dds/generic.rkt

#lang racket

;;; dds/generic

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

(require racket/generic graph)

(provide
 ;; Generics
 gen:dds
 ;; Functions
 (contract-out [dds-step-one (-> dds? any/c (set/c any/c))]
               [dds-step-one-annotated (-> dds? any/c (set/c (cons/c any/c any/c)))]
               [dds-step (-> dds? (set/c any/c #:kind 'dont-care) (set/c any/c))]
               [dds-build-state-graph (-> dds? (set/c any/c #:kind 'dont-care) graph?)]
               [dds-build-n-step-state-graph (-> dds? (set/c any/c #:kind 'dont-care) number? graph?)])
 ;; 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))))

;;; Given a dds, a set of starting states, and a range whose length
;;; determines the number of steps to run, produces the state graph
;;; reachable from the starting steps in this many steps.  This is a
;;; fallback for dds-build-state-graph and dds-build-n-step-state
;;; graph.
(define (fallback-dds-build-state-graph dds states step-range)
  (for/fold ([edges empty]
             [current-states states]
             [visited-states states]
             #:result (directed-graph edges))
            ([i step-range]
             #:break (set-empty? current-states))
    (for/fold ([new-edges empty]
               [new-states (set)]
               #:result (values
                         (append edges new-edges)
                         (set-subtract new-states visited-states)
                         (set-union current-states visited-states)))
              ([s current-states])
      (let ([ss-next (dds-step-one dds s)])
        (values
         (append new-edges (for/list ([s-next ss-next]) (list s s-next)))
         (set-union ss-next new-states))))))

;;; A discrete dynamical system.
(define-generics dds
  ;; Given a dds and a state, produce the next states of the dds.
  ;; This method has no fallback.
  (dds-step-one dds state)
  ;; Given a dds and a state, produce the next states paired with some
  ;; annotation.  Typical usage would include including the
  ;; information about the update mode.  This method has no fallback.
  (dds-step-one-annotated 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)
  ;; Given a dds and a set of starting states, produces the state
  ;; graph reachable from the starting states.  This method falls back
  ;; to exploring the state graph with dds-step-one.
  (dds-build-state-graph dds states)
  ;; Given a dds, a set of starting states, and a number of steps to
  ;; run, produces the state graph reachable from the starting states
  ;; in this many steps.  This method falls back to exploring the
  ;; state graph with dds-step-one.
  (dds-build-n-step-state-graph dds states nsteps)

  #:defined-predicate dds-implements?
  #:fallbacks
  [(define dds-step fallback-dds-step)
   (define (dds-build-state-graph dds states)
     ;; Run fallback-dds-build-state-graph with an infinite range,
     ;; which will make it stop only when it has explored all the
     ;; state graph.
     (fallback-dds-build-state-graph dds states (in-naturals)))
   (define (dds-build-n-step-state-graph dds states nsteps)
     (fallback-dds-build-state-graph dds states (in-range nsteps)))])