dds/scribblings/functions.scrbl

#lang scribble/manual
@(require scribble/example racket/sandbox
	  (for-label typed/racket/base "../functions.rkt" dds/utils
	  	     typed/racket/unsafe))

@title[#:tag "functions"]{dds/functions: Formal Functions}

@defmodule[dds/functions]

This modules provides some definitions for working with functions: tabulating,
(re)constructing from tables, generating random functions, etc.
Some definitions of particular kinds of functions are also provided (threshold
Boolean functions, etc.).

@(define functions-evaluator
  (parameterize ([sandbox-output 'string]
  		 [sandbox-error-output 'string]
		 [sandbox-memory-limit 50])
   (make-evaluator 'typed/racket #:requires '((submod "functions.rkt" typed)))))

@section{Tabulating functions}

@defproc[(tabulate [func (-> a ... b)]
		   [doms (List (Listof a) ... a)])
		   (Listof (Listof (U Any b)))]{

Given a function @racket[func] and a list of domains @racket[doms] for each of
its arguments, in order, produces a list of lists giving the values of
arguments and the value of the functions for these inputs.

@examples[#:eval functions-evaluator
(tabulate (λ (x y) (and x y)) '((#f #t) (#f #t)))
]}

@defproc[(tabulate/strict [func (-> a ... b)]
		   	  [doms (List (Listof a) ... a)])
		   	  (Listof (List (List a ...) (Listof b)))]{

Like @racket[tabulate], but the types of the arguments of @racket[func]
explicitly appear in the return type.

As of 2022-03-06, I am not able to write the type of a list first containing
elements of types @racket[a ...], followed by an element of type @racket[b].
This is why this function returns a list of lists, each containing first a list
of inputs, and then the output of @racket[func].

@examples[#:eval functions-evaluator
(tabulate/strict (λ (x y) (and x y)) '((#f #t) (#f #t)))
]}

@defproc[(tabulate/untyped [funcs procedure?]
		           [doms (listof list?)])
		           (listof list?)]{

A version of @racket[tabulate] without type checking.

As of 2022-03-06, Typed Racket cannot generate contracts for polymorphic
variable-arity functions.  This means that @racket[tabulate] cannot be used
directly in untyped code and should be replaced by @racket[tabulate/untyped],
which is simply an @racket[unsafe-provide] of @racket[tabulate].

@examples[#:eval functions-evaluator
(tabulate/untyped (λ (x y) (and x y)) '((#f #t) (#f #t)))
]

The contracts in the documentation entry are provided for explanatory purposes
and are not actually enforced.  Some contracts on the functions
@racket[tabulate] uses internally are still checked.  For example, trying to
tabulate a function of wrong arity will still raise an error.

@examples[#:eval functions-evaluator
(module tabulate/untyped-test racket/base
  (require "functions.rkt")
  (tabulate/untyped (λ (x y z) (and x y z)) '((#f #t) (#f #t))))
(eval:error (require 'tabulate/untyped-test))
]}

@defproc[(tabulate* [funcs (Listof (-> a ... b))]
		    [doms (List (Listof a) ... a)])
		    (Listof (Listof (U Any b)))]{

Like @racket[tabulate], but @racket[funcs] is a list of functions taking the
same arguments over the same domains.

@examples[#:eval functions-evaluator
(tabulate* (list (λ (x y) (and x y))
                 (λ (x y) (or x y)))
           '((#f #t) (#f #t)))
]}

@defproc[(tabulate*/strict [funcs (Listof (-> a ... b))]
			   [doms (List (Listof a) ... a)])
			   (Listof (List (List a ...) (Listof b)))]{

Like @racket[tabulate*], but the types of the arguments of the functions
explicitly appear in the return type.

As of 2022-03-06, I am not able to write the type of a list first containing
elements of types @racket[a ...], followed by a list of elements of type
@racket[b].  This is why this function returns a list of lists, each containing
first a list of inputs, and then the list of outputs of @racket[funcs].

@examples[#:eval functions-evaluator
(tabulate*/strict (list (λ (x y) (and x y))
                  	(λ (x y) (or x y)))
           	   '((#f #t) (#f #t)))
]

The result of @racket[tabulate*] can be obtained by applying
@racket[append-lists]:

@examples[#:eval functions-evaluator
(require (only-in "utils.rkt" append-lists))
(append-lists (tabulate*/strict (list (λ (x y) (and x y))
                                      (λ (x y) (or x y)))
                                '((#f #t) (#f #t))))
]}

@defproc[(tabulate*/untyped [funcs (listof procedure?)]
			    [doms (listof list?)])
			    (listof list?)]{

A version of @racket[tabulate*] without type checking.

As of 2022-03-06, Typed Racket cannot generate contracts for polymorphic
variable-arity functions.  This means that @racket[tabulate*] cannot be used
directly in untyped code and should be replaced by @racket[tabulate*/untyped],
which is simply an @racket[unsafe-provide] of @racket[tabulate*].

@examples[#:eval functions-evaluator
(tabulate*/untyped (list (λ (x y) (and x y))
                         (λ (x y) (or x y)))
                   '((#f #t) (#f #t)))
]

The contracts in the documentation entry are provided for explanatory purposes
and are not actually enforced.  Some contracts on the functions
@racket[tabulate*] uses internally are still checked.  For example, trying to
tabulate a function of wrong arity will still raise an error.

@examples[#:eval functions-evaluator
(module untyped-test racket/base
  (require "functions.rkt")
  (tabulate*/untyped (list (λ (x y z) (and x y z)))
                     '((#f #t) (#f #t))))
(eval:error (require 'untyped-test))
]}

@section{Constructing functions}

@section{Random functions}

@section{Threshold Boolean functions}