#lang racket

;;; dds/generic

;;; Provides the definition of several generic interfaces for discrete
;;; dynamical systems.

(require racket/generic)

(provide
 ;; Generics
 gen:dds
 ;; Functions
 (contract-out [dds-step-one (-> dds? any/c (set/c any/c))]
               [dds-step (-> dds? (set/c any/c) (set/c any/c))])
 ;; Predicates
 (contract-out [dds? (-> any/c boolean?)]))

;;; Given a dds and a set of starting states, produce the set of
;;; states reachable in one step.  This is a fallback for dds-step.
(define (fallback-dds-step dds ss)
  (apply set-union (for/list ([s ss]) (dds-step-one dds s))))

;;; A discrete dynamical system.
(define-generics dds
  ;; Given a dds and a state, produce the next states of the dds.
  (dds-step-one dds state)
  ;; Given a dds and a set of starting states, produce the set of
  ;; states reachable in one step.  This method falls back to running
  ;; dds-step-one for all states.
  (dds-step dds states)

  #:defined-predicate dds-implements?
  #:fallbacks
  [(define dds-step fallback-dds-step)])