Theory Asig

theory Asig
imports Main
(*  Title:      HOL/IOA/Asig.thy
Author: Tobias Nipkow & Konrad Slind
Copyright 1994 TU Muenchen
*)


header {* Action signatures *}

theory Asig
imports Main
begin

type_synonym
'a signature = "('a set * 'a set * 'a set)"

consts
"actions" :: "'action signature => 'action set"
"inputs" :: "'action signature => 'action set"
"outputs" :: "'action signature => 'action set"
"internals" :: "'action signature => 'action set"
externals :: "'action signature => 'action set"

is_asig ::"'action signature => bool"
mk_ext_asig ::"'action signature => 'action signature"


defs

asig_inputs_def: "inputs == fst"
asig_outputs_def: "outputs == (fst o snd)"
asig_internals_def: "internals == (snd o snd)"

actions_def:
"actions(asig) == (inputs(asig) Un outputs(asig) Un internals(asig))"

externals_def:
"externals(asig) == (inputs(asig) Un outputs(asig))"

is_asig_def:
"is_asig(triple) ==
((inputs(triple) Int outputs(triple) = {}) &
(outputs(triple) Int internals(triple) = {}) &
(inputs(triple) Int internals(triple) = {}))"



mk_ext_asig_def:
"mk_ext_asig(triple) == (inputs(triple), outputs(triple), {})"


lemmas asig_projections = asig_inputs_def asig_outputs_def asig_internals_def

lemma int_and_ext_is_act: "[| a~:internals(S) ;a~:externals(S)|] ==> a~:actions(S)"
apply (simp add: externals_def actions_def)
done

lemma ext_is_act: "[|a:externals(S)|] ==> a:actions(S)"
apply (simp add: externals_def actions_def)
done

end