dds/scribblings/dynamics.scrbl

118 lines
3.3 KiB
Text
Raw Normal View History

2022-07-06 00:00:17 +02:00
#lang scribble/manual
@(require scribble/example racket/sandbox
2022-08-23 10:17:58 +02:00
(for-label "../dynamics.rkt" typed/racket/base
(only-in racket/class object%)))
2022-07-06 00:00:17 +02:00
@(define-syntax-rule (deftypeform . args)
(defform #:kind "type" . args))
@(define-syntax-rule (deftype . args)
(defidform #:kind "polymorphic type" . args))
@title[#:tag "dynamics"]{dds/dynamics: Dynamics of DDS}
@defmodule[dds/dynamics]
This module provides a number of general definitions for building and analyzing
the dynamics of discrete dynamical systems.
2022-08-23 10:17:58 +02:00
@defclass[dds% object% ()]{
The abstract base class for discrete dynamical systems.
This class has two type parameters:
@itemize[
@item{@racket[State] --- a state of the discrete dynamical system,}
@item{@racket[Modality] --- a description of the way in which the discrete
dynamical system transitions from a given state @italic{s} to another state
@italic{s}. For systems whose states are described by a set of variables,
a @racket[Modality] is typically a list of variables updated during the
state transition.}
]
@defmethod[(step [st State]) (Listof State)]{
Given a state @racket[st], produces the next states of the state.
This method falls back to calling @method[dds% step/annotated], and then
discarding the annotations.
}
@defmethod[(step/annotated [st State]) (Listof (Pairof Modality State))]{
Given a state, produces the next states paired with the corresponding
modalities. Typical usage would include giving the information about the
update mode.
This method has no fallback and must be overridden.
}
@defmethod[(step* [sts (Listof State)]) (Listof State)]{
Given a set of starting states, produce the set of states reachable in
one step.
This method falls back to running @method[dds% step] for all states.
Note that @method[dds% step*] has no direct @tt{/annotated} counterpart.
This is because producing a list of @racket[(Pairof Modality State)] would not
give enough information to identify to which particular transition the modality
corresponds to.
}
@defmethod[(build-state-graph [sts (Listof State)]) Graph]{
Given a set of starting states, produces the state graph reachable from the
starting states.
This method falls back to exploring the state graph with @method[dds% step].
}
@defmethod[(build-state-graph/annotated [sts (Listof State)]) Graph]{
Given a set of starting states, produces the labelled state graph reachable
from the starting states.
This method falls back to exploring the state graph with @method[dds%
step/annotated].
}
@defmethod[(build-state-graph* [sts (Listof State)]
[nsteps (U Positive-Integer 'full)])
Graph]{
2022-08-23 10:17:58 +02:00
Given a set of starting states and a number @racket[nsteps] of steps to run,
produces the state graph reachable from the starting states @racket[nsteps]
steps. If @racket[nsteps] is @racket['full], constructs the full state
graph instead.
2022-08-23 10:17:58 +02:00
This method falls back to exploring the state graph with @method[dds% step].
}
@defmethod[(build-state-graph*/annotated [sts (Listof State)]
[nsteps (U Positive-Integer 'full)])
2022-08-23 10:17:58 +02:00
Graph]{
Given a set of starting states and a number @racket[nsteps] of steps to run,
produces the labelled state graph reachable from the starting states
@racket[nsteps] steps. If @racket[nsteps] is @racket['full], constructs the
full state graph instead.
2022-08-23 10:17:58 +02:00
This method falls back to exploring the state graph with @method[dds%
step/annotated].
}
}