118 lines
3.3 KiB
Racket
118 lines
3.3 KiB
Racket
#lang scribble/manual
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@(require scribble/example racket/sandbox
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(for-label "../dynamics.rkt" typed/racket/base
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(only-in racket/class object%)))
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@(define-syntax-rule (deftypeform . args)
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(defform #:kind "type" . args))
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@(define-syntax-rule (deftype . args)
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(defidform #:kind "polymorphic type" . args))
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@title[#:tag "dynamics"]{dds/dynamics: Dynamics of DDS}
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@defmodule[dds/dynamics]
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This module provides a number of general definitions for building and analyzing
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the dynamics of discrete dynamical systems.
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@defclass[dds% object% ()]{
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The abstract base class for discrete dynamical systems.
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This class has two type parameters:
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@itemize[
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@item{@racket[State] --- a state of the discrete dynamical system,}
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@item{@racket[Modality] --- a description of the way in which the discrete
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dynamical system transitions from a given state @italic{s} to another state
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@italic{s}. For systems whose states are described by a set of variables,
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a @racket[Modality] is typically a list of variables updated during the
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state transition.}
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]
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@defmethod[(step [st State]) (Listof State)]{
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Given a state @racket[st], produces the next states of the state.
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This method falls back to calling @method[dds% step/annotated], and then
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discarding the annotations.
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}
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@defmethod[(step/annotated [st State]) (Listof (Pairof Modality State))]{
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Given a state, produces the next states paired with the corresponding
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modalities. Typical usage would include giving the information about the
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update mode.
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This method has no fallback and must be overridden.
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}
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@defmethod[(step* [sts (Listof State)]) (Listof State)]{
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Given a set of starting states, produce the set of states reachable in
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one step.
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This method falls back to running @method[dds% step] for all states.
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Note that @method[dds% step*] has no direct @tt{/annotated} counterpart.
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This is because producing a list of @racket[(Pairof Modality State)] would not
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give enough information to identify to which particular transition the modality
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corresponds to.
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}
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@defmethod[(build-state-graph [sts (Listof State)]) Graph]{
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Given a set of starting states, produces the state graph reachable from the
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starting states.
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This method falls back to exploring the state graph with @method[dds% step].
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}
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@defmethod[(build-state-graph/annotated [sts (Listof State)]) Graph]{
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Given a set of starting states, produces the labelled state graph reachable
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from the starting states.
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This method falls back to exploring the state graph with @method[dds%
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step/annotated].
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}
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@defmethod[(build-state-graph* [sts (Listof State)]
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[nsteps (U Positive-Integer 'full)])
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Graph]{
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Given a set of starting states and a number @racket[nsteps] of steps to run,
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produces the state graph reachable from the starting states @racket[nsteps]
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steps. If @racket[nsteps] is @racket['full], constructs the full state
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graph instead.
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This method falls back to exploring the state graph with @method[dds% step].
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}
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@defmethod[(build-state-graph*/annotated [sts (Listof State)]
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[nsteps (U Positive-Integer 'full)])
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Graph]{
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Given a set of starting states and a number @racket[nsteps] of steps to run,
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produces the labelled state graph reachable from the starting states
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@racket[nsteps] steps. If @racket[nsteps] is @racket['full], constructs the
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full state graph instead.
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This method falls back to exploring the state graph with @method[dds%
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step/annotated].
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}
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}
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