author | haftmann |
Wed, 19 Feb 2014 22:05:05 +0100 | |
changeset 55599 | 6535c537b243 |
parent 52046 | bc01725d7918 |
child 55600 | 3c7610b8dcfc |
permissions | -rw-r--r-- |
44656 | 1 |
(* Author: Tobias Nipkow *) |
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theory Abs_Int_den0_const |
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imports Abs_Int_den0 |
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begin |
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subsection "Constant Propagation" |
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datatype cval = Const val | Any |
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fun rep_cval where |
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"rep_cval (Const n) = {n}" | |
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"rep_cval (Any) = UNIV" |
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fun plus_cval where |
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"plus_cval (Const m) (Const n) = Const(m+n)" | |
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"plus_cval _ _ = Any" |
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instantiation cval :: SL_top |
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begin |
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fun le_cval where |
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"_ \<sqsubseteq> Any = True" | |
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"Const n \<sqsubseteq> Const m = (n=m)" | |
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"Any \<sqsubseteq> Const _ = False" |
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fun join_cval where |
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"Const m \<squnion> Const n = (if n=m then Const m else Any)" | |
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"_ \<squnion> _ = Any" |
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definition "Top = Any" |
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instance |
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proof |
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case goal1 thus ?case by (cases x) simp_all |
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next |
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case goal2 thus ?case by(cases z, cases y, cases x, simp_all) |
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next |
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case goal3 thus ?case by(cases x, cases y, simp_all) |
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next |
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case goal4 thus ?case by(cases y, cases x, simp_all) |
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next |
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case goal5 thus ?case by(cases z, cases y, cases x, simp_all) |
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next |
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case goal6 thus ?case by(simp add: Top_cval_def) |
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qed |
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end |
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55599
6535c537b243
aggiornamento for "interpretation with definitions": operate uniformly on theory and locale level under the brand of "permanent interpretation"
haftmann
parents:
52046
diff
changeset
|
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permanent_interpretation Rep rep_cval |
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proof |
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case goal1 thus ?case |
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by(cases a, cases b, simp, simp, cases b, simp, simp) |
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qed |
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||
55599
6535c537b243
aggiornamento for "interpretation with definitions": operate uniformly on theory and locale level under the brand of "permanent interpretation"
haftmann
parents:
52046
diff
changeset
|
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permanent_interpretation Val_abs rep_cval Const plus_cval |
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proof |
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case goal1 show ?case by simp |
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next |
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case goal2 thus ?case |
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by(cases a1, cases a2, simp, simp, cases a2, simp, simp) |
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qed |
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||
55599
6535c537b243
aggiornamento for "interpretation with definitions": operate uniformly on theory and locale level under the brand of "permanent interpretation"
haftmann
parents:
52046
diff
changeset
|
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permanent_interpretation Abs_Int rep_cval Const plus_cval "(iter' 3)" |
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defines AI_const is AI |
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and aval'_const is aval' |
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proof qed (auto simp: iter'_pfp_above) |
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text{* Straight line code: *} |
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definition "test1_const = |
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bc01725d7918
replaced `;' by `;;' to disambiguate syntax; unexpected slight increase in build time
nipkow
parents:
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changeset
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''y'' ::= N 7;; |
bc01725d7918
replaced `;' by `;;' to disambiguate syntax; unexpected slight increase in build time
nipkow
parents:
45200
diff
changeset
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''z'' ::= Plus (V ''y'') (N 2);; |
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''y'' ::= Plus (V ''x'') (N 0)" |
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text{* Conditional: *} |
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definition "test2_const = |
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IF Less (N 41) (V ''x'') THEN ''x'' ::= N 5 ELSE ''x'' ::= N 5" |
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text{* Conditional, test is ignored: *} |
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definition "test3_const = |
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bc01725d7918
replaced `;' by `;;' to disambiguate syntax; unexpected slight increase in build time
nipkow
parents:
45200
diff
changeset
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''x'' ::= N 42;; |
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IF Less (N 41) (V ''x'') THEN ''x'' ::= N 5 ELSE ''x'' ::= N 6" |
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text{* While: *} |
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definition "test4_const = |
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52046
bc01725d7918
replaced `;' by `;;' to disambiguate syntax; unexpected slight increase in build time
nipkow
parents:
45200
diff
changeset
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''x'' ::= N 0;; WHILE Bc True DO ''x'' ::= N 0" |
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text{* While, test is ignored: *} |
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definition "test5_const = |
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52046
bc01725d7918
replaced `;' by `;;' to disambiguate syntax; unexpected slight increase in build time
nipkow
parents:
45200
diff
changeset
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''x'' ::= N 0;; WHILE Less (V ''x'') (N 1) DO ''x'' ::= N 1" |
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text{* Iteration is needed: *} |
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definition "test6_const = |
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52046
bc01725d7918
replaced `;' by `;;' to disambiguate syntax; unexpected slight increase in build time
nipkow
parents:
45200
diff
changeset
|
94 |
''x'' ::= N 0;; ''y'' ::= N 0;; ''z'' ::= N 2;; |
bc01725d7918
replaced `;' by `;;' to disambiguate syntax; unexpected slight increase in build time
nipkow
parents:
45200
diff
changeset
|
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WHILE Less (V ''x'') (N 1) DO (''x'' ::= V ''y'';; ''y'' ::= V ''z'')" |
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text{* More iteration would be needed: *} |
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definition "test7_const = |
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52046
bc01725d7918
replaced `;' by `;;' to disambiguate syntax; unexpected slight increase in build time
nipkow
parents:
45200
diff
changeset
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''x'' ::= N 0;; ''y'' ::= N 0;; ''z'' ::= N 0;; ''u'' ::= N 3;; |
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WHILE Less (V ''x'') (N 1) |
52046
bc01725d7918
replaced `;' by `;;' to disambiguate syntax; unexpected slight increase in build time
nipkow
parents:
45200
diff
changeset
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DO (''x'' ::= V ''y'';; ''y'' ::= V ''z'';; ''z'' ::= V ''u'')" |
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value [code] "list (AI_const test1_const Top)" |
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value [code] "list (AI_const test2_const Top)" |
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value [code] "list (AI_const test3_const Top)" |
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value [code] "list (AI_const test4_const Top)" |
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value [code] "list (AI_const test5_const Top)" |
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value [code] "list (AI_const test6_const Top)" |
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value [code] "list (AI_const test7_const Top)" |
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end |