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(*              The Compcert verified compiler                         *)
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(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
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(*  Copyright Institut National de Recherche en Informatique et en     *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  under the terms of the GNU General Public License as published by  *)
(*  the Free Software Foundation, either version 2 of the License, or  *)
(*  (at your option) any later version.  This file is also distributed *)
(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
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(** Constructions of semi-lattices. *)
(* To avoid useless definitions of inductors in extracted code. *)
Local Unset Elimination Schemes.
Local Unset Case Analysis Schemes.
(** * Signatures of semi-lattices *)
(** A semi-lattice is a type [t] equipped with an equivalence relation [eq], a boolean equivalence test [beq], a partial order [ge], a smallest element [bot], and an upper bound operation [lub]. Note that we do not demand that [lub] computes the least upper bound. *)
Module Type SEMILATTICE.
Parameter t: Type.
Parameter eq: t -> t -> Prop.

Axiom ge_lub_left: forall x y, ge (lub x y) x.