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Diffstat (limited to 'test-suite')
-rw-r--r-- | test-suite/bugs/closed/5683.v | 71 |
1 files changed, 71 insertions, 0 deletions
diff --git a/test-suite/bugs/closed/5683.v b/test-suite/bugs/closed/5683.v new file mode 100644 index 000000000..b5c6a48ec --- /dev/null +++ b/test-suite/bugs/closed/5683.v @@ -0,0 +1,71 @@ +Require Import Program.Tactics. +Require Import FunctionalExtensionality. + +Inductive Succ A := +| Succ_O : Succ A +| Succ_S : A -> Succ A. +Arguments Succ_O {A}. +Arguments Succ_S {A} _. + +Inductive Zero : Type :=. + +Inductive ty := +| ty_nat : ty +| ty_arr : ty -> ty -> ty. + +Inductive term A := +| term_abs : ty -> term (Succ A) -> term A +| term_app : term A -> term A -> term A +| term_var : A -> term A +| term_nat : nat -> term A. +Arguments term_abs {A} _ _. +Arguments term_app {A} _ _. +Arguments term_var {A} _. +Arguments term_nat {A} _. + +Class Functor F := +{ + ret : forall {A}, A -> F A; + fmap : forall {A B}, (A -> B) -> F A -> F B; + fmap_id : forall {A} (fa : F A), fmap (@id A) fa = fa; + fmap_compose : forall {A B C} (fa : F A) (g : B -> C) (h : A -> B), fmap (fun +a => g (h a)) fa = fmap g (fmap h fa) +}. + +Class Monad M `{Functor M} := +{ + bind : forall {A B}, M A -> (A -> M B) -> M B; + ret_left_id : forall {A B} (a : A) (f : A -> M B), bind (ret a) f = f a; + ret_right_id : forall {A} (m : M A), bind m ret = m; + bind_assoc : forall {A B C} (m : M A) (f : A -> M B) (g : B -> M C), bind +(bind m f) g = bind m (fun x => bind (f x) g) +}. + +Instance Succ_Functor : Functor Succ. +Proof. + unshelve econstructor. + - intros A B f fa. + destruct fa. + + apply Succ_O. + + apply Succ_S. tauto. + - intros. apply Succ_S. assumption. + - intros A [|a]; reflexivity. + - intros A B C [|a] g h; reflexivity. +Defined. + +(* Anomaly: Not an arity *) +Program Fixpoint term_bind {A B} (tm : term A) (f : A -> term B) : term B := + let Succ_f (var : Succ A) := + match var with + | Succ_O => term_var Succ_O + | Succ_S var' => _ + end in + match tm with + | term_app tm1 tm2 => term_app (term_bind tm1 f) (term_bind tm2 f) + | term_abs ty body => term_abs ty (term_bind body Succ_f) + | term_var a => f a + | term_nat n => term_nat n + end. +Next Obligation. + intros. +Admitted. |