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

@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* [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))))
]}

@section{Constructing functions}

@section{Random functions}

@section{Threshold Boolean functions}