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Diffstat (limited to 'test-suite/bugs/closed/3567.v')
| -rw-r--r-- | test-suite/bugs/closed/3567.v | 68 |
1 files changed, 68 insertions, 0 deletions
diff --git a/test-suite/bugs/closed/3567.v b/test-suite/bugs/closed/3567.v new file mode 100644 index 00000000..cb16b3ae --- /dev/null +++ b/test-suite/bugs/closed/3567.v @@ -0,0 +1,68 @@ + +(* File reduced by coq-bug-finder from original input, then from 2901 lines to 69 lines, then from 80 lines to 63 lines *) +(* coqc version trunk (September 2014) compiled on Sep 2 2014 2:7:1 with OCaml 4.01.0 + coqtop version cagnode17:/afs/csail.mit.edu/u/j/jgross/coq-trunk,trunk (3c5daf4e23ee20f0788c0deab688af452e83ccf0) *) + +Set Primitive Projections. +Set Implicit Arguments. +Record prod (A B : Type) := pair { fst : A ; snd : B }. +Arguments fst {A B} _ / . +Arguments snd {A B} _ / . +Add Printing Let prod. +Notation "x * y" := (prod x y) : type_scope. +Notation "( x , y , .. , z )" := (pair .. (pair x y) .. z) : core_scope. +Unset Implicit Arguments. +Inductive paths {A : Type} (a : A) : A -> Type := idpath : paths a a where "x = y" := (@paths _ x y) : type_scope. +Arguments idpath {A a} , [A] a. +Definition ap {A B:Type} (f:A -> B) {x y:A} (p:x = y) : f x = f y := match p with idpath => idpath end. +Definition Sect {A B : Type} (s : A -> B) (r : B -> A) := forall x : A, r (s x) = x. +Class IsEquiv {A B : Type} (f : A -> B) := + { equiv_inv : B -> A ; + eisretr : Sect equiv_inv f; + eissect : Sect f equiv_inv; + eisadj : forall x : A, eisretr (f x) = ap f (eissect x) }. +Definition path_prod_uncurried {A B : Type} (z z' : A * B) (pq : (fst z = fst z') * (snd z = snd z')) +: (z = z') + := match fst pq in (_ = z'1), snd pq in (_ = z'2) return z = (z'1, z'2) with + | idpath, idpath => idpath + end. +Definition path_prod {A B : Type} (z z' : A * B) : + (fst z = fst z') -> (snd z = snd z') -> (z = z') + := fun p q => path_prod_uncurried z z' (p,q). +Definition path_prod' {A B : Type} {x x' : A} {y y' : B} +: (x = x') -> (y = y') -> ((x,y) = (x',y')) + := fun p q => path_prod (x,y) (x',y') p q. +Axiom ap_fst_path_prod : forall {A B : Type} {z z' : A * B} + (p : fst z = fst z') (q : snd z = snd z'), + ap fst (path_prod _ _ p q) = p. +Axiom ap_snd_path_prod : forall {A B : Type} {z z' : A * B} + (p : fst z = fst z') (q : snd z = snd z'), + ap snd (path_prod _ _ p q) = q. +Axiom eta_path_prod : forall {A B : Type} {z z' : A * B} (p : z = z'), + path_prod _ _(ap fst p) (ap snd p) = p. +Definition isequiv_path_prod {A B : Type} {z z' : A * B} : IsEquiv (path_prod_uncurried z z'). +Proof. + refine (Build_IsEquiv + _ _ _ + (fun r => (ap fst r, ap snd r)) + eta_path_prod + (fun pq => match pq with + | (p,q) => path_prod' + (ap_fst_path_prod p q) (ap_snd_path_prod p q) + end) _). + destruct z as [x y], z' as [x' y']. simpl. +(* Toplevel input, characters 15-50: +Error: Abstracting over the term "z" leads to a term +fun z0 : A * B => +forall x : (fst z0 = fst z') * (snd z0 = snd z'), +eta_path_prod (path_prod_uncurried z0 z' x) = +ap (path_prod_uncurried z0 z') + (let (p, q) as pq + return + ((ap (fst) (path_prod_uncurried z0 z' pq), + ap (snd) (path_prod_uncurried z0 z' pq)) = pq) := x in + path_prod' (ap_fst_path_prod p q) (ap_snd_path_prod p q)) +which is ill-typed. +Reason is: Pattern-matching expression on an object of inductive type prod +has invalid information. + *)
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