% Author(s): Aad Mathijssen, Jeroen Keiren
% Copyright: see the accompanying file COPYING or copy at
% https://github.com/mCRL2org/mCRL2/blob/master/COPYING
%
% Distributed under the Boost Software License, Version 1.0.
% (See accompanying file LICENSE_1_0.txt or copy at
% http://www.boost.org/LICENSE_1_0.txt)
%
% Specification of the Bool data sort.
sort Bool;
cons true: Bool;
false: Bool;
map !: Bool -> Bool;
&&: Bool # Bool -> Bool;
||: Bool # Bool -> Bool;
=>: Bool # Bool -> Bool;
var b:Bool;
eqn !true = false;
!false = true;
!!b = b;
b && true = b;
b && false = false;
true && b = b;
false && b = false;
b || true = true;
b || false = b;
true || b = true;
false || b = b;
b => true = true;
b => false = !(b);
true => b = b;
false => b = true;
true == b = b;
false == b = !(b);
b == true = b;
b == false = !b;
false < b = b;
true < b = false;
b < false = false;
b < true = !b;
false <= b = true;
true <= b = b;
b <= false = !b;
b <= true = true;