1859 lines
80 KiB
Racket
1859 lines
80 KiB
Racket
#lang racket
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(module typed typed/racket
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(require "utils.rkt" "functions.rkt" "dynamics.rkt"
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typed/graph racket/random)
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(module+ test
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(require typed/rackunit)
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(define skip-expensive-tests? #t)
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(unless skip-expensive-tests?
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(displayln "Running the complete test suite...")))
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(provide
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State UpdateFunction Domain DomainMapping
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01->boolean/state
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(struct-out network) Network
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make-same-domains make-boolean-domains make-boolean-network
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make-01-domains make-01-network update
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UpdateFunctionForm (struct-out network-form) NetworkForm
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update-function-form->update-function/any
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update-function-form->update-function/boolean
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update-function-form->update-function/01
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network-form->network/any network-form->network/boolean
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network-form->network/01 make-boolean-network-form
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forms->boolean-network
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build-all-states build-all-boolean-states build-all-01-states
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list-syntactic-interactions build-syntactic-interaction-graph
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interaction? get-interaction-sign build-interaction-graph
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build-interaction-graph/form build-signed-interaction-graph
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build-signed-interaction-graph/form
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Modality Mode dynamics%
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)
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(define-type (State a) (VariableMapping a))
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(define-type (UpdateFunction a) (-> (State a) a))
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(define-type (Domain a) (Listof a))
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(define-type (DomainMapping a) (VariableMapping (Domain a)))
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(: 01->boolean/state (-> (State (U Zero One)) (State Boolean)))
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(define (01->boolean/state s)
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(for/hash ([(x val) (in-hash s)]) : (State Boolean)
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(if (eq? val 1) (values x #t) (values x #f))))
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(module+ test
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(test-case "01->boolean/state"
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(check-equal? (01->boolean/state (hash 'a 0 'b 1))
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(hash 'a #f 'b #t))))
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(struct (a) network ([functions : (VariableMapping (UpdateFunction a))]
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[domains : (DomainMapping a)])
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#:transparent
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#:type-name Network)
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(: make-same-domains (All (a) (-> (Listof Variable) (Domain a)
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(DomainMapping a))))
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(define (make-same-domains vars domain)
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(for/hash ([var vars]) : (DomainMapping a)
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(values var domain)))
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(module+ test
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(test-case "make-same-domains"
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(check-equal? (make-same-domains '(a b) '(1 2))
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#hash((a . (1 2)) (b . (1 2))))))
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(: make-boolean-domains (-> (Listof Variable) (DomainMapping Boolean)))
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(define (make-boolean-domains vars)
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(make-same-domains vars '(#f #t)))
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(module+ test
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(test-case "make-boolean-domains"
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(check-equal? (make-boolean-domains '(a b))
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#hash((a . (#f #t)) (b . (#f #t))))))
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(: make-boolean-network (-> (VariableMapping (UpdateFunction Boolean))
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(Network Boolean)))
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(define (make-boolean-network funcs)
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(network funcs (make-boolean-domains (hash-keys funcs))))
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(module+ test
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(test-case "make-boolean-network"
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(define f1 (λ ([s : (State Boolean)])
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(and (hash-ref s 'x1) (not (hash-ref s 'x2)))))
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(define f2 (λ ([s : (State Boolean)])
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(not (hash-ref s 'x2))))
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(define bn (make-boolean-network (hash 'x1 f1 'x2 f2)))
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(check-equal? (network-domains bn) (hash 'x1 '(#f #t) 'x2 '(#f #t)))))
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(: make-01-domains (-> (Listof Variable) (DomainMapping (U Zero One))))
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(define (make-01-domains vars)
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(make-same-domains vars '(0 1)))
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(module+ test
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(test-case "make-01-domains"
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(check-equal? (make-01-domains '(a b))
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'#hash((a . (0 1)) (b . (0 1))))))
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(: make-01-network (-> (VariableMapping (UpdateFunction (U Zero One)))
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(Network (U Zero One))))
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(define (make-01-network funcs)
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(network funcs (make-01-domains (hash-keys funcs))))
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(module+ test
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(test-case "make-01-network"
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(define f1 (λ ([s : (State (U Zero One))])
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(assert-type (max (hash-ref s 'a) (hash-ref s 'b))
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(U Zero One))))
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(define f2 (λ ([s : (State (U Zero One))])
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(assert-type (min (hash-ref s 'a) (hash-ref s 'b))
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(U Zero One))))
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(define n (make-01-network (hash 'a f1 'b f2)))
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(check-equal? (network-domains n) (hash 'a '(0 1) 'b '(0 1)))))
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(: update (All (a) (-> (Network a) (State a) (Listof Variable) (State a))))
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(define (update network s xs)
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(define funcs (network-functions network))
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(for/fold ([new-s : (State a) s])
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([x xs])
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(define fx (hash-ref funcs x))
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(hash-set new-s x (fx s))))
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(module+ test
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(test-case "update"
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(define f1 (λ ([s : (State Boolean)])
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(and (hash-ref s 'x1) (not (hash-ref s 'x2)))))
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(define f2 (λ ([s : (State Boolean)])
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(not (hash-ref s 'x2))))
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(define bn (make-boolean-network (hash 'x1 f1 'x2 f2)))
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(check-equal? (update bn (hash 'x1 #f 'x2 #f) '(x1))
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#hash((x1 . #f) (x2 . #f)))
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(check-equal? (update bn (hash 'x1 #f 'x2 #f) '(x1 x2))
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#hash((x1 . #f) (x2 . #t)))))
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(define-type UpdateFunctionForm Any)
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(struct (a) network-form ([forms : (VariableMapping UpdateFunctionForm)]
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[domains : (DomainMapping a)])
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#:transparent
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#:type-name NetworkForm)
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(: update-function-form->update-function/any (-> UpdateFunctionForm (UpdateFunction Any)))
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(define (update-function-form->update-function/any form)
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(λ (s) (eval1-with s form)))
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(module+ test
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(test-case "update-function-form->update-function/any"
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(define s (hash 'x #t 'y #f))
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(define f (update-function-form->update-function/any '(and x y)))
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(check-equal? (f s) #f)))
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(: update-function-form->update-function/boolean (-> UpdateFunctionForm (UpdateFunction Boolean)))
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(define (update-function-form->update-function/boolean form)
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(λ (s) (assert-type (eval1-with s form) Boolean)))
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(module+ test
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(test-case "update-function-form->update-function/boolean"
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(define s (hash 'x #t 'y #f))
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(define f (update-function-form->update-function/boolean '(and x y)))
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(check-equal? (f s) #f)))
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(: update-function-form->update-function/01 (-> UpdateFunctionForm (UpdateFunction (U Zero One))))
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(define (update-function-form->update-function/01 form)
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(λ (s) (assert-type (eval1-with s form) (U Zero One))))
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(module+ test
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(test-case "update-function-form->update-function/01"
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(define s (hash 'x 0 'y 1))
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(define f (update-function-form->update-function/01 '(max x y)))
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(check-equal? (f s) 1)))
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(: network-form->network/any (-> (NetworkForm Any) (Network Any)))
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(define (network-form->network/any nf)
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(network
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(for/hash ([(x form) (in-hash (network-form-forms nf))])
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: (VariableMapping (UpdateFunction Any))
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(values x (update-function-form->update-function/any form)))
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(network-form-domains nf)))
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(module+ test
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(test-case "network-form->network/any"
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(define bn (network-form->network/any
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(network-form (hash 'a '(and a b)
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'b '(not b))
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(hash 'a '(#f #t)
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'b '(#f #t)))))
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(define s (hash 'a #t 'b #t))
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(check-equal? ((hash-ref (network-functions bn) 'a) s) #t)))
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(: network-form->network/boolean (-> (NetworkForm Boolean) (Network Boolean)))
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(define (network-form->network/boolean nf)
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(network
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(for/hash ([(x form) (in-hash (network-form-forms nf))])
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: (VariableMapping (UpdateFunction Boolean))
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(values x (update-function-form->update-function/boolean form)))
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(network-form-domains nf)))
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(module+ test
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(test-case "network-form->network/boolean"
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(define bn (network-form->network/boolean
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(network-form (hash 'a '(and a b)
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'b '(not b))
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(hash 'a '(#f #t)
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'b '(#f #t)))))
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(define s (hash 'a #t 'b #t))
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(check-equal? ((hash-ref (network-functions bn) 'a) s) #t)))
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(: network-form->network/01 (-> (NetworkForm (U Zero One)) (Network (U Zero One))))
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(define (network-form->network/01 nf)
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(network
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(for/hash ([(x form) (in-hash (network-form-forms nf))])
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: (VariableMapping (UpdateFunction (U Zero One)))
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(values x (update-function-form->update-function/01 form)))
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(network-form-domains nf)))
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(module+ test
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(test-case "network-form->network/01"
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(define bn (network-form->network/01
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(network-form (hash 'a '(min a b)
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'b '(- 1 b))
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(hash 'a '(0 1)
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'b '(0 1)))))
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(define s (hash 'a 1 'b 1))
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(check-equal? ((hash-ref (network-functions bn) 'a) s) 1)))
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(: make-boolean-network-form (-> (VariableMapping UpdateFunctionForm)
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(NetworkForm Boolean)))
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(define (make-boolean-network-form forms)
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(network-form forms (make-boolean-domains (hash-keys forms))))
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(module+ test
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(test-case "make-boolean-network-form"
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(check-equal? (make-boolean-network-form (hash 'a '(and a b)
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'b '(not b)))
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(network-form
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'#hash((a . (and a b)) (b . (not b)))
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'#hash((a . (#f #t)) (b . (#f #t)))))))
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(: forms->boolean-network (-> (VariableMapping UpdateFunctionForm)
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(Network Boolean)))
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(define forms->boolean-network
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(compose network-form->network/boolean make-boolean-network-form))
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(module+ test
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(test-case "forms->boolean-network"
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(define n (forms->boolean-network (hash 'a '(and a b)
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'b '(not b))))
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(check-equal? (network-domains n) (hash 'a '(#f #t)
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'b '(#f #t)))))
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(: build-all-states (All (a) (-> (DomainMapping a) (Listof (State a)))))
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(define (build-all-states vars-domains)
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;; TODO: Use hash-keys and hash-values when Typed Racket will have
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;; caught up with the new argument try-order?.
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(define vdlist (hash-map vars-domains (inst cons Variable (Domain a)) #t))
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(define vars (map (inst car Variable (Domain a)) vdlist))
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(define doms (map (inst cdr Variable (Domain a)) vdlist))
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(for/list ([s (apply cartesian-product doms)])
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(make-immutable-hash (map (inst cons Variable a) vars s))))
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(module+ test
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(test-case "build-all-states"
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(check-equal? (build-all-states #hash((a . (#t #f)) (b . (1 2 3))))
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'(#hash((a . #t) (b . 1))
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#hash((a . #t) (b . 2))
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#hash((a . #t) (b . 3))
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#hash((a . #f) (b . 1))
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#hash((a . #f) (b . 2))
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#hash((a . #f) (b . 3))))))
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(: build-all-boolean-states (-> (Listof Variable) (Listof (State Boolean))))
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(define (build-all-boolean-states vars)
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(build-all-states (make-boolean-domains vars)))
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(module+ test
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(test-case "build-all-boolean-states"
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(check-equal? (build-all-boolean-states '(a b))
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'(#hash((a . #f) (b . #f))
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#hash((a . #f) (b . #t))
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#hash((a . #t) (b . #f))
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#hash((a . #t) (b . #t))))))
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(: build-all-01-states (-> (Listof Variable) (Listof (State (U Zero One)))))
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(define (build-all-01-states vars)
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(build-all-states (make-01-domains vars)))
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(module+ test
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(test-case "build-all-01-states"
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(check-equal? (build-all-01-states '(a b))
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'(#hash((a . 0) (b . 0))
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#hash((a . 0) (b . 1))
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#hash((a . 1) (b . 0))
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#hash((a . 1) (b . 1))))))
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(: list-syntactic-interactions
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(All (a) (-> (NetworkForm a) Variable (Listof Variable))))
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(define (list-syntactic-interactions nf x)
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(set-intersect
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(extract-symbols (hash-ref (network-form-forms nf) x))
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(hash-keys (network-form-forms nf))))
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(module+ test
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(test-case "list-syntactic-interactions"
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(define n (make-boolean-network-form #hash((a . (+ a b c))
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(b . (- b c)))))
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(check-true (set=? (list-syntactic-interactions n 'a) '(a b)))
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(check-true (set=? (list-syntactic-interactions n 'b) '(b)))))
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(: build-syntactic-interaction-graph (All (a) (-> (NetworkForm a) Graph)))
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(define (build-syntactic-interaction-graph n)
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(transpose
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(unweighted-graph/adj
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(for/list ([(var _) (in-hash (network-form-forms n))])
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(cons var (list-syntactic-interactions n var))))))
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(module+ test
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(test-case "build-syntactic-interaction-graph"
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(define n (make-boolean-network-form #hash((a . (+ a b c))
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(b . (- b c)))))
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(define ig (build-syntactic-interaction-graph n))
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(check-true (has-vertex? ig 'a))
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(check-true (has-vertex? ig 'b))
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(check-false (has-vertex? ig 'c))
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(check-true (has-edge? ig 'a 'a))
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(check-true (has-edge? ig 'b 'a))
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(check-true (has-edge? ig 'b 'b))
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(check-false (has-edge? ig 'c 'b))
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(check-false (has-edge? ig 'c 'a))))
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(: interaction? (All (a) (-> (Network a) Variable Variable Boolean)))
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(define (interaction? network x y)
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(define doms (network-domains network))
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(define states-not-x (build-all-states (hash-remove doms x)))
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(define dom-x (hash-ref doms x))
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(define y-func (hash-ref (network-functions network) y))
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(: different-ys-exist? (-> (State a) Boolean))
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(define (different-ys-exist? st)
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(define x-states (for/list ([x-val (in-list dom-x)])
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: (Listof (State a))
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(hash-set st x x-val)))
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;; TODO: Replace with for*/first when/if it is fixed.
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(for*/first/typed : (Option Boolean)
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([st1 : (State a) x-states]
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[st2 : (State a) x-states]
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#:unless (equal? (hash-ref st1 x) (hash-ref st2 x))
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#:unless (equal? (y-func st1) (y-func st2)))
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#t))
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;; TODO: Replace with for/first when/if it is fixed.
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(for/first/typed : (Option Boolean)
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([st (in-list states-not-x)]
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#:when (different-ys-exist? st))
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#t))
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|
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(module+ test
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(test-case "interaction?"
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(define n1 (forms->boolean-network
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(hash 'x '(not y)
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'y 'x
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'z '(and y z))))
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(check-true (interaction? n1 'x 'y))
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(check-true (interaction? n1 'y 'x))
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(check-false (interaction? n1 'x 'z))
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(define n-multi (hash 'x '(max (+ y 1) 2)
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'y '(min (- y 1) 0)))
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(define 123-doms (make-same-domains '(x y) '(0 1 2)))
|
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(define n2 (network-form->network/any (network-form n-multi 123-doms)))
|
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(check-false (interaction? n2 'x 'y))
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(check-true (interaction? n2 'y 'x))))
|
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|
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(: get-interaction-sign (All (a) (-> (Network a) Variable Variable (Option Integer))))
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(define (get-interaction-sign network x y)
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(define doms (network-domains network))
|
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(define dom-x (hash-ref doms x))
|
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(define dom-y (hash-ref doms y))
|
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(define y-func (hash-ref (network-functions network) y))
|
||
(define (collect-impacts-on-y [st : (State a)])
|
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;; The way in which the values are ordered in the domains gives
|
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;; a total order on these values. This means that considering
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;; pairs of consecutive values of x is sufficient for testing the
|
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;; sign of the interaction.
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(define x-states (for/list : (Listof (State a))
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([x-val (in-list dom-x)])
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(hash-set st x x-val)))
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(for/list : (Listof (U '< '> '=))
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([st1 (in-list x-states)]
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[st2 (in-list (cdr x-states))])
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(define y1-idx (assert-type (index-of dom-y (y-func st1)) Index))
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(define y2-idx (assert-type (index-of dom-y (y-func st2)) Index))
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||
(cond
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[(< y1-idx y2-idx) '<]
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[(> y1-idx y2-idx) '>]
|
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[else '=])))
|
||
(define states-not-x (build-all-states (hash-remove doms x)))
|
||
(define interactions
|
||
(remove-duplicates
|
||
(for/list : (Listof (U '< '> '= Zero))
|
||
([st (in-list states-not-x)])
|
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(define impacts (remove-duplicates (collect-impacts-on-y st)))
|
||
(cond
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||
[(and (member '< impacts) (not (member '> impacts))) '<]
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[(and (member '> impacts) (not (member '< impacts))) '>]
|
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[(equal? impacts '(=)) '=]
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[else 0]))))
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(cond
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[(and (member '< interactions) (not (member '> interactions))) 1]
|
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[(and (member '> interactions) (not (member '< interactions))) -1]
|
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[(equal? interactions '(=)) #f]
|
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[else 0]))
|
||
|
||
(module+ test
|
||
(test-case "get-interaction-sign"
|
||
(define n1 (forms->boolean-network
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(hash 'x '(not y)
|
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'y 'x
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'z '(and y z)
|
||
't '(or (and (not x) y)
|
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(and x (not y))))))
|
||
(check-equal? (get-interaction-sign n1 'x 'y) 1)
|
||
(check-equal? (get-interaction-sign n1 'y 'x) -1)
|
||
(check-false (get-interaction-sign n1 'x 'z))
|
||
(check-equal? (get-interaction-sign n1 'y 'z) 1)
|
||
(check-equal? (get-interaction-sign n1 'x 't) 0)
|
||
(define n-multi (hash 'x '(min (+ y 1) 2)
|
||
'y '(max (- y 1) 0)
|
||
'z '(- 2 y)
|
||
't '(abs (- y 1))))
|
||
(define 123-doms (make-same-domains '(x y z t) '(0 1 2)))
|
||
(define n2 (network-form->network/any (network-form n-multi 123-doms)))
|
||
(check-false (get-interaction-sign n2 'x 'y))
|
||
(check-equal? (get-interaction-sign n2 'y 'x) 1)
|
||
(check-equal? (get-interaction-sign n2 'y 'z) -1)
|
||
(check-equal? (get-interaction-sign n2 'y 't) 0)
|
||
(check-equal? (get-interaction-sign n2 'y 'y) 1)))
|
||
|
||
(: build-interaction-graph (All (a) (-> (Network a) Graph)))
|
||
(define (build-interaction-graph network)
|
||
(define vars (hash-keys (network-functions network)))
|
||
(unweighted-graph/directed
|
||
(for*/list : (Listof (List Any Any))
|
||
([x (in-list vars)]
|
||
[y (in-list vars)]
|
||
#:when (interaction? network x y))
|
||
(list x y))))
|
||
|
||
(: build-interaction-graph/form (All (a) (-> (NetworkForm a) Graph)))
|
||
(define (build-interaction-graph/form form)
|
||
(build-interaction-graph (network-form->network/any form)))
|
||
|
||
(module+ test
|
||
(test-case "build-interaction-graph"
|
||
(cond
|
||
[skip-expensive-tests?
|
||
(displayln "Skipping test case build-interaction-graph.")]
|
||
[else
|
||
(define n1 (make-boolean-network-form
|
||
(hash 'x '(not y)
|
||
'y 'x
|
||
'z '(and y z)
|
||
't '(or (and (not x) y)
|
||
(and x (not y))))))
|
||
(check-equal? (graphviz (build-interaction-graph/form n1))
|
||
"digraph G {\n\tnode0 [label=\"y\"];\n\tnode1 [label=\"t\"];\n\tnode2 [label=\"z\"];\n\tnode3 [label=\"x\"];\n\tsubgraph U {\n\t\tedge [dir=none];\n\t\tnode0 -> node3 [];\n\t\tnode2 -> node2 [];\n\t}\n\tsubgraph D {\n\t\tnode0 -> node1 [];\n\t\tnode0 -> node2 [];\n\t\tnode3 -> node1 [];\n\t}\n}\n")
|
||
(define n-multi (hash 'x '(min (+ y 1) 2)
|
||
'y '(max (- y 1) 0)
|
||
'z '(- 2 y)
|
||
't '(abs (- y 1))))
|
||
(define 123-doms (make-same-domains '(x y z t) '(0 1 2)))
|
||
(define n2 (network-form n-multi 123-doms))
|
||
(check-equal? (graphviz (build-interaction-graph/form n2))
|
||
"digraph G {\n\tnode0 [label=\"y\"];\n\tnode1 [label=\"t\"];\n\tnode2 [label=\"z\"];\n\tnode3 [label=\"x\"];\n\tsubgraph U {\n\t\tedge [dir=none];\n\t\tnode0 -> node0 [];\n\t}\n\tsubgraph D {\n\t\tnode0 -> node1 [];\n\t\tnode0 -> node2 [];\n\t\tnode0 -> node3 [];\n\t}\n}\n")])))
|
||
|
||
(: build-signed-interaction-graph (All (a) (-> (Network a) Graph)))
|
||
(define (build-signed-interaction-graph network)
|
||
(define vars (hash-keys (network-functions network)))
|
||
(weighted-graph/directed
|
||
(for*/list : (Listof (List Integer Any Any))
|
||
([x (in-list vars)]
|
||
[y (in-list vars)]
|
||
[sign (in-value (get-interaction-sign network x y))]
|
||
#:unless (eq? sign #f))
|
||
(list sign x y))))
|
||
|
||
(: build-signed-interaction-graph/form (All (a) (-> (NetworkForm a) Graph)))
|
||
(define (build-signed-interaction-graph/form nf)
|
||
(build-signed-interaction-graph (network-form->network/any nf)))
|
||
|
||
(module+ test
|
||
(test-case "build-signed-interaction-graph"
|
||
(cond
|
||
[skip-expensive-tests?
|
||
(displayln "Skipping test case build-signed-interaction-graph.")]
|
||
[else
|
||
(define n1 (make-boolean-network-form
|
||
(hash 'x '(not y)
|
||
'y 'x
|
||
'z '(and y z)
|
||
't '(or (and (not x) y)
|
||
(and x (not y))))))
|
||
(check-equal? (graphviz (build-signed-interaction-graph/form n1))
|
||
"digraph G {\n\tnode0 [label=\"y\"];\n\tnode1 [label=\"t\"];\n\tnode2 [label=\"z\"];\n\tnode3 [label=\"x\"];\n\tsubgraph U {\n\t\tedge [dir=none];\n\t\tnode2 -> node2 [label=\"1\"];\n\t}\n\tsubgraph D {\n\t\tnode0 -> node1 [label=\"0\"];\n\t\tnode0 -> node2 [label=\"1\"];\n\t\tnode0 -> node3 [label=\"-1\"];\n\t\tnode3 -> node1 [label=\"0\"];\n\t\tnode3 -> node0 [label=\"1\"];\n\t}\n}\n")
|
||
(define n-multi (hash 'x '(min (+ y 1) 2)
|
||
'y '(max (- y 1) 0)
|
||
'z '(- 2 y)
|
||
't '(abs (- y 1))))
|
||
(define 123-doms (make-same-domains '(x y z t) '(0 1 2)))
|
||
(define n2 (network-form n-multi 123-doms))
|
||
(check-equal? (graphviz (build-signed-interaction-graph/form n2))
|
||
"digraph G {\n\tnode0 [label=\"y\"];\n\tnode1 [label=\"t\"];\n\tnode2 [label=\"z\"];\n\tnode3 [label=\"x\"];\n\tsubgraph U {\n\t\tedge [dir=none];\n\t\tnode0 -> node0 [label=\"1\"];\n\t}\n\tsubgraph D {\n\t\tnode0 -> node1 [label=\"0\"];\n\t\tnode0 -> node2 [label=\"-1\"];\n\t\tnode0 -> node3 [label=\"1\"];\n\t}\n}\n")])))
|
||
|
||
(define-type Modality (Listof Variable))
|
||
(define-type Mode (Listof Modality))
|
||
|
||
(define dynamics%
|
||
;; TODO: Fix the parameter of State when Typed Racket supports
|
||
;; passing type parameters to the parent.
|
||
(class (inst dds% (State Any) Modality)
|
||
#:forall (a)
|
||
(super-new)
|
||
|
||
(init-field [network : (Network a) network]
|
||
[mode : Mode mode])
|
||
|
||
(: step/annotated (-> (State a) (Listof (Pairof Modality (State a)))))
|
||
(define/override (step/annotated s)
|
||
(for/list ([m mode])
|
||
(cons m (update network s m))))))
|
||
|
||
(module+ test
|
||
(let* ([n1 : (Network Boolean)
|
||
(forms->boolean-network (hash 'x '(not y)
|
||
'y 'x
|
||
'z '(and y z)))]
|
||
[syn : Mode '((x y z))]
|
||
[asyn : Mode '((x) (y) (z))]
|
||
[dyn-syn (new (inst dynamics% Boolean) [network n1] [mode syn])]
|
||
[dyn-asyn (new (inst dynamics% Boolean) [network n1] [mode asyn])]
|
||
[s1 (hash 'x #f 'y #f 'z #f)]
|
||
[s2 (hash 'x #t 'y #t 'z #t)])
|
||
(test-case "dynamics%"
|
||
(check-equal? (send dyn-syn step/annotated s1)
|
||
'(((x y z) . #hash((x . #t) (y . #f) (z . #f)))))
|
||
(check-equal? (send dyn-asyn step/annotated s1)
|
||
'(((x) . #hash((x . #t) (y . #f) (z . #f)))
|
||
((y) . #hash((x . #f) (y . #f) (z . #f)))
|
||
((z) . #hash((x . #f) (y . #f) (z . #f))))))
|
||
|
||
(test-case "dynamics%:step"
|
||
(check-equal? (send dyn-syn step s1)
|
||
'(#hash((x . #t) (y . #f) (z . #f))))
|
||
(check-equal? (send dyn-asyn step s1)
|
||
'(#hash((x . #t) (y . #f) (z . #f))
|
||
#hash((x . #f) (y . #f) (z . #f))
|
||
#hash((x . #f) (y . #f) (z . #f)))))
|
||
(test-case "dynamics%:step*"
|
||
(check-equal? (list->set (send dyn-syn step* (list s1 s2)))
|
||
(list->set (append (send dyn-syn step s1)
|
||
(send dyn-syn step s2))))
|
||
(check-equal? (list->set (send dyn-asyn step* (list s1 s2)))
|
||
(list->set (append (send dyn-asyn step s1)
|
||
(send dyn-asyn step s2)))))
|
||
)
|
||
)
|
||
)
|
||
|
||
(require 'typed)
|
||
|
||
|
||
(require (except-in "utils.rkt" lists-transpose) (submod "utils.rkt" untyped)
|
||
"generic.rkt" "functions.rkt"
|
||
graph racket/random racket/hash)
|
||
|
||
(provide
|
||
;; Structures
|
||
(contract-out [struct tbf/state ([weights (hash/c variable? number?)]
|
||
[threshold number?])]
|
||
[struct dynamics ([network network?]
|
||
[mode mode?])])
|
||
;; Functions
|
||
(contract-out [build-signed-interaction-graph (-> network? graph?)]
|
||
[build-signed-interaction-graph/form (-> network-form? graph?)]
|
||
[make-asyn (-> (listof variable?) mode?)]
|
||
[make-syn (-> (listof variable?) mode?)]
|
||
[make-dynamics-from-func (-> network? (-> (listof variable?) mode?) dynamics?)]
|
||
[make-asyn-dynamics (-> network? dynamics?)]
|
||
[make-syn-dynamics (-> network? dynamics?)]
|
||
[dds-step-one (-> dynamics? state? (set/c state?))]
|
||
[dds-step-one-annotated (-> dynamics? state? (set/c (cons/c modality? state?)))]
|
||
[dds-step (-> dynamics? (set/c state? #:kind 'dont-care) (set/c state?))]
|
||
[dds-build-state-graph (-> dynamics? (set/c state? #:kind 'dont-care) graph?)]
|
||
[dds-build-n-step-state-graph (-> dynamics? (set/c state? #:kind 'dont-care) number? graph?)]
|
||
[dds-build-state-graph-annotated (-> dynamics? (set/c state? #:kind 'dont-care) graph?)]
|
||
[dds-build-n-step-state-graph-annotated (-> dynamics? (set/c state? #:kind 'dont-care) number? graph?)]
|
||
[pretty-print-state (-> state? string?)]
|
||
[pretty-print-boolean-state (-> state? string?)]
|
||
[pretty-print-state-graph-with (-> graph? (-> state? string?) graph?)]
|
||
[pretty-print-state-graph (-> graph? graph?)]
|
||
[ppsg (-> graph? graph?)]
|
||
[pretty-print-boolean-state-graph (-> graph? graph?)]
|
||
[ppsgb (-> graph? graph?)]
|
||
[build-full-state-graph (-> dynamics? graph?)]
|
||
[build-full-state-graph-annotated (-> dynamics? graph?)]
|
||
[tabulate-state (->* (procedure? domain-mapping/c) (#:headers boolean?)
|
||
(listof (listof any/c)))]
|
||
[tabulate-state* (->* ((non-empty-listof procedure?) domain-mapping/c) (#:headers boolean?)
|
||
(listof (listof any/c)))]
|
||
[tabulate-state/boolean (->* (procedure? (listof variable?)) (#:headers boolean?)
|
||
(listof (listof any/c)))]
|
||
[tabulate-state*/boolean (->* ((non-empty-listof procedure?) (listof variable?)) (#:headers boolean?)
|
||
(listof (listof any/c)))]
|
||
[tabulate-network (->* (network?) (#:headers boolean?)
|
||
(listof (listof any/c)))]
|
||
[table->network (->* ((listof (*list/c any/c any/c))) (#:headers boolean?) network?)]
|
||
[random-function/state (domain-mapping/c generic-set? . -> . procedure?)]
|
||
[random-boolean-function/state ((listof variable?) . -> . procedure?)]
|
||
[random-network (domain-mapping/c . -> . network?)]
|
||
[random-boolean-network ((listof variable?) . -> . network?)]
|
||
[random-boolean-network/vars (number? . -> . network?)]
|
||
[apply-tbf-to-state (-> tbf? state? (or/c 0 1))]
|
||
[tbf/state-w (-> tbf/state? (hash/c variable? number?))]
|
||
[tbf/state-θ (-> tbf/state? number?)]
|
||
[make-tbf/state (-> (listof (cons/c variable? number?)) number? tbf/state?)]
|
||
[make-sbf/state (-> (listof (cons/c variable? number?)) sbf/state?)]
|
||
[apply-tbf/state (-> tbf/state? (hash/c variable? (or/c 0 1)) (or/c 0 1))]
|
||
[lists->tbfs/state (->* ((listof (listof (or/c number? symbol?))))
|
||
(#:headers boolean?)
|
||
(listof tbf/state?))]
|
||
[lists->sbfs/state (->* ((listof (listof (or/c number? symbol?))))
|
||
(#:headers boolean?)
|
||
(listof sbf/state?))]
|
||
[read-org-tbfs/state (->* (string?) (#:headers boolean?) (listof tbf/state?))]
|
||
[read-org-sbfs/state (->* (string?) (#:headers boolean?) (listof sbf/state?))]
|
||
[print-org-tbfs/state (->* ((non-empty-listof tbf/state?)) (#:headers boolean?)
|
||
(listof (listof (or/c number? symbol?))))]
|
||
[print-org-sbfs/state (->* ((non-empty-listof tbf/state?)) (#:headers boolean?)
|
||
(listof (listof (or/c number? symbol?))))]
|
||
[tbf/state-tabulate* (->* ((non-empty-listof tbf/state?)) (#:headers boolean?)
|
||
(listof (listof (or/c symbol? number?))))]
|
||
[tbf/state-tabulate (->* (tbf/state?) (#:headers boolean?)
|
||
(listof (listof (or/c symbol? number?))))]
|
||
[group-truth-table-by-nai (-> (listof (listof (or/c 0 1))) (listof (listof (listof (or/c 0 1)))))]
|
||
[make-tbn (-> (listof (cons/c variable? tbf/state?)) tbn?)]
|
||
[tbn->network (-> tbn? network?)]
|
||
[make-sbn (-> (listof (cons/c variable? tbf/state?)) sbn?)]
|
||
[parse-org-tbn (->* ((listof any/c))
|
||
(#:headers boolean? #:func-names boolean?)
|
||
tbn?)]
|
||
[read-org-tbn (->* (string?)
|
||
(#:headers boolean? #:func-names boolean?)
|
||
tbn?)]
|
||
[read-org-sbn (->* (string?)
|
||
(#:headers boolean? #:func-names boolean?)
|
||
tbn?)]
|
||
[build-tbn-state-graph (-> tbn? graph?)]
|
||
[normalized-tbn? (-> tbn? boolean?)]
|
||
[normalize-tbn (-> tbn? normalized-tbn?)]
|
||
[compact-tbf (-> tbf/state? tbf/state?)]
|
||
[compact-tbn (-> tbn? tbn?)]
|
||
[print-org-tbn (->* (tbn?) (#:headers boolean? #:func-names boolean?)
|
||
(listof (listof (or/c number? symbol?))))]
|
||
[print-org-sbn (->* (sbn?) (#:headers boolean? #:func-names boolean?)
|
||
(listof (listof (or/c number? symbol?))))]
|
||
[tbn-interaction-graph (->* (tbn?) (#:zero-edges boolean?)
|
||
graph?)]
|
||
[pretty-print-tbn-interaction-graph (-> graph? graph?)]
|
||
[sbn-interaction-graph (->* (sbn?) (#:zero-edges boolean?)
|
||
graph?)])
|
||
;; Predicates
|
||
(contract-out [variable? (-> any/c boolean?)]
|
||
[state? (-> any/c boolean?)]
|
||
[update-function-form? (-> any/c boolean?)]
|
||
[modality? (-> any/c boolean?)]
|
||
[mode? (-> any/c boolean?)]
|
||
[sbf/state? (-> any/c boolean?)])
|
||
;; Contracts
|
||
(contract-out [state/c contract?]
|
||
[update-function/c contract?]
|
||
[domain-mapping/c contract?]
|
||
[tbn? contract?]
|
||
[sbn? contract?]))
|
||
|
||
(module+ test
|
||
(require rackunit)
|
||
;; When this variable is set to #t, some particularly expensive test
|
||
;; cases are omitted.
|
||
(define skip-expensive-tests? #t)
|
||
(unless skip-expensive-tests?
|
||
(displayln "Running the complete test suite...")))
|
||
|
||
|
||
;;; =================
|
||
;;; Basic definitions
|
||
;;; =================
|
||
|
||
(define variable? symbol?)
|
||
|
||
;;; A state of a network is a mapping from the variables of the
|
||
;;; network to their values.
|
||
(define state? variable-mapping?)
|
||
(define state/c (flat-named-contract 'state state?))
|
||
|
||
;;; An update function is a function computing a value from the given
|
||
;;; state.
|
||
(define update-function/c (-> state? any/c))
|
||
|
||
;;; A domain mapping is a hash set mapping variables to the lists of
|
||
;;; values in their domains.
|
||
(define domain-mapping/c (hash/c variable? list?))
|
||
|
||
|
||
;;; =================================
|
||
;;; Syntactic description of networks
|
||
;;; =================================
|
||
|
||
(define update-function-form? any/c)
|
||
|
||
|
||
;;; ====================
|
||
;;; Dynamics of networks
|
||
;;; ====================
|
||
|
||
(define modality? (set/c variable?))
|
||
(define mode? (set/c modality?))
|
||
|
||
;;; A network dynamics is a network plus a mode.
|
||
(struct dynamics (network mode)
|
||
#:methods gen:dds
|
||
[;; Annotates each result state with the modality which lead to it.
|
||
(define/match (dds-step-one-annotated dyn s)
|
||
[((dynamics network mode) s)
|
||
(for/set ([m mode]) (cons m (update network s m)))])])
|
||
|
||
;;; Given a list of variables, builds the asynchronous mode (a set of
|
||
;;; singletons).
|
||
(define (make-asyn vars)
|
||
(for/set ([v vars]) (set v)))
|
||
|
||
;;; Given a list of variables, builds the synchronous mode (a set
|
||
;;; containing the set of variables).
|
||
(define (make-syn vars) (set (list->set vars)))
|
||
|
||
(module+ test
|
||
(test-case "make-asyn, make-syn"
|
||
(define vars '(a b c))
|
||
(check-equal? (make-asyn vars) (set (set 'a) (set 'b) (set 'c)))
|
||
(check-equal? (make-syn vars) (set (set 'a 'b 'c)))))
|
||
|
||
;;; Given a network, applies a function for building a mode to its
|
||
;;; variables and returns the corresponding network dynamics.
|
||
(define (make-dynamics-from-func network mode-func)
|
||
(dynamics network (mode-func (hash-keys (network-functions network)))))
|
||
|
||
;;; Creates the asynchronous dynamics for a given network.
|
||
(define (make-asyn-dynamics network)
|
||
(make-dynamics-from-func network make-asyn))
|
||
|
||
;;; Creates the synchronous dynamics for a given network.
|
||
(define (make-syn-dynamics network)
|
||
(make-dynamics-from-func network make-syn))
|
||
|
||
(module+ test
|
||
(test-case "make-asyn-dynamics, make-syn-dynamics"
|
||
(define n (forms->boolean-network #hash((a . (not a)) (b . b))))
|
||
(define asyn (make-asyn-dynamics n))
|
||
(define syn (make-syn-dynamics n))
|
||
(check-equal? (dynamics-network asyn) n)
|
||
(check-equal? (dynamics-mode asyn) (set (set 'a) (set 'b)))
|
||
(check-equal? (dynamics-network syn) n)
|
||
(check-equal? (dynamics-mode syn) (set (set 'a 'b)))))
|
||
|
||
;;; Pretty-prints a state of the network.
|
||
(define (pretty-print-state s)
|
||
(string-join (hash-map s (λ (key val) (format "~a:~a" key val)) #t)))
|
||
|
||
(module+ test
|
||
(test-case "pretty-print-state"
|
||
(check-equal? (pretty-print-state (hash 'a #f 'b 3 'c 4))
|
||
"a:#f b:3 c:4")))
|
||
|
||
;;; Pretty-prints a state of the network to Boolean values 0 or 1.
|
||
(define (pretty-print-boolean-state s)
|
||
(string-join (hash-map s (λ (key val) (format "~a:~a" key (any->01 val))) #t)))
|
||
|
||
(module+ test
|
||
(test-case "pretty-print-boolean-state"
|
||
(check-equal?
|
||
(pretty-print-boolean-state (hash 'a #f 'b #t 'c #t))
|
||
"a:0 b:1 c:1")))
|
||
|
||
;;; Given a state graph and a pretty-printer for states build a new
|
||
;;; state graph with pretty-printed vertices and edges.
|
||
(define (pretty-print-state-graph-with gr pprinter)
|
||
(update-graph gr #:v-func pprinter #:e-func pretty-print-set-sets))
|
||
|
||
;;; Pretty prints a state graph with pretty-print-state.
|
||
(define (pretty-print-state-graph gr)
|
||
(pretty-print-state-graph-with gr pretty-print-state))
|
||
|
||
;;; A shortcut for pretty-print-state-graph.
|
||
(define ppsg pretty-print-state-graph)
|
||
|
||
;;; Pretty prints a state graph with pretty-print-boolean-state.
|
||
(define (pretty-print-boolean-state-graph gr)
|
||
(pretty-print-state-graph-with gr pretty-print-boolean-state))
|
||
|
||
;;; A shortcut for pretty-print-boolean-state-graph.
|
||
(define ppsgb pretty-print-boolean-state-graph)
|
||
|
||
;;; Builds the full state graph of a Boolean network.
|
||
(define (build-full-state-graph dyn)
|
||
(dds-build-state-graph
|
||
dyn
|
||
((compose list->set
|
||
build-all-states
|
||
network-domains
|
||
dynamics-network) dyn)))
|
||
|
||
;;; Build the full annotated state graph of a Boolean network.
|
||
(define (build-full-state-graph-annotated dyn)
|
||
(dds-build-state-graph-annotated
|
||
dyn
|
||
((compose list->set
|
||
build-all-states
|
||
network-domains
|
||
dynamics-network) dyn)))
|
||
|
||
(module+ test
|
||
(test-case "Dynamics of networks"
|
||
(define n (forms->boolean-network #hash((a . (not a)) (b . b))))
|
||
(define asyn (make-asyn-dynamics n))
|
||
(define syn (make-syn-dynamics n))
|
||
(define s (hash 'a #t 'b #f))
|
||
(define ss (set (hash 'a #t 'b #t)
|
||
(hash 'a #f 'b #t)))
|
||
(define gr1 (dds-build-n-step-state-graph asyn (set s) 1))
|
||
(define gr-full (dds-build-state-graph asyn (set s)))
|
||
(define gr-full-pp (pretty-print-state-graph gr-full))
|
||
(define gr-full-ppb (pretty-print-boolean-state-graph gr-full))
|
||
(define gr-complete-bool (build-full-state-graph asyn))
|
||
(define gr-complete-bool-ann (build-full-state-graph-annotated asyn))
|
||
(check-equal? (dds-step-one asyn s) (set (hash 'a #f 'b #f)
|
||
(hash 'a #t 'b #f)))
|
||
(check-equal? (dds-step-one-annotated asyn s)
|
||
(set (cons (set 'b) '#hash((a . #t) (b . #f)))
|
||
(cons (set 'a) '#hash((a . #f) (b . #f)))))
|
||
(check-equal? (dds-step-one syn s) (set (hash 'a #f 'b #f)))
|
||
(check-equal? (dds-step asyn ss)
|
||
(set (hash 'a #f 'b #t)
|
||
(hash 'a #t 'b #t)))
|
||
(check-true (has-vertex? gr1 #hash((a . #t) (b . #f))))
|
||
(check-true (has-vertex? gr1 #hash((a . #f) (b . #f))))
|
||
(check-false (has-vertex? gr1 #hash((a . #t) (b . #t))))
|
||
(check-true (has-edge? gr1 #hash((a . #t) (b . #f)) #hash((a . #f) (b . #f))))
|
||
(check-true (has-edge? gr1 #hash((a . #t) (b . #f)) #hash((a . #t) (b . #f))))
|
||
(check-false (has-edge? gr1 #hash((a . #f) (b . #f)) #hash((a . #t) (b . #f))))
|
||
|
||
(check-true (has-vertex? gr-full #hash((a . #t) (b . #f))))
|
||
(check-true (has-vertex? gr-full #hash((a . #f) (b . #f))))
|
||
(check-false (has-vertex? gr-full #hash((a . #t) (b . #t))))
|
||
(check-true (has-edge? gr-full #hash((a . #t) (b . #f)) #hash((a . #f) (b . #f))))
|
||
(check-true (has-edge? gr-full #hash((a . #t) (b . #f)) #hash((a . #t) (b . #f))))
|
||
(check-true (has-edge? gr-full #hash((a . #f) (b . #f)) #hash((a . #t) (b . #f))))
|
||
(check-true (has-edge? gr-full #hash((a . #f) (b . #f)) #hash((a . #f) (b . #f))))
|
||
|
||
(check-true (has-vertex? gr-full-pp "a:#f b:#f"))
|
||
(check-true (has-vertex? gr-full-pp "a:#t b:#f"))
|
||
(check-true (has-vertex? gr-full-ppb "a:0 b:0"))
|
||
(check-true (has-vertex? gr-full-ppb "a:1 b:0"))
|
||
|
||
(check-true (set=?
|
||
(get-edges gr-complete-bool)
|
||
'((#hash((a . #f) (b . #f)) #hash((a . #t) (b . #f)))
|
||
(#hash((a . #f) (b . #f)) #hash((a . #f) (b . #f)))
|
||
(#hash((a . #t) (b . #f)) #hash((a . #t) (b . #f)))
|
||
(#hash((a . #t) (b . #f)) #hash((a . #f) (b . #f)))
|
||
(#hash((a . #t) (b . #t)) #hash((a . #f) (b . #t)))
|
||
(#hash((a . #t) (b . #t)) #hash((a . #t) (b . #t)))
|
||
(#hash((a . #f) (b . #t)) #hash((a . #f) (b . #t)))
|
||
(#hash((a . #f) (b . #t)) #hash((a . #t) (b . #t))))))
|
||
|
||
(check-true (set=?
|
||
(get-edges gr-complete-bool-ann)
|
||
'((#hash((a . #f) (b . #f)) #hash((a . #t) (b . #f)))
|
||
(#hash((a . #f) (b . #f)) #hash((a . #f) (b . #f)))
|
||
(#hash((a . #t) (b . #f)) #hash((a . #t) (b . #f)))
|
||
(#hash((a . #t) (b . #f)) #hash((a . #f) (b . #f)))
|
||
(#hash((a . #t) (b . #t)) #hash((a . #f) (b . #t)))
|
||
(#hash((a . #t) (b . #t)) #hash((a . #t) (b . #t)))
|
||
(#hash((a . #f) (b . #t)) #hash((a . #f) (b . #t)))
|
||
(#hash((a . #f) (b . #t)) #hash((a . #t) (b . #t))))))
|
||
(check-equal? (edge-weight gr-complete-bool-ann
|
||
#hash((a . #f) (b . #f)) #hash((a . #t) (b . #f)))
|
||
(set (set 'a)))
|
||
(check-equal? (edge-weight gr-complete-bool-ann
|
||
#hash((a . #f) (b . #f)) #hash((a . #f) (b . #f)))
|
||
(set (set 'b)))
|
||
(check-equal? (edge-weight gr-complete-bool-ann
|
||
#hash((a . #t) (b . #f)) #hash((a . #t) (b . #f)))
|
||
(set (set 'b)))
|
||
(check-equal? (edge-weight gr-complete-bool-ann
|
||
#hash((a . #t) (b . #f)) #hash((a . #f) (b . #f)))
|
||
(set (set 'a)))
|
||
(check-equal? (edge-weight gr-complete-bool-ann
|
||
#hash((a . #t) (b . #t)) #hash((a . #f) (b . #t)))
|
||
(set (set 'a)))
|
||
(check-equal? (edge-weight gr-complete-bool-ann
|
||
#hash((a . #t) (b . #t)) #hash((a . #t) (b . #t)))
|
||
(set (set 'b)))
|
||
(check-equal? (edge-weight gr-complete-bool-ann
|
||
#hash((a . #f) (b . #t)) #hash((a . #f) (b . #t)))
|
||
(set (set 'b)))
|
||
(check-equal? (edge-weight gr-complete-bool-ann
|
||
#hash((a . #f) (b . #t)) #hash((a . #t) (b . #t)))
|
||
(set (set 'a)))))
|
||
|
||
|
||
;;; =================================
|
||
;;; Tabulating functions and networks
|
||
;;; =================================
|
||
|
||
|
||
;;; Like tabulate, but supposes that the function works on states.
|
||
;;;
|
||
;;; The argument domains defines the domains of each of the component
|
||
;;; of the states. If headers it true, the resulting list starts with
|
||
;;; a listing the names of the variables of the domain and ending with
|
||
;;; the symbol 'f, which indicates the values of the function.
|
||
(define (tabulate-state func domains #:headers [headers #t])
|
||
(define tab (tabulate-state* `(,func) domains #:headers headers))
|
||
(cond
|
||
[headers
|
||
;; Replace 'f1 in the headers by 'f.
|
||
(match tab [(cons hdrs vals)
|
||
(cons (append (drop-right hdrs 1) '(f)) vals)])]
|
||
[else tab]))
|
||
|
||
;;; Like tabulate-state, but assumes the function is a Boolean
|
||
;;; function. args is a list of names of the arguments which can
|
||
;;; appear in the states.
|
||
(define (tabulate-state/boolean func args #:headers [headers #t])
|
||
(tabulate-state func (make-boolean-domains args) #:headers headers))
|
||
|
||
(module+ test
|
||
(test-case "tabulate-state/boolean"
|
||
(define func (λ (st) (not (hash-ref st 'a))))
|
||
(check-equal? (tabulate-state/boolean func '(a)) '((a f) (#f #t) (#t #f)))))
|
||
|
||
;;; Like tabulate-state, but takes a list of functions over the same
|
||
;;; domain. If headers is #t, the first list of the result enumerates
|
||
;;; the variable names, and then contains a symbol 'fi for each of the
|
||
;;; functions, where i is replaced by the number of the function in
|
||
;;; the list.
|
||
(define (tabulate-state* funcs domains #:headers [headers #t])
|
||
(define tab (for/list ([st (build-all-states domains)])
|
||
(append (hash-map st (λ (x y) y) #t)
|
||
(for/list ([f funcs]) (f st)))))
|
||
(cond
|
||
[headers
|
||
(define var-names (hash-map domains (λ (x y) x) #t))
|
||
(define func-names (for/list ([_ funcs] [i (in-naturals 1)]) (string->symbol (format "f~a" i))))
|
||
(cons (append var-names func-names) tab)]
|
||
[else tab]))
|
||
|
||
;;; Like tabulate-state/boolean, but takes a list of functions.
|
||
(define (tabulate-state*/boolean funcs args #:headers [headers #t])
|
||
(tabulate-state* funcs (make-boolean-domains args) #:headers headers))
|
||
|
||
(module+ test
|
||
(test-case "tabulate-state*/boolean"
|
||
(define f1 (λ (st) (and (hash-ref st 'a) (hash-ref st 'b))))
|
||
(define f2 (λ (st) (or (hash-ref st 'a) (hash-ref st 'b))))
|
||
(check-equal? (tabulate-state*/boolean (list f1 f2) '(a b))
|
||
'((a b f1 f2)
|
||
(#f #f #f #f)
|
||
(#f #t #f #t)
|
||
(#t #f #f #t)
|
||
(#t #t #t #t)))))
|
||
|
||
;;; Tabulates a given network.
|
||
;;;
|
||
;;; For a Boolean network with n variables, returns a table with 2n
|
||
;;; columns and 2^n rows. The first n columns correspond to the
|
||
;;; different values of the variables of the networks. The last n
|
||
;;; columns represent the values of the n update functions of the
|
||
;;; network. If headers is #t, prepends a list of variable names and
|
||
;;; update functions (f-x, where x is the name of the corresponding
|
||
;;; variable) to the result.
|
||
(define (tabulate-network network #:headers [headers #t])
|
||
;; I use hash-map with try-order? set to #t to ask the hash table to
|
||
;; sort the keys for me.
|
||
(define-values (vars funcs) (for/lists (l1 l2)
|
||
([pair (hash-map (network-functions network) cons #t)])
|
||
(values (car pair) (cdr pair))))
|
||
(define tab (tabulate-state* funcs (network-domains network) #:headers headers))
|
||
(cond
|
||
[headers
|
||
;; Replace the names of the functions tabulate-state* gave us by
|
||
;; what we promise in the comment.
|
||
(define fnames (for/list ([x (in-list vars)])
|
||
(string->symbol (format "f-~a" x))))
|
||
(match tab [(cons hdrs vals)
|
||
(cons (append (take hdrs (length vars)) fnames) vals)])]
|
||
[else tab]))
|
||
|
||
(module+ test
|
||
(test-case "tabulate-network"
|
||
(define bn (forms->boolean-network #hash((a . (not a)) (b . b))))
|
||
(check-equal? (tabulate-network bn)
|
||
'((a b f-a f-b) (#f #f #t #f) (#f #t #t #t) (#t #f #f #f) (#t #t #f #t)))
|
||
(check-equal? (tabulate-network bn #:headers #f)
|
||
'((#f #f #t #f) (#f #t #t #t) (#t #f #f #f) (#t #t #f #t)))))
|
||
|
||
|
||
;;; ===================================
|
||
;;; Constructing functions and networks
|
||
;;; ===================================
|
||
|
||
;;; Given a table like the one produced by tabulate-network,
|
||
;;; constructs a Boolean network having this behaviour. If headers is
|
||
;;; #t, considers that the first element of the list are the headers
|
||
;;; and reads the names of the variables from them. Otherwise
|
||
;;; generates names for variables of the form xi, where 0 ≤ i < number
|
||
;;; of variables, and treats all rows in the table as defining the
|
||
;;; behaviour of the functions of the network. The columns defining
|
||
;;; the functions are taken to be in the same order as the variables
|
||
;;; in the first half of the function. The headers of the columns
|
||
;;; defining the functions are therefore discarded.
|
||
;;;
|
||
;;; This function relies on table->function, so the same caveats
|
||
;;; apply.
|
||
;;;
|
||
;;; The domains of the network is a mapping assigning to each variable
|
||
;;; the set of values which can appear in its column in the table.
|
||
;;; This function does not check whether the table is complete.
|
||
(define (table->network table #:headers [headers #t])
|
||
(define n (/ (length (car table)) 2))
|
||
;; Get the variable names from the table or generate them, if
|
||
;; necessary.
|
||
(define var-names (cond [headers (take (car table) n)]
|
||
[else (for ([i (in-range n)])
|
||
(symbol->string (format "x~a" i)))]))
|
||
;; Drop the headers if they are present.
|
||
(define tab (cond [headers (cdr table)]
|
||
[else table]))
|
||
;; Split the table into the inputs and the outputs of the functions.
|
||
(define-values (ins outs) (multi-split-at tab n))
|
||
;; Transpose outs to have functions define by lines instead of by
|
||
;; columns.
|
||
(define func-lines (lists-transpose outs))
|
||
;; Make states out of inputs.
|
||
(define st-ins (for/list ([in ins]) (make-immutable-hash (map cons var-names in))))
|
||
;; Construct the functions.
|
||
(define funcs (for/list ([out func-lines])
|
||
(table->function (for/list ([in st-ins] [o out])
|
||
(list in o)))))
|
||
;; Infer the domains.
|
||
(define domains (for/hash [(dom (in-list (lists-transpose ins)))
|
||
(x (in-list var-names))]
|
||
(values x (remove-duplicates dom))))
|
||
;; Construct the network.
|
||
(network (for/hash ([x (in-list var-names)]
|
||
[f (in-list funcs)])
|
||
(values x f))
|
||
domains))
|
||
|
||
(module+ test
|
||
(test-case "table->network"
|
||
(define n (table->network '((x1 x2 f1 f2)
|
||
(#f #f #f #f)
|
||
(#f #t #f #t)
|
||
(#t #f #t #f)
|
||
(#t #t #t #t))))
|
||
(define f1 (hash-ref (network-functions n) 'x1))
|
||
(define f2 (hash-ref (network-functions n) 'x2))
|
||
|
||
(check-false (f1 (hash 'x1 #f 'x2 #f)))
|
||
(check-false (f1 (hash 'x1 #f 'x2 #t)))
|
||
(check-true (f1 (hash 'x1 #t 'x2 #f)))
|
||
(check-true (f1 (hash 'x1 #t 'x2 #t)))
|
||
|
||
(check-false (f2 (hash 'x1 #f 'x2 #f)))
|
||
(check-true (f2 (hash 'x1 #f 'x2 #t)))
|
||
(check-false (f2 (hash 'x1 #t 'x2 #f)))
|
||
(check-true (f2 (hash 'x1 #t 'x2 #t)))
|
||
|
||
(check-equal? (network-domains n)
|
||
#hash((x1 . (#f #t)) (x2 . (#f #t))))))
|
||
|
||
|
||
;;; =============================
|
||
;;; Random functions and networks
|
||
;;; =============================
|
||
|
||
;;; Generates a random function accepting a state over the domains
|
||
;;; given by arg-domains and producing values in func-domain.
|
||
(define (random-function/state arg-domains func-domain)
|
||
(table->function (for/list ([st (build-all-states arg-domains)])
|
||
(list st (random-ref func-domain)))))
|
||
|
||
;;; Like random-function/state, but the domains of the arguments and
|
||
;;; of the function are Boolean. args is a list of names of the
|
||
;;; variables appearing in the state.
|
||
(define (random-boolean-function/state args)
|
||
(random-function/state (make-boolean-domains args) '(#f #t)))
|
||
|
||
(module+ test
|
||
(test-case "random-boolean-function/state"
|
||
(random-seed 0)
|
||
(define f (random-boolean-function/state '(x1 x2)))
|
||
(check-equal? (tabulate-state/boolean f '(x1 x2))
|
||
'((x1 x2 f) (#f #f #f) (#f #t #f) (#t #f #t) (#t #t #t)))
|
||
(check-equal? (tabulate-state/boolean f '(x1 x2) #:headers #f)
|
||
'((#f #f #f) (#f #t #f) (#t #f #t) (#t #t #t)))
|
||
(define bn (random-boolean-network/vars 3))
|
||
(check-equal? (tabulate-network bn)
|
||
'((x0 x1 x2 f-x0 f-x1 f-x2)
|
||
(#f #f #f #f #t #f)
|
||
(#f #f #t #t #f #f)
|
||
(#f #t #f #f #t #t)
|
||
(#f #t #t #t #f #f)
|
||
(#t #f #f #t #f #t)
|
||
(#t #f #t #f #f #t)
|
||
(#t #t #f #f #f #f)
|
||
(#t #t #t #t #t #t)))))
|
||
|
||
;;; Generates a random network from the given domain mapping.
|
||
(define (random-network domains)
|
||
(network (for/hash ([(x x-dom) (in-hash domains)])
|
||
(values x (random-function/state domains x-dom)))
|
||
domains))
|
||
|
||
;;; Generates a random Boolean network with the given variables.
|
||
(define (random-boolean-network vars)
|
||
(random-network (make-boolean-domains vars)))
|
||
|
||
;;; Like random-boolean-network, but also generates the names of the
|
||
;;; variables for the network. The variables have the names x0 to xk,
|
||
;;; where k = n - 1.
|
||
(define (random-boolean-network/vars n)
|
||
(random-boolean-network (for/list ([i (in-range n)]) (string->symbol (format "x~a" i)))))
|
||
|
||
|
||
;;; ===================
|
||
;;; TBF/TBN and SBF/SBN
|
||
;;; ===================
|
||
|
||
;;; Applies a TBF to a state.
|
||
;;;
|
||
;;; The values of the variables of the state are ordered by hash-map
|
||
;;; and fed to the TBF in order. The number of the inputs of the TBF
|
||
;;; must match the number of variables in the state.
|
||
(define (apply-tbf-to-state tbf st)
|
||
(apply-tbf tbf (list->vector (hash-map st (λ (_ val) val)))))
|
||
|
||
(module+ test
|
||
(test-case "apply-tbf-to-state"
|
||
(define st (hash 'x1 0 'x2 1))
|
||
(define f (tbf #(1 1) 1))
|
||
(check-equal? (apply-tbf-to-state f st) 0)))
|
||
|
||
;;; A state TBF is a TBF with named inputs. A state TBF can be
|
||
;;; applied to states in an unambiguous ways.
|
||
(struct tbf/state (weights threshold) #:transparent)
|
||
|
||
;;; Shortcuts for acessing fields of a state/tbf.
|
||
(define tbf/state-w tbf/state-weights)
|
||
(define tbf/state-θ tbf/state-threshold)
|
||
|
||
;;; Makes a state/tbf from a list of pairs of names of variables and
|
||
;;; weights, as well as a threshold.
|
||
(define (make-tbf/state pairs threshold)
|
||
(tbf/state (make-immutable-hash pairs) threshold))
|
||
|
||
(module+ test
|
||
(test-case "tbf/state"
|
||
(define f (make-tbf/state '((x1 . 1) (x2 . 1)) 1))
|
||
(check-equal? (tbf/state-w f) #hash((x1 . 1) (x2 . 1)))
|
||
(check-equal? (tbf/state-θ f) 1)))
|
||
|
||
;;; A sign Boolean function (SBF) is a TBF whose threshold is 0.
|
||
(define sbf/state? (and/c tbf/state? (λ (tbf) (zero? (tbf/state-θ tbf)))))
|
||
|
||
(module+ test
|
||
(test-case "sbf/state?"
|
||
(check-true (sbf/state? (tbf/state #hash((a . -1) (b . 1)) 0)))))
|
||
|
||
;;; Makes a state/tbf which is an SBF from a list of pairs of names of
|
||
;;; variables and weights.
|
||
(define (make-sbf/state pairs)
|
||
(make-tbf/state pairs 0))
|
||
|
||
(module+ test
|
||
(test-case "make-sbf/state"
|
||
(check-equal? (make-sbf/state '((a . -1) (b . 1)))
|
||
(make-tbf/state '((a . -1) (b . 1)) 0))))
|
||
|
||
;;; Applies a state TBF to its inputs.
|
||
;;;
|
||
;;; Applying a TBF consists in multiplying the weights by the
|
||
;;; corresponding inputs and comparing the sum of the products to the
|
||
;;; threshold.
|
||
;;;
|
||
;;; This function is similar to apply-tbf, but applies a state TBF (a
|
||
;;; TBF with explicitly named inputs) to a state whose values are 0
|
||
;;; and 1.
|
||
(define (apply-tbf/state tbf st)
|
||
(any->01 (> (foldl + 0 (hash-values
|
||
(hash-intersect (tbf/state-w tbf)
|
||
st
|
||
#:combine *)))
|
||
(tbf/state-θ tbf))))
|
||
|
||
(module+ test
|
||
(test-case "apply-tbf/state"
|
||
(define st1 (hash 'a 1 'b 0 'c 1))
|
||
(define st2 (hash 'a 1 'b 1 'c 0))
|
||
(define tbf (make-tbf/state '((a . 2) (b . -2)) 1))
|
||
(check-equal? (apply-tbf/state tbf st1) 1)
|
||
(check-equal? (apply-tbf/state tbf st2) 0)))
|
||
|
||
;;; Reads a list of tbf/state from a list of list of numbers.
|
||
;;;
|
||
;;; The last element of each list is taken to be the threshold of the
|
||
;;; TBFs, and the rest of the elements are taken to be the weights.
|
||
;;;
|
||
;;; If headers is #t, the names of the variables to appear as the
|
||
;;; inputs of the TBF are taken from the first list. The last element
|
||
;;; of this list is discarded.
|
||
;;;
|
||
;;; If headers is #f, the names of the variables are generated as xi,
|
||
;;; where i is the index of the variable.
|
||
(define (lists->tbfs/state lsts #:headers [headers #t])
|
||
(define-values (var-names rows)
|
||
(if headers
|
||
(values (car lsts) (cdr lsts))
|
||
(values (for/list ([i (in-range (length (car lsts)))])
|
||
(string->symbol (format "x~a" i)))
|
||
lsts)))
|
||
(for/list ([lst (in-list rows)])
|
||
(define-values (ws θ) (split-at-right lst 1))
|
||
(make-tbf/state (for/list ([x (in-list var-names)]
|
||
[w (in-list ws)])
|
||
(cons x w))
|
||
(car θ))))
|
||
|
||
(module+ test
|
||
(test-case "lists->tbfs/state"
|
||
(define tbfs '((1 2 3) (1 1 2)))
|
||
(check-equal? (lists->tbfs/state tbfs #:headers #f)
|
||
(list
|
||
(tbf/state '#hash((x0 . 1) (x1 . 2)) 3)
|
||
(tbf/state '#hash((x0 . 1) (x1 . 1)) 2)))
|
||
(check-equal? (lists->tbfs/state (cons '(a b f) tbfs))
|
||
(list
|
||
(tbf/state '#hash((a . 1) (b . 2)) 3)
|
||
(tbf/state '#hash((a . 1) (b . 1)) 2)))))
|
||
|
||
;;; Like lists->tbfs/state, but does not expect thresholds in the
|
||
;;; input.
|
||
;;;
|
||
;;; Every lists in the list contains the weights of the SBF. If
|
||
;;; headers is #t, the names of the variables to appear as the inputs
|
||
;;; of the TBF are taken from the first list.
|
||
;;;
|
||
;;; If headers is #f, the names of the variables are generated as xi,
|
||
;;; where i is the index of the variable.
|
||
(define (lists->sbfs/state lsts #:headers [headers #t])
|
||
(define rows (if headers (cdr lsts) lsts))
|
||
(define rows-θ (for/list ([lst (in-list rows)]) (append lst '(0))))
|
||
(lists->tbfs/state (if headers (cons (car lsts) rows-θ) rows-θ)
|
||
#:headers headers))
|
||
|
||
(module+ test
|
||
(test-case "lists->sbfs/state"
|
||
(define tbfs '((1 2) (1 -1)))
|
||
(check-equal? (lists->sbfs/state tbfs #:headers #f)
|
||
(list
|
||
(tbf/state '#hash((x0 . 1) (x1 . 2)) 0)
|
||
(tbf/state '#hash((x0 . 1) (x1 . -1)) 0)))
|
||
(check-equal? (lists->sbfs/state (cons '(a b) tbfs) #:headers #t)
|
||
(list
|
||
(tbf/state '#hash((a . 1) (b . 2)) 0)
|
||
(tbf/state '#hash((a . 1) (b . -1)) 0)))))
|
||
|
||
;;; Reads a list of tbf/state from an Org-mode string containing a
|
||
;;; sexp, containing a list of lists of numbers. As in
|
||
;;; lists->tbfs/state, the last element of each list is taken to be
|
||
;;; the threshold of the TBFs, and the rest of the elements are taken
|
||
;;; to be the weights.
|
||
;;;
|
||
;;; If headers is #t, the names of the variables to appear as the
|
||
;;; inputs of the TBF are taken from the first list. The last element
|
||
;;; of this list is discarded.
|
||
;;;
|
||
;;; If headers is #f, the names of the variables are generated as xi,
|
||
;;; where i is the index of the variable.
|
||
(define (read-org-tbfs/state str #:headers [headers #t])
|
||
(lists->tbfs/state (read-org-sexp str) #:headers headers))
|
||
|
||
(module+ test
|
||
(test-case "read-org-tbfs/state"
|
||
(check-equal? (read-org-tbfs/state "((a b f) (1 2 3) (1 1 2))")
|
||
(list
|
||
(tbf/state '#hash((a . 1) (b . 2)) 3)
|
||
(tbf/state '#hash((a . 1) (b . 1)) 2)))
|
||
(check-equal? (read-org-tbfs/state "((1 2 3) (1 1 2))" #:headers #f)
|
||
(list
|
||
(tbf/state '#hash((x0 . 1) (x1 . 2)) 3)
|
||
(tbf/state '#hash((x0 . 1) (x1 . 1)) 2)))))
|
||
|
||
;;; Like read-org-tbfs/state, but reads a list of SBFs. Therefore,
|
||
;;; the lists of numbers in the sexp are taken to be the weights of
|
||
;;; the SBFs.
|
||
;;;
|
||
;;; If headers is #t, the names of the variables to appear as the
|
||
;;; inputs of the TBF are taken from the first list. If headers is
|
||
;;; #f, the names of the variables are generated as xi, where i is the
|
||
;;; index of the variable.
|
||
(define (read-org-sbfs/state str #:headers [headers #t])
|
||
(lists->sbfs/state (read-org-sexp str) #:headers headers))
|
||
|
||
(module+ test
|
||
(test-case "read-org-sbfs/state"
|
||
(check-equal? (read-org-sbfs/state "((a b) (-1 2) (1 1))")
|
||
(list
|
||
(tbf/state '#hash((a . -1) (b . 2)) 0)
|
||
(tbf/state '#hash((a . 1) (b . 1)) 0)))
|
||
(check-equal? (read-org-sbfs/state "((-1 2) (1 1))" #:headers #f)
|
||
(list
|
||
(tbf/state '#hash((x0 . -1) (x1 . 2)) 0)
|
||
(tbf/state '#hash((x0 . 1) (x1 . 1)) 0)))))
|
||
|
||
;;; Given a list of tbf/state, produces a sexp that Org-mode can
|
||
;;; interpret as a table.
|
||
;;;
|
||
;;; All tbf/state in the list must have the same inputs. The function
|
||
;;; does not check this property.
|
||
;;;
|
||
;;; If #:headers is #f, does not print the names of the inputs of the
|
||
;;; TBFs. If #:headers is #t, the output starts by a list giving the
|
||
;;; names of the variables, as well as the symbol 'θ to represent the
|
||
;;; column giving the thresholds of the TBF.
|
||
(define (print-org-tbfs/state tbfs #:headers [headers #t])
|
||
(define table (for/list ([tbf (in-list tbfs)])
|
||
(append (hash-map (tbf/state-w tbf) (λ (_ w) w) #t)
|
||
(list (tbf/state-θ tbf)))))
|
||
(if headers
|
||
(cons (append (hash-map (tbf/state-w (car tbfs)) (λ (x _) x) #t) '(θ))
|
||
table)
|
||
table))
|
||
|
||
(module+ test
|
||
(test-case "print-org-tbfs/state"
|
||
(define tbfs (list (make-tbf/state '((a . 1) (b . 2)) 3)
|
||
(make-tbf/state '((a . -2) (b . 1)) 1)))
|
||
(check-equal? (print-org-tbfs/state tbfs)
|
||
'((a b θ) (1 2 3) (-2 1 1)))))
|
||
|
||
;;; Like print-org-tbfs/state, but expects a list of SBFs. The
|
||
;;; thresholds are therefore not included in the output.
|
||
;;;
|
||
;;; All sbf/state in the list must have the same inputs. The function
|
||
;;; does not check this property.
|
||
;;;
|
||
;;; If #:headers is #f, does not print the names of the inputs of the
|
||
;;; TBFs. If #:headers is #t, the output starts by a list giving the
|
||
;;; names of the variables.
|
||
(define (print-org-sbfs/state sbfs #:headers [headers #t])
|
||
(define table (for/list ([sbf (in-list sbfs)])
|
||
(hash-map (tbf/state-w sbf) (λ (_ w) w) #t)))
|
||
(if headers
|
||
(cons (hash-map (tbf/state-w (car sbfs)) (λ (x _) x) #t)
|
||
table)
|
||
table))
|
||
|
||
(module+ test
|
||
(define sbfs (list (make-sbf/state '((a . 1) (b . 2)))
|
||
(make-sbf/state '((a . -2) (b . 1)))))
|
||
(check-equal? (print-org-sbfs/state sbfs)
|
||
'((a b) (1 2) (-2 1)))
|
||
(check-equal? (print-org-sbfs/state sbfs #:headers #f)
|
||
'((1 2) (-2 1))))
|
||
|
||
;;; Tabulates a list of tbf/state.
|
||
;;;
|
||
;;; As in the case of tbf-tabulate*, the result is a list of lists
|
||
;;; giving the truth tables of the given TBFs. The first elements of
|
||
;;; each row give the values of the inputs, while the last elements
|
||
;;; give the values of each function corresponding to the input.
|
||
;;;
|
||
;;; All the TBFs must have exactly the same inputs. This function
|
||
;;; does not check this property.
|
||
;;;
|
||
;;; If #:headers is #t, the output starts by a list giving the names
|
||
;;; of the variables, and then the symbols 'fi, where i is the number
|
||
;;; of the TBF in the list.
|
||
(define (tbf/state-tabulate* tbfs #:headers [headers #t])
|
||
(define vars (hash-map (tbf/state-w (car tbfs)) (λ (x _) x) #t))
|
||
(tabulate-state* (map (curry apply-tbf/state) tbfs)
|
||
(make-same-domains vars '(0 1))
|
||
#:headers headers))
|
||
|
||
(module+ test
|
||
(test-case "tbf/state-tabulate*"
|
||
(define tbfs (list (make-tbf/state '((a . 1) (b . 2)) 1)
|
||
(make-tbf/state '((a . -2) (b . 3)) 1)))
|
||
(check-equal? (tbf/state-tabulate* tbfs)
|
||
'((a b f1 f2)
|
||
(0 0 0 0)
|
||
(0 1 1 1)
|
||
(1 0 0 0)
|
||
(1 1 1 0)))))
|
||
|
||
;;; Like tbf/state-tabulate*, but only tabulates a single TBF.
|
||
(define (tbf/state-tabulate tbf #:headers [headers #t])
|
||
(tbf/state-tabulate* (list tbf) #:headers headers))
|
||
|
||
(module+ test
|
||
(test-case "tbf/state-tabulate"
|
||
(define tbf (make-tbf/state '((a . -2) (b . 3)) 1))
|
||
(check-equal? (tbf/state-tabulate tbf)
|
||
'((a b f1)
|
||
(0 0 0)
|
||
(0 1 1)
|
||
(1 0 0)
|
||
(1 1 0)))))
|
||
|
||
;;; Given a truth table of a Boolean function, groups the lines by the
|
||
;;; "number of activated inputs"—the number of inputs which are 1 in
|
||
;;; the input vector.
|
||
;;;
|
||
;;; The truth table must not include the header line.
|
||
(define (group-truth-table-by-nai tt)
|
||
(define sum (((curry foldl) +) 0))
|
||
(group-by (λ (row) (drop-right row 1))
|
||
tt
|
||
(λ (in1 in2) (= (sum in1) (sum in2)))))
|
||
|
||
(module+ test
|
||
(test-case "group-truth-table-by-nai"
|
||
(check-equal? (group-truth-table-by-nai '((0 0 0 1)
|
||
(0 0 1 1)
|
||
(0 1 0 0)
|
||
(0 1 1 1)
|
||
(1 0 0 0)
|
||
(1 0 1 0)
|
||
(1 1 0 1)
|
||
(1 1 1 0)))
|
||
'(((0 0 0 1))
|
||
((0 0 1 1) (0 1 0 0) (1 0 0 0))
|
||
((0 1 1 1) (1 0 1 0) (1 1 0 1))
|
||
((1 1 1 0))))))
|
||
|
||
;;; A TBN is a network form mapping variables to tbf/state.
|
||
;;;
|
||
;;; The tbf/state must only reference variables appearing in the
|
||
;;; network. This contract does not check this condition.
|
||
(define tbn? (hash/c variable? tbf/state?))
|
||
|
||
;;; Builds a TBN from a list of pairs (variable, tbf/state).
|
||
(define make-tbn make-immutable-hash)
|
||
|
||
(module+ test
|
||
(test-case "make-tbn"
|
||
(define tbf-not (make-tbf/state '((a . -1)) -1))
|
||
(define tbf-id (make-sbf/state '((a . 1))))
|
||
(check-equal? (make-tbn `((a . ,tbf-not) (b . ,tbf-id)))
|
||
(hash 'a (tbf/state '#hash((a . -1)) -1)
|
||
'b (tbf/state '#hash((a . 1)) 0)))))
|
||
|
||
;;; A SBN is a network form mapping variables to sbf/state.
|
||
;;;
|
||
;;; The tbf/state must only reference variables appearing in the
|
||
;;; network. This contract does not check this condition.
|
||
(define sbn? (hash/c variable? sbf/state?))
|
||
|
||
;;; Builds an SBN from a list of pairs (variable, sbf/state).
|
||
(define make-sbn make-immutable-hash)
|
||
|
||
(module+ test
|
||
(test-case "make-sbn"
|
||
(define sbf1 (make-sbf/state '((a . -1))))
|
||
(define sbf2 (make-sbf/state '((a . 1))))
|
||
(check-equal? (make-sbn `((a . ,sbf1) (b . ,sbf2)))
|
||
(hash 'a (tbf/state '#hash((a . -1)) 0)
|
||
'b (tbf/state '#hash((a . 1)) 0)))))
|
||
|
||
;;; Constructs a network from a network form defining a TBN.
|
||
(define (tbn->network tbn)
|
||
(make-01-network (for/hash ([(var tbf) (in-hash tbn)])
|
||
(values var ((curry apply-tbf/state) tbf)))))
|
||
|
||
(module+ test
|
||
(test-case "tbn->network"
|
||
(define tbn (make-tbn `((a . ,(make-sbf/state '((b . 1))))
|
||
(b . ,(make-tbf/state '((a . -1)) -1)))))
|
||
(define n (tbn->network tbn))
|
||
(define s1 (hash 'a 0 'b 0))
|
||
(check-equal? (update n s1 '(a b))
|
||
(hash 'a 0 'b 1))
|
||
(check-equal? (network-domains n) #hash((a . (0 1)) (b . (0 1))))
|
||
|
||
(define sbn (make-sbn `((a . ,(make-sbf/state '((b . -1))))
|
||
(b . ,(make-sbf/state '((a . 1)))))))
|
||
(define sn (tbn->network sbn))
|
||
(define s2 (hash 'a 1 'b 1))
|
||
(check-equal? (update sn s2 '(a b))
|
||
(hash 'a 0 'b 1))
|
||
(check-equal? (network-domains sn) #hash((a . (0 1)) (b . (0 1))))))
|
||
|
||
;;; A helper function for read-org-tbn and read-org-sbn. It reads a
|
||
;;; TBN from an Org-mode sexp containing a list of lists of numbers.
|
||
;;; As in lists->tbfs/state, the last element of each list is taken to
|
||
;;; be the threshold of the TBFs, and the rest of the elements are
|
||
;;; taken to be the weights.
|
||
;;;
|
||
;;; As in read-org-tbfs/state, if headers is #t, the names of the
|
||
;;; variables to appear as the inputs of the TBF are taken from the
|
||
;;; first list. The last element of this list is discarded.
|
||
;;; If headers is #f, the names of the variables are generated as xi,
|
||
;;; where i is the index of the variable.
|
||
;;;
|
||
;;; If func-names is #t, the first element in every row except the
|
||
;;; first one, are taken to be the name of the variable to which the
|
||
;;; TBF should be associated. If func-names is #f, the functions are
|
||
;;; assigned to variables in alphabetical order.
|
||
;;;
|
||
;;; func-names cannot be #t if headers is #f. The function does not
|
||
;;; check this condition.
|
||
(define (parse-org-tbn sexp
|
||
#:headers [headers #t]
|
||
#:func-names [func-names #t])
|
||
(cond
|
||
[(eq? func-names #t)
|
||
(define-values (vars rows) (multi-split-at sexp 1))
|
||
(define tbfs (lists->tbfs/state rows #:headers headers))
|
||
(for/hash ([tbf (in-list tbfs)] [var (in-list (cdr vars))])
|
||
(values (car var) tbf))]
|
||
[else
|
||
(define tbfs (lists->tbfs/state sexp #:headers headers))
|
||
(define vars (hash-map (tbf/state-w (car tbfs)) (λ (x _) x) #t))
|
||
(for/hash ([tbf (in-list tbfs)] [var (in-list vars)])
|
||
(values var tbf))]))
|
||
|
||
;;; Reads a TBN from an Org-mode string containing a sexp, containing
|
||
;;; a list of lists of numbers. As in lists->tbfs/state, the last
|
||
;;; element of each list is taken to be the threshold of the TBFs, and
|
||
;;; the rest of the elements are taken to be the weights.
|
||
;;;
|
||
;;; As in read-org-tbfs/state, if headers is #t, the names of the
|
||
;;; variables to appear as the inputs of the TBF are taken from the
|
||
;;; first list. The last element of this list is discarded.
|
||
;;; If headers is #f, the names of the variables are generated as xi,
|
||
;;; where i is the index of the variable.
|
||
;;;
|
||
;;; If func-names is #t, the first element in every row except the
|
||
;;; first one, are taken to be the name of the variable to which the
|
||
;;; TBF should be associated. If func-names is #f, the functions are
|
||
;;; assigned to variables in alphabetical order.
|
||
;;;
|
||
;;; func-names cannot be #t if headers is #f. The function does not
|
||
;;; check this condition.
|
||
(define (read-org-tbn str
|
||
#:headers [headers #t]
|
||
#:func-names [func-names #t])
|
||
(parse-org-tbn (read-org-sexp str)
|
||
#:headers headers
|
||
#:func-names func-names))
|
||
|
||
(module+ test
|
||
(test-case "read-org-tbn, parse-org-tbn"
|
||
(check-equal? (read-org-tbn "((\"-\" \"x\" \"y\" \"θ\") (\"y\" -1 0 -1) (\"x\" 0 -1 -1))")
|
||
(hash
|
||
'x
|
||
(tbf/state '#hash((x . 0) (y . -1)) -1)
|
||
'y
|
||
(tbf/state '#hash((x . -1) (y . 0)) -1)))
|
||
(check-equal? (read-org-tbn "((\"x\" \"y\" \"θ\") (-1 0 -1) (0 -1 -1))" #:func-names #f)
|
||
(hash
|
||
'x
|
||
(tbf/state '#hash((x . -1) (y . 0)) -1)
|
||
'y
|
||
(tbf/state '#hash((x . 0) (y . -1)) -1)))
|
||
(check-equal? (read-org-tbn "((-1 0 -1) (0 -1 -1))" #:headers #f #:func-names #f)
|
||
(hash
|
||
'x0
|
||
(tbf/state '#hash((x0 . -1) (x1 . 0)) -1)
|
||
'x1
|
||
(tbf/state '#hash((x0 . 0) (x1 . -1)) -1)))))
|
||
|
||
;;; Like read-org-tbn, but reads an SBN from an Org-mode string
|
||
;;; containing a sexp, containing a list of lists of numbers.
|
||
;;;
|
||
;;; As in read-org-sbfs/state, if headers is #t, the names of the
|
||
;;; variables to appear as the inputs of the SBF are taken from the
|
||
;;; first list. The last element of this list is discarded.
|
||
;;; If headers is #f, the names of the variables are generated as xi,
|
||
;;; where i is the index of the variable.
|
||
;;;
|
||
;;; If func-names is #t, the first element in every row except the
|
||
;;; first one, are taken to be the name of the variable to which the
|
||
;;; TBF should be associated. If func-names is #f, the functions are
|
||
;;; assigned to variables in alphabetical order.
|
||
;;;
|
||
;;; func-names cannot be #t if headers is #f. The function does not
|
||
;;; check this condition.
|
||
(define (read-org-sbn str
|
||
#:headers [headers #t]
|
||
#:func-names [func-names #t])
|
||
(define sexp (read-org-sexp str))
|
||
;; Inject the 0 thresholds into the rows of the sexp we have just read.
|
||
(define (inject-0 rows) (for/list ([row (in-list rows)]) (append row '(0))))
|
||
(define sexp-ready (if headers
|
||
(cons (car sexp) (inject-0 (cdr sexp)))
|
||
(inject-0 sexp)))
|
||
(parse-org-tbn sexp-ready #:headers headers #:func-names func-names))
|
||
|
||
(module+ test
|
||
(test-case "read-org-sbn, parse-org-tbn"
|
||
(check-equal? (read-org-sbn "((\"-\" \"x\" \"y\") (\"y\" -1 0) (\"x\" 0 -1))")
|
||
(hash
|
||
'x
|
||
(tbf/state '#hash((x . 0) (y . -1)) 0)
|
||
'y
|
||
(tbf/state '#hash((x . -1) (y . 0)) 0)))
|
||
(check-equal? (read-org-sbn "((\"x\" \"y\") (-1 0) (0 -1))" #:func-names #f)
|
||
(hash
|
||
'x
|
||
(tbf/state '#hash((x . -1) (y . 0)) 0)
|
||
'y
|
||
(tbf/state '#hash((x . 0) (y . -1)) 0)))
|
||
(check-equal? (read-org-sbn "((-1 0) (0 -1))" #:headers #f #:func-names #f)
|
||
(hash
|
||
'x0
|
||
(tbf/state '#hash((x0 . -1) (x1 . 0)) 0)
|
||
'x1
|
||
(tbf/state '#hash((x0 . 0) (x1 . -1)) 0)))))
|
||
|
||
;;; A shortcut for building the state graphs of TBN.
|
||
(define build-tbn-state-graph
|
||
(compose pretty-print-state-graph
|
||
build-full-state-graph
|
||
make-syn-dynamics
|
||
tbn->network))
|
||
|
||
;;; Checks whether a TBN is normalized: whether all of the functions
|
||
;;; have the same inputs, and whether these inputs are exactly the
|
||
;;; variables of the TBN.
|
||
(define (normalized-tbn? tbn)
|
||
(define tbn-vars (hash-keys tbn))
|
||
(for/and ([tbf (in-list (hash-values tbn))])
|
||
(set=? tbn-vars (hash-keys (tbf/state-w tbf)))))
|
||
|
||
(module+ test
|
||
(test-case "normalized-tbn?"
|
||
(check-false (normalized-tbn?
|
||
(make-tbn `((a . ,(make-sbf/state '((b . 1))))
|
||
(b . ,(make-tbf/state '((a . -1)) -1))))))
|
||
(check-true (normalized-tbn?
|
||
(make-tbn `((a . ,(make-sbf/state '((a . 1) (b . -1))))
|
||
(b . ,(make-tbf/state '((a . -1) (b . 1)) -1))))))))
|
||
|
||
;;; Normalizes a TBN.
|
||
;;;
|
||
;;; For every TBF, removes the inputs that are not in the variables of
|
||
;;; the TBN, and adds missing inputs with 0 weight.
|
||
(define (normalize-tbn tbn)
|
||
(define vars-0 (for/hash ([(x _) (in-hash tbn)]) (values x 0)))
|
||
(define (normalize-tbf tbf)
|
||
;; Only keep the inputs which are also the variables of tbn.
|
||
(define w-pruned (hash-intersect tbn (tbf/state-w tbf)
|
||
#:combine (λ (_ w) w)))
|
||
;; Put in the missing inputs with weight 0.
|
||
(define w-complete (hash-union vars-0 w-pruned #:combine (λ (_ w) w)))
|
||
(tbf/state w-complete (tbf/state-θ tbf)))
|
||
(for/hash ([(x tbf) (in-hash tbn)]) (values x (normalize-tbf tbf))))
|
||
|
||
(module+ test
|
||
(test-case "normalize-tbn"
|
||
(check-equal? (normalize-tbn
|
||
(hash 'a (make-sbf/state '((b . 1) (c . 3)))
|
||
'b (make-tbf/state '((a . -1)) -1)))
|
||
(hash
|
||
'a
|
||
(tbf/state '#hash((a . 0) (b . 1)) 0)
|
||
'b
|
||
(tbf/state '#hash((a . -1) (b . 0)) -1)))))
|
||
|
||
;;; Compacts (and denormalizes) a TBF by removing all inputs which
|
||
;;; are 0.
|
||
(define (compact-tbf tbf)
|
||
(tbf/state
|
||
(for/hash ([(k v) (in-hash (tbf/state-w tbf))]
|
||
#:unless (zero? v))
|
||
(values k v))
|
||
(tbf/state-θ tbf)))
|
||
|
||
(module+ test
|
||
(test-case "compact-tbf"
|
||
(check-equal? (compact-tbf (tbf/state (hash 'a 0 'b 1 'c 2 'd 0) 2))
|
||
(tbf/state '#hash((b . 1) (c . 2)) 2))))
|
||
|
||
;;; Compacts a TBN by removing all inputs which are 0 or which are not
|
||
;;; variables of the network.
|
||
(define (compact-tbn tbn)
|
||
(define (remove-0-non-var tbf)
|
||
(tbf/state
|
||
(for/hash ([(x w) (in-hash (tbf/state-w tbf))]
|
||
#:when (hash-has-key? tbn x)
|
||
#:unless (zero? w))
|
||
(values x w))
|
||
(tbf/state-θ tbf)))
|
||
(for/hash ([(x tbf) (in-hash tbn)])
|
||
(values x (remove-0-non-var tbf))))
|
||
|
||
(module+ test
|
||
(test-case "compact-tbn"
|
||
(check-equal?
|
||
(compact-tbn (hash 'a (tbf/state (hash 'a 0 'b 1 'c 3 'd 0) 0)
|
||
'b (tbf/state (hash 'a -1 'b 1) -1)))
|
||
(hash
|
||
'a
|
||
(tbf/state '#hash((b . 1)) 0)
|
||
'b
|
||
(tbf/state '#hash((a . -1) (b . 1)) -1)))))
|
||
|
||
;;; Given TBN, produces a sexp containing the description of the
|
||
;;; functions of the TBN that Org-mode can interpret as a table.
|
||
;;;
|
||
;;; Like print-org-tbfs/state, if #:headers is #f, does not print the
|
||
;;; names of the inputs of the TBFs. If #:headers is #t, the output
|
||
;;; starts by a list giving the names of the variables, as well as the
|
||
;;; symbol 'θ to represent the column giving the thresholds of the
|
||
;;; TBF.
|
||
;;;
|
||
;;; If #:func-names is #t, the first column of the table gives the
|
||
;;; variable which the corresponding TBF updates.
|
||
;;;
|
||
;;; If both #:func-names and #:headers are #t, the first cell of the
|
||
;;; first column contains the symbol '-.
|
||
(define (print-org-tbn tbn
|
||
#:headers [headers #t]
|
||
#:func-names [func-names #t])
|
||
(define ntbn (normalize-tbn tbn))
|
||
(define vars-tbfs (hash-map ntbn (λ (x tbf) (cons x tbf)) #t))
|
||
(define tbfs (map cdr vars-tbfs))
|
||
(define tbfs-table (print-org-tbfs/state tbfs #:headers headers))
|
||
(cond
|
||
[(eq? func-names #t)
|
||
(define vars (map car vars-tbfs))
|
||
(define col-1 (if headers (cons '- vars) vars))
|
||
(for/list ([var (in-list col-1)] [row (in-list tbfs-table)])
|
||
(cons var row))]
|
||
[else
|
||
tbfs-table]))
|
||
|
||
(module+ test
|
||
(test-case "print-org-tbn"
|
||
(define tbn (make-tbn `((a . ,(make-sbf/state '((b . 1))))
|
||
(b . ,(make-tbf/state '((a . -1)) -1)))))
|
||
(check-equal? (print-org-tbn tbn)
|
||
'((- a b θ) (a 0 1 0) (b -1 0 -1)))))
|
||
|
||
;;; Given an SBN, produces a sexp containing the description of the
|
||
;;; functions of the SBN that Org-mode can interpret as a table.
|
||
;;; This function is therefore very similar to print-org-tbn.
|
||
;;;
|
||
;;; Like print-org-tbfs/state, if #:headers is #f, does not print the
|
||
;;; names of the inputs of the TBFs. If #:headers is #t, the output
|
||
;;; starts by a list giving the names of the variables.
|
||
;;;
|
||
;;; If #:func-names is #t, the first column of the table gives the
|
||
;;; variable which the corresponding TBF updates.
|
||
;;;
|
||
;;; If both #:func-names and #:headers are #t, the first cell of the
|
||
;;; first column contains the symbol '-.
|
||
(define (print-org-sbn sbn
|
||
#:headers [headers #t]
|
||
#:func-names [func-names #t])
|
||
(define tab (print-org-tbn sbn #:headers headers #:func-names func-names))
|
||
(define-values (tab-no-θ _) (multi-split-at
|
||
tab
|
||
(- (length (car tab)) 1)))
|
||
tab-no-θ)
|
||
|
||
(module+ test
|
||
(test-case "print-org-sbn"
|
||
(define sbn (hash
|
||
'a
|
||
(tbf/state (hash 'b 2) 0)
|
||
'b
|
||
(tbf/state (hash 'a 2) 0)))
|
||
(check-equal? (print-org-sbn sbn)
|
||
'((- a b) (a 0 2) (b 2 0)))))
|
||
|
||
;;; Given a TBN, constructs its interaction graph. The nodes of this
|
||
;;; graph are labeled with pairs (variable name . threshold), while
|
||
;;; the edges are labelled with the weights.
|
||
;;;
|
||
;;; If #:zero-edges is #t, the edges with zero weights will appear in
|
||
;;; the interaction graph.
|
||
(define (tbn-interaction-graph tbn
|
||
#:zero-edges [zero-edges #t])
|
||
(define ntbn (normalize-tbn tbn))
|
||
(define ig (weighted-graph/directed
|
||
(if zero-edges
|
||
(for*/list ([(tar tbf) (in-hash ntbn)]
|
||
[(src w) (in-hash (tbf/state-w tbf))])
|
||
(list w src tar))
|
||
(for*/list ([(tar tbf) (in-hash ntbn)]
|
||
[(src w) (in-hash (tbf/state-w tbf))]
|
||
#:unless (zero? w))
|
||
(list w src tar)))))
|
||
(update-graph ig #:v-func (λ (x) (cons x (tbf/state-θ (hash-ref ntbn x))))))
|
||
|
||
(module+ test
|
||
(test-case "tbn-interaction-graph"
|
||
(define tbn (make-tbn `((a . ,(make-sbf/state '((b . 1))))
|
||
(b . ,(make-tbf/state '((a . -1)) -1)))))
|
||
(check-equal? (graphviz (tbn-interaction-graph tbn))
|
||
"digraph G {\n\tnode0 [label=\"'(b . -1)\\n\"];\n\tnode1 [label=\"'(a . 0)\\n\"];\n\tsubgraph U {\n\t\tedge [dir=none];\n\t\tnode0 -> node0 [label=\"0\"];\n\t\tnode1 -> node1 [label=\"0\"];\n\t}\n\tsubgraph D {\n\t\tnode0 -> node1 [label=\"1\"];\n\t\tnode1 -> node0 [label=\"-1\"];\n\t}\n}\n")
|
||
(check-equal? (graphviz (tbn-interaction-graph tbn #:zero-edges #f))
|
||
"digraph G {\n\tnode0 [label=\"'(b . -1)\\n\"];\n\tnode1 [label=\"'(a . 0)\\n\"];\n\tsubgraph U {\n\t\tedge [dir=none];\n\t}\n\tsubgraph D {\n\t\tnode0 -> node1 [label=\"1\"];\n\t\tnode1 -> node0 [label=\"-1\"];\n\t}\n}\n")))
|
||
|
||
;;; Pretty prints the node labels of the interaction graph of a TBN.
|
||
(define (pretty-print-tbn-interaction-graph ig)
|
||
(update-graph ig #:v-func (match-lambda
|
||
[(cons var weight) (~a var ":" weight)])))
|
||
|
||
(module+ test
|
||
(test-case "pretty-print-tbn-interaction-graph"
|
||
(define tbn (make-tbn `((a . ,(make-sbf/state '((b . 1))))
|
||
(b . ,(make-tbf/state '((a . -1)) -1)))))
|
||
(check-equal? (graphviz (pretty-print-tbn-interaction-graph (tbn-interaction-graph tbn)))
|
||
"digraph G {\n\tnode0 [label=\"b:-1\"];\n\tnode1 [label=\"a:0\"];\n\tsubgraph U {\n\t\tedge [dir=none];\n\t\tnode0 -> node0 [label=\"0\"];\n\t\tnode1 -> node1 [label=\"0\"];\n\t}\n\tsubgraph D {\n\t\tnode0 -> node1 [label=\"1\"];\n\t\tnode1 -> node0 [label=\"-1\"];\n\t}\n}\n")))
|
||
|
||
;;; Given an SBN, constructs its interaction graph. As in
|
||
;;; tbn-interaction-graph, the nodes of this graph are labeled with
|
||
;;; the variable names, while the edges are labelled with the weights.
|
||
;;;
|
||
;;; If #:zero-edges is #t, the edges with zero weights will appear in
|
||
;;; the interaction graph.
|
||
(define (sbn-interaction-graph sbn
|
||
#:zero-edges [zero-edges #t])
|
||
(update-graph (tbn-interaction-graph sbn #:zero-edges zero-edges)
|
||
#:v-func (match-lambda
|
||
[(cons var _) var])))
|
||
|
||
(module+ test
|
||
(test-case "sbn-interaction-graph"
|
||
(define sbn (hash
|
||
'a
|
||
(tbf/state (hash 'b 2) 0)
|
||
'b
|
||
(tbf/state (hash 'a 2) 0)))
|
||
(check-equal? (graphviz (sbn-interaction-graph sbn))
|
||
"digraph G {\n\tnode0 [label=\"b\"];\n\tnode1 [label=\"a\"];\n\tsubgraph U {\n\t\tedge [dir=none];\n\t\tnode0 -> node1 [label=\"2\"];\n\t\tnode0 -> node0 [label=\"0\"];\n\t\tnode1 -> node1 [label=\"0\"];\n\t}\n\tsubgraph D {\n\t}\n}\n")))
|