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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).
(* This one could eventually be solved, the "Fail" is just to ensure *)
(* that it does not fail with an anomaly, as it did at some time *)
Fail Check (fun x : I' 0 => match x return _ x with
| C2' _ _ => 0
| niln => 0
| _ => 0
end).
(* Check insertion of coercions around matched subterm *)
Parameter A:Set.
Parameter f:> A -> nat.
Inductive J : Set := D : A -> J.
Check (fun x => match x with
| D 0 => 0
| D _ => 1
end).
(* Check coercions against the type of the term to match *)
(* Used to fail in V8.1beta *)
Inductive C : Set := c : C.
Inductive E : Set := e :> C -> E.
Check fun (x : E) => match x with c => e c end.
(* Check coercions with uniform parameters (cf bug #1168) *)
Inductive C' : bool -> Set := c' : C' true.
Inductive E' (b : bool) : Set := e' :> C' b -> E' b.
Check fun (x : E' true) => match x with c' => e' true c' end.
(* Check use of the no-dependency strategy when a type constraint is
given (and when the "inversion-and-dependencies-as-evars" strategy
is not strong enough because of a constructor with a type whose
pattern structure is not refined enough for it to be captured by
the inversion predicate) *)
Inductive K : bool -> bool -> Type := F : K true true | G x : K x x.
Check fun z P Q (y:K true z) (H1 H2:P y) (f:forall y, P y -> Q y z) =>
match y with
| F => f y H1
| G _ => f y H2
end : Q y z.
(* Check use of the maximal-dependency-in-variable strategy even when
no explicit type constraint is given (and when the
"inversion-and-dependencies-as-evars" strategy is not strong enough
because of a constructor with a type whose pattern structure is not
refined enough for it to be captured by the inversion predicate) *)
Check fun z P Q (y:K true z) (H1 H2:P y) (f:forall y z, P y -> Q y z) =>
match y with
| F => f y true H1
| G b => f y b H2
end.
(* Check use of the maximal-dependency-in-variable strategy for "Var"
variables *)
Goal forall z P Q (y:K true z) (H1 H2:P y) (f:forall y z, P y -> Q y z), Q y z.
intros z P Q y H1 H2 f.
Show.
refine (match y with
| F => f y true H1
| G b => f y b H2
end).
Qed.
|
