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|
(* Check coercions in patterns *)
Inductive I : Set :=
| C1 : nat -> I
| C2 : I -> I.
Coercion C1 : nat >-> I.
(* Coercion at the root of pattern *)
Check (fun x => match x with
| C2 n => 0
| O => 0
| S n => n
end).
(* Coercion not at the root of pattern *)
Check (fun x => match x with
| C2 O => 0
| _ => 0
end).
(* Unification and coercions inside patterns *)
Check
(fun x : option nat => match x with
| None => 0
| Some O => 0
| _ => 0
end).
(* Coercion up to delta-conversion, and unification *)
Coercion somenat := Some (A:=nat).
Check (fun x => match x with
| None => 0
| O => 0
| S n => n
end).
(* Coercions with parameters *)
Inductive listn : nat -> Set :=
| niln : listn 0
| consn : forall n : nat, nat -> listn n -> listn (S n).
Inductive I' : nat -> Set :=
| C1' : forall n : nat, listn n -> I' n
| C2' : forall n : nat, I' n -> I' n.
Coercion C1' : listn >-> I'.
Check (fun x : I' 0 => match x with
| C2' _ _ => 0
| niln => 0
| _ => 0
end).
Check (fun x : I' 0 => match x with
| C2' _ niln => 0
| _ => 0
end).
|
