160 lines
7.0 KiB
Racket
160 lines
7.0 KiB
Racket
#lang racket
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;;; dds/generic
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;;; Provides the definition of several generic interfaces for discrete
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;;; dynamical systems.
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(require racket/generic graph "utils.rkt")
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(provide
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;; Generics
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gen:dds
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;; Functions
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(contract-out [dds-step-one (-> dds? any/c (set/c any/c))]
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[dds-step-one-annotated (-> dds? any/c (set/c (cons/c any/c any/c)))]
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[dds-step (-> dds? (set/c any/c #:kind 'dont-care) (set/c any/c))]
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[dds-build-state-graph (-> dds? (set/c any/c #:kind 'dont-care) graph?)]
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[dds-build-n-step-state-graph (-> dds? (set/c any/c #:kind 'dont-care) number? graph?)]
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[dds-build-state-graph-annotated (-> dds? (set/c any/c #:kind 'dont-care) graph?)]
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[dds-build-n-step-state-graph-annotated (-> dds? (set/c any/c #:kind 'dont-care) number? graph?)])
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;; Predicates
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(contract-out [dds? (-> any/c boolean?)]))
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;;; Given a dds and a set of starting states, produce the set of
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;;; states reachable in one step. This is a fallback for dds-step.
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(define (fallback-dds-step dds ss)
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(apply set-union (for/list ([s ss]) (dds-step-one dds s))))
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;;; Given a dds, a set of starting states, and a range whose length
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;;; determines the number of steps to run, produces the edges (and the
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;;; edge labels) of the state graph reachable from the starting states
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;;; in this many steps. The last argument is a function similar do
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;;; dds-step-one-annotated: given a state, it should produce the set
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;;; of next states, labelled with appropriate labels.
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;;;
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;;; This is a fallback for dds-build-state-graph,
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;;; dds-build-n-step-state-graph, dds-build-state-graph-annotated, and
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;;; dds-build-n-step-state-graph-annotated.
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(define (fallback-dds-build-state-graph-edges dds states step-range step-func)
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(for/fold ([edges empty]
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[labels empty]
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[current-states states]
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[visited-states states]
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#:result (collect-by-key/sets edges labels))
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([i step-range]
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#:break (set-empty? current-states))
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(for/fold ([new-edges empty]
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[new-labels empty]
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[new-states (set)]
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#:result (values
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(append edges new-edges)
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(append labels new-labels)
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(set-subtract new-states visited-states)
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(set-union current-states visited-states)))
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([s current-states])
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(for/fold ([edges-to-add empty]
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[labels-to-add empty]
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[states-to-add empty]
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#:result (values
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(append new-edges edges-to-add)
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(append new-labels labels-to-add)
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(set-union (list->set states-to-add) new-states)))
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([next (set->list (step-func dds s))])
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(match next
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[(cons label s-next)
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(values
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(cons (list s s-next) edges-to-add)
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(cons label labels-to-add)
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(cons s-next states-to-add))])))))
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;;; Run dds-step-one, and produce a set of new states annotated with a
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;;; 'dummy annotation.
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(define (dummy-annotated-dds-step-one dds s)
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(for/set ([new-s (dds-step-one dds s)])
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(cons 'dummy new-s)))
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;;; A poor man's fallback for dds-step-one-annotated.
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(define (fallback-dds-step-one-annotated dds s) (dds-step-one-annotated dds s))
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;;; Run dds-step-one-annotated, but then discard the annotations.
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;;; This is a fallback for dds-step-one.
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(define (fallback-dds-step-one dds state)
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(for/set ([annotation-state (dds-step-one-annotated dds state)])
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(match annotation-state
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[(cons a s) s])))
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;;; A discrete dynamical system.
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(define-generics dds
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;; Given a dds and a state, produce the next states of the dds.
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;; This method falls back to calling dds-step-one-annotated,
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;; discarding the annotations.
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(dds-step-one dds state)
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;; Given a dds and a state, produce the next states paired with some
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;; annotation. Typical usage would include including the
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;; information about the update mode. This method has no fallback.
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(dds-step-one-annotated dds state)
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;; Given a dds and a set of starting states, produce the set of
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;; states reachable in one step. This method falls back to running
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;; dds-step-one for all states.
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(dds-step dds states)
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;; Given a dds and a set of starting states, produces the state
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;; graph reachable from the starting states. This method falls back
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;; to exploring the state graph with dds-step-one.
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(dds-build-state-graph dds states)
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;; Given a dds, a set of starting states, and a number of steps to
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;; run, produces the state graph reachable from the starting states
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;; in this many steps. This method falls back to exploring the
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;; state graph with dds-step-one.
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(dds-build-n-step-state-graph dds states nsteps)
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;; Given a dds and a set of starting states, produces the labelled
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;; state graph reachable from the starting states. This method
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;; falls back to exploring the state graph with
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;; dds-step-one-annotated.
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(dds-build-state-graph-annotated dds states)
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;; Given a dds, a set of starting states, and a number of steps to
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;; run, produces the labelled state graph reachable from the
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;; starting states in this many steps. This method falls back to
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;; exploring the state graph with dds-step-one-annotated.
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(dds-build-n-step-state-graph-annotated dds states nsteps)
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#:defined-predicate dds-implements?
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#:fallbacks
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[(define dds-step fallback-dds-step)
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(define dds-step-one fallback-dds-step-one)
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;; Run fallback-dds-build-state-graph-edges with an infinite range,
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;; which will make it stop only when it has explored all the state
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;; graph. Use dummy-annotated-dds-step-one to produce dummy edge
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;; labels and then discard them.
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(define (dds-build-state-graph dds states)
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(let-values ([(edges labels)
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(fallback-dds-build-state-graph-edges
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dds states (in-naturals)
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dummy-annotated-dds-step-one)])
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(directed-graph edges)))
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;; Run fallback-dds-build-state-graph-edges within the given range.
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;; Use dummy-annotated-dds-step-one to produce dummy edge labels
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;; and then discard them.
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(define (dds-build-n-step-state-graph dds states nsteps)
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(let-values ([(edges labels)
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(fallback-dds-build-state-graph-edges
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dds states (in-range nsteps)
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dummy-annotated-dds-step-one)])
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(directed-graph edges)))
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(define (dds-build-state-graph-annotated dds states)
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(let-values ([(edges labels)
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(fallback-dds-build-state-graph-edges
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dds states (in-naturals)
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fallback-dds-step-one-annotated)])
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(directed-graph edges labels)))
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(define (dds-build-n-step-state-graph-annotated dds states nsteps)
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(let-values ([(edges labels)
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(fallback-dds-build-state-graph-edges
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dds states (in-range nsteps)
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fallback-dds-step-one-annotated)])
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(directed-graph edges labels)))])
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