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reduction.rkt
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reduction.rkt
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#lang racket
(require redex)
(require "./peg.rkt")
(provide (all-defined-out))
(define-extended-language Reduct Grammar
(C (/ C e)
(/ e C)
(• C e)
(• e C)
(* C)
(! C)
(NT x)
h)
(D ⊥
suc)
(nat 0
(⊕ nat))
(dir ↓
↑)
(s (natural ...))
(state (G ⊢ (C ...) e dir s_1 s_2 D (natural ...)))
)
;up-arrow - coming out of the expression - finished the analysis
;down-arrow: entering
;dir -> setinha
;state é o input e o output da red
;nat ser transformado em uma lista de numeros
;quando aparecer um choice, colocar um 0 na frente
;quando sair do choice com sucesso, tira o topo da lista
(define-metafunction Reduct
input-grammar : state -> G ;type
[(input-grammar (G ⊢ (C ...) e dir s_1 s_2 D (natural ...))) G])
(define-metafunction Reduct
input-peg : state -> e
[(input-peg (G ⊢ (C ...) e dir s_1 s_2 D (natural ...))) e])
(define-metafunction Reduct
input-result : state -> s
[(input-result (G ⊢ (C ...) e dir s_1 s_2 ⊥ (natural ...))) ⊥]
[(input-result (G ⊢ (C ...) e dir s_1 s_2 D (natural ...))) s_1])
(define-metafunction Reduct
input-term : state -> s
[(input-term (G ⊢ (C ...) e dir s_1 s_2 D (natural ...))) s_1])
;
(define red
(reduction-relation
Reduct
#:domain state
;Terminal
(--> (G ⊢ (C ...) natural_1 ↓ (natural_1 natural_2 ...) (natural_3 ...) D (natural_4 natural_5 ...))
(G ⊢ (C ...) natural_1 ↑ (natural_2 ...) (natural_1 natural_3 ...) suc ((inc natural_4) natural_5 ...))
"Terminal")
(--> (G ⊢ (C ...) natural_1 ↓ (natural_2 natural ...) s_1 D (natural_3 ...))
(G ⊢ (C ...) natural_1 ↑ (natural_2 natural ...) s_1 ⊥ (natural_3 ...))
(side-condition (term (diff-exp? natural_1 natural_2)))
"Terminal ⊥")
(--> (G ⊢ (C ...) natural_1 ↓ () s_1 D (natural_2 ...))
(G ⊢ (C ...) natural_1 ↑ () s_1 ⊥ (natural_2 ...))
"Terminal () ⊥")
;Empty
(--> (G ⊢ (C ...) ε ↓ (natural ...) s_1 D (natural_1 ...))
(G ⊢ (C ...) ε ↑ (natural ...) s_1 suc (natural_1 ...))
"Empty")
#|
quando falhar, a gnt tem que voltar até o (nat ...) ser 0.
quando ele ta saindo com bot ou entrando, vai voltando ate chegar na setinha pra baixo com 0.
faz voltar com a redução
quando tiver oplus, tira o oplus, tira de uma lista e coloca no começo da outra, até ter 0 no (nat ...)
ai muda a setinha pra cima e ver se da certo ou errado
|#
;Choice
;esquerdo deu certo:
(--> (G ⊢ (C ...) (/ e_1 e_2) ↓ (natural_1 ...) (natural ...) D (natural_2 ...))
(G ⊢ ((/ h e_2) C ...) e_1 ↓ (natural_1 ...) (natural ...) D (0 natural_2 ...)) ;h serve tentar e e_2 para memorizar
"Alternancia-Entra")
(--> (G ⊢ ((/ h e_2) C ...) e_1 ↑ (natural_1 ...) (natural_2 ...) suc (natural_3 natural_4 natural_5 ...))
(G ⊢ (C ...) (/ e_1 e_2) ↑ (natural_1 ...) (natural_2 ...) suc ((⊕ natural_3 natural_4) natural_5 ...))
"Alternancia-SUC-first")
(--> (G ⊢ ((/ h e_2) C ...) e_1 ↑ (natural ...) s_1 ⊥ (0 natural_2 ...))
(G ⊢ ((/ e_1 h) C ...) e_2 ↓ (natural ...) s_1 ⊥ (0 natural_2 ...))
"Alternancia-BOT-first")
(--> (G ⊢ ((/ h e_2) C ...) e_1 ↑ (natural ...) (natural_1 natural_2 ...) ⊥ (natural_3 natural_4 ...))
(G ⊢ ((/ h e_2) C ...) e_1 ↑ (natural_1 natural ...) (natural_2 ...) ⊥ ((dec natural_3) natural_4 ...))
(side-condition (term (diff-exp? natural_3 0)))
"Alternancia-BOT-first-restore")
(--> (G ⊢ ((/ e_1 h) C ...) e_2 ↑ (natural_1 ...) (natural_2 ...) suc (natural_3 natural_4 natural_5 ...))
(G ⊢ (C ...) (/ e_1 e_2) ↑ (natural_1 ...) (natural_2 ...) suc ((⊕ natural_3 natural_4) natural_5 ...))
"Alternancia-SUC-second")
(--> (G ⊢ ((/ e_1 h) C ...) e_2 ↑ (natural ...) s_1 ⊥ (0 natural_1 ...))
(G ⊢ (C ...) (/ e_1 e_2) ↑ (natural ...) s_1 ⊥ (natural_1 ...))
"Alternancia-BOT-second")
(--> (G ⊢ ((/ e_1 h) C ...) e_2 ↑ (natural ...) (natural_1 natural_2 ...) ⊥ (natural_3 natural_4 ...))
(G ⊢ ((/ e_1 h) C ...) e_2 ↑ (natural_1 natural ...) (natural_2 ...) ⊥ ((dec natural_3) natural_4 ...))
(side-condition (term (diff-exp? natural_3 0)))
"Alternancia-BOT-second-restore")
;Sequence
(--> (G ⊢ (C ...) (• e_1 e_2) ↓ (natural_1 ...) (natural ...) D (natural_2 ...))
(G ⊢ ((• h e_2) C ...) e_1 ↓ (natural_1 ...) (natural ...) D (natural_2 ...))
"Sequencia-Entra")
;saindo do e_1 deu bom
(--> (G ⊢ ((• h e_2) C ...) e_1 ↑ (natural_1 ...) (natural_3 ...) suc (natural_4 ...))
(G ⊢ ((• e_1 h) C ...) e_2 ↓ (natural_1 ...) (natural_3 ...) suc (natural_4 ...)) ;soma 1, pq ele consome 1
"Sequencia-SUC-first")
;saindo do e_1 deu ruim
(--> (G ⊢ ((• h e_2) C ...) e_1 ↑ (natural_1 ...) (natural_3 ...) ⊥ (natural_4 ...))
(G ⊢ (C ...) (• e_1 e_2) ↑ (natural_1 ...) (natural_3 ...) ⊥ (natural_4 ...))
"Sequencia-BOT-first")
;saindo do e_2 deu bom
(--> (G ⊢ ((• e_1 h) C ...) e_2 ↑ (natural_1 ...) (natural_3 ...) suc (natural_4 ...))
(G ⊢ (C ...) (• e_1 e_2) ↑ (natural_1 ...) (natural_3 ...) suc (natural_4 ...))
"Sequencia-SUC-second")
;saindo do e_2 deu ruim
(--> (G ⊢ ((• e_1 h) C ...) e_2 ↑ (natural_1 ...) (natural_3 ...) ⊥ (natural_5 ...))
(G ⊢ (C ...) (• e_1 e_2) ↑ (natural_1 ...) (natural_3 ...) ⊥ (natural_5 ...))
"Sequencia-BOT-second")
;volta na repetição quando dá falha
;cada vez que a repet dá certo, podemos tirar do topo
;Repetition
(--> (G ⊢ (C ...) (* e_1) ↓ s_1 s_2 D (natural_4 ...))
(G ⊢ ((* h) C ...) e_1 ↓ s_1 s_2 D (0 natural_4 ...))
"Repetition-Entra")
(--> (G ⊢ ((* h) C ...) e_1 ↑ () (natural ...) suc (natural_4 ...))
(G ⊢ (C ...) (* e_1) ↑ () (natural ...) suc (natural_4 ...))
"Repetition-SUC-Sai")
(--> (G ⊢ ((* h) C ...) e_1 ↑ (natural_1 natural_2 ...) (natural ...) suc (natural_3 natural_4 natural_5 ...))
(G ⊢ (C ...) (* e_1) ↓ (natural_1 natural_2 ...) (natural ...) suc ((⊕ natural_3 natural_4) natural_5 ...))
(side-condition (term (not (diff-exp? e_1 natural_1))))
"Repetition-SUC")
(--> (G ⊢ ((* h) C ...) e_1 ↑ s_1 s_2 ⊥ (0 natural_4 ...))
(G ⊢ (C ...) (* e_1) ↑ s_1 s_2 suc (natural_4 ...))
"Repetition-BOT")
(--> (G ⊢ ((* h) C ...) e_1 ↑ (natural_2 ...) (natural_1 natural_3 ...) ⊥ (natural_4 natural_5 ...))
(G ⊢ ((* h) C ...) e_1 ↑ (natural_1 natural_2 ...) (natural_3 ...) ⊥ ((dec natural_4) natural_5 ...))
(side-condition (term (diff-exp? natural_4 0)))
"Repetition-BOT-restore")
;Not
(--> (G ⊢ (C ...) (! e_1) ↓ (natural_1 ...) (natural ...) D (natural_4 ... ))
(G ⊢ ((! h) C ...) e_1 ↓ (natural_1 ...) (natural ...) D (0 natural_4 ...))
"Not-Entra")
(--> (G ⊢ ((! h) C ...) e_1 ↑ (natural_1 ...) (natural ...) suc (0 natural_4 ...))
(G ⊢ (C ...) (! e_1) ↑ (natural_1 ...) (natural ...) ⊥ (natural_4 ...))
"Not-BOT")
(--> (G ⊢ ((! h) C ...) e_1 ↑ (natural ...) (natural_1 natural_2 ...) suc (natural_3 natural_4 ...))
(G ⊢ ((! h) C ...) e_1 ↑ (natural_1 natural ...) (natural_2 ...) suc ((dec natural_3) natural_4 ...))
(side-condition (term (diff-exp? natural_3 0)))
"Not-BOT-restore")
(--> (G ⊢ ((! h) C ...) e_1 ↑ (natural_1 ...) (natural ...) ⊥ (0 natural_4 ...))
(G ⊢ (C ...) (! e_1) ↑ (natural_1 ...) (natural ...) suc (natural_4 ...))
"Not-SUC")
(--> (G ⊢ ((! h) C ...) e_1 ↑ (natural ...) (natural_1 natural_2 ...) ⊥ (natural_3 natural_4 ...))
(G ⊢ ((! h) C ...) e_1 ↑ (natural_1 natural ...) (natural_2 ...) ⊥ ((dec natural_3) natural_4 ...))
(side-condition (term (diff-exp? natural_3 0)))
"Not-SUC-restore")
;Non-terminals
(--> (G ⊢ (C ...) x ↓ (natural_1 ...) (natural ...) D (natural_4 ...))
(G ⊢ ((NT x) C ...) (lookup-red G x) ↓ (natural_1 ...) (natural ...) D (natural_4 ...))
"Non-terminals-entra")
(--> (G ⊢ ((NT x) C ...) e ↑ (natural_1 ...) (natural ...) D (natural_4 ...))
(G ⊢ (C ...) x ↑ (natural_1 ...) (natural ...) D (natural_4 ...))
"Non-terminals-sai")
)
)
(define-metafunction Reduct
[(diff-exp? e_1 e_1) #f]
[(diff-exp? e_1 e_2) #t]
)
(define-metafunction Reduct
[(lookup-red (x e G) x) e]
[(lookup-red (x_1 e G) x_2) (lookup-red G x_2)]
[(lookup-red ∅ x) ,(error 'lookup-red "not found: ~e" (term x))]
)
(define-metafunction Reduct
[(inc natural) ,(add1 (term natural))]
)
(define-metafunction Reduct
[(dec natural) ,(sub1 (term natural))]
)
(define-metafunction Reduct
[(⊕ natural_1 natural_2) ,(+ (term natural_1) (term natural_2))]
)
;Terminal
;(stepper red (term (∅ ⊢ () 1 ↓ (1 2 3) () ⊥ (0))))
;(traces red (term (∅ ⊢ () 1 ↓ (2 3) () ⊥ (0))))
;Choice
;(traces red (term (∅ ⊢ () (/ 1 2) ↓ (1 2 3) () ⊥ (0))))
;(traces red (term (∅ ⊢ () (/ 1 2) ↓ (2 3) () ⊥ (0))))
;Sequence
;(traces red (term (∅ ⊢ () (• 1 3) ↓ (1 2 3) () ⊥ (0))))
;(traces red (term (∅ ⊢ () (• (• 1 2) (• 1 3)) ↓ (1 2 1 5 5) () ⊥ (0))))
;Repetition
;(traces red (term (∅ ⊢ () (* 1) ↓ (1 1 1 1 2) () ⊥ (0))))
;(traces red (term (∅ ⊢ () (* 1) ↓ (1 1 1 1) () ⊥ (0))))
;Not
;(traces red (term (∅ ⊢ () (! 1) ↓ (1 1 2) () ⊥ (0))))
;(traces red (term (∅ ⊢ () (! 2) ↓ (1 1 2) () ⊥ (0))))
;ALTERNANCIA COM REPETIÇÃO E TERMINAL
;(traces red (term (∅ ⊢ () (/ (* 1) 1) ↓ (1 1 1 1 2) () ⊥ (0))))
;SEQUENCIAS E ALTERNANCIAS
;(traces red (term (∅ ⊢ () (• 1 (• 2 (/ (• 3 4) (• 3 5)))) ↓ (1 2 3 5) () ⊥ (0))))
;ALTERNANCIA COM SEQUENCIA
;(stepper red (term (∅ ⊢ () (/ (• 1 2) (• 1 3)) ↓ (1 3 3) () ⊥ (0))))
;NON-TERMINAL
;(traces red (term ((A 2 ∅) ⊢ () A ↓ (2 3 4 5 6 7) () ⊥ (0))))
;(traces red (term ((A 2 ∅) ⊢ () A ↓ (3 4 5 6 7) () ⊥ (0))))
;(traces red (term ((A 2 ∅) ⊢ () B ↓ (2 3 4 5 6 7) () ⊥ (0))))
;(traces red (term ((A 2 ∅) ⊢ () (/ A 1) ↓ (1 1 2 3) () ⊥ (0))))
;(stepper red (term (∅ ⊢ () (• (! 0) (• 1 2)) ↓ (1 2 3) () ⊥ (0)))) ;esse da certo
;(traces red (term (∅ ⊢ () (• (• 1 2) (! 0)) ↓ (1 2 3) () ⊥ (0))))
;(stepper red (term (∅ ⊢ () (* (• 1 2)) ↓ (1 2 1 2 1 2 1 3) () ⊥ (0))))
;(traces red (term (∅ ⊢ () (/ (! (• 1 2)) (• 1 0)) ↓ (1 2 3) () ⊥ (0)))); esse da certo tb
;(traces red (term (∅ ⊢ () (! 1) ↓ (1 2 3) () ⊥ (0))))
;(stepper red (term (∅ ⊢ () (! (• 1 3)) ↓ (1 2 3) () ⊥ (0))))
;(traces red (term (∅ ⊢ () (* (! (• 1 2))) ↓ (1 3) () ⊥ (0))))
#;(stepper red (term ((A (/ (• 0 (• A 1)) ε)
(B (/ (• 1 (• B 2)) ε)
(C (/ 0 (/ 1 2))
(S (• (! (! A)) (• (* 0) (• B (! C)))) ∅))))
⊢ () S ↓ (0 1 2) () ⊥ (0))))
#;(stepper red (term ((A (/ (• 0 A) ε) ∅)
⊢ () (! (/ (• 0 0) ε)) ↓ (0 0 0 1 2) () ⊥ (0))))
;(stepper red (term (∅ ⊢ () (/ (• (/ (• 0 0) (/ (• 0 1) (• 0 2))) (• 1 3)) (• 0 1)) ↓ (0 1 1 4) () ⊥ (0))))
;(apply-reduction-relation* red (term (∅ ⊢ () (* (• 1 2)) ↓ (1 2 1 2 1 2 1 3) () ⊥ (0))))