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(** Examples of extraction with manually-declared implicit arguments *)
(** NB: we should someday check the produced code instead of
extracting and just compiling. *)
Require Coq.extraction.Extraction.
(** Bug #4243, part 1 *)
Inductive dnat : nat -> Type :=
| d0 : dnat 0
| ds : forall n m, n = m -> dnat n -> dnat (S n).
Extraction Implicit ds [m].
Lemma dnat_nat: forall n, dnat n -> nat.
Proof.
intros n d.
induction d as [| n m Heq d IHn].
exact 0. exact (S IHn).
Defined.
Recursive Extraction dnat_nat.
Extraction TestCompile dnat_nat.
Extraction Implicit dnat_nat [n].
Recursive Extraction dnat_nat.
Extraction TestCompile dnat_nat.
(** Same, with a Fixpoint *)
Fixpoint dnat_nat' n (d:dnat n) :=
match d with
| d0 => 0
| ds n m _ d => S (dnat_nat' n d)
end.
Recursive Extraction dnat_nat'.
Extraction TestCompile dnat_nat'.
Extraction Implicit dnat_nat' [n].
Recursive Extraction dnat_nat'.
Extraction TestCompile dnat_nat'.
(** Bug #4243, part 2 *)
Inductive enat: nat -> Type :=
e0: enat 0
| es: forall n, enat n -> enat (S n).
Lemma enat_nat: forall n, enat n -> nat.
Proof.
intros n e.
induction e as [| n e IHe].
exact (O).
exact (S IHe).
Defined.
Extraction Implicit es [n].
Extraction Implicit enat_nat [n].
Recursive Extraction enat_nat.
Extraction TestCompile enat_nat.
(** Same, with a Fixpoint *)
Fixpoint enat_nat' n (e:enat n) : nat :=
match e with
| e0 => 0
| es n e => S (enat_nat' n e)
end.
Extraction Implicit enat_nat' [n].
Recursive Extraction enat_nat'.
Extraction TestCompile enat_nat'.
(** Bug #4228 *)
Module Food.
Inductive Course :=
| main: nat -> Course
| dessert: nat -> Course.
Inductive Meal : Course -> Type :=
| one_course : forall n:nat, Meal (main n)
| two_course : forall n m, Meal (main n) -> Meal (dessert m).
Extraction Implicit two_course [n].
End Food.
Recursive Extraction Food.Meal.
Extraction TestCompile Food.Meal.
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