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%------------------------------------------------------------------------------
% Semigroups definition file
%
% Author: Rick Butler
% David Lester, Manchester University & NIA
%
% Version 1.0 3/1/02
% Version 1.1 12/3/03 New library structure
% Version 1.2 5/5/04 Reworked for definition files DRL
%------------------------------------------------------------------------------
semigroup_def[T:Type,*:[T,T->T]]: THEORY
BEGIN
IMPORTING groupoid_def[T,*]
S: VAR set[T]
semigroup?(S): MACRO bool = groupoid?(S) AND
associative?[(S)](*)
finite_semigroup?(S): bool = semigroup?(S) AND is_finite(S)
commutative_semigroup?(S): bool = semigroup?(S) AND
commutative?[(S)](*)
finite_commutative_semigroup?(S): bool = finite_semigroup?(S) AND
commutative?[(S)](*)
END semigroup_def
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