Procedures

Function: apply proc [arg1 ...] args

Args must be a sequence (list, vector, or string) or a primitive Java array. (This is an extension over standard Scheme, which requires that args be a list.) Calls the proc (which must be a procedure), using as arguments the arg1... values plus all the elements of args.

Syntax: constant-fold proc arg1 ...

Same as (proc arg1 ...), unless proc and all the following arguments are compile-time constants. (That is: They are either constant, or symbols that have a global binding and no lexical binding.) In that case, proc is applied to the arguments at compile-time, and the result replaces the constant-fold form. If the application raises an exception, a compile-time error is reported. For example:
(constant-fold vector 'a 'b 'c)
is equivalent to (quote #(a b c)), assuming vector has not been re-bound.

Procedure properties

You can associate arbitrary properties with any procedure. Each property is a (key, value)-pair. Usually the key is a symbol, but it can be any object.

The system uses certain internal properties: 'name refers to the name used when a procedure is printed; 'emacs-interactive is used to implement Emacs interactive specification; 'setter is used to associate a setter prcedure.

Function: procedure-property proc key [default]

Get the property value corresponding to the given key. If proc has no property with the given key, return default (which defaults to #f) instead.

Function: set-procedure-property! proc key value

Associate the given value with the key property of proc.

To change the print name of the standard + procedure (probably not a good idea!), you could do:

(set-procedure-property! + 'name 'PLUS)

Note this only changes the name property used for printing:

+ => #<procedure PLUS>
(+ 2 3) => 5
(PLUS 3 4) => ERROR

As a matter of style, it is cleaner to use the define-procedure form, as it is a more declarative interface.

Syntax: define-procedure name [propname: propvalue] ... method ...

Defines name as a compound procedure consisting of the specified methods, with the associated properties. Applying name select the "best" method, and applies that. See the following section on generic procedures.

For example, the standard vector-ref procedure specifies one method, as well as the setter property:
(define-procedure vector-ref
  setter: vector-set!
  (lambda ((vector :: <vector>) (k :: <int>))
    (invoke vector 'get k)))

Generic (dynamically overloaded) procedures

A generic procedure is a collection of method procedures. (A "method procedure" is not the same as a Java method, but the terms are related.) You can call a generic procedure, which selects the "closest match" among the component method procedures: I.e. the most specific method procedure that is applicable given the actual arguments.

Warning: The current implementation of selecting the "best" method is not reliable if there is more than one method. It can select depending on argument count, and it can select between primitive Java methods. However, it cannot yet do what you probably hope for: select between different Scheme procedures based on parameter types.

Function: make-procedure [keyword: value]... method...

Create a generic procedure given the specific methods. You can also specify property values for the result.

The keywords specify how the arguments are used. A method: keyword is optional and specifies that the following argument is a method. A name: keyword specifies the name of the resulting procedure, when used for printing. Unrecognized keywords are used to set the procedure properties of the result.
(define plus10 (make-procedure foo: 33 name: 'Plus10
                            method: (lambda (x y) (+ x y 10))
                            method: (lambda () 10)))

Extended Formal Arguments List

The formal arguments list of a lambda expression has two extendsions over standard Scheme: Kawa borrows the extended formal argument list of DSSSL, and Kawa allows you to declare the type of the parameter.

lambda-expression ::= (lambda formals [rtype] body)

where

formals ::= (formal-arguments) | rest-arg

You can of course also use the extended format in a define:

(define (name formal-arguments) [rtype] body)

formal-arguments ::=
req-opt-args (rest-key-args | . rest-arg)

req-opt-args ::= req-arg ... [#!optional opt-arg ...]
rest-key-args ::= [#!rest rest-arg] [#!key key-arg ...]
req-arg ::= variable [:: type] | (variable [[::] type] )
opt-arg ::= arg-with-default
key-arg ::= arg-with-default
arg-with-default ::= variable [:: type]
| ( variable [:: type [initializer] | initializer [[::] type]] )
rest-arg ::= variable

When the procedure is applied to a list of actual arguments, the formal and actual arguments are processed from left to right as follows:

The req-args are bound to actual arguments starting with the first actual argument. It shall be an error if there are fewer actual arguments then there are req-args.
Next the opt-args are bound to remaining actual arguemnts. If there are fewer remaining actual arguments than there are opt-args, then the remaining variables are bound to the corresponding initializer, if one was specified, and otherwise to #f. The initializer is evaluated in an environment in which all the previous formal parameters have been bound.
If there is a rest-arg, it is bound to a list of all the remaining actual arguments. These remaining actual arguments are also eligible to be bound to keyword arguments. If there is no rest-arg and there are no key-args, then it shall be an error if there are any remaining actual arguments.
If #!key was specified, then there shall be an even number of remaining actual arguments. These are interpreted as a series of pairs, where the first member of each pair is a keyword specifying the argument name, and the second is the corresponding value. It shall be an error if the first member of a pair is not a keyword. It shall be an error if the argument name is not the same as a variable in a key-args, unless there is a rest-arg. If the same argument name occurs more than once in the list of actual arguments, then the first value is used. If there is no actual argument for a particular key-arg, then the variable is bound to the corresponding initializer, if one was specified, and otherwise to #f. The initializer is evaluated in an environment in which all the previous formal parameters have been bound.

If a type is specified, the corresponding actual argument (or the initializer default value) is coerced to the specified type. In the function body, the parameter has the specified type.

If rtype (the first form of the function body) is an unbound identifier of the form <TYPE> (that is the first character is ‘<’ and the last is ‘>’), then that specifies the function's return type. It is syntactic sugar for (as <TYPE> (begin BODY)).

Syntax: cut slot-or-expr slot-or-expr* [<...>]

where each slot-or-expr is either an expression or the literal symbol <>.

It is frequently necessary to specialize some of the parameters of a multi-parameter procedure. For example, from the binary operation cons one might want to obtain the unary operation (lambda (x) (cons 1 x)). This specialization of parameters is also known as partial application, operator section, or projection. The macro cut specializes some of the parameters of its first argument. The parameters that are to show up as formal variables of the result are indicated by the symbol <>, pronouced as "slot". In addition, the symbol <...>, pronounced as "rest-slot", matches all residual arguments of a variable argument procedure.

A cut-expression is transformed into a lambda expression with as many formal variables as there are slots in the list slot-or-expr*. The body of the resulting lambda expression calls the first slot-or-expr with arguments from the slot-or-expr* list in the order they appear. In case there is a rest-slot symbol, the resulting procedure is also of variable arity, and the body calls the first slot-or-expr with remaining arguments provided to the actual call of the specialized procedure.

Here are some examples:

(cut cons (+ a 1) <>) is the same as (lambda (x2) (cons (+ a 1) x2))

(cut list 1 <> 3 <> 5) is the same as (lambda (x2 x4) (list 1 x2 3 x4 5))

(cut list) is the same as (lambda () (list))

(cut list 1 <> 3 <...>) is the same as (lambda (x2 . xs) (apply list 1 x2 3 xs))

The first argument can also be a slot, as one should expect in Scheme: (cut <> a b) is the same as (lambda (f) (f a b))

Syntax: cute slot-or-expr slot-or-expr* [<...>]

The macro cute (a mnemonic for "cut with evaluated non-slots") is similar to cut, but it evaluates the non-slot expressions at the time the procedure is specialized, not at the time the specialized procedure is called.

For example (cute cons (+ a 1) <>) is the same as (let ((a1 (+ a 1))) (lambda (x2) (cons a1 x2)))

As you see from comparing this example with the first example above, the cute-variant will evaluate (+ a 1) once, while the cut-variant will evaluate it during every invocation of the resulting procedure.