src/HOL/HOLCF/IOA/meta_theory/Asig.thy

--- a/src/HOL/HOLCF/IOA/meta_theory/Asig.thy	Thu Dec 31 12:37:16 2015 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,101 +0,0 @@
-(*  Title:      HOL/HOLCF/IOA/meta_theory/Asig.thy
-    Author:     Olaf Müller, Tobias Nipkow & Konrad Slind
-*)
-
-section \<open>Action signatures\<close>
-
-theory Asig
-imports Main
-begin
-
-type_synonym
-  'a signature = "('a set * 'a set * 'a set)"
-
-definition
-  inputs :: "'action signature => 'action set" where
-  asig_inputs_def: "inputs = fst"
-
-definition
-  outputs :: "'action signature => 'action set" where
-  asig_outputs_def: "outputs = (fst o snd)"
-
-definition
-  internals :: "'action signature => 'action set" where
-  asig_internals_def: "internals = (snd o snd)"
-
-definition
-  actions :: "'action signature => 'action set" where
-  "actions(asig) = (inputs(asig) Un outputs(asig) Un internals(asig))"
-
-definition
-  externals :: "'action signature => 'action set" where
-  "externals(asig) = (inputs(asig) Un outputs(asig))"
-
-definition
-  locals :: "'action signature => 'action set" where
-  "locals asig = ((internals asig) Un (outputs asig))"
-
-definition
-  is_asig :: "'action signature => bool" where
-  "is_asig(triple) =
-     ((inputs(triple) Int outputs(triple) = {}) &
-      (outputs(triple) Int internals(triple) = {}) &
-      (inputs(triple) Int internals(triple) = {}))"
-
-definition
-  mk_ext_asig :: "'action signature => 'action signature" where
-  "mk_ext_asig(triple) = (inputs(triple), outputs(triple), {})"
-
-
-lemmas asig_projections = asig_inputs_def asig_outputs_def asig_internals_def
-
-lemma asig_triple_proj:
- "(outputs    (a,b,c) = b)   &
-  (inputs     (a,b,c) = a) &
-  (internals  (a,b,c) = c)"
-  apply (simp add: asig_projections)
-  done
-
-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
-
-lemma int_is_act: "[|a:internals S|] ==> a:actions S"
-apply (simp add: asig_internals_def actions_def)
-done
-
-lemma inp_is_act: "[|a:inputs S|] ==> a:actions S"
-apply (simp add: asig_inputs_def actions_def)
-done
-
-lemma out_is_act: "[|a:outputs S|] ==> a:actions S"
-apply (simp add: asig_outputs_def actions_def)
-done
-
-lemma ext_and_act: "(x: actions S & x : externals S) = (x: externals S)"
-apply (fast intro!: ext_is_act)
-done
-
-lemma not_ext_is_int: "[|is_asig S;x: actions S|] ==> (x~:externals S) = (x: internals S)"
-apply (simp add: actions_def is_asig_def externals_def)
-apply blast
-done
-
-lemma not_ext_is_int_or_not_act: "is_asig S ==> (x~:externals S) = (x: internals S | x~:actions S)"
-apply (simp add: actions_def is_asig_def externals_def)
-apply blast
-done
-
-lemma int_is_not_ext:
- "[| is_asig (S); x:internals S |] ==> x~:externals S"
-apply (unfold externals_def actions_def is_asig_def)
-apply simp
-apply blast
-done
-
-
-end