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authorGravatar Stephane Glondu <steph@glondu.net>2010-07-21 09:46:51 +0200
committerGravatar Stephane Glondu <steph@glondu.net>2010-07-21 09:46:51 +0200
commit5b7eafd0f00a16d78f99a27f5c7d5a0de77dc7e6 (patch)
tree631ad791a7685edafeb1fb2e8faeedc8379318ae /contrib/subtac/test/ListDep.v
parentda178a880e3ace820b41d38b191d3785b82991f5 (diff)
Imported Upstream snapshot 8.3~beta0+13298
Diffstat (limited to 'contrib/subtac/test/ListDep.v')
-rw-r--r--contrib/subtac/test/ListDep.v49
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diff --git a/contrib/subtac/test/ListDep.v b/contrib/subtac/test/ListDep.v
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-(* -*- coq-prog-args: ("-emacs-U" "-debug") -*- *)
-Require Import List.
-Require Import Coq.Program.Program.
-
-Set Implicit Arguments.
-
-Definition sub_list (A : Set) (l' l : list A) := (forall v, In v l' -> In v l) /\ length l' <= length l.
-
-Lemma sub_list_tl : forall A : Set, forall x (l l' : list A), sub_list (x :: l) l' -> sub_list l l'.
-Proof.
- intros.
- inversion H.
- split.
- intros.
- apply H0.
- auto with datatypes.
- auto with arith.
-Qed.
-
-Section Map_DependentRecursor.
- Variable U V : Set.
- Variable l : list U.
- Variable f : { x : U | In x l } -> V.
-
- Obligations Tactic := unfold sub_list in * ;
- program_simpl ; intuition.
-
- Program Fixpoint map_rec ( l' : list U | sub_list l' l )
- { measure length l' } : { r : list V | length r = length l' } :=
- match l' with
- | nil => nil
- | cons x tl => let tl' := map_rec tl in
- f x :: tl'
- end.
-
- Next Obligation.
- destruct_call map_rec.
- simpl in *.
- subst l'.
- simpl ; auto with arith.
- Qed.
-
- Program Definition map : list V := map_rec l.
-
-End Map_DependentRecursor.
-
-Extraction map.
-Extraction map_rec.
-