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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* $Id: Field_Compl.v,v 1.2.2.1 2004/07/16 19:30:17 herbelin Exp $ *)
Inductive listT [A:Type] : Type :=
nilT : (listT A) | consT : A->(listT A)->(listT A).
Fixpoint appT [A:Type][l:(listT A)] : (listT A) -> (listT A) :=
[m:(listT A)]
Cases l of
| nilT => m
| (consT a l1) => (consT A a (appT A l1 m))
end.
Inductive prodT [A,B:Type] : Type :=
pairT: A->B->(prodT A B).
Definition assoc_2nd :=
Fix assoc_2nd_rec
{assoc_2nd_rec
[A:Type;B:Set;eq_dec:(e1,e2:B){e1=e2}+{~e1=e2};lst:(listT (prodT A B))]
: B->A->A:=
[key:B;default:A]
Cases lst of
| nilT => default
| (consT (pairT v e) l) =>
(Cases (eq_dec e key) of
| (left _) => v
| (right _) => (assoc_2nd_rec A B eq_dec l key default)
end)
end}.
Definition fstT [A,B:Type;c:(prodT A B)] :=
Cases c of
| (pairT a _) => a
end.
Definition sndT [A,B:Type;c:(prodT A B)] :=
Cases c of
| (pairT _ a) => a
end.
Definition mem :=
Fix mem {mem [A:Set;eq_dec:(e1,e2:A){e1=e2}+{~e1=e2};a:A;l:(listT A)] : bool :=
Cases l of
| nilT => false
| (consT a1 l1) =>
Cases (eq_dec a a1) of
| (left _) => true
| (right _) => (mem A eq_dec a l1)
end
end}.
Inductive field_rel_option [A:Type] : Type :=
| Field_None : (field_rel_option A)
| Field_Some : (A -> A -> A) -> (field_rel_option A).
|
