-------------------------------------------------------------------------------- -- Copyright 2008 Chantal Keller -- School of Computer Science -- University of Nottingham -- This program is free software: you can redistribute it and/or modify -- it under the terms of the GNU General Public License as published by -- the Free Software Foundation, either version 3 of the License, or -- (at your option) any later version. -- This program is distributed in the hope that it will be useful, -- but WITHOUT ANY WARRANTY; without even the implied warranty of -- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -- GNU General Public License for more details. -- You should have received a copy of the GNU General Public License -- along with this program. If not, see . -------------------------------------------------------------------------------- module Equality where data _≡_ {A : Set} : A -> A -> Set where refl : {a : A} -> a ≡ a infix 10 _≡_ sym : {A : Set} -> {a b : A} -> a ≡ b -> b ≡ a sym refl = refl trans : {A : Set} -> {a b c : A} -> a ≡ b -> b ≡ c -> a ≡ c trans refl refl = refl