diff options
Diffstat (limited to 'test-suite/bugs/closed/shouldsucceed/1918.v')
| -rw-r--r-- | test-suite/bugs/closed/shouldsucceed/1918.v | 39 |
1 files changed, 19 insertions, 20 deletions
diff --git a/test-suite/bugs/closed/shouldsucceed/1918.v b/test-suite/bugs/closed/shouldsucceed/1918.v index 9d4a3e04..9d92fe12 100644 --- a/test-suite/bugs/closed/shouldsucceed/1918.v +++ b/test-suite/bugs/closed/shouldsucceed/1918.v @@ -35,7 +35,7 @@ Definition mon (X:k1) : Type := forall (A B:Set), (A -> B) -> X A -> X B. (** extensionality *) Definition ext (X:k1)(h: mon X): Prop := - forall (A B:Set)(f g:A -> B), + forall (A B:Set)(f g:A -> B), (forall a, f a = g a) -> forall r, h _ _ f r = h _ _ g r. (** first functor law *) @@ -44,7 +44,7 @@ Definition fct1 (X:k1)(m: mon X) : Prop := (** second functor law *) Definition fct2 (X:k1)(m: mon X) : Prop := - forall (A B C:Set)(f:A -> B)(g:B -> C)(x:X A), + forall (A B C:Set)(f:A -> B)(g:B -> C)(x:X A), m _ _ (g o f) x = m _ _ g (m _ _ f x). (** pack up the good properties of the approximation into @@ -60,20 +60,20 @@ Definition pEFct (F:k2) : Type := forall (X:k1), EFct X -> EFct (F X). -(** we show some closure properties of pEFct, depending on such properties +(** we show some closure properties of pEFct, depending on such properties for EFct *) Definition moncomp (X Y:k1)(mX:mon X)(mY:mon Y): mon (fun A => X(Y A)). Proof. red. - intros X Y mX mY A B f x. + intros A B f x. exact (mX (Y A)(Y B) (mY A B f) x). Defined. (** closure under composition *) Lemma compEFct (X Y:k1): EFct X -> EFct Y -> EFct (fun A => X(Y A)). Proof. - intros X Y ef1 ef2. + intros ef1 ef2. apply (mkEFct(m:=moncomp (m ef1) (m ef2))); red; intros; unfold moncomp. (* prove ext *) apply (e ef1). @@ -92,7 +92,7 @@ Proof. apply (f2 ef2). Defined. -Corollary comppEFct (F G:k2): pEFct F -> pEFct G -> +Corollary comppEFct (F G:k2): pEFct F -> pEFct G -> pEFct (fun X A => F X (G X A)). Proof. red. @@ -103,8 +103,8 @@ Defined. (** closure under sums *) Lemma sumEFct (X Y:k1): EFct X -> EFct Y -> EFct (fun A => X A + Y A)%type. Proof. - intros X Y ef1 ef2. - set (m12:=fun (A B:Set)(f:A->B) x => match x with + intros ef1 ef2. + set (m12:=fun (A B:Set)(f:A->B) x => match x with | inl y => inl _ (m ef1 f y) | inr y => inr _ (m ef2 f y) end). @@ -133,7 +133,7 @@ Proof. rewrite (f2 ef2); reflexivity. Defined. -Corollary sumpEFct (F G:k2): pEFct F -> pEFct G -> +Corollary sumpEFct (F G:k2): pEFct F -> pEFct G -> pEFct (fun X A => F X A + G X A)%type. Proof. red. @@ -144,8 +144,8 @@ Defined. (** closure under products *) Lemma prodEFct (X Y:k1): EFct X -> EFct Y -> EFct (fun A => X A * Y A)%type. Proof. - intros X Y ef1 ef2. - set (m12:=fun (A B:Set)(f:A->B) x => match x with + intros ef1 ef2. + set (m12:=fun (A B:Set)(f:A->B) x => match x with (x1,x2) => (m ef1 f x1, m ef2 f x2) end). apply (mkEFct(m:=m12)); red; intros. (* prove ext *) @@ -168,7 +168,7 @@ Proof. apply (f2 ef2). Defined. -Corollary prodpEFct (F G:k2): pEFct F -> pEFct G -> +Corollary prodpEFct (F G:k2): pEFct F -> pEFct G -> pEFct (fun X A => F X A * G X A)%type. Proof. red. @@ -220,7 +220,6 @@ Defined. (** constants in k1 *) Lemma constEFct (C:Set): EFct (fun _ => C). Proof. - intro. set (mC:=fun A B (f:A->B)(x:C) => x). apply (mkEFct(m:=mC)); red; intros; unfold mC; reflexivity. Defined. @@ -248,19 +247,19 @@ Module Type LNMIt_Type. Parameter F:k2. Parameter FpEFct: pEFct F. -Parameter mu20: k1. +Parameter mu20: k1. Definition mu2: k1:= fun A => mu20 A. Parameter mapmu2: mon mu2. Definition MItType: Type := forall G : k1, (forall X : k1, X c_k1 G -> F X c_k1 G) -> mu2 c_k1 G. Parameter MIt0 : MItType. -Definition MIt : MItType:= fun G s A t => MIt0 s t. -Definition InType : Type := - forall (X:k1)(ef:EFct X)(j: X c_k1 mu2), +Definition MIt : MItType:= fun G s A t => MIt0 s t. +Definition InType : Type := + forall (X:k1)(ef:EFct X)(j: X c_k1 mu2), NAT j (m ef) mapmu2 -> F X c_k1 mu2. Parameter In : InType. Axiom mapmu2Red : forall (A:Set)(X:k1)(ef:EFct X)(j: X c_k1 mu2) - (n: NAT j (m ef) mapmu2)(t: F X A)(B:Set)(f:A->B), + (n: NAT j (m ef) mapmu2)(t: F X A)(B:Set)(f:A->B), mapmu2 f (In ef n t) = In ef n (m (FpEFct ef) f t). Axiom MItRed : forall (G : k1) (s : forall X : k1, X c_k1 G -> F X c_k1 G)(X : k1)(ef:EFct X)(j: X c_k1 mu2) @@ -327,8 +326,8 @@ Fixpoint Pow (X:k1)(k:nat){struct k}:k1:= Fixpoint POW (k:nat)(X:k1)(m:mon X){struct k} : mon (Pow X k) := match k return mon (Pow X k) - with 0 => fun _ _ f => f - | S k' => fun _ _ f => m _ _ (POW k' m f) + with 0 => fun _ _ f => f + | S k' => fun _ _ f => m _ _ (POW k' m f) end. Module Type BushkToList_Type. |