diff options
Diffstat (limited to 'test-suite/success')
| -rw-r--r-- | test-suite/success/abstract_chain.v | 43 | ||||
| -rw-r--r-- | test-suite/success/change_pattern.v | 34 | ||||
| -rw-r--r-- | test-suite/success/decl_mode.v | 182 | ||||
| -rw-r--r-- | test-suite/success/decl_mode2.v | 249 | ||||
| -rw-r--r-- | test-suite/success/old_typeclass.v | 13 | ||||
| -rw-r--r-- | test-suite/success/rewrite_evar.v | 8 |
6 files changed, 98 insertions, 431 deletions
diff --git a/test-suite/success/abstract_chain.v b/test-suite/success/abstract_chain.v new file mode 100644 index 000000000..0ff61e87f --- /dev/null +++ b/test-suite/success/abstract_chain.v @@ -0,0 +1,43 @@ +Lemma foo1 : nat -> True. +Proof. +intros _. +assert (H : True -> True). +{ abstract (exact (fun x => x)) using bar. } +assert (H' : True). +{ abstract (exact (bar I)) using qux. } +exact H'. +Qed. + +Lemma foo2 : True. +Proof. +assert (H : True -> True). +{ abstract (exact (fun x => x)) using bar. } +assert (H' : True). +{ abstract (exact (bar I)) using qux. } +assert (H'' : True). +{ abstract (exact (bar qux)) using quz. } +exact H''. +Qed. + +Set Universe Polymorphism. + +Lemma foo3 : nat -> True. +Proof. +intros _. +assert (H : True -> True). +{ abstract (exact (fun x => x)) using bar. } +assert (H' : True). +{ abstract (exact (bar I)) using qux. } +exact H'. +Qed. + +Lemma foo4 : True. +Proof. +assert (H : True -> True). +{ abstract (exact (fun x => x)) using bar. } +assert (H' : True). +{ abstract (exact (bar I)) using qux. } +assert (H'' : True). +{ abstract (exact (bar qux)) using quz. } +exact H''. +Qed. diff --git a/test-suite/success/change_pattern.v b/test-suite/success/change_pattern.v new file mode 100644 index 000000000..874abf49f --- /dev/null +++ b/test-suite/success/change_pattern.v @@ -0,0 +1,34 @@ +Set Implicit Arguments. +Unset Strict Implicit. + +Axiom vector : Type -> nat -> Type. + +Record KleeneStore i j a := kleeneStore + { dim : nat + ; peek : vector j dim -> a + ; pos : vector i dim + }. + +Definition KSmap i j a b (f : a -> b) (s : KleeneStore i j a) : KleeneStore i j b := + kleeneStore (fun v => f (peek v)) (pos s). + +Record KleeneCoalg (i o : Type -> Type) := kleeneCoalg + { coalg :> forall a b, (o a) -> KleeneStore (i a) (i b) (o b) }. + +Axiom free_b_dim : forall i o (k : KleeneCoalg i o) a b b' (x : o a), dim (coalg k b x) = dim (coalg k b' x). +Axiom t : Type -> Type. +Axiom traverse : KleeneCoalg (fun x => x) t. + +Definition size a (x:t a) : nat := dim (traverse a a x). + +Lemma iso1_iso2_2 a (y : {x : t unit & vector a (size x)}) : False. +Proof. +destruct y. +pose (X := KSmap (traverse a unit) (traverse unit a x)). +set (e :=(eq_sym (free_b_dim traverse (a:=unit) a unit x))). +clearbody e. +(** The pattern generated by change must have holes where there were implicit + arguments in the original user-provided term. This particular example fails + if this is not the case because the inferred argument does not coincide with + the one in the considered term. *) +progress (change (dim (traverse unit a x)) with (dim X) in e). diff --git a/test-suite/success/decl_mode.v b/test-suite/success/decl_mode.v deleted file mode 100644 index e569bcb49..000000000 --- a/test-suite/success/decl_mode.v +++ /dev/null @@ -1,182 +0,0 @@ -(* \sqrt 2 is irrationnal, (c) 2006 Pierre Corbineau *) - -Set Firstorder Depth 1. -Require Import ArithRing Wf_nat Peano_dec Div2 Even Lt. - -Lemma double_div2: forall n, div2 (double n) = n. -proof. - assume n:nat. - per induction on n. - suppose it is 0. - suffices (0=0) to show thesis. - thus thesis. - suppose it is (S m) and Hrec:thesis for m. - have (div2 (double (S m))= div2 (S (S (double m)))). - ~= (S (div2 (double m))). - thus ~= (S m) by Hrec. - end induction. -end proof. -Show Script. -Qed. - -Lemma double_inv : forall n m, double n = double m -> n = m . -proof. - let n, m be such that H:(double n = double m). -have (n = div2 (double n)) by double_div2,H. - ~= (div2 (double m)) by H. - thus ~= m by double_div2. -end proof. -Qed. - -Lemma double_mult_l : forall n m, (double (n * m)=n * double m). -proof. - assume n:nat and m:nat. - have (double (n * m) = n*m + n * m). - ~= (n * (m+m)) by * using ring. - thus ~= (n * double m). -end proof. -Qed. - -Lemma double_mult_r : forall n m, (double (n * m)=double n * m). -proof. - assume n:nat and m:nat. - have (double (n * m) = n*m + n * m). - ~= ((n + n) * m) by * using ring. - thus ~= (double n * m). -end proof. -Qed. - -Lemma even_is_even_times_even: forall n, even (n*n) -> even n. -proof. - let n be such that H:(even (n*n)). - per cases of (even n \/ odd n) by even_or_odd. - suppose (odd n). - hence thesis by H,even_mult_inv_r. - end cases. -end proof. -Qed. - -Lemma main_thm_aux: forall n,even n -> -double (double (div2 n *div2 n))=n*n. -proof. - given n such that H:(even n). - *** have (double (double (div2 n * div2 n)) - = double (div2 n) * double (div2 n)) - by double_mult_l,double_mult_r. - thus ~= (n*n) by H,even_double. -end proof. -Qed. - -Require Import Omega. - -Lemma even_double_n: (forall m, even (double m)). -proof. - assume m:nat. - per induction on m. - suppose it is 0. - thus thesis. - suppose it is (S mm) and thesis for mm. - then H:(even (S (S (mm+mm)))). - have (S (S (mm + mm)) = S mm + S mm) using omega. - hence (even (S mm +S mm)) by H. - end induction. -end proof. -Qed. - -Theorem main_theorem: forall n p, n*n=double (p*p) -> p=0. -proof. - assume n0:nat. - define P n as (forall p, n*n=double (p*p) -> p=0). - claim rec_step: (forall n, (forall m,m<n-> P m) -> P n). - let n be such that H:(forall m : nat, m < n -> P m) and p:nat . - per cases of ({n=0}+{n<>0}) by eq_nat_dec. - suppose H1:(n=0). - per cases on p. - suppose it is (S p'). - assume (n * n = double (S p' * S p')). - =~ 0 by H1,mult_n_O. - ~= (S ( p' + p' * S p' + S p'* S p')) - by plus_n_Sm. - hence thesis . - suppose it is 0. - thus thesis. - end cases. - suppose H1:(n<>0). - assume H0:(n*n=double (p*p)). - have (even (double (p*p))) by even_double_n . - then (even (n*n)) by H0. - then H2:(even n) by even_is_even_times_even. - then (double (double (div2 n *div2 n))=n*n) - by main_thm_aux. - ~= (double (p*p)) by H0. - then H':(double (div2 n *div2 n)= p*p) by double_inv. - have (even (double (div2 n *div2 n))) by even_double_n. - then (even (p*p)) by even_double_n,H'. - then H3:(even p) by even_is_even_times_even. - have (double(double (div2 n * div2 n)) = n*n) - by H2,main_thm_aux. - ~= (double (p*p)) by H0. - ~= (double(double (double (div2 p * div2 p)))) - by H3,main_thm_aux. - then H'':(div2 n * div2 n = double (div2 p * div2 p)) - by double_inv. - then (div2 n < n) by lt_div2,neq_O_lt,H1. - then H4:(div2 p=0) by (H (div2 n)),H''. - then (double (div2 p) = double 0). - =~ p by even_double,H3. - thus ~= 0. - end cases. - end claim. - hence thesis by (lt_wf_ind n0 P). -end proof. -Qed. - -Require Import Reals Field. -(*Coercion INR: nat >->R. -Coercion IZR: Z >->R.*) - -Open Scope R_scope. - -Lemma square_abs_square: - forall p,(INR (Z.abs_nat p) * INR (Z.abs_nat p)) = (IZR p * IZR p). -proof. - assume p:Z. - per cases on p. - suppose it is (0%Z). - thus thesis. - suppose it is (Zpos z). - thus thesis. - suppose it is (Zneg z). - have ((INR (Z.abs_nat (Zneg z)) * INR (Z.abs_nat (Zneg z))) = - (IZR (Zpos z) * IZR (Zpos z))). - ~= ((- IZR (Zpos z)) * (- IZR (Zpos z))). - thus ~= (IZR (Zneg z) * IZR (Zneg z)). - end cases. -end proof. -Admitted. - -Definition irrational (x:R):Prop := - forall (p:Z) (q:nat),q<>0%nat -> x<> (IZR p/INR q). - -Theorem irrationnal_sqrt_2: irrational (sqrt (INR 2%nat)). -proof. - let p:Z,q:nat be such that H:(q<>0%nat) - and H0:(sqrt (INR 2%nat)=(IZR p/INR q)). - have H_in_R:(INR q<>0:>R) by H. - have triv:((IZR p/INR q* INR q) =IZR p :>R) by * using field. - have sqrt2:((sqrt (INR 2%nat) * sqrt (INR 2%nat))= INR 2%nat:>R) by sqrt_def. - have (INR (Z.abs_nat p * Z.abs_nat p) - = (INR (Z.abs_nat p) * INR (Z.abs_nat p))) - by mult_INR. - ~= (IZR p* IZR p) by square_abs_square. - ~= ((IZR p/INR q*INR q)*(IZR p/INR q*INR q)) by triv. (* we have to factor because field is too weak *) - ~= ((IZR p/INR q)*(IZR p/INR q)*(INR q*INR q)) using ring. - ~= (sqrt (INR 2%nat) * sqrt (INR 2%nat)*(INR q*INR q)) by H0. - ~= (INR (2%nat * (q*q))) by sqrt2,mult_INR. - then (Z.abs_nat p * Z.abs_nat p = 2* (q * q))%nat. - ~= ((q*q)+(q*q))%nat. - ~= (Div2.double (q*q)). - then (q=0%nat) by main_theorem. - hence thesis by H. -end proof. -Qed. diff --git a/test-suite/success/decl_mode2.v b/test-suite/success/decl_mode2.v deleted file mode 100644 index 46174e481..000000000 --- a/test-suite/success/decl_mode2.v +++ /dev/null @@ -1,249 +0,0 @@ -Theorem this_is_trivial: True. -proof. - thus thesis. -end proof. -Qed. - -Theorem T: (True /\ True) /\ True. - split. split. -proof. (* first subgoal *) - thus thesis. -end proof. -trivial. (* second subgoal *) -proof. (* third subgoal *) - thus thesis. -end proof. -Abort. - -Theorem this_is_not_so_trivial: False. -proof. -end proof. (* here a warning is issued *) -Fail Qed. (* fails: the proof in incomplete *) -Admitted. (* Oops! *) - -Theorem T: True. -proof. -escape. -auto. -return. -Abort. - -Theorem T: let a:=false in let b:= true in ( if a then True else False -> if b then True else False). -intros a b. -proof. -assume H:(if a then True else False). -reconsider H as False. -reconsider thesis as True. -Abort. - -Theorem T: forall x, x=2 -> 2+x=4. -proof. -let x be such that H:(x=2). -have H':(2+x=2+2) by H. -Abort. - -Theorem T: forall x, x=2 -> 2+x=4. -proof. -let x be such that H:(x=2). -then (2+x=2+2). -Abort. - -Theorem T: forall x, x=2 -> x + x = x * x. -proof. -let x be such that H:(x=2). -have (4 = 4). - ~= (2 * 2). - ~= (x * x) by H. - =~ (2 + 2). - =~ H':(x + x) by H. -Abort. - -Theorem T: forall x, x + x = x * x -> x = 0 \/ x = 2. -proof. -let x be such that H:(x + x = x * x). -claim H':((x - 2) * x = 0). -thus thesis. -end claim. -Abort. - -Theorem T: forall (A B:Prop), A -> B -> A /\ B. -intros A B HA HB. -proof. -hence B. -Abort. - -Theorem T: forall (A B C:Prop), A -> B -> C -> A /\ B /\ C. -intros A B C HA HB HC. -proof. -thus B by HB. -Abort. - -Theorem T: forall (A B C:Prop), A -> B -> C -> A /\ B. -intros A B C HA HB HC. -proof. -Fail hence C. (* fails *) -Abort. - -Theorem T: forall (A B:Prop), B -> A \/ B. -intros A B HB. -proof. -hence B. -Abort. - -Theorem T: forall (A B C D:Prop), C -> D -> (A /\ B) \/ (C /\ D). -intros A B C D HC HD. -proof. -thus C by HC. -Abort. - -Theorem T: forall (P:nat -> Prop), P 2 -> exists x,P x. -intros P HP. -proof. -take 2. -Abort. - -Theorem T: forall (P:nat -> Prop), P 2 -> exists x,P x. -intros P HP. -proof. -hence (P 2). -Abort. - -Theorem T: forall (P:nat -> Prop) (R:nat -> nat -> Prop), P 2 -> R 0 2 -> exists x, exists y, P y /\ R x y. -intros P R HP HR. -proof. -thus (P 2) by HP. -Abort. - -Theorem T: forall (A B:Prop) (P:nat -> Prop), (forall x, P x -> B) -> A -> A /\ B. -intros A B P HP HA. -proof. -suffices to have x such that HP':(P x) to show B by HP,HP'. -Abort. - -Theorem T: forall (A:Prop) (P:nat -> Prop), P 2 -> A -> A /\ (forall x, x = 2 -> P x). -intros A P HP HA. -proof. -(* BUG: the next line fails when it should succeed. -Waiting for someone to investigate the bug. -focus on (forall x, x = 2 -> P x). -let x be such that (x = 2). -hence thesis by HP. -end focus. -*) -Abort. - -Theorem T: forall x, x = 0 -> x + x = x * x. -proof. -let x be such that H:(x = 0). -define sqr x as (x * x). -reconsider thesis as (x + x = sqr x). -Abort. - -Theorem T: forall (P:nat -> Prop), forall x, P x -> P x. -proof. -let P:(nat -> Prop). -let x:nat. -assume HP:(P x). -Abort. - -Theorem T: forall (P:nat -> Prop), forall x, P x -> P x. -proof. -let P:(nat -> Prop). -Fail let x. (* fails because x's type is not clear *) -let x be such that HP:(P x). (* here x's type is inferred from (P x) *) -Abort. - -Theorem T: forall (P:nat -> Prop), forall x, P x -> P x -> P x. -proof. -let P:(nat -> Prop). -let x:nat. -assume (P x). (* temporary name created *) -Abort. - -Theorem T: forall (P:nat -> Prop), forall x, P x -> P x. -proof. -let P:(nat -> Prop). -let x be such that (P x). (* temporary name created *) -Abort. - -Theorem T: forall (P:nat -> Prop) (A:Prop), (exists x, (P x /\ A)) -> A. -proof. -let P:(nat -> Prop),A:Prop be such that H:(exists x, P x /\ A). -consider x such that HP:(P x) and HA:A from H. -Abort. - -(* Here is an example with pairs: *) - -Theorem T: forall p:(nat * nat)%type, (fst p >= snd p) \/ (fst p < snd p). -proof. -let p:(nat * nat)%type. -consider x:nat,y:nat from p. -reconsider thesis as (x >= y \/ x < y). -Abort. - -Theorem T: forall P:(nat -> Prop), (forall n, P n -> P (n - 1)) -> -(exists m, P m) -> P 0. -proof. -let P:(nat -> Prop) be such that HP:(forall n, P n -> P (n - 1)). -given m such that Hm:(P m). -Abort. - -Theorem T: forall (A B C:Prop), (A -> C) -> (B -> C) -> (A \/ B) -> C. -proof. -let A:Prop,B:Prop,C:Prop be such that HAC:(A -> C) and HBC:(B -> C). -assume HAB:(A \/ B). -per cases on HAB. -suppose A. - hence thesis by HAC. -suppose HB:B. - thus thesis by HB,HBC. -end cases. -Abort. - -Section Coq. - -Hypothesis EM : forall P:Prop, P \/ ~ P. - -Theorem T: forall (A C:Prop), (A -> C) -> (~A -> C) -> C. -proof. -let A:Prop,C:Prop be such that HAC:(A -> C) and HNAC:(~A -> C). -per cases of (A \/ ~A) by EM. -suppose (~A). - hence thesis by HNAC. -suppose A. - hence thesis by HAC. -end cases. -Abort. - -Theorem T: forall (A C:Prop), (A -> C) -> (~A -> C) -> C. -proof. -let A:Prop,C:Prop be such that HAC:(A -> C) and HNAC:(~A -> C). -per cases on (EM A). -suppose (~A). -Abort. -End Coq. - -Theorem T: forall (A B:Prop) (x:bool), (if x then A else B) -> A \/ B. -proof. -let A:Prop,B:Prop,x:bool. -per cases on x. -suppose it is true. - assume A. - hence A. -suppose it is false. - assume B. - hence B. -end cases. -Abort. - -Theorem T: forall (n:nat), n + 0 = n. -proof. -let n:nat. -per induction on n. -suppose it is 0. - thus (0 + 0 = 0). -suppose it is (S m) and H:thesis for m. - then (S (m + 0) = S m). - thus =~ (S m + 0). -end induction. -Abort.
\ No newline at end of file diff --git a/test-suite/success/old_typeclass.v b/test-suite/success/old_typeclass.v new file mode 100644 index 000000000..01e35810b --- /dev/null +++ b/test-suite/success/old_typeclass.v @@ -0,0 +1,13 @@ +Require Import Setoid Coq.Classes.Morphisms. +Set Typeclasses Legacy Resolution. + +Declare Instance and_Proper_eq: Proper (Logic.eq ==> Logic.eq ==> Logic.eq) and. + +Axiom In : Prop. +Axiom union_spec : In <-> True. + +Lemma foo : In /\ True. +Proof. +progress rewrite union_spec. +repeat constructor. +Qed. diff --git a/test-suite/success/rewrite_evar.v b/test-suite/success/rewrite_evar.v new file mode 100644 index 000000000..f7ad261cb --- /dev/null +++ b/test-suite/success/rewrite_evar.v @@ -0,0 +1,8 @@ +Require Import Coq.Setoids.Setoid. + +Goal forall (T2 MT1 MT2 : Type) (x : T2) (M2 m2 : MT2) (M1 m1 : MT1) (F : T2 -> MT1 -> MT2 -> Prop), + (forall (defaultB : T2) (m3 : MT1) (m4 : MT2), F defaultB m3 m4 <-> True) -> F x M1 M2 -> F x m1 m2. + intros ????????? H' H. + rewrite (H' _) in *. + (** The above rewrite should also rewrite in H. *) + Fail progress rewrite H' in H. |