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#lang racket
(provide falsifiable-cnf?)
(require "props.rkt")
(define (prop? f)
(or (var? f)
(and (neg? f)
(prop? (neg-subf f)))
(and (disj? f)
(prop? (disj-left f))
(prop? (disj-right f)))
(and (conj? f)
(prop? (conj-left f))
(prop? (conj-right f)))))
(define (lit-var f)
(cond [(var? f) f]
[(neg? f) (neg-subf f)]
[else (error "Złe dane ze znacznikiem -- LIT-VAR" f)]))
(define (free-vars f)
(cond [(null? f) null]
[(var? f) (list f)]
[(neg? f) (free-vars (neg-subf f))]
[(conj? f) (append (free-vars (conj-left f))
(free-vars (conj-right f)))]
[(disj? f) (append (free-vars (disj-left f))
(free-vars (disj-right f)))]
[else (error "Zła formula -- FREE-VARS" f)]))
(define (gen-vals xs)
(if (null? xs)
(list null)
(let*
((vss (gen-vals (cdr xs)))
(x (car xs))
(vst (map (λ (vs) (cons (list x true) vs)) vss))
(vsf (map (λ (vs) (cons (list x false) vs)) vss)))
(append vst vsf))))
(define (eval-formula f evaluation)
(cond [(var? f)
(let ((val (assoc f evaluation)))
(if (not val)
(error "Zmienna wolna nie wystepuje w wartościowaniu -- EVAL-FORMULA" f evaluation)
(cadr val)))]
[(neg? f) (not (eval-formula (neg-subf f) evaluation))]
[(disj? f) (or (eval-formula (disj-left f) evaluation)
(eval-formula (disj-right f) evaluation))]
[(conj? f) (and (eval-formula (conj-left f) evaluation)
(eval-formula (conj-right f) evaluation))]
[else (error "Zła formuła -- EVAL-FORMULA" f evaluation)]))
(define (falsifiable-eval? f)
(let* ((evaluations (gen-vals (free-vars f)))
(results (map (λ (evaluation) (eval-formula f evaluation)) evaluations)))
(ormap false? results)))
(define (nff? f)
(cond [(lit? f) true]
[(neg? f) false]
[(conj? f) (and (nff? (conj-left f))
(nff? (conj-right f)))]
[(disj? f) (and (nff? (disj-left f))
(nff? (disj-right f)))]
[else (error "Zła formuła -- NFF?" f)]))
(define (convert-to-nnf f)
(cond [(lit? f) f]
[(neg? f) (convert-negation (neg-subf f))]
[(conj? f) (conj (convert-to-nnf (conj-left f))
(convert-to-nnf (conj-right f)))]
[(disj? f) (disj (convert-to-nnf (disj-left f))
(convert-to-nnf (disj-right f)))]
[else (error "Zła formuła -- CONVERT" f)]))
(define (convert-negation f)
(cond [(lit? f)
(if (var? f)
(neg f)
(neg-subf f))]
[(neg? f) (convert-to-nnf (neg-subf f))]
[(conj? f) (disj (convert-negation (conj-left f))
(convert-negation (conj-right f)))]
[(disj? f) (conj (convert-negation (disj-left f))
(convert-negation (disj-right f)))]
[else (error "Zła formuła -- CONVERT-NEGATION" f)]))
(define (clause? x)
(and (list? x)
(andmap lit? x)))
(define (clause-empty? x)
(and (clause? x)
(null? x)))
(define (cnf? x)
(and (list? x)
(andmap clause? x)))
(define (flatmap proc seq)
(foldl append null (map proc seq)))
(define (convert-to-cnf f)
(define (convert f)
(cond [(lit? f) (list (list f))]
[(conj? f) (append (convert-to-cnf (conj-left f))
(convert-to-cnf (conj-right f)))]
[(disj? f)
(let ((clause-left (convert-to-cnf (disj-left f)))
(clause-right (convert-to-cnf (disj-right f))))
(flatmap (λ (clause)
(map (λ (clause2)
(append clause2 clause)) clause-left))
clause-right))]))
(convert (convert-to-nnf f)))
(define (falsifiable-clause? clause)
(cond [(clause-empty? clause) true]
[(lit? (findf (λ (l) (equal?
l
(convert-to-nnf (neg (car clause)))))
clause)) false]
[else (falsifiable-clause? (cdr clause))]))
(define (falsifiable-cnf? f)
(define (neg-value lit)
(if (var? lit)
(list lit false)
(list (neg-subf lit) true)))
(ormap (λ (clause) (if (falsifiable-clause? clause)
(map neg-value clause)
false))
(convert-to-cnf f)))
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