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Diffstat (limited to 'test-suite/bugs/closed/2117.v')
-rw-r--r-- | test-suite/bugs/closed/2117.v | 56 |
1 files changed, 56 insertions, 0 deletions
diff --git a/test-suite/bugs/closed/2117.v b/test-suite/bugs/closed/2117.v new file mode 100644 index 00000000..6377a8b7 --- /dev/null +++ b/test-suite/bugs/closed/2117.v @@ -0,0 +1,56 @@ +(* Check pattern-unification on evars in apply unification *) + +Axiom app : forall tau tau':Type, (tau -> tau') -> tau -> tau'. + +Axiom copy : forall tau:Type, tau -> tau -> Prop. +Axiom copyr : forall tau:Type, tau -> tau -> Prop. +Axiom copyf : forall tau:Type, tau -> tau -> Prop. +Axiom eq : forall tau:Type, tau -> tau -> Prop. +Axiom subst : forall tau tau':Type, (tau -> tau') -> tau -> tau' -> Prop. + +Axiom copy_atom : forall tau:Type, forall t t':tau, eq tau t t' -> copy tau t t'. +Axiom copy_fun: forall tau tau':Type, forall t t':(tau->tau'), +(forall x:tau, copyr tau x x->copy tau' (t x) (t' x)) +->copy (tau->tau') t t'. + +Axiom copyr_atom : forall tau:Type, forall t t':tau, copyr tau t t' -> eq tau t t'. +Axiom copyr_fun: forall tau tau':Type, forall t t':(tau->tau'), +copyr (tau->tau') t t' +->(forall x y:tau, copy tau x y->copyr tau' (t x) (t' y)). + +Axiom copyf_atom : forall tau:Type, forall t t':tau, copyf tau t t' -> eq tau t t'. +Axiom copyf_fun: forall tau tau':Type, forall t t':(tau->tau'), +copyr (tau->tau') t t' +->(forall x y:tau, forall z1 z2:tau', +(copy tau x y)-> +(subst tau tau' t x z1)-> +(subst tau tau' t' y z2)-> +copyf tau' z1 z2). + +Axiom eqappg: forall tau tau':Type, forall t:tau->tau', forall q:tau, forall r:tau',forall t':tau', +( ((subst tau tau' t q t') /\ (eq tau' t' r)) +->eq tau' (app tau tau' t q) r). + +Axiom eqappd: forall tau tau':Type, forall t:tau->tau', forall q:tau, forall r:tau', +forall t':tau', ((subst tau tau' t q t') /\ (eq tau' r t')) +->eq tau' r (app tau tau' t q). + +Axiom substcopy: forall tau tau':Type, forall t:tau->tau', forall q:tau, forall r:tau', +(forall x:tau, (copyf tau x q) -> (copy tau' (t x) r)) +->subst tau tau' t q r. + +Ltac EtaLong := (apply copy_fun;intros;EtaLong)|| apply copy_atom.
+Ltac Subst := apply substcopy;intros;EtaLong. +Ltac Rigid_aux := fun A => apply A|| Rigid_aux (copyr_fun _ _ _ _ A). +Ltac Rigid := fun A => apply copyr_atom; Rigid_aux A. + +Theorem church0: forall i:Type, exists X:(i->i)->i->i, +copy ((i->i)->i->i) (fun f:i->i => fun x:i=>f (X f x)) (fun f:i->i=>fun x:i=>app i i (X f) (f x)). +intros. +esplit. +EtaLong. +eapply eqappd;split. +Subst. +apply copyf_atom. +Show Existentials. +apply H1. |