dds/tbn.rkt

#lang racket

(require (except-in "utils.rkt" lists-transpose) (submod "utils.rkt" untyped)
         "functions.rkt" "networks.rkt"
         graph racket/random racket/hash)

(module typed typed/racket
  (require (except-in "utils.rkt" lists-transpose)
         "utils.rkt" "functions.rkt" "networks.rkt"
         typed/graph typed/racket/random)

  (require/typed racket/hash
    [hash-intersect
     (->* ((HashTable Variable Real))
          (#:combine (-> Real Real Real))
          #:rest (HashTable Variable Real)
          (HashTable Variable Real))])

  (module+ test
    (require typed/rackunit))

  (provide
   apply-tbf-to-state

   (struct-out tbf/state) TBF/State tbf/state-w tbf/state-θ make-tbf/state
   sbf/state? apply-tbf/state

   lists+vars->tbfs/state lists+headers->tbfs/state lists->tbfs/state
   lists+vars->sbfs/state lists+headers->sbfs/state lists->sbfs/state
   )

  (: apply-tbf-to-state (-> TBF (State (U Zero One)) (U Zero One)))
  (define (apply-tbf-to-state tbf st)
    (apply-tbf tbf (list->vector
                    (hash-map st (λ (_ [val : (U Zero One)]) val) #t))))

  (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)))

  (struct tbf/state ([weights : (VariableMapping Real)]
                     [threshold : Real])
    #:transparent
    #:type-name TBF/State)
  (define tbf/state-w tbf/state-weights)
  (define tbf/state-θ tbf/state-threshold)

  (: make-tbf/state (-> (Listof (Pairof Variable Real)) Real TBF/State))
  (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)))

  (: sbf/state? (-> TBF/State Boolean))
  (define (sbf/state? tbfs) (zero? (tbf/state-θ tbfs)))

  (module+ test
    (test-case "sbf/state?"
      (check-true (sbf/state? (tbf/state (hash 'a -1 'b 1) 0)))
      (check-false (sbf/state? (tbf/state (hash 'a -1 'b 1) 1)))))

  (: apply-tbf/state (-> TBF/State (State (U Zero One)) (U Zero One)))
  (define (apply-tbf/state tbfs st)
    (any->01
     (> (apply + (hash-values (hash-intersect (tbf/state-w tbfs) st #:combine *)))
        (tbf/state-θ tbfs))))

  (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)))

  (: lists+vars->tbfs/state (-> (Listof Variable) (Listof (Listof Real))
                                (Listof TBF/State)))
  (define (lists+vars->tbfs/state vars lsts)
    (for/list ([lst (in-list lsts)])
      (define-values (ws θ) (split-at-right lst 1))
      (make-tbf/state (for/list ([x (in-list vars)]
                                 [w (in-list ws)])
                        (cons x w))
                      (car θ))))

  (module+ test
    (test-case "lists+vars->tbfs/state"
      (check-equal? (lists+vars->tbfs/state '(x y) '((1 2 3) (1 1 2)))
                    (list (tbf/state '#hash((x . 1) (y . 2)) 3)
                          (tbf/state '#hash((x . 1) (y . 1)) 2)))))

  (: lists+headers->tbfs/state (-> (Pairof (Listof Variable) (Listof (Listof Real)))
                                   (Listof TBF/State)))
  (define (lists+headers->tbfs/state lsts+headers)
    (lists+vars->tbfs/state (drop-right (car lsts+headers) 1)
                            (cdr lsts+headers)))

  (module+ test
    (test-case "lists+headers->tbfs/state"
      (check-equal? (lists+headers->tbfs/state '((x y f) (1 2 3) (1 1 2)))
                    (list (tbf/state '#hash((x . 1) (y . 2)) 3)
                          (tbf/state '#hash((x . 1) (y . 1)) 2)))))

  (: lists->tbfs/state (-> (Listof (Listof Real)) (Listof TBF/State)))
  (define (lists->tbfs/state lsts)
    (lists+vars->tbfs/state
     (for/list ([i (in-range (length (car lsts)))])
       (string->symbol (format "x~a" i)))
     lsts))

  (module+ test
    (test-case "lists->tbfs/state"
      (check-equal? (lists->tbfs/state '((1 2 3) (1 1 2)))
                    (list (tbf/state '#hash((x0 . 1) (x1 . 2)) 3)
                          (tbf/state '#hash((x0 . 1) (x1 . 1)) 2)))))

  (: lists+vars->sbfs/state (-> (Listof Variable) (Listof (Listof Real))
                                (Listof TBF/State)))
  (define (lists+vars->sbfs/state vars lsts)
    (for/list ([lst (in-list lsts)])
      (make-tbf/state (map (inst cons Variable Real) vars lst) 0)))

  (module+ test
    (test-case "lists+vars->sbfs/state"
      (check-equal? (lists+vars->sbfs/state '(x y) '((1 2) (1 1)))
                    (list (tbf/state '#hash((x . 1) (y . 2)) 0)
                          (tbf/state '#hash((x . 1) (y . 1)) 0)))))

  (: lists+headers->sbfs/state (-> (Pairof (Listof Variable) (Listof (Listof Real)))
                                   (Listof TBF/State)))
  (define (lists+headers->sbfs/state lsts)
    (lists+vars->sbfs/state (car lsts) (cdr lsts)))

  (module+ test
    (test-case "lists+headers->sbfs/state"
      (check-equal? (lists+headers->sbfs/state '((x y) (1 2) (1 1)))
                    (list (tbf/state '#hash((x . 1) (y . 2)) 0)
                          (tbf/state '#hash((x . 1) (y . 1)) 0)))))

  (: lists->sbfs/state (-> (Listof (Listof Real)) (Listof TBF/State)))
  (define (lists->sbfs/state lsts)
    (lists+vars->sbfs/state
     (for/list ([i (in-range (length (car lsts)))])
       (string->symbol (format "x~a" i)))
     lsts))

  (module+ test
    (test-case "lists->sbfs/state"
      (check-equal? (lists->sbfs/state '((1 2) (1 1)))
                    (list
                     (tbf/state '#hash((x0 . 1) (x1 . 2)) 0)
                     (tbf/state '#hash((x0 . 1) (x1 . 1)) 0)))))
  )

(module+ test
  (require rackunit))

;;; ===================
;;; 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 symbol? 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 symbol? 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")))