dds/bn.rkt

#lang typed/racket

;;; dds/bn

;;; This module provides some quick definitions for running Boolean
;;; networks.  A Boolean network is a set of Boolean variables which
;;; are updated according to their corresponding update functions.
;;; The variables to be updated at each step are given by the mode.

(require "utils.rkt")

(provide Variable State UpdateFunc Network
         update make-state make-bn-funcs update-func-form->update-func
         bn-form->bn make-bn-forms)


;;; =================
;;; Basic definitions
;;; =================

(define-type Variable Symbol)

;;; A state of a Boolean network is a mapping from the variables of the
;;; network to their Boolean values.
(define-type State (HashTable Variable Boolean))

;;; An update function is a Boolean function computing a Boolean value
;;; from the given state.
(define-type UpdateFunc (-> State Boolean))

;;; A Boolean network is a mapping from its variables to its update
;;; functions.
(define-type Network (HashTable Variable UpdateFunc))

;;; Given a state s updates all the variables from xs.  This
;;; corresponds to a parallel mode.
(: update (-> Network State (Listof Variable) State))
(define (update bn  ; the Boolean network
                s   ; the state to operate on
                xs) ; the variables to update
  (let ([new-s : State (hash-copy s)])
    (for ([x xs])
      (let ([f (hash-ref bn x)])
        (hash-set! new-s x (f s))))
    new-s))

;;; A version of make-hash restricted to creating Boolean states.
(: make-state (-> (Listof (Pairof Variable Boolean)) State))
(define (make-state mappings)
  (make-hash mappings))

;;; A version of make-hash restricted to creating Boolean networks.
(: make-bn-funcs (-> (Listof (Pairof Variable UpdateFunc)) Network))
(define (make-bn-funcs funcs)
  (make-hash funcs))


;;; =========================================
;;; Syntactic description of Boolean networks
;;; =========================================

;;; An UpdateFuncForm is any form which can appear as a body of a
;;; Boolean function and which can be evaluated with eval.  For
;;; example, '(and x y (not z)).
(define-type UpdateFuncForm Any)

;;; A Boolean network form is a mapping from its variables to the
;;; forms of their update functions.
(define-type NetworkForm (HashTable Variable UpdateFuncForm))

;;; Build an update function from an update function form.
#;(: update-func-form->update-func (-> UpdateFuncForm UpdateFunc))
(define (update-func-form->update-func form)
  (lambda ([s : State])
    (cast (eval-with1 (cast s (HashTable Variable Any)) form) Boolean)))

;;; Build a Network from a Network form.
(: bn-form->bn (-> NetworkForm Network))
(define (bn-form->bn bnf)
  (make-hash
   (hash-map bnf (lambda ([x : Variable] [form : UpdateFuncForm])
                   (cons x (update-func-form->update-func form))))))

;;; Build a network from a list of pairs of forms of update functions.
(: make-bn-forms (-> (Listof (Pairof Variable UpdateFuncForm)) Network))
(define (make-bn-forms forms)
  (bn-form->bn (make-hash forms)))

(let ([bn (make-bn-forms '((a . (and a b))
                           (b . (not b))))]
      [s (make-state '((a . #t)
                       (b . #t)))])
  ((hash-ref bn 'a) s))