dds/networks.rkt

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#lang racket
;;; dds/networks
;;; This module provides some quick definitions for and analysing
;;; network models. A network is a set of variables which are updated
;;; according to their corresponding update functions. The variables
;;; to be updated at each step are given by the mode.
;;;
;;; This model can generalise Boolean networks, TBANs, multivalued
;;; networks, etc.
(require "utils.rkt" "generic.rkt" graph)
(provide
;; Structures
(struct-out dynamics)
;; Functions
(contract-out [update (-> network? state? (set/c variable? #:kind 'dont-care) state?)]
[make-state (-> (listof (cons/c symbol? any/c)) state?)]
[make-network-from-functions (-> (listof (cons/c symbol? update-function/c)) network?)]
[update-function-form->update-function (-> update-function-form? update-function/c)]
[network-form->network (-> network-form? network?)]
[make-network-from-forms (-> (listof (cons/c symbol? update-function-form?))
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network?)]
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[list-interactions (-> network-form? variable? (listof variable?))]
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[build-interaction-graph (-> network-form? graph?)]
[build-all-states (-> domain-mapping/c (listof state?))]
[make-same-domains (-> (listof variable?) generic-set? domain-mapping/c)]
[make-boolean-domains (-> (listof variable?) (hash/c variable? (list/c #f #t)))]
[build-all-boolean-states (-> (listof variable?) (listof state?))]
[get-interaction-sign (-> network-form? domain-mapping/c variable? variable? (or/c '+ '- '0))]
[build-signed-interaction-graph (-> network-form? domain-mapping/c graph?)]
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[build-boolean-signed-interaction-graph (-> 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?)]
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[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?)]
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[dds-build-n-step-state-graph (-> dynamics? (set/c state? #:kind 'dont-care) number? graph?)]
[pretty-print-state (-> state? string?)]
[any->boolean (-> any/c boolean?)]
[pretty-print-boolean-state (-> state? string?)]
[pretty-print-state-graph-with (-> graph? (-> state? string?) graph?)]
[pretty-print-state-graph (-> graph? graph?)]
[pretty-print-boolean-state-graph (-> graph? graph?)]
[build-full-boolean-state-graph (-> dynamics? graph?)])
;; Predicates
(contract-out [variable? (-> any/c boolean?)]
[state? (-> any/c boolean?)]
[update-function-form? (-> any/c boolean?)]
[network-form? (-> any/c boolean?)]
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[modality? (-> any/c boolean?)]
[mode? (-> any/c boolean?)])
;; Contracts
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(contract-out [state/c contract?]
[network/c contract?]
[update-function/c contract?]
[domain-mapping/c contract?])
;; Syntax
st nn ppsg ppsgb)
;;; =================
;;; 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 network is a mapping from its variables to its update functions.
(define network? variable-mapping?)
(define network/c (flat-named-contract 'network network?))
;;; Given a state s updates all the variables from xs. This
;;; corresponds to a parallel mode.
(define (update network s xs)
(for/fold ([new-s s])
([x xs])
(let ([f (hash-ref network x)])
(hash-set new-s x (f s)))))
;;; A version of make-immutable-hash restricted to creating network
;;; states (see contract).
(define (make-state mappings) (make-immutable-hash mappings))
;;; A shortcut for make-state.
(define-syntax-rule (st mappings) (make-state mappings))
;;; A version of make-immutable-hash restricted to creating networks.
(define (make-network-from-functions funcs) (make-immutable-hash funcs))
;;; =================================
;;; Syntactic description of networks
;;; =================================
;;; An update function form is any form which can appear as a body of
;;; a function and which can be evaluated with eval. For example,
;;; '(and x y (not z)) or '(+ 1 a (- b 10)).
(define update-function-form? any/c)
;;; A Boolean network form is a mapping from its variables to the
;;; forms of their update functions.
(define network-form? variable-mapping?)
;;; Build an update function from an update function form.
(define (update-function-form->update-function form)
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(λ (s) (eval-with s form)))
;;; Build a network from a network form.
(define (network-form->network bnf)
(for/hash ([(x form) bnf])
(values x (update-function-form->update-function form))))
;;; Build a network from a list of pairs of forms of update functions.
(define (make-network-from-forms forms)
(network-form->network (make-immutable-hash forms)))
;;; A shortcut for network-form->network.
(define-syntax-rule (nn forms) (network-form->network forms))
;;; ============================
;;; Inferring interaction graphs
;;; ============================
;;; I allow any syntactic forms in definitions of Boolean functions.
;;; I can still find out which Boolean variables appear in those
;;; syntactic form, but I have no reliable syntactic means of finding
;;; out what kind of action do they have (inhibition or activation)
;;; since I cannot do Boolean minimisation (e.g., I cannot rely on not
;;; appearing before a variable, since (not (not a)) is equivalent
;;; to a). On the other hand, going through all Boolean states is
;;; quite resource-consuming and thus not always useful.
;;;
;;; In this section I provide inference of both unsigned and signed
;;; interaction graphs, but since the inference of signed interaction
;;; graphs is based on analysing the dynamics of the networks, it may
;;; be quite resource-consuming.
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;;; Lists the variables of the network form appearing in the update
;;; function form for x.
(define (list-interactions nf x)
(set-intersect
(extract-symbols (hash-ref nf x))
(hash-keys nf)))
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;;; Builds the graph in which the vertices are the variables of a
;;; given network, and which contains an arrow from a to b whenever a
;;; appears in (list-interactions a).
(define (build-interaction-graph n)
(transpose
(unweighted-graph/adj
(for/list ([(var _) n]) (cons var (list-interactions n var))))))
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;;; 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?))
;;; Given a hash-set mapping variables to generic sets of their
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;;; possible values, constructs the list of all possible states.
(define (build-all-states vars-domains)
(let* ([var-dom-list (hash->list vars-domains)]
[vars (map car var-dom-list)]
[domains (map cdr var-dom-list)])
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(for/list ([s (apply cartesian-product domains)])
(make-state (for/list ([var vars] [val s])
(cons var val))))))
;;; Makes a hash set mapping all variables to a single domain.
(define (make-same-domains vars domain)
(for/hash ([var vars]) (values var domain)))
;;; Makes a hash set mapping all variables to the Boolean domain.
(define (make-boolean-domains vars)
(make-same-domains vars '(#f #t)))
;;; Builds all boolean states possible over a given set of variables.
(define (build-all-boolean-states vars)
(build-all-states (make-boolean-domains vars)))
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;;; Given two interacting variables of a network form and the domains
;;; of the variables, returns '+ if the interaction is monotonously
;;; increasing, '- if it is monotonously decreasing, and '0 otherwise.
;;;
;;; This function does not check whether the two variables indeed
;;; interact. Its behaviour is undefined if the variables do not
;;; interact.
;;;
;;; /!\ This function iterates through almost all of the states of the
;;; network, so its performance decreases very quickly with network
;;; size.
(define (get-interaction-sign network-form doms x y)
(let* ([dom-x (hash-ref doms x)]
[dom-y (hash-ref doms y)]
[network (network-form->network network-form)]
;; Replace the domain of x by a dummy singleton.
[doms-no-x (hash-set doms x '(#f))]
;; Build all the states, but as if x were not there: since I
;; replace its domain by a singleton, all states will contain
;; the same value for x.
[states-no-x (build-all-states doms-no-x)]
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;; Go through all states, then through all ordered pairs of
;; values of x, generate pairs of states (s1, s2) such that x
;; has a smaller value in s1, and check that updating y in s1
;; yields a smaller value than updating y in s2. I rely on
;; the fact that the domains are ordered.
[x-y-interactions (for*/list ([s states-no-x]
[x1 dom-x] ; ordered pairs of values of x
[x2 (cdr (member x1 dom-x))])
(let* ([s1 (hash-set s x x1)] ; s1(x) < s2(x)
[s2 (hash-set s x x2)]
[y1 ((hash-ref network y) s1)]
[y2 ((hash-ref network y) s2)])
;; y1 <= y2?
(<= (index-of dom-y y1) (index-of dom-y y2))))])
(cond
;; If, in all interactions, y1 <= y2, then we have an
;; increasing/promoting interaction between x and y.
[(andmap (λ (x) (eq? x #t)) x-y-interactions) '+]
;; If, in all interactions, y1 > y2, then we have an
;; decreasing/inhibiting interaction between x and y.
[(andmap (λ (x) (eq? x #f)) x-y-interactions) '-]
;; Otherwise the interaction is neither increasing nor
;; decreasing.
[else '0])))
;;; Constructs a signed interaction graph of a given network form,
;;; given the ordered domains of its variables. The order on the
;;; domains determines the signs which will appear on the interaction
;;; graph.
;;;
;;; /!\ This function iterates through almost all states of the
;;; network for every arrow in the unsigned interaction graph, so its
;;; performance decreases very quickly with the size of the network.
(define (build-signed-interaction-graph network-form doms)
(let ([ig (build-interaction-graph network-form)])
(weighted-graph/directed
(for/list ([e (in-edges ig)])
(match-let ([(list x y) e])
(list (match (get-interaction-sign network-form doms x y)
['+ 1] ['- -1] ['0 0])
x y))))))
;;; Calls build-signed-interaction-graph with the Boolean domain for
;;; all variable.
;;;
;;; /!\ The same performance warning applies as for
;;; build-signed-interaction-graph.
(define (build-boolean-signed-interaction-graph network-form)
(build-signed-interaction-graph network-form
(make-boolean-domains (hash-keys network-form))))
;;; ====================
;;; Dynamics of networks
;;; ====================
;;; This section contains definitions for building and analysing the
;;; dynamics of networks.
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;;; A modality is a set of variable.
(define modality? (set/c variable?))
;;; A mode is a set of modalities.
(define mode? (set/c modality?))
;;; A network dynamics is a network plus a mode.
(struct dynamics (network mode)
#:methods gen:dds
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[(define/match (dds-step-one dyn s)
[((dynamics network mode) s)
(for/set ([m mode]) (update network s m))])
;; 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)))])])
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;;; 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)))
;;; 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))))
;;; 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))
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;;; Pretty-prints a state of the network.
(define (pretty-print-state s)
(string-join (for/list ([(key val) s]) (format "~a:~a" key val))))
;;; Converts any non-#f value to 1 and #f to 0.
(define (any->boolean x) (if x 1 0))
;;; Pretty-prints a state of the network to Boolean values 0 or 1.
(define (pretty-print-boolean-state s)
(string-join (for/list ([(key val) s]) (format "~a:~a" key (any->boolean val)))))
;;; Given a state graph and a pretty-printer for states build a new
;;; state graph with pretty-printed vertices.
(define (pretty-print-state-graph-with gr pprinter)
(update-vertices/unweighted gr pprinter))
;;; 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-syntax-rule (ppsg gr) (pretty-print-state-graph gr))
;;; 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-syntax-rule (ppsgb gr) (pretty-print-boolean-state-graph gr))
;;; Builds the full state graph of a Boolean network.
(define (build-full-boolean-state-graph dyn)
(dds-build-state-graph
dyn
(list->set (build-all-boolean-states (hash-keys (dynamics-network dyn))))))