#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" "functions.rkt" graph racket/random)

(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-state-booleanize (-> (listof (cons/c symbol? (or/c 0 1))) state?)]
               [booleanize-state (-> state? 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?))
                                            network?)]
               [list-interactions (-> network-form? variable? (listof variable?))]
               [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? domain-mapping/c variable? variable? (or/c '+ '- '0))]
               [build-signed-interaction-graph/form (-> network-form? domain-mapping/c graph?)]
               [build-boolean-signed-interaction-graph/form (-> network-form? graph?)]
               [build-signed-interaction-graph (-> network? domain-mapping/c graph?)]
               [build-boolean-signed-interaction-graph (-> network? 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?)]
               [read-org-network-make-asyn (-> string? dynamics?)]
               [read-org-network-make-syn (-> string? 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-boolean-state-graph (-> dynamics? graph?)]
               [build-full-boolean-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? domain-mapping/c) (#:headers boolean?)
                                      (listof (listof any/c)))]
               [tabulate-boolean-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?)])
 ;; Predicates
 (contract-out [variable? (-> any/c boolean?)]
               [state? (-> any/c boolean?)]
               [update-function-form? (-> any/c boolean?)]
               [network-form? (-> any/c boolean?)]
               [modality? (-> any/c boolean?)]
               [mode? (-> any/c boolean?)])
 ;; Contracts
 (contract-out [state/c contract?]
               [update-function/c contract?]
               [domain-mapping/c contract?]))

(module+ test
  (require rackunit))


;;; =================
;;; 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? (hash/c variable? procedure?))

;;; 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)))))

(module+ test
  (test-case "basic definitions"
    (define f1 (λ (s) (let ([x1 (hash-ref s 'x1)]
                            [x2 (hash-ref s 'x2)])
                        (and x1 (not x2)))))
    (define f2 (λ (s) (let ([x2 (hash-ref s 'x2)])
                        (not x2))))
    (define bn (make-network-from-functions `((x1 . ,f1) (x2 . ,f2))))
    (define s1 (make-state '((x1 . #t) (x2 . #f))))
    (define new-s1 (update bn s1 '(x2 x1)))
    (define s2 (make-state '((x1 . #f) (x2 . #f))))
    (define new-s2 (update bn s2 '(x2)))

    (check-equal? s1 #hash((x1 . #t) (x2 . #f)))
    (check-equal? new-s1 #hash((x1 . #t) (x2 . #t)))
    (check-equal? s2 #hash((x1 . #f) (x2 . #f)))
    (check-equal? new-s2 #hash((x1 . #f) (x2 . #t)))))

;;; A version of make-immutable-hash restricted to creating network
;;; states (see contract).
(define (make-state mappings) (make-immutable-hash mappings))

;;; Makes a new Boolean states from a state with numerical values 0
;;; and 1.
(define (make-state-booleanize mappings)
  (make-state (for/list ([mp mappings])
                (match mp
                  [(cons var 0) (cons var #f)]
                  [(cons var 1) (cons var #t)]))))

(module+ test
  (test-case "make-state, make-state-booleanize, booleanize-state"
    (check-equal? (make-state-booleanize '((a . 0) (b . 1)))
                  (make-state '((a . #f) (b . #t))))
    (check-equal? (booleanize-state (make-state '((a . 0) (b . 1))))
                  (make-state '((a . #f) (b . #t))))))

;;; Booleanizes a given state: replaces 0 with #f and 1 with #t.
(define (booleanize-state s)
  (for/hash ([(x val) s]) (match val [0 (values x #f)] [1 (values x #t)])))

;;; 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)
  (λ (s) (eval-with s form)))

(module+ test
  (test-case "update-function-form->update-function"
    (define s (make-state '((x . #t) (y . #f))))
    (define f (update-function-form->update-function '(and x y)))
    (check-equal? (f s) #f)))

;;; 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))))

(module+ test
  (test-case "network-form->network"
    (define bn (network-form->network
         (make-hash '((a . (and a b)) (b . (not b))))))
    (define s (make-state '((a . #t) (b . #t))))
    (check-equal? ((hash-ref bn 'a) s) #t)))

;;; 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)))

(module+ test
  (test-case "make-network-from-forms"
    (define bn (make-network-from-forms '((a . (and a b))
                                          (b . (not b)))))
    (define s (make-state '((a . #t) (b . #t))))
    (check-equal? ((hash-ref bn 'a) s) #t)))


;;; ============================
;;; 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.

;;; 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)))

(module+ test
  (test-case "list-interactions"
    (define n #hash((a . (+ a b c))
                    (b . (- b c))))
    (check-true (set=? (list-interactions n 'a) '(a b)))
    (check-true (set=? (list-interactions n 'b) '(b)))))

;;; 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))))))

(module+ test
  (test-case "build-interaction-graph"
    (define n #hash((a . (+ a b c))
             (b . (- b c))))
    (define ig (build-interaction-graph n))
    (check-true (has-vertex? ig 'a))
    (check-true (has-vertex? ig 'b))
    (check-false (has-vertex? ig 'c))
    (check-true (has-edge? ig 'a 'a))
    (check-true (has-edge? ig 'b 'a))
    (check-true (has-edge? ig 'b 'b))
    (check-false (has-edge? ig 'c 'b))
    (check-false (has-edge? ig 'c 'a))))

;;; 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
;;; possible values, constructs the list of all possible states.
(define (build-all-states vars-domains)
  (let* ([var-dom-list (hash-map vars-domains (λ (x y) (cons x y)) #t)]
         [vars (map car var-dom-list)]
         [domains (map cdr var-dom-list)])
    (for/list ([s (apply cartesian-product domains)])
      (make-state (for/list ([var vars] [val s])
                    (cons var val))))))

(module+ test
  (test-case "build-all-states"
    (check-equal? (build-all-states #hash((a . (#t #f)) (b . (1 2 3))))
                  '(#hash((a . #t) (b . 1))
                    #hash((a . #t) (b . 2))
                    #hash((a . #t) (b . 3))
                    #hash((a . #f) (b . 1))
                    #hash((a . #f) (b . 2))
                    #hash((a . #f) (b . 3))))))

;;; 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)))

(module+ test
  (test-case "make-same-domains, make-boolean-domains"
    (check-equal? (make-boolean-domains '(a b))
                  #hash((a . (#f #t)) (b . (#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)))

(module+ test
  (test-case "build-all-boolean-states"
    (check-equal? (build-all-boolean-states '(a b))
                  '(#hash((a . #f) (b . #f))
                    #hash((a . #f) (b . #t))
                    #hash((a . #t) (b . #f))
                    #hash((a . #t) (b . #t))))))

;;; Given two interacting variables of a network 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 doms x y)
  (let* ([dom-x (hash-ref doms x)]
         [dom-y (hash-ref doms y)]
         ;; 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)]
         ;; 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])))

(module+ test
  (test-case "get-interaction-sign"
    (define n #hash((a . (not b)) (b . a)))
    (define doms (make-boolean-domains '(a b)))
    (check-equal? (get-interaction-sign (network-form->network n) doms 'a 'b) '+)
    (check-equal? (get-interaction-sign (network-form->network n) doms 'b 'a) '-)))

;;; 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/form network-form doms)
  (let ([ig (build-interaction-graph network-form)]
        [network (network-form->network network-form)])
    ;; Label every edge of the interaction graph with the sign.
    (define sig
      (weighted-graph/directed
       (for/list ([e (in-edges ig)])
         (match-let ([(list x y) e])
           (list (get-interaction-sign network doms x y)
                 x y)))))
    ;; Ensure that every variable of the network appears in the signed
    ;; interaction graph as well.
    (for ([v (in-vertices ig)])
      (add-vertex! sig v))
    sig))

(module+ test
  (test-case "build-signed-interaction-graph/form"
    (define n #hash((a . (not b)) (b . a)))
    (define doms (make-boolean-domains '(a b)))
    (define sig1 (build-signed-interaction-graph/form n doms))
    (check-true (has-vertex? sig1 'a))
    (check-true (has-vertex? sig1 'b))
    (check-false (has-vertex? sig1 'c))
    (check-false (has-edge? sig1 'a 'a))
    (check-true (has-edge? sig1 'b 'a))
    (check-false (has-edge? sig1 'b 'b))
    (check-false (has-edge? sig1 'c 'b))
    (check-false (has-edge? sig1 'c 'a))
    (check-equal? (edge-weight sig1 'a 'b) '+)
    (check-equal? (edge-weight sig1 'b 'a) '-)))

;;; 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/form network-form)
  (build-signed-interaction-graph/form
   network-form
   (make-boolean-domains (hash-keys network-form))))

(module+ test
  (test-case "build-boolean-signed-interaction-graph/form"
    (define n #hash((a . (not b)) (b . a)))
    (define sig2 (build-boolean-signed-interaction-graph/form n))
    (check-true (has-vertex? sig2 'a))
    (check-true (has-vertex? sig2 'b))
    (check-false (has-vertex? sig2 'c))
    (check-false (has-edge? sig2 'a 'a))
    (check-true (has-edge? sig2 'b 'a))
    (check-false (has-edge? sig2 'b 'b))
    (check-false (has-edge? sig2 'c 'b))
    (check-false (has-edge? sig2 'c 'a))
    (check-equal? (edge-weight sig2 'a 'b) '+)
    (check-equal? (edge-weight sig2 'b 'a) '-)))

;;; Similar to build-signed-interaction-graph/form, but operates on a
;;; network rather than a form.  The resulting graph only includes the
;;; edges for positive or negative interactions.
;;;
;;; This function has operates with much less knowledge than
;;; build-signed-interaction-graph/form, so prefer using the latter
;;; when you can get a network form.
;;;
;;; /!\ This function iterates through 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 doms)
  (define sig
    (weighted-graph/directed
     (for*/fold ([edges '()])
                ([(x _) (in-hash network)]
                 [(y _) (in-hash network)])
       (match (get-interaction-sign network doms x y)
         ['0 edges]
         [sign (cons (list sign x y) edges)]))))
  ;; Ensure that all variables of the network appear in the signed
  ;; interaction graph.
  (for ([(v _) (in-hash network)])
      (add-vertex! sig v))
    sig)

;;; Calls build-signed-interaction-graph assuming that the domains of
;;; all variables are Boolean.
;;;
;;; This function has operates with much less knowledge than
;;; build-boolean-signed-interaction-graph/form, so prefer using the
;;; latter when you can get a network form.
;;;
;;; /!\ This function iterates through 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-boolean-signed-interaction-graph network)
  (build-signed-interaction-graph network (make-boolean-domains (hash-keys network))))

(module+ test
  (test-case "build-signed-interaction-graph, build-boolean-signed-interaction-graph"
    (define n #hash((a . (not b)) (b . a)))
    (define sig3 (build-boolean-signed-interaction-graph (network-form->network n)))
    (check-true (has-vertex? sig3 'a))
    (check-true (has-vertex? sig3 'b))
    (check-equal? (edge-weight sig3 'a 'a) '+)
    (check-equal? (edge-weight sig3 'b 'b) '+)
    (check-equal? (edge-weight sig3 'a 'b) '+)
    (check-equal? (edge-weight sig3 'b 'a) '-)))

;;; Interaction graphs for networks without interactions must still
;;; contain all nodes.
(module+ test
  (test-case "Interaction must graphs always contain all nodes."
    (define n #hash((a . #t) (b . #t)))
    (define ig (build-interaction-graph n))
    (define sig-nf (build-boolean-signed-interaction-graph/form n))
    (define sig (build-boolean-signed-interaction-graph (network-form->network n)))
    (check-equal? (get-vertices ig) '(b a))
    (check-true (empty? (get-edges ig)))
    (check-equal? (get-vertices sig-nf) '(b a))
    (check-true (empty? (get-edges sig-nf)))
    (check-equal? (get-vertices sig) '(b a))))


;;; ====================
;;; Dynamics of networks
;;; ====================

;;; This section contains definitions for building and analysing the
;;; dynamics of networks.

;;; 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
  [;; 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))))

;;; 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 (network-form->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)))))

;;; Reads an Org-mode-produced sexp, converts it into a network, and
;;; builds the asyncronous dynamics out of it.
(define read-org-network-make-asyn (compose make-asyn-dynamics network-form->network read-org-variable-mapping))

;;; Reads an Org-mode-produced sexp, converts it into a network, and
;;; builds the synchronous dynamics out of it.
(define read-org-network-make-syn (compose make-syn-dynamics network-form->network read-org-variable-mapping))

;;; 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 (make-state '((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 (make-state '((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-boolean-state-graph dyn)
  (dds-build-state-graph
   dyn
   (list->set (build-all-boolean-states (hash-keys (dynamics-network dyn))))))

;;; Build the full annotated state graph of a Boolean network.
(define (build-full-boolean-state-graph-annotated dyn)
  (dds-build-state-graph-annotated
   dyn
   (list->set (build-all-boolean-states (hash-keys (dynamics-network dyn))))))

(module+ test
  (test-case "Dynamics of networks"
    (define n (network-form->network #hash((a . (not a)) (b . b))))
    (define asyn (make-asyn-dynamics n))
    (define syn (make-syn-dynamics n))
    (define s (make-state '((a . #t) (b . #f))))
    (define ss (set (make-state '((a . #t) (b . #t)))
                    (make-state '((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-boolean-state-graph asyn))
    (define gr-complete-bool-ann (build-full-boolean-state-graph-annotated asyn))
    (check-equal? (dds-step-one asyn s) (set (make-state '((a . #f) (b . #f)))
                                             (make-state '((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 (make-state '((a . #f) (b . #f)))))
    (check-equal? (dds-step asyn ss)
                  (set (make-state '((a . #f) (b . #t)))
                       (make-state '((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 domains #: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 cons #t)])
                                (values (car pair) (cdr pair))))
  (define tab (tabulate-state* funcs domains #: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]))

;;; Like tabulate-network, but assumes all the variables are Boolean.
(define (tabulate-boolean-network bn #:headers [headers #t])
  (tabulate-network bn (make-boolean-domains (hash-map bn (λ (x y) x) #t))
                    #:headers headers))

(module+ test
  (test-case "tabulate-boolean-network"
    (define bn (network-form->network #hash((a . (not a)) (b . b))))
    (check-equal? (tabulate-boolean-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-boolean-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.
(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-state (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)))))
  ;; Construct the network.
  (make-network-from-functions (map cons var-names funcs)))

(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 n 'x1))
    (define f2 (hash-ref n 'x2))

    (check-false (f1 (make-state '((x1 . #f) (x2 . #f)))))
    (check-false (f1 (make-state '((x1 . #f) (x2 . #t)))))
    (check-true (f1 (make-state '((x1 . #t) (x2 . #f)))))
    (check-true (f1 (make-state '((x1 . #t) (x2 . #t)))))

    (check-false (f2 (make-state '((x1 . #f) (x2 . #f)))))
    (check-true (f2 (make-state '((x1 . #f) (x2 . #t)))))
    (check-false (f2 (make-state '((x1 . #t) (x2 . #f)))))
    (check-true (f2 (make-state '((x1 . #t) (x2 . #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-boolean-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)
  (for/hash ([(x x-dom) (in-hash domains)])
    (values x (random-function/state domains x-dom))))

;;; 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)))))