author | wenzelm |
Fri, 22 Nov 2013 20:37:19 +0100 | |
changeset 54560 | 7f36da77130d |
parent 42174 | d0be2722ce9f |
child 58889 | 5b7a9633cfa8 |
permissions | -rw-r--r-- |
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(* Title: HOL/IOA/Asig.thy |
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Author: Tobias Nipkow & Konrad Slind |
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Copyright 1994 TU Muenchen |
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*) |
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header {* Action signatures *} |
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theory Asig |
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imports Main |
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begin |
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type_synonym |
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'a signature = "('a set * 'a set * 'a set)" |
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consts |
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"actions" :: "'action signature => 'action set" |
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"inputs" :: "'action signature => 'action set" |
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"outputs" :: "'action signature => 'action set" |
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"internals" :: "'action signature => 'action set" |
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externals :: "'action signature => 'action set" |
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is_asig ::"'action signature => bool" |
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mk_ext_asig ::"'action signature => 'action signature" |
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defs |
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asig_inputs_def: "inputs == fst" |
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asig_outputs_def: "outputs == (fst o snd)" |
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asig_internals_def: "internals == (snd o snd)" |
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actions_def: |
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"actions(asig) == (inputs(asig) Un outputs(asig) Un internals(asig))" |
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externals_def: |
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"externals(asig) == (inputs(asig) Un outputs(asig))" |
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is_asig_def: |
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"is_asig(triple) == |
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((inputs(triple) Int outputs(triple) = {}) & |
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(outputs(triple) Int internals(triple) = {}) & |
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(inputs(triple) Int internals(triple) = {}))" |
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mk_ext_asig_def: |
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"mk_ext_asig(triple) == (inputs(triple), outputs(triple), {})" |
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lemmas asig_projections = asig_inputs_def asig_outputs_def asig_internals_def |
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lemma int_and_ext_is_act: "[| a~:internals(S) ;a~:externals(S)|] ==> a~:actions(S)" |
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apply (simp add: externals_def actions_def) |
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done |
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lemma ext_is_act: "[|a:externals(S)|] ==> a:actions(S)" |
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apply (simp add: externals_def actions_def) |
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done |
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end |