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src/HOL/ex/MonoidGroup.thy

changeset 11019 | e968e5bfe98d |

parent 10357 | 0d0cac129618 |

child 11939 | c5e69470f03b |

--- a/src/HOL/ex/MonoidGroup.thy Thu Feb 01 20:43:41 2001 +0100 +++ b/src/HOL/ex/MonoidGroup.thy Thu Feb 01 20:43:59 2001 +0100 @@ -11,23 +11,23 @@ theory MonoidGroup = Main: record 'a monoid_sig = - times :: "['a, 'a] => 'a" + times :: "'a => 'a => 'a" one :: 'a record 'a group_sig = "'a monoid_sig" + inv :: "'a => 'a" constdefs - monoid :: "(| times :: ['a, 'a] => 'a, one :: 'a, ... :: 'b::more |) => bool" - "monoid M == ALL x y z. - times M (times M x y) z = times M x (times M y z) & - times M (one M) x = x & times M x (one M) = x" + monoid :: "(| times :: 'a => 'a => 'a, one :: 'a, ... :: 'b::more |) => bool" + "monoid M == \<forall>x y z. + times M (times M x y) z = times M x (times M y z) \<and> + times M (one M) x = x \<and> times M x (one M) = x" - group :: "(| times :: ['a, 'a] => 'a, one :: 'a, inv :: 'a => 'a, ... :: 'b::more |) => bool" - "group G == monoid G & (ALL x. times G (inv G x) x = one G)" + group :: "(| times :: 'a => 'a => 'a, one :: 'a, inv :: 'a => 'a, ... :: 'b::more |) => bool" + "group G == monoid G \<and> (\<forall>x. times G (inv G x) x = one G)" - reverse :: "(| times :: ['a, 'a] => 'a, one :: 'a, ... :: 'b::more |) => - (| times :: ['a, 'a] => 'a, one :: 'a, ... :: 'b |)" - "reverse M == M (| times := %x y. times M y x |)" + reverse :: "(| times :: 'a => 'a => 'a, one :: 'a, ... :: 'b::more |) => + (| times :: 'a => 'a => 'a, one :: 'a, ... :: 'b |)" + "reverse M == M (| times := \<lambda>x y. times M y x |)" end