Removed tests from hybrid-core
Tests are now in cur-test, so removed from hybrid-core
This commit is contained in:
William J. Bowman
parent
23d0cf3e6f
commit
c99b44bc09
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@ -51,57 +51,6 @@
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(define U? (redex-match? ttL U))
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(define Δ? (redex-match? ttL Δ))
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(module+ test
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(define-term Type (Unv 0))
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(check-true (x? (term T)))
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(check-true (x? (term A)))
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(check-true (x? (term truth)))
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(check-true (x? (term zero)))
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(check-true (x? (term s)))
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(check-true (t? (term zero)))
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(check-true (t? (term s)))
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(check-true (x? (term nat)))
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(check-true (t? (term nat)))
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(check-true (t? (term A)))
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(check-true (t? (term S)))
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(check-true (U? (term (Unv 0))))
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(check-true (U? (term Type)))
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(check-true (e? (term (λ (x_0 : (Unv 0)) x_0))))
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(check-true (t? (term (λ (x_0 : (Unv 0)) x_0))))
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(check-true (t? (term (λ (x_0 : (Unv 0)) x_0))))
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;; TODO: Rename these signatures, and use them in all future tests.
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(define Δ (term ((∅ (nat : (Unv 0) ((zero : nat) (s : (Π (x : nat) nat)))))
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(bool : (Unv 0) ((true : bool) (false : bool))))))
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(define Δ0 (term ∅))
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(define Δ3 (term (∅ (and : (Π (A : (Unv 0)) (Π (B : (Unv 0)) (Unv 0))) ()))))
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(define Δ4 (term (∅ (and : (Π (A : (Unv 0)) (Π (B : (Unv 0)) (Unv 0)))
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((conj : (Π (A : (Unv 0)) (Π (B : (Unv 0)) (Π (a : A) (Π (b : B) ((and A) B)))))))))))
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(check-true (Δ? Δ0))
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(check-true (Δ? Δ))
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(check-true (Δ? Δ4))
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(check-true (Δ? Δ3))
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(check-true (Δ? Δ4))
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(define sigma (term ((((((∅ (true : (Unv 0) ((T : true))))
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(false : (Unv 0) ()))
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(equal : (Π (A : (Unv 0)) (Π (B : (Unv 0)) (Unv 0)))
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()))
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(nat : (Unv 0) ()))
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(heap : (Unv 0) ()))
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(pre : (Π (temp808 : heap) (Unv 0)) ()))))
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(check-true (Δ? (term (∅ (true : (Unv 0) ((T : true)))))))
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(check-true (Δ? (term (∅ (false : (Unv 0) ())))))
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(check-true (Δ? (term (∅ (equal : (Π (A : (Unv 0)) (Π (B : (Unv 0)) (Unv 0)))
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())))))
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(check-true (Δ? (term (∅ (nat : (Unv 0) ())))))
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(check-true (Δ? (term (∅ (pre : (Π (temp808 : heap) (Unv 0)) ())))))
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(check-true (Δ? (term ((∅ (true : (Unv 0) ((T : true)))) (false : (Unv 0) ())))))
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(check-true (Δ? (term (((∅ (true : (Unv 0) ((T : true)))) (false : (Unv 0) ()))
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(equal : (Π (A : (Unv 0)) (Π (B : (Unv 0)) (Unv 0)))
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())))))
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(check-true (Δ? sigma)))
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;;; ------------------------------------------------------------------------
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;;; Universe typing
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@ -130,23 +79,12 @@
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[(α-equivalent? t_0 t_1)
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,(alpha-equivalent? ttL (term t_0) (term t_1))])
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(module+ test
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(default-equiv (lambda (x y) (term (α-equivalent? ,x ,y)))))
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;; Replace x by t_1 in t_0
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(define-metafunction ttL
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subst : t x t -> t
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[(subst t_0 x t_1)
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(substitute t_0 x t_1)])
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(module+ test
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(check-true (t? (term (Π (a : A) (Π (b : B) ((and A) B))))))
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(check-true
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(term
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(α-equivalent?
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(Π (a : S) (Π (b : B) ((and S) B)))
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(subst (Π (a : A) (Π (b : B) ((and A) B))) A S)))))
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(define-metafunction ttL
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subst-all : t (x ...) (e ...) -> t
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[(subst-all t () ()) t]
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@ -186,14 +124,6 @@
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[(Δ-key-by-constructor (Δ (x_1 : t_1 any)) x)
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(Δ-key-by-constructor Δ x)])
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(module+ test
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(check-equal?
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(term (Δ-key-by-constructor ,Δ zero))
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(term nat))
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(check-equal?
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(term (Δ-key-by-constructor ,Δ s))
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(term nat)))
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;; Returns the constructor map for the inductively defined type x_D in the signature Δ
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(define-metafunction ttL
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Δ-ref-constructor-map : Δ x -> ((x : t) ...) or #f
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@ -204,14 +134,6 @@
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[(Δ-ref-constructor-map (Δ (x_1 : t_1 any)) x_D)
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(Δ-ref-constructor-map Δ x_D)])
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(module+ test
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(check-equal?
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(term (Δ-ref-constructor-map ,Δ nat))
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(term ((zero : nat) (s : (Π (x : nat) nat)))))
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(check-equal?
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(term (Δ-ref-constructor-map ,sigma false))
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(term ())))
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;; TODO: Should not use Δ-ref-type
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(define-metafunction ttL
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Δ-ref-constructor-type : Δ x x -> t
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@ -257,15 +179,6 @@
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(define Φ? (redex-match? tt-ctxtL Φ))
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(define Θ? (redex-match? tt-ctxtL Θ))
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(module+ test
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;; Are these telescopes the same when filled with alpha-equivalent, and equivalently renamed, termed
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(define (telescope-equiv x y)
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(alpha-equivalent? ttL (term (in-hole ,x (Unv 0))) (term (in-hole ,y (Unv 0)))))
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(define-syntax-rule (check-telescope-equiv? e1 e2)
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(check telescope-equiv e1 e2))
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(define-syntax-rule (check-telescope-not-equiv? e1 e2)
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(check (compose not telescope-equiv) e1 e2)))
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;; TODO: Might be worth it to actually maintain the above bijections, for performance reasons.
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;; Return the parameters of x_D as a telescope Ξ
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@ -277,14 +190,6 @@
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[(Δ-ref-parameter-Ξ (Δ (x_1 : t_1 any)) x_D)
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(Δ-ref-parameter-Ξ Δ x_D)])
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(module+ test
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(check-telescope-equiv?
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(term (Δ-ref-parameter-Ξ ,Δ nat))
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(term hole))
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(check-telescope-equiv?
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(term (Δ-ref-parameter-Ξ ,Δ4 and))
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(term (Π (A : Type) (Π (B : Type) hole)))))
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;; Applies the term t to the telescope Ξ.
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;; TODO: Test
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#| TODO:
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@ -304,13 +209,6 @@
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[(Ξ-compose Ξ_0 Ξ_1 Ξ_rest ...)
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(Ξ-compose (in-hole Ξ_0 Ξ_1) Ξ_rest ...)])
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(module+ test
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(check-telescope-equiv?
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(term (Ξ-compose
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(Π (x : t_0) (Π (y : t_1) hole))
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(Π (z : t_2) (Π (a : t_3) hole))))
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(term (Π (x : t_0) (Π (y : t_1) (Π (z : t_2) (Π (a : t_3) hole)))))))
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;; Compute the number of arguments in a Ξ
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(define-metafunction tt-ctxtL
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Ξ-length : Ξ -> natural
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@ -423,37 +321,6 @@
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[(Δ-methods-telescope Δ x_D t_P)
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(method-loop Δ x_D t_P (Δ-ref-constructors Δ x_D))])
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(module+ test
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(check-telescope-equiv?
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(term (Δ-methods-telescope ,Δ nat (λ (x : nat) nat)))
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(term (Π (m-zero : ((λ (x : nat) nat) zero))
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(Π (m-s : (Π (x : nat) (Π (x-ih : ((λ (x : nat) nat) x)) ((λ (x : nat) nat) (s x))))) hole))))
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(check-telescope-equiv?
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(term (Δ-methods-telescope ,Δ nat P))
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(term (Π (m-zero : (P zero))
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(Π (m-s : (Π (x : nat) (Π (ih-x : (P x)) (P (s x)))))
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hole))))
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(check-telescope-equiv?
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(term (Δ-methods-telescope ,Δ nat (λ (x : nat) nat)))
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(term (Π (m-zero : ((λ (x : nat) nat) zero))
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(Π (m-s : (Π (x : nat) (Π (ih-x : ((λ (x : nat) nat) x)) ((λ (x : nat) nat) (s x)))))
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hole))))
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(check-telescope-equiv?
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(term (Δ-methods-telescope ,Δ4 and (λ (A : Type) (λ (B : Type) (λ (x : ((and A) B)) true)))))
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(term (Π (m-conj : (Π (A : Type) (Π (B : Type) (Π (a : A) (Π (b : B)
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((((λ (A : Type) (λ (B : Type) (λ (x : ((and A) B)) true)))
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A)
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B)
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((((conj A) B) a) b)))))))
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hole)))
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(check-true (x? (term false)))
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(check-true (Ξ? (term hole)))
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(check-true (t? (term (λ (y : false) (Π (x : Type) x)))))
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(check-true (redex-match? ttL ((x : t) ...) (term ())))
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(check-telescope-equiv?
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(term (Δ-methods-telescope ,sigma false (λ (y : false) (Π (x : Type) x))))
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(term hole)))
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;; Computes the type of the eliminator for the inductively defined type x_D with a motive whose result
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;; is in universe U.
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;;
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@ -506,27 +373,6 @@
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(side-condition (memq (term x_ci) (term (Δ-ref-constructors Δ x_D))))]
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[(Δ-inductive-elim Δ x_D U t_P Θ_p Θ_m Θ_nr) hole])
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;; TODO: Insufficient tests, no tests of inductives with parameters, or complex induction.
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(module+ test
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(check-true
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(redex-match? tt-ctxtL (in-hole Θ_i (hole (in-hole Θ_r zero))) (term (hole zero))))
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(check-telescope-equiv?
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(term (Δ-inductive-elim ,Δ nat Type (λ (x : nat) nat) hole
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((hole (s zero)) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
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(hole zero)))
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(term (hole (((((elim nat Type) (λ (x : nat) nat))
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(s zero))
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(λ (x : nat) (λ (ih-x : nat) (s (s x)))))
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zero))))
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(check-telescope-equiv?
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(term (Δ-inductive-elim ,Δ nat Type (λ (x : nat) nat) hole
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((hole (s zero)) (λ (x : nat) (λ (ih-x : nat) (s (s x)))))
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(hole (s zero))))
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(term (hole (((((elim nat Type) (λ (x : nat) nat))
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(s zero))
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(λ (x : nat) (λ (ih-x : nat) (s (s x)))))
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(s zero))))))
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;;; ------------------------------------------------------------------------
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;;; Dynamic semantics
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;;; The majority of this section is dedicated to evaluation of (elim x U), the eliminator for the
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@ -544,11 +390,6 @@
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(define E? (redex-match? tt-redL E))
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(define v? (redex-match? tt-redL v))
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(module+ test
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(check-true (v? (term (λ (x_0 : (Unv 0)) x_0))))
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(check-true (v? (term (refl Nat))))
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(check-true (v? (term ((refl Nat) z)))))
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(define current-Δ (make-parameter (term ∅)))
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(define tt-->
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(reduction-relation tt-redL
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@ -614,70 +455,6 @@
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(dict-set! reduce-memoize (term e_r) x)
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x)))))])
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;; TODO: Move equivalence up here, and use in these tests.
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(module+ test
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(check-equiv? (term (reduce ∅ (Unv 0))) (term (Unv 0)))
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(check-equiv? (term (reduce ∅ ((λ (x : t) x) (Unv 0)))) (term (Unv 0)))
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(check-not-equiv? (term (reduce ∅ ((Π (x : t) x) (Unv 0)))) (term (Unv 0)))
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(check-not-equiv? (term (reduce ∅ (Π (x : t) ((Π (x_0 : t) x_0) (Unv 0)))))
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(term (Π (x : t) (Unv 0))))
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(check-not-equiv? (term (reduce ∅ (Π (x : t) ((Π (x_0 : t) (x_0 x)) x))))
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(term (Π (x : t) (x x))))
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(check-equiv? (term (reduce ,Δ (((((elim nat Type) (λ (x : nat) nat))
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(s zero))
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(λ (x : nat) (λ (ih-x : nat)
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(s (s x)))))
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zero)))
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(term (s zero)))
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(check-equiv? (term (reduce ,Δ (((((elim nat Type) (λ (x : nat) nat))
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(s zero))
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(λ (x : nat) (λ (ih-x : nat)
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(s (s x)))))
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(s zero))))
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(term (s (s zero))))
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(check-equiv? (term (reduce ,Δ (((((elim nat Type) (λ (x : nat) nat))
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(s zero))
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(λ (x : nat) (λ (ih-x : nat) (s (s x)))))
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(s (s (s zero))))))
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(term (s (s (s (s zero))))))
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(check-equiv?
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(term (reduce ,Δ
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(((((elim nat Type) (λ (x : nat) nat))
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(s (s zero)))
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(λ (x : nat) (λ (ih-x : nat) (s ih-x))))
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(s (s zero)))))
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(term (s (s (s (s zero))))))
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(check-equiv?
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(term (step ,Δ
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(((((elim nat Type) (λ (x : nat) nat))
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(s (s zero)))
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(λ (x : nat) (λ (ih-x : nat) (s ih-x))))
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(s (s zero)))))
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(term
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(((λ (x : nat) (λ (ih-x : nat) (s ih-x)))
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(s zero))
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(((((elim nat Type) (λ (x : nat) nat))
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(s (s zero)))
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(λ (x : nat) (λ (ih-x : nat) (s ih-x))))
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(s zero)))))
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(check-equiv?
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(term (step ,Δ (step ,Δ
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(((λ (x : nat) (λ (ih-x : nat) (s ih-x)))
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(s zero))
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(((((elim nat Type) (λ (x : nat) nat))
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(s (s zero)))
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(λ (x : nat) (λ (ih-x : nat) (s ih-x))))
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(s zero))))))
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(term
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((λ (ih-x1 : nat) (s ih-x1))
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(((λ (x : nat) (λ (ih-x : nat) (s ih-x)))
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zero)
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(((((elim nat Type) (λ (x : nat) nat))
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(s (s zero)))
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(λ (x : nat) (λ (ih-x : nat) (s ih-x))))
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zero))))))
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(define-judgment-form tt-redL
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#:mode (equivalent I I I)
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#:contract (equivalent Δ t t)
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@ -687,13 +464,6 @@
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(side-condition (α-equivalent? t_2 t_3))
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----------------- "≡-αβ"
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(equivalent Δ t_0 t_1)])
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(module+ test
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(define-syntax-rule (check-equivalent e1 e2)
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(check-holds (equivalent ∅ e1 e2)))
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(check-equivalent
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(λ (x : Type) x) (λ (y : Type) y))
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(check-equivalent
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(Π (x : Type) x) (Π (y : Type) y)))
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;;; ------------------------------------------------------------------------
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;;; Type checking and synthesis
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@ -757,22 +527,6 @@
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,(and (term (positive x_D (in-hole Ξ (Unv 0)))) (term (positive* x_D (t_rest ...))))
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(where (in-hole Ξ (in-hole Θ x_D)) t_c)])
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;; NB: These tests may or may not fail because positivity checking is not implemented.
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(module+ test
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(check-true (term (positive* nat (nat))))
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(check-true (term (positive* nat ((Π (x : (Unv 0)) (Π (y : (Unv 0)) nat))))))
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(check-true (term (positive* nat ((Π (x : nat) nat)))))
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;; (nat -> nat) -> nat
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;; Not sure if this is actually supposed to pass
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(check-false (term (positive* nat ((Π (x : (Π (y : nat) nat)) nat)))))
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;; ((Unv 0) -> nat) -> nat
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(check-true (term (positive* nat ((Π (x : (Π (y : (Unv 0)) nat)) nat)))))
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;; (((nat -> (Unv 0)) -> nat) -> nat)
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(check-true (term (positive* nat ((Π (x : (Π (y : (Π (x : nat) (Unv 0))) nat)) nat)))))
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;; Not sure if this is actually supposed to pass
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;; ((nat -> nat) -> nat) -> nat
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(check-false (term (positive* nat ((Π (x : (Π (y : (Π (x : nat) nat)) nat)) nat))))))
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;; Holds when the signature Δ and typing context Γ are well-formed.
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(define-judgment-form tt-typingL
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#:mode (wf I I)
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@ -798,63 +552,6 @@
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;; the constructor is well-formed.
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((x_c : (name t_c (in-hole Ξ (in-hole Θ x_D*)))) ...))) ∅)])
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(module+ test
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(check-true (judgment-holds (wf ,Δ0 ∅)))
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(check-true (redex-match? tt-redL (in-hole Ξ (Unv 0)) (term (Unv 0))))
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(check-true (redex-match? tt-redL (in-hole Ξ (in-hole Φ (in-hole Θ nat)))
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(term (Π (x : nat) nat))))
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(define (bindings-equal? l1 l2)
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(map set=? l1 l2))
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(check-pred
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(curry bindings-equal?
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(list (list
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(make-bind 'Ξ (term (Π (x : nat) hole)))
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(make-bind 'Φ (term hole))
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(make-bind 'Θ (term hole)))
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(list
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(make-bind 'Ξ (term hole))
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(make-bind 'Φ (term (Π (x : nat) hole)))
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(make-bind 'Θ (term hole)))))
|
||||
(map match-bindings (redex-match tt-redL (in-hole Ξ (in-hole Φ (in-hole Θ nat)))
|
||||
(term (Π (x : nat) nat)))))
|
||||
(check-pred
|
||||
(curry bindings-equal?
|
||||
(list
|
||||
(list
|
||||
(make-bind 'Φ (term (Π (x : nat) hole)))
|
||||
(make-bind 'Θ (term hole)))))
|
||||
(map match-bindings (redex-match tt-redL (in-hole hole (in-hole Φ (in-hole Θ nat)))
|
||||
(term (Π (x : nat) nat)))))
|
||||
|
||||
(check-true
|
||||
(redex-match? tt-redL
|
||||
(in-hole hole (in-hole hole (in-hole hole nat)))
|
||||
(term nat)))
|
||||
(check-true
|
||||
(redex-match? tt-redL
|
||||
(in-hole hole (in-hole (Π (x : nat) hole) (in-hole hole nat)))
|
||||
(term (Π (x : nat) nat))))
|
||||
(check-holds (wf (∅ (nat : (Unv 0) ())) ∅))
|
||||
|
||||
(check-holds (wf ,Δ0 ∅))
|
||||
(check-holds (type-infer ∅ ∅ (Unv 0) U))
|
||||
(check-holds (type-infer ∅ (∅ nat : (Unv 0)) nat U))
|
||||
(check-holds (type-infer ∅ (∅ nat : (Unv 0)) (Π (x : nat) nat) U))
|
||||
(check-true (term (positive* nat (nat (Π (x : nat) nat)))))
|
||||
(check-holds
|
||||
(wf (∅ (nat : (Unv 0) ((zero : nat)))) ∅))
|
||||
(check-holds
|
||||
(wf (∅ (nat : (Unv 0) ((s : (Π (x : nat) nat))))) ∅))
|
||||
(check-holds (wf ,Δ ∅))
|
||||
|
||||
(check-holds (wf ,Δ3 ∅))
|
||||
(check-holds (wf ,Δ4 ∅))
|
||||
(check-holds (wf (∅ (truth : (Unv 0) ())) ∅))
|
||||
(check-holds (wf ∅ (∅ x : (Unv 0))))
|
||||
(check-holds (wf (∅ (nat : (Unv 0) ())) (∅ x : nat)))
|
||||
(check-holds (wf (∅ (nat : (Unv 0) ())) (∅ x : (Π (x : nat) nat)))))
|
||||
|
||||
|
||||
;; TODO: Bi-directional and inference?
|
||||
;; TODO: http://www.cs.ox.ac.uk/ralf.hinze/WG2.8/31/slides/stephanie.pdf
|
||||
|
||||
|
|
@ -908,339 +605,3 @@
|
|||
(equivalent Δ t t_0)
|
||||
----------------- "DTR-Check"
|
||||
(type-check Δ Γ e t)])
|
||||
|
||||
(module+ test
|
||||
(check-holds (type-infer ∅ ∅ (Unv 0) (Unv 1)))
|
||||
(check-holds (type-infer ∅ (∅ x : (Unv 0)) (Unv 0) (Unv 1)))
|
||||
(check-holds (type-infer ∅ (∅ x : (Unv 0)) x (Unv 0)))
|
||||
(check-holds (type-infer ∅ ((∅ x_0 : (Unv 0)) x_1 : (Unv 0))
|
||||
(Π (x_3 : x_0) x_1) (Unv 0)))
|
||||
(check-holds (type-infer ∅ (∅ x_0 : (Unv 0)) x_0 U_1))
|
||||
(check-holds (type-infer ∅ ((∅ x_0 : (Unv 0)) x_2 : x_0) (Unv 0) U_2))
|
||||
(check-holds (unv-pred (Unv 0) (Unv 0) (Unv 0)))
|
||||
(check-holds (type-infer ∅ (∅ x_0 : (Unv 0)) (Π (x_2 : x_0) (Unv 0)) t))
|
||||
|
||||
(check-holds (type-check ∅ ∅ (λ (x : (Unv 0)) x) (Π (x : (Unv 0)) (Unv 0))))
|
||||
(check-holds (type-check ∅ ∅ (λ (y : (Unv 0)) (λ (x : y) x))
|
||||
(Π (y : (Unv 0)) (Π (x : y) y))))
|
||||
|
||||
(check-equal? (list (term (Unv 1)))
|
||||
(judgment-holds
|
||||
(type-infer ∅ ((∅ x1 : (Unv 0)) x2 : (Unv 0)) (Π (t6 : x1) (Π (t2 : x2) (Unv 0)))
|
||||
U)
|
||||
U))
|
||||
;; ---- Elim
|
||||
;; TODO: Clean up/Reorganize these tests
|
||||
(check-true
|
||||
(redex-match? tt-typingL
|
||||
(in-hole Θ_m (((elim x_D U) e_D) e_P))
|
||||
(term ((((elim truth Type) T) (Π (x : truth) (Unv 1))) (Unv 0)))))
|
||||
(define Δtruth (term (∅ (truth : (Unv 0) ((T : truth))))))
|
||||
(check-holds (type-infer ,Δtruth ∅ truth (in-hole Ξ U)))
|
||||
(check-holds (type-infer ,Δtruth ∅ T (in-hole Θ_ai truth)))
|
||||
(check-holds (type-infer ,Δtruth ∅ (λ (x : truth) (Unv 1))
|
||||
(in-hole Ξ (Π (x : (in-hole Θ truth)) U))))
|
||||
|
||||
(check-telescope-equiv?
|
||||
(term (Δ-methods-telescope ,Δtruth truth (λ (x : truth) (Unv 1))))
|
||||
(term (Π (m-T : ((λ (x : truth) (Unv 1)) T)) hole)))
|
||||
(check-holds (type-infer ,Δtruth ∅ (elim truth Type) t))
|
||||
(check-holds (type-check (∅ (truth : (Unv 0) ((T : truth))))
|
||||
∅
|
||||
((((elim truth (Unv 2)) (λ (x : truth) (Unv 1))) (Unv 0))
|
||||
T)
|
||||
(Unv 1)))
|
||||
(check-not-holds (type-check (∅ (truth : (Unv 0) ((T : truth))))
|
||||
∅
|
||||
((((elim truth (Unv 1)) Type) Type) T)
|
||||
(Unv 1)))
|
||||
(check-holds
|
||||
(type-infer ∅ ∅ (Π (x2 : (Unv 0)) (Unv 0)) U))
|
||||
(check-holds
|
||||
(type-infer ∅ (∅ x1 : (Unv 0)) (λ (x2 : (Unv 0)) (Π (t6 : x1) (Π (t2 : x2) (Unv 0))))
|
||||
t))
|
||||
(check-holds
|
||||
(type-infer ,Δ ∅ nat (in-hole Ξ U)))
|
||||
(check-holds
|
||||
(type-infer ,Δ ∅ zero (in-hole Θ_ai nat)))
|
||||
(check-holds
|
||||
(type-infer ,Δ ∅ (λ (x : nat) nat)
|
||||
(in-hole Ξ (Π (x : (in-hole Θ nat)) U))))
|
||||
(define-syntax-rule (nat-test syn ...)
|
||||
(check-holds (type-check ,Δ syn ...)))
|
||||
(nat-test ∅ (Π (x : nat) nat) (Unv 0))
|
||||
(nat-test ∅ (λ (x : nat) x) (Π (x : nat) nat))
|
||||
(nat-test ∅ (((((elim nat Type) (λ (x : nat) nat)) zero)
|
||||
(λ (x : nat) (λ (ih-x : nat) x))) zero)
|
||||
nat)
|
||||
(nat-test ∅ nat (Unv 0))
|
||||
(nat-test ∅ zero nat)
|
||||
(nat-test ∅ s (Π (x : nat) nat))
|
||||
(nat-test ∅ (s zero) nat)
|
||||
;; TODO: Meta-function auto-currying and such
|
||||
(check-holds
|
||||
(type-infer ,Δ ∅ ((((elim nat (Unv 0)) (λ (x : nat) nat))
|
||||
zero)
|
||||
(λ (x : nat) (λ (ih-x : nat) x)))
|
||||
t))
|
||||
(nat-test ∅ (((((elim nat (Unv 0)) (λ (x : nat) nat))
|
||||
zero)
|
||||
(λ (x : nat) (λ (ih-x : nat) x)))
|
||||
zero)
|
||||
nat)
|
||||
(nat-test ∅ (((((elim nat (Unv 0)) (λ (x : nat) nat))
|
||||
(s zero))
|
||||
(λ (x : nat) (λ (ih-x : nat) (s (s x)))))
|
||||
zero)
|
||||
nat)
|
||||
(nat-test ∅ (((((elim nat Type) (λ (x : nat) nat))
|
||||
(s zero))
|
||||
(λ (x : nat) (λ (ih-x : nat) (s (s x))))) zero)
|
||||
nat)
|
||||
(nat-test (∅ n : nat)
|
||||
(((((elim nat (Unv 0)) (λ (x : nat) nat)) zero) (λ (x : nat) (λ (ih-x : nat) x))) n)
|
||||
nat)
|
||||
(check-holds
|
||||
(type-check (,Δ (bool : (Unv 0) ((btrue : bool) (bfalse : bool))))
|
||||
(∅ n2 : nat)
|
||||
(((((elim nat (Unv 0)) (λ (x : nat) bool))
|
||||
btrue)
|
||||
(λ (x : nat) (λ (ih-x : bool) bfalse)))
|
||||
n2)
|
||||
bool))
|
||||
(check-not-holds
|
||||
(type-check ,Δ ∅
|
||||
((((elim nat (Unv 0)) nat) (s zero)) zero)
|
||||
nat))
|
||||
(define lam (term (λ (nat : (Unv 0)) nat)))
|
||||
(check-equivalent
|
||||
(Π (nat : (Unv 0)) (Unv 0))
|
||||
,(car (judgment-holds (type-infer ,Δ0 ∅ ,lam t) t)))
|
||||
(check-equivalent
|
||||
(Π (nat : (Unv 0)) (Unv 0))
|
||||
,(car (judgment-holds (type-infer ,Δ ∅ ,lam t) t)))
|
||||
(check-equivalent
|
||||
(Π (x : (Π (y : (Unv 0)) y)) nat)
|
||||
,(car (judgment-holds (type-infer (∅ (nat : (Unv 0) ())) ∅ (λ (x : (Π (y : (Unv 0)) y)) (x nat))
|
||||
t) t)))
|
||||
(check-equivalent
|
||||
(Π (y : (Unv 0)) (Unv 0))
|
||||
,(car (judgment-holds (type-infer (∅ (nat : (Unv 0) ())) ∅ (λ (y : (Unv 0)) y) t) t)))
|
||||
(check-equivalent
|
||||
(Unv 0)
|
||||
,(car (judgment-holds (type-infer (∅ (nat : (Unv 0) ())) ∅
|
||||
((λ (x : (Π (y : (Unv 0)) (Unv 0))) (x nat))
|
||||
(λ (y : (Unv 0)) y))
|
||||
t) t)))
|
||||
(check-equal?
|
||||
(list (term (Unv 0)) (term (Unv 1)))
|
||||
(judgment-holds
|
||||
(type-infer ,Δ4 ∅ (Π (S : (Unv 0)) (Π (B : (Unv 0)) (Π (a : S) (Π (b : B) ((and S) B)))))
|
||||
U) U))
|
||||
(check-holds
|
||||
(type-check ,Δ4 (∅ S : (Unv 0)) conj (Π (A : (Unv 0)) (Π (B : (Unv 0)) (Π (a : A) (Π (b : B) ((and A) B)))))))
|
||||
(check-holds
|
||||
(type-check ,Δ4 (∅ S : (Unv 0))
|
||||
conj (Π (P : (Unv 0)) (Π (Q : (Unv 0)) (Π (x : P) (Π (y : Q) ((and P) Q)))))))
|
||||
(check-holds
|
||||
(type-check ,Δ4 (∅ S : (Unv 0)) S (Unv 0)))
|
||||
(check-holds
|
||||
(type-check ,Δ4 (∅ S : (Unv 0)) (conj S)
|
||||
(Π (B : (Unv 0)) (Π (a : S) (Π (b : B) ((and S) B))))))
|
||||
(check-holds
|
||||
(type-check ,Δ4 (∅ S : (Unv 0)) (conj S)
|
||||
(Π (B : (Unv 0)) (Π (a : S) (Π (b : B) ((and S) B))))))
|
||||
(check-holds
|
||||
(type-check ,Δ4 ∅ (λ (S : (Unv 0)) (conj S))
|
||||
(Π (S : (Unv 0)) (Π (B : (Unv 0)) (Π (a : S) (Π (b : B) ((and S) B)))))))
|
||||
(check-holds
|
||||
(type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
|
||||
((((conj true) true) tt) tt)
|
||||
((and true) true)))
|
||||
(check-holds
|
||||
(type-infer ,Δ4 ∅ and (in-hole Ξ U_D)))
|
||||
(check-holds
|
||||
(type-infer (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
|
||||
((((conj true) true) tt) tt)
|
||||
(in-hole Θ and)))
|
||||
(check-holds
|
||||
(type-infer (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
|
||||
(λ (A : Type) (λ (B : Type) (λ (x : ((and A) B)) true)))
|
||||
(in-hole Ξ (Π (x : (in-hole Θ_Ξ and)) U_P))))
|
||||
(check-holds
|
||||
(type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
|
||||
((((((elim and (Unv 0))
|
||||
(λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
|
||||
true))))
|
||||
(λ (A : (Unv 0))
|
||||
(λ (B : (Unv 0))
|
||||
(λ (a : A)
|
||||
(λ (b : B) tt)))))
|
||||
true) true)
|
||||
((((conj true) true) tt) tt))
|
||||
true))
|
||||
(check-true (Γ? (term (((∅ P : (Unv 0)) Q : (Unv 0)) ab : ((and P) Q)))))
|
||||
(check-holds
|
||||
(type-infer ,Δ4 ∅ and (in-hole Ξ U)))
|
||||
(check-holds
|
||||
(type-infer ,Δ4 (((∅ P : Type) Q : Type) ab : ((and P) Q))
|
||||
ab (in-hole Θ and)))
|
||||
(check-true
|
||||
(redex-match? tt-redL
|
||||
(in-hole Ξ (Π (x : (in-hole Θ and)) U))
|
||||
(term (Π (A : (Unv 0)) (Π (B : (Unv 0)) (Π (x : ((and A) B)) (Unv 0)))))))
|
||||
(check-holds
|
||||
(type-infer ,Δ4 (((∅ P : Type) Q : Type) ab : ((and P) Q))
|
||||
(λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
|
||||
((and B) A))))
|
||||
(in-hole Ξ (Π (x : (in-hole Θ and)) U))))
|
||||
(check-holds
|
||||
(equivalent ,Δ4
|
||||
(Π (A : (Unv 0)) (Π (B : (Unv 0)) (Π (x : ((and A) B)) (Unv 0))))
|
||||
(Π (P : (Unv 0)) (Π (Q : (Unv 0)) (Π (x : ((and P) Q)) (Unv 0))))))
|
||||
(check-holds
|
||||
(type-infer ,Δ4 ∅
|
||||
(λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
|
||||
((and B) A))))
|
||||
(in-hole Ξ (Π (x : (in-hole Θ_Ξ and)) U_P))))
|
||||
(check-holds
|
||||
(type-check ,Δ4
|
||||
(((∅ P : (Unv 0)) Q : (Unv 0)) ab : ((and P) Q))
|
||||
((((((elim and (Unv 0))
|
||||
(λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
|
||||
((and B) A)))))
|
||||
(λ (A : (Unv 0))
|
||||
(λ (B : (Unv 0))
|
||||
(λ (a : A)
|
||||
(λ (b : B) ((((conj B) A) b) a))))))
|
||||
P) Q) ab)
|
||||
((and Q) P)))
|
||||
(check-holds
|
||||
(type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
|
||||
(λ (A : Type) (λ (B : Type) (λ (x : ((and A) B)) ((and B) A))))
|
||||
(Π (A : (Unv 0)) (Π (B : (Unv 0)) (Π (x : ((and A) B)) (Unv 0))))))
|
||||
(check-holds
|
||||
(type-infer (,Δ4 (true : (Unv 0) ((tt : true))))
|
||||
((∅ A : Type) B : Type)
|
||||
(conj B)
|
||||
t))
|
||||
(check-holds
|
||||
(type-check (,Δ4 (true : (Unv 0) ((tt : true)))) ∅
|
||||
((((((elim and (Unv 0))
|
||||
(λ (A : Type) (λ (B : Type) (λ (x : ((and A) B))
|
||||
((and B) A)))))
|
||||
(λ (A : (Unv 0))
|
||||
(λ (B : (Unv 0))
|
||||
(λ (a : A)
|
||||
(λ (b : B) ((((conj B) A) b) a))))))
|
||||
true) true)
|
||||
((((conj true) true) tt) tt))
|
||||
((and true) true)))
|
||||
(define gamma (term (∅ temp863 : pre)))
|
||||
(check-holds (wf ,sigma ∅))
|
||||
(check-holds (wf ,sigma ,gamma))
|
||||
(check-holds
|
||||
(type-infer ,sigma ,gamma (Unv 0) t))
|
||||
(check-holds
|
||||
(type-infer ,sigma ,gamma pre t))
|
||||
(check-holds
|
||||
(type-check ,sigma (,gamma tmp863 : pre) (Unv 0) (Unv 1)))
|
||||
(check-holds
|
||||
(type-infer ,sigma ,gamma pre t))
|
||||
(check-holds
|
||||
(type-check ,sigma (,gamma tmp863 : pre) (Unv 0) (Unv 1)))
|
||||
(check-holds
|
||||
(type-infer ,sigma (,gamma x : false) false (in-hole Ξ U_D)))
|
||||
(check-holds
|
||||
(type-infer ,sigma (,gamma x : false) x (in-hole Θ false)))
|
||||
(check-holds
|
||||
(type-infer ,sigma (,gamma x : false) (λ (y : false) (Π (x : Type) x))
|
||||
(in-hole Ξ (Π (x : (in-hole Θ false)) U))))
|
||||
(check-true
|
||||
(redex-match? tt-typingL
|
||||
((in-hole Θ_m ((elim x_D U) e_P)) e_D)
|
||||
(term (((elim false (Unv 1)) (λ (y : false) (Π (x : Type) x)))
|
||||
x))))
|
||||
(check-holds
|
||||
(type-check ,sigma (,gamma x : false)
|
||||
(((elim false (Unv 0)) (λ (y : false) (Π (x : Type) x))) x)
|
||||
(Π (x : (Unv 0)) x)))
|
||||
|
||||
;; nat-equal? tests
|
||||
(define zero?
|
||||
(term ((((elim nat Type) (λ (x : nat) bool))
|
||||
true)
|
||||
(λ (x : nat) (λ (x_ih : bool) false)))))
|
||||
(check-holds
|
||||
(type-check ,Δ ∅ ,zero? (Π (x : nat) bool)))
|
||||
(check-equal?
|
||||
(term (reduce ,Δ (,zero? zero)))
|
||||
(term true))
|
||||
(check-equal?
|
||||
(term (reduce ,Δ (,zero? (s zero))))
|
||||
(term false))
|
||||
(define ih-equal?
|
||||
(term ((((elim nat Type) (λ (x : nat) bool))
|
||||
false)
|
||||
(λ (x : nat) (λ (y : bool) (x_ih x))))))
|
||||
(check-holds
|
||||
(type-check ,Δ (∅ x_ih : (Π (x : nat) bool))
|
||||
,ih-equal?
|
||||
(Π (x : nat) bool)))
|
||||
(check-holds
|
||||
(type-infer ,Δ ∅ nat (Unv 0)))
|
||||
(check-holds
|
||||
(type-infer ,Δ ∅ bool (Unv 0)))
|
||||
(check-holds
|
||||
(type-infer ,Δ ∅ (λ (x : nat) (Π (x : nat) bool)) (Π (x : nat) (Unv 0))))
|
||||
(define nat-equal?
|
||||
(term ((((elim nat Type) (λ (x : nat) (Π (x : nat) bool)))
|
||||
,zero?)
|
||||
(λ (x : nat) (λ (x_ih : (Π (x : nat) bool))
|
||||
,ih-equal?)))))
|
||||
(check-holds
|
||||
(type-check ,Δ (∅ nat-equal? : (Π (x-D«4158» : nat) ((λ (x«4159» : nat) (Π (x«4160» : nat) bool)) x-D«4158»)))
|
||||
((nat-equal? zero) zero)
|
||||
bool))
|
||||
(check-holds
|
||||
(type-check ,Δ ∅
|
||||
,nat-equal?
|
||||
(Π (x : nat) (Π (y : nat) bool))))
|
||||
(check-equal?
|
||||
(term (reduce ,Δ ((,nat-equal? zero) (s zero))))
|
||||
(term false))
|
||||
(check-equal?
|
||||
(term (reduce ,Δ ((,nat-equal? (s zero)) zero)))
|
||||
(term false))
|
||||
|
||||
;; == tests
|
||||
(define Δ= (term (,Δ (== : (Π (A : (Unv 0)) (Π (a : A) (Π (b : A) (Unv 0))))
|
||||
((refl : (Π (A : (Unv 0)) (Π (a : A) (((== A) a) a)))))))))
|
||||
(check-true (Δ? Δ=))
|
||||
|
||||
(define refl-elim
|
||||
(term (((((((elim == (Unv 0)) (λ (A1 : (Unv 0)) (λ (x1 : A1) (λ (y1 : A1) (λ (p2 : (((==
|
||||
A1)
|
||||
x1)
|
||||
y1))
|
||||
nat)))))
|
||||
(λ (A1 : (Unv 0)) (λ (x1 : A1) zero))) bool) true) true) ((refl bool) true))))
|
||||
(check-holds
|
||||
(type-check ,Δ= ∅ ,refl-elim nat))
|
||||
(check-true
|
||||
(redex-match?
|
||||
tt-redL
|
||||
(Δ (in-hole E (in-hole Θ ((elim x_D U) e_P))))
|
||||
(term (,Δ= ,refl-elim))))
|
||||
(check-true
|
||||
(redex-match?
|
||||
tt-redL
|
||||
(in-hole (Θ_p (in-hole Θ_i x_ci)) Θ_m)
|
||||
(term (((((hole
|
||||
(λ (A1 : (Unv 0)) (λ (x1 : A1) zero))) bool) true) true) ((refl bool) true)))))
|
||||
(check-telescope-equiv?
|
||||
(term (Δ-ref-parameter-Ξ ,Δ= ==))
|
||||
(term (Π (A : Type) (Π (a : A) (Π (b : A) hole)))))
|
||||
(check-equal?
|
||||
(term (reduce ,Δ= ,refl-elim))
|
||||
(term zero)))
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user