121 lines
4.3 KiB
Racket
121 lines
4.3 KiB
Racket
|
#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")
|
|||
|
|
|||
|
(provide
|
|||
|
;; Functions with contracts
|
|||
|
(contract-out [update (-> network? state? (listof variable?) state?)]
|
|||
|
[make-state (-> (listof (cons/c symbol? any/c)) state?)]
|
|||
|
[make-network-from-functions (-> (listof (cons/c symbol? update-function?)) network?)]
|
|||
|
[update-function-form->update-function (-> update-function-form? update-function?)]
|
|||
|
[network-form->network (-> network-form? network?)]
|
|||
|
[make-network-from-forms (-> (listof (cons/c symbol? update-function-form?))
|
|||
|
network?)])
|
|||
|
;; Functions
|
|||
|
variable? state? update-function? update-function-form? network-form?
|
|||
|
;; Contracts
|
|||
|
state/c network/c
|
|||
|
;; Syntax
|
|||
|
st nn)
|
|||
|
|
|||
|
|
|||
|
;;; =================
|
|||
|
;;; 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? (-> 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 bn ; the Boolean network
|
|||
|
s ; the state to operate on
|
|||
|
xs) ; the variables to update
|
|||
|
(let ([new-s (hash-copy s)])
|
|||
|
(for ([x xs])
|
|||
|
(let ([f (hash-ref bn x)])
|
|||
|
(hash-set! new-s x (f s))))
|
|||
|
new-s))
|
|||
|
|
|||
|
;;; A version of make-hash restricted to creating network states (see
|
|||
|
;;; contract).
|
|||
|
(define (make-state mappings) (make-hash mappings))
|
|||
|
|
|||
|
;;; A shortcut for make-state.
|
|||
|
(define-syntax-rule (st mappings) (make-state mappings))
|
|||
|
|
|||
|
;;; A version of make-hash restricted to creating networks.
|
|||
|
(define (make-network-from-functions funcs) (make-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)
|
|||
|
(lambda (s) (eval-with s form)))
|
|||
|
|
|||
|
;;; Build a network from a network form.
|
|||
|
(define (network-form->network bnf)
|
|||
|
(make-hash
|
|||
|
(hash-map bnf (lambda (x form)
|
|||
|
(cons 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-hash forms)))
|
|||
|
|
|||
|
;;; A shortcut for make-network-from-forms.
|
|||
|
(define-syntax-rule (nn forms) (make-network-from-forms 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.
|