ppredicates returns trueif the object is a thread descriptor.

const thr (launch (nil))
println   (thread-p thr) # true

The thread result can be obtained with the help of the resultmethod. Although the result can be accessed at any time, the returned value will be niluntil the thread as completed its execution.

const thr (launch (nil))
println   (thr:result)   # nilp

Although the engine will ensure that the result is niluntil the thread has completed its execution, it does not mean that it is a reliable approach to test until the result is not nil. The engine provides various mechanisms to synchronize a thread and eventually wait for its completion.

Shared objects
The whole purpose of using a multi-threaded environment is to provide a concurrent execution with some shared variables. Although, several threads can execute concurrently without sharing data, the most common situation is that one or more global variable are accessed -- and even changed -- by one or more threads. Various scenarios are possible. For example, a variable is changed by one thread, the other thread just read its value. Another scenario is one read, multiple write, or even more complicated, multiple read and multiple write. In any case, the interpreter subsystem must ensure that each objects are in a good state when such operation do occur.The engine provides an automatic synchronization mechanism for global objects, where only one thread can modify an object, but several thread can read it. This mechanism known as read-write lockingguarantees that there is only one writer, but eventually multiple reader. When a thread starts to modify an object, no other thread are allowed to read or write this object until the transaction has been completed. On the opposite, no thread is allowed to change (i.e. write) an object, until all thread which access (i.e. read) the object value have completed the transaction. Because a context switch can occur at any time, the object read-write locking will ensure a safe protection during each concurrent access.

Shared protection access
We illustrate the previous discussion with an interesting example and some variations around it. Let's consider a form which increase an integer object and another form which decrease the same integer object. If the integer is initialized to 0, and the two forms run in two separate threads, we might expect to see the value bounded by the time allocated for each thread. In other word, this simple example is a very good illustration of your machine scheduler.

# shared variable access
const var 0
# increase method
const incr nil {
  while true (println "increase: " (var:= (+ var 1)))
}
# decrease method
const decr nil {
  while true (println "decrease: " (var:= (- var 1)))
}
# start both threads
launch (decr)
launch (incr)

In the previous example, varis initialized to 0. The incrthread increments varwhile the decrthread decrements var. Depending on the operating system, the result stays bounded within a certain range. The previous example can be changed by using the main thread or a third thread to print the variable value. The end result is the same, except that there is more threads competing for the shared variable.

# shared variable access
const var 0	
# incrementer, decrementer and printer
const incr nil (while true (var:= (+ var 1)))
const decr nil (while true (var:= (- var 1)))
const prtv nil (while true (println "value = " var))
# start all threads
launch (decr)
launch (incr)
launch (prtv)

Synchronization
Although, there is an automatic synchronization mechanism for reading or writing an object, it is sometimes necessary to control the execution flow. There are basically two techniques to do so. First, protect a form from being executed by several threads. Second, wait for one or several threads to complete their task before going to the next execution step.

Form synchronization
The reserved keyword synccan be used to synchronize a form. When a form, is synchronized, the engine guarantees that only one thread will execute this form.

const print-message (code mesg) (
  sync {
    errorln "error  : " code
    errorln "message: " mesg
  }
)

The previous example creates a gamma expression which make sure that both the error code and error message are printed in one group, when several threads call it.

Thread completion
The other piece of synchronization is the thread completion indicator. The thread descriptor contains a method called waitwhich suspend the calling thread until the thread attached to the descriptor has been completed. If the thread is already completed, the method returns immediately.

# simple flag
const flag false
# simple tester
const ftest (bval) (flag:= bval)
# run the thread and wait
const thr (launch (ftest true))
thr:wait
assert true flag

This example is taken from the test suites. It checks that a boolean variable is set when started in a thread. Note the use of the waitmethod to make sure the thread has completed before checking for the flag value. It is also worth to note that waitis one of the method which guarantees that a thread result is valid. Another use of the waitmethod can be made with a vector of thread descriptors when one wants to wait until all of them have completed.

# shared vector of threads descriptors
const thr-group (Vector)
# wait until all threads in the group are finished
const wait-all nil (for (thr) (thr-group) (thr:wait))

Complete example
We illustrate the previous discussion with a complete example. The idea is to perform a matrix multiplication. A thread is launched when when multiplying one line with one column. The result is stored in the thread descriptor. A vector of thread descriptor is used to store the result.

# initialize the shared library
interp:library "afnix-sys"
# shared vector of threads descriptors
const thr-group (Vector)
# waits until all threads in the group are finished
const wait-all nil (for (thr) (thr-group) (thr:wait))

The group of threads is represented as a vector. Based on the the previous discussion, a simple loop that blocks until all threads are completed is designed as a simple gamma expression.

# initializes a matrix with random numbers
const init-matrix (n) {
  trans i (Integer 0)
  const m (Vector)
  do {
    trans v (m:add (Vector))
    trans j (Integer)
    do {
      v:add (afnix:sys:get-random)
    } (< (j:++) n)
  } (< (i:++) n)
  eval m
}

The matrix initialization is quite straightforward. The matrix is represented as a vector of lines. Each line is also a vector of random integer number. It is here worth to note that the standard mathmodule provides a native implementation of real matrix.

# this procedure multiply one line with one column
const mult-line-column (u v) {
  assert (u:length) (v:length)
  trans result 0
  for (x y) (u v) (result:+= (* x y))
  eval result
}
# this procedure multiply two vectors assuming one 
# is a line and one is a column from the matrix
const mult-matrix (mx my) {
  for (lv) (mx) {
    assert true (vector-p lv)
    for (cv) (my) {
      assert true (vector-p cv)
      thr-group:add (launch (mult-line-column lv cv))
    }
  }
}

The matrix vector multiplication is at the heart of the example. Each line-column multiplication is started into a thread and the thread object is placed into the thread group vector.

# check for some arguments
# note the use of errorln method
if (== 0 (interp:argv:length)) {
  errorln "usage: axi 0607.als size"
  afnix:sys:exit 1
}
# get the integer and multiply
const n (Integer (interp:argv:get 0))
mult-matrix (init-matrix n) (init-matrix n)
# wait for all threads to complete
wait-all
# make sure we have the right number
assert (* n n) (thr-group:length)

The main execution is started with the matrix size as the first argument. Two random matrices are then created and the multi-threaded multiplication is launched. The main thread is blocked until all threads in the thread group are completed.

Condition variable
A condition variableis another mechanism to synchronize several threads. A condition variable is modeled with the Condvarobject. At construction, the condition variable is initialized to false. A thread calling the waitmethod will block until the condition becomes true. The markmethod can be used by a thread to change the state of a condition variable and eventually awake some threads which are blocked on it. The following example shows how the main thread blocks until another change the state of the condition.

# create a condition variable
const cv (Condvar)
# this function runs in a thread - does some 
# computation and mark the condition variable
const do-something nil {
  # do some computation
  ....
  # mark the condition
  cv:mark
}
# start some computation in a thread
launch (do-something)
# block until the condition is changed
cv:wait-unlock
# continue here

In this example, the condition variable is created at the beginning. The thread is started and the main thread blocks until the thread change the state of the condition variable. It is important to note the use of the wait-unlockmethod. When the main thread is re-started (after the condition variable has been marked), the main thread owns the lock associated with the condition variable. The wait-unlockmethod unlocks that lock when the main thread is restarted. Note also that the wait-unlockmethod reset the condition variable. if the waitmethod was used instead of wait-unlockthe lock would still be owned by the main thread. Any attempt by other thread to call the mark method would result in the calling thread to block until the lock is released.The Condvarclass has several methods which can be used to control the behavior of the condition variable. Most of them are related to lock control. The resetmethod reset the condition variable. The lockand unlockcontrol the condition variable locking. The mark, waitand wait-unlockmethod controls the synchronization among several threads.

Function expression
A lambda expression or a gamma expression can be seen like a function object with no name. During the evaluation process, the expression object is evaluated as well as the arguments -- from left to right -- and a result is produced by applying those arguments to the function object. An expression can be built dynamically as part of the evaluation process.

(axi) println ((lambda (n) (+n 1)) 1)
2

The difference between a lambda expression and a gamma expression is only in the nameset binding during the evaluation process. The lambda expression nameset is linked with the calling one, while the gamma expression nameset is linked with the top level nameset. The use of gamma expression is particularly interesting with recursive functions as it can generate a significant execution speedup. The previous example will behaves the same with a gamma expression.

(axi) println ((gamma (n) (+n 1)) 1)
2

Self reference
When combining a function expression with recursion, the need for the function to call itself is becoming a problem since that function expression does not have a name. For this reason, the writing system provides the reserved keyword selfthat is a reference to the function expression. We illustrate this capability with the well-known factorial expression written in pure functional style.

(axi) println ((gamma (n) 
    (if (<= n 1) 1 (* n (self (- n 1))))) 5)
120

The use of a gamma expression versus a lambda expression is a matter of speed. Since the gamma expression does not have free variables, the symbol resolution is not a concern here.

Closed variables
One of the writing system characteristic is the treatment of free variables. A variable is said to be free if it is not bound in the expression environment or its children at the time of the symbol resolution. For example, the expression ((lambda (n) (+ n x)) 1)computes the sum of the argument nwith the free variable x. The evaluation will succeeds if xis defined in one of the parent environment. Actually this example can also illustrates the difference between a lambda expression and a gamma expression. Let's consider the following forms.

trans x 1
const do-print nil {
  trans x 2
  println ((lambda (n) (+ n x)) 1)
}

The gamma expression do-printwill produce 3since it sums the argument nbound to 1, with the free variable xwhich is defined in the calling environment as 2. Now if we rewrite the previous example with a gamma expression the result will be one, since the expression parent will be the top level environment that defines xas 1.

trans x 1
const do-print nil {
  trans x 2
  println ((gamma (n) (+ n x)) 1)
}

With this example, it is easy to see that there is a need to be able to determine a particular symbol value during the expression construction. Doing so is called closing a variable. Closing a variable is a mechanism that binds into the expression a particular symbol with a value and such symbol is called a closed variable, since its value is closed under the current environment evaluation. For example, the previous example can be rewritten to close the symbol x.

trans x 1
const do-print nil {
  trans x 2
  println ((gamma (n) (x) (+ n x)) 1)
}

Note that the list of closed variable immediately follow the argument list. In this particular case, the function do-printwill print 3since xhas been closed with the value 2has defined in the function do-print.

Dynamic binding
Because there is a dynamic binding symbol resolution, it is possible to have under some circumstances a free or closed variable. This kind of situation can happen when a particular symbol is defined under a condition.

lambda (n) {
  if (<= n 1) (trans x 1)
  println (+ n x)
}

With this example, the symbol xis a free variable if the argument nis greater than 1. While this mechanism can be powerful, extreme caution should be made when using such feature.

Lexical and qualified names
The basic forms elements are the lexical and qualified names. Lexical and qualified names are constructed by the parser. Although the evaluation process make that lexical object transparent, it is possible to manipulate them directly.

(axi) const sym (protect lex)
(axi) println   (sym:repr)
Lexical

In this example, the protectreserved keyword is used to avoid the evaluation of the lexical object named lex. Therefore the symbol symrefers to a lexical object. Since a lexical -- and a qualified -- object is a also a literal object, the printlnreserved function will work and print the object name. In fact, a literal object provides the to-stringmethod that returns the string representation of a literal object.

(axi) const sym (protect lex)
(axi) println   (sym:to-string)
lex

Symbol and argument access
Each nameset maintains a table of symbols. A symbol is a binding between a name and an object. Eventually, the symbol carries the constflag. During the lexical evaluation process, the lexical object tries to find an object in the nameset hierarchy. Such object can be either a symbol or an argument. Again, this process is transparent, but can be controlled manually. Both lexical and qualified named object have the mapmethod that returns the first object associated in the nameset hierarchy.

(axi) const obj 0
(axi) const lex (protect obj)
(axi) const sym (lex:map)
(axi) println   (sym:repr)
Symbol

A symbol is also a literal object, so the to-stringand to-literalmethods will return the symbol name. Symbol methods are provided to access or modify the symbol values. It is also possible to change the constsymbol flag with the set-constmethod.

(axi) println (sym:get-const)
true
(axi) println (sym:get-object)
0
(axi) sym:set-object true
(axi) println (sym:get-object)
true

A symbol name cannot be modified, since the name must be synchronized with the nameset association. On the other hand, a symbol can be explicitly constructed. As any object, the =operator can be used to assign a symbol value. The operator will behaves like the set-objectmethod.

(axi) const sym (Symbol "symbol")
(axi) println sym
symbol
(axi) sym:= 0
(axi) println (eval sym)
0

Closure
As an object, the Closurecan be manipulated outside the traditional declarative way. A closure is a special object that holds an argument list, a set of closed variables and a form to execute. The mechanic of a closure evaluation has been described earlier. What we are interested here is the ability to manipulate a closure as an object and eventually modify it. Note that by default a closure is constructed as a lambda expression. With a boolean argument set to true the same result is obtained. With false, a gamma expression is created.

(axi) const f (Closure)
(axi) println (closure-p f)
true

This example creates an empty closure. The default closure is equivalent to the trans f nil nil. The same can be obtained with const f (Closure true). For a gamma expression, the following forms are equivalent, const f (Closure false)and const f nil nil. Remember that it is transand constthat differentiate between a lambda and a gamma expression. Once the closure object is defined, the set-formmethod can be used to bind a form.

# the simple way
trans f nil (println "hello world")
# the complex way
const f    (Closure)
f:set-form (protect (println "hello world"))

There are numerous situations where it is desirable to mute dynamically a closure expression. The simplest one is the closure that mute itself based on some context. With the use of self, a new form can be set to the one that is executed. Another use is a mechanism call advice, where some new computation are inserted prior the closure execution. Note that appending to a closure can lead to some strange results if the existing closure expression uses returnspecial forms. In a multi-threaded environment, the ability to change a closure expression is particularly handy. For example a special thread could be used to monitor some context. When a particular situation develops, that threads might trigger some closure expression changes. Note that changing a closure expression does not affect the one that is executed. If such change occurs during a recursive call, that change is seen only at the next call.