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lib/maude/conditional.sx — condition-aware reducer. ceq fires only when its guard holds: equational guards (l=r reduce to same normal form) and boolean guards (term reduces to true), evaluated by recursing through the same reducer. Verified on gcd, insertion sort, max, even. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
109 lines
4.6 KiB
Plaintext
109 lines
4.6 KiB
Plaintext
;; lib/maude/tests/conditional.sx — Phase 4: conditional equations.
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(define mct-pass 0)
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(define mct-fail 0)
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(define mct-failures (list))
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(define
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mct-check!
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(fn
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(name got expected)
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(if
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(= got expected)
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(set! mct-pass (+ mct-pass 1))
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(do
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(set! mct-fail (+ mct-fail 1))
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(append!
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mct-failures
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(str name " expected: " expected " got: " got))))))
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;; ---- gcd (equational guard, recursive) ----
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(define
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mct-gcd
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(mau/parse-module
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"fmod GCD is\n sorts Nat Bool .\n op 0 : -> Nat .\n op s_ : Nat -> Nat .\n op true : -> Bool .\n op false : -> Bool .\n op _>_ : Nat Nat -> Bool .\n op _-_ : Nat Nat -> Nat .\n op gcd : Nat Nat -> Nat .\n vars X Y : Nat .\n eq 0 > Y = false .\n eq s X > 0 = true .\n eq s X > s Y = X > Y .\n eq X - 0 = X .\n eq 0 - Y = 0 .\n eq s X - s Y = X - Y .\n eq gcd(X, 0) = X .\n eq gcd(0, Y) = Y .\n eq gcd(X, X) = X .\n ceq gcd(X, Y) = gcd(X - Y, Y) if X > Y = true .\n ceq gcd(X, Y) = gcd(Y, X) if Y > X = true .\nendfm"))
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(mct-check!
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"gcd-6-4"
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(mau/creduce->str mct-gcd "gcd(s s s s s s 0, s s s s 0)")
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"s_(s_(0))")
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(mct-check!
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"gcd-3-6"
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(mau/creduce->str mct-gcd "gcd(s s s 0, s s s s s s 0)")
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"s_(s_(s_(0)))")
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(mct-check!
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"gcd-base-zero"
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(mau/creduce->str mct-gcd "gcd(s s 0, 0)")
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"s_(s_(0))")
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(mct-check!
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"gcd-equal"
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(mau/creduce->str mct-gcd "gcd(s s 0, s s 0)")
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"s_(s_(0))")
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(mct-check!
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"gcd-coprime"
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(mau/creduce->str mct-gcd "gcd(s s s 0, s s 0)")
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"s_(0)")
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;; guard predicate reductions
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(mct-check! "gt-true" (mau/creduce->str mct-gcd "s s 0 > s 0") "true")
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(mct-check! "gt-false" (mau/creduce->str mct-gcd "s 0 > s s 0") "false")
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;; ---- insertion sort (true/false guards) ----
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(define
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mct-sort
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(mau/parse-module
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"fmod SORT is\n sorts Nat List Bool .\n op 0 : -> Nat .\n op s_ : Nat -> Nat .\n op true : -> Bool .\n op false : -> Bool .\n op _<=_ : Nat Nat -> Bool .\n op nil : -> List .\n op _:_ : Nat List -> List .\n op insert : Nat List -> List .\n op sort : List -> List .\n vars M N : Nat .\n var L : List .\n eq 0 <= N = true .\n eq s M <= 0 = false .\n eq s M <= s N = M <= N .\n eq insert(N, nil) = N : nil .\n ceq insert(N, M : L) = N : (M : L) if N <= M = true .\n ceq insert(N, M : L) = M : insert(N, L) if N <= M = false .\n eq sort(nil) = nil .\n eq sort(N : L) = insert(N, sort(L)) .\nendfm"))
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(mct-check!
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"sort-321"
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(mau/creduce->str mct-sort "sort(s s s 0 : (s 0 : (s s 0 : nil)))")
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"_:_(s_(0), _:_(s_(s_(0)), _:_(s_(s_(s_(0))), nil)))")
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(mct-check! "sort-empty" (mau/creduce->str mct-sort "sort(nil)") "nil")
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(mct-check!
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"sort-singleton"
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(mau/creduce->str mct-sort "sort(s s 0 : nil)")
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"_:_(s_(s_(0)), nil)")
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(mct-check!
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"insert-front"
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(mau/creduce->str mct-sort "insert(0, s 0 : (s s 0 : nil))")
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"_:_(0, _:_(s_(0), _:_(s_(s_(0)), nil)))")
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(mct-check!
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"insert-back"
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(mau/creduce->str mct-sort "insert(s s s 0, s 0 : (s s 0 : nil))")
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"_:_(s_(0), _:_(s_(s_(0)), _:_(s_(s_(s_(0))), nil)))")
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;; ---- max (conditional simplification, both branches) ----
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(define
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mct-max
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(mau/parse-module
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"fmod MAX is\n sorts Nat Bool .\n op 0 : -> Nat .\n op s_ : Nat -> Nat .\n op true : -> Bool .\n op false : -> Bool .\n op _<=_ : Nat Nat -> Bool .\n op max : Nat Nat -> Nat .\n vars M N : Nat .\n eq 0 <= N = true .\n eq s M <= 0 = false .\n eq s M <= s N = M <= N .\n ceq max(M, N) = M if N <= M = true .\n ceq max(M, N) = N if N <= M = false .\nendfm"))
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(mct-check!
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"max-left"
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(mau/creduce->str mct-max "max(s s s 0, s 0)")
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"s_(s_(s_(0)))")
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(mct-check!
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"max-right"
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(mau/creduce->str mct-max "max(s 0, s s 0)")
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"s_(s_(0))")
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(mct-check!
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"max-equal"
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(mau/creduce->str mct-max "max(s s 0, s s 0)")
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"s_(s_(0))")
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;; ---- boolean-kind condition (`if pred`) ----
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(define
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mct-even
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(mau/parse-module
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"fmod EVEN is\n sorts Nat Bool Tag .\n op 0 : -> Nat .\n op s_ : Nat -> Nat .\n op true : -> Bool .\n op false : -> Bool .\n op even : Nat -> Bool .\n op evn : -> Tag .\n op odd : -> Tag .\n op tag : Nat -> Tag .\n var N : Nat .\n eq even(0) = true .\n eq even(s 0) = false .\n eq even(s s N) = even(N) .\n ceq tag(N) = evn if even(N) .\n ceq tag(N) = odd if even(N) = false .\nendfm"))
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(mct-check! "even-4" (mau/creduce->str mct-even "even(s s s s 0)") "true")
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(mct-check! "even-3" (mau/creduce->str mct-even "even(s s s 0)") "false")
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(mct-check! "tag-even-bool" (mau/creduce->str mct-even "tag(s s 0)") "evn")
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(mct-check! "tag-odd" (mau/creduce->str mct-even "tag(s s s 0)") "odd")
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(define mau-conditional-tests-run! (fn () {:failures mct-failures :total (+ mct-pass mct-fail) :passed mct-pass :failed mct-fail}))
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