isabelle: src/HOLCF/IMP/HoareEx.thy@e5418eec375c (annotated)

3664 2dced1ac2d8e Example from HOLCF paper. nipkow parents: diff changeset	1	(* Title: HOLCF/IMP/HoareEx.thy
2dced1ac2d8e Example from HOLCF paper. nipkow parents: diff changeset	2	Author: Tobias Nipkow, TUM
2dced1ac2d8e Example from HOLCF paper. nipkow parents: diff changeset	3	Copyright 1997 TUM
2dced1ac2d8e Example from HOLCF paper. nipkow parents: diff changeset	4	*)
2dced1ac2d8e Example from HOLCF paper. nipkow parents: diff changeset	5
12431 07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	6	header "Correctness of Hoare by Fixpoint Reasoning"
07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	7
16417 9bc16273c2d4 migrated theory headers to new format haftmann parents: 12600 diff changeset	8	theory HoareEx imports Denotational begin
3664 2dced1ac2d8e Example from HOLCF paper. nipkow parents: diff changeset	9
12431 07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	10	text {*
12546 0c90e581379f tuned; wenzelm parents: 12431 diff changeset	11	An example from the HOLCF paper by M�ller, Nipkow, Oheimb, Slotosch
0c90e581379f tuned; wenzelm parents: 12431 diff changeset	12	\cite{MuellerNvOS99}. It demonstrates fixpoint reasoning by showing
0c90e581379f tuned; wenzelm parents: 12431 diff changeset	13	the correctness of the Hoare rule for while-loops.
12431 07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	14	*}
3664 2dced1ac2d8e Example from HOLCF paper. nipkow parents: diff changeset	15
12431 07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	16	types assn = "state => bool"
07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	17
19737 3b8920131be2 tuned; wenzelm parents: 16417 diff changeset	18	definition
21404 eb85850d3eb7 more robust syntax for definition/abbreviation/notation; wenzelm parents: 19737 diff changeset	19	hoare_valid :: "[assn, com, assn] => bool" ("\|= {(1_)}/ (_)/ {(1_)}" 50) where
19737 3b8920131be2 tuned; wenzelm parents: 16417 diff changeset	20	"\|= {A} c {B} = (\<forall>s t. A s \<and> D c $(Discr s) = Def t --> B t)"
3664 2dced1ac2d8e Example from HOLCF paper. nipkow parents: diff changeset	21
12431 07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	22	lemma WHILE_rule_sound:
12600 30ec65eaaf5f tuned; wenzelm parents: 12546 diff changeset	23	"\|= {A} c {A} ==> \|= {A} \<WHILE> b \<DO> c {\<lambda>s. A s \<and> \<not> b s}"
12431 07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	24	apply (unfold hoare_valid_def)
07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	25	apply (simp (no_asm))
07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	26	apply (rule fix_ind)
12600 30ec65eaaf5f tuned; wenzelm parents: 12546 diff changeset	27	apply (simp (no_asm)) -- "simplifier with enhanced @{text adm}-tactic"
12431 07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	28	apply (simp (no_asm))
07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	29	apply (simp (no_asm))
07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	30	apply blast
07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	31	done
07ec657249e5 converted to Isar kleing parents: 10835 diff changeset	32
3664 2dced1ac2d8e Example from HOLCF paper. nipkow parents: diff changeset	33	end

author	haftmann
	Wed, 11 Aug 2010 13:31:29 +0200
changeset 38343	e5418eec375c
parent 35174	e15040ae75d7
permissions	-rw-r--r--