--- a/src/HOL/IMP/Abs_Int_Den/Abs_Int0_const.thy Wed Sep 28 08:51:55 2011 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,111 +0,0 @@
-(* Author: Tobias Nipkow *)
-
-theory Abs_Int0_const
-imports Abs_Int0
-begin
-
-subsection "Constant Propagation"
-
-datatype cval = Const val | Any
-
-fun rep_cval where
-"rep_cval (Const n) = {n}" |
-"rep_cval (Any) = UNIV"
-
-fun plus_cval where
-"plus_cval (Const m) (Const n) = Const(m+n)" |
-"plus_cval _ _ = Any"
-
-instantiation cval :: SL_top
-begin
-
-fun le_cval where
-"_ \<sqsubseteq> Any = True" |
-"Const n \<sqsubseteq> Const m = (n=m)" |
-"Any \<sqsubseteq> Const _ = False"
-
-fun join_cval where
-"Const m \<squnion> Const n = (if n=m then Const m else Any)" |
-"_ \<squnion> _ = Any"
-
-definition "Top = Any"
-
-instance
-proof
- case goal1 thus ?case by (cases x) simp_all
-next
- case goal2 thus ?case by(cases z, cases y, cases x, simp_all)
-next
- case goal3 thus ?case by(cases x, cases y, simp_all)
-next
- case goal4 thus ?case by(cases y, cases x, simp_all)
-next
- case goal5 thus ?case by(cases z, cases y, cases x, simp_all)
-next
- case goal6 thus ?case by(simp add: Top_cval_def)
-qed
-
-end
-
-interpretation Rep rep_cval
-proof
- case goal1 thus ?case
- by(cases a, cases b, simp, simp, cases b, simp, simp)
-qed
-
-interpretation Val_abs rep_cval Const plus_cval
-proof
- case goal1 show ?case by simp
-next
- case goal2 thus ?case
- by(cases a1, cases a2, simp, simp, cases a2, simp, simp)
-qed
-
-interpretation Abs_Int rep_cval Const plus_cval "(iter' 3)"
-defines AI_const is AI
-and aval'_const is aval'
-proof qed (auto simp: iter'_pfp_above)
-
-text{* Straight line code: *}
-definition "test1_const =
- ''y'' ::= N 7;
- ''z'' ::= Plus (V ''y'') (N 2);
- ''y'' ::= Plus (V ''x'') (N 0)"
-
-text{* Conditional: *}
-definition "test2_const =
- IF Less (N 41) (V ''x'') THEN ''x'' ::= N 5 ELSE ''x'' ::= N 5"
-
-text{* Conditional, test is ignored: *}
-definition "test3_const =
- ''x'' ::= N 42;
- IF Less (N 41) (V ''x'') THEN ''x'' ::= N 5 ELSE ''x'' ::= N 6"
-
-text{* While: *}
-definition "test4_const =
- ''x'' ::= N 0; WHILE B True DO ''x'' ::= N 0"
-
-text{* While, test is ignored: *}
-definition "test5_const =
- ''x'' ::= N 0; WHILE Less (V ''x'') (N 1) DO ''x'' ::= N 1"
-
-text{* Iteration is needed: *}
-definition "test6_const =
- ''x'' ::= N 0; ''y'' ::= N 0; ''z'' ::= N 2;
- WHILE Less (V ''x'') (N 1) DO (''x'' ::= V ''y''; ''y'' ::= V ''z'')"
-
-text{* More iteration would be needed: *}
-definition "test7_const =
- ''x'' ::= N 0; ''y'' ::= N 0; ''z'' ::= N 0; ''u'' ::= N 3;
- WHILE Less (V ''x'') (N 1)
- DO (''x'' ::= V ''y''; ''y'' ::= V ''z''; ''z'' ::= V ''u'')"
-
-value [code] "list (AI_const test1_const Top)"
-value [code] "list (AI_const test2_const Top)"
-value [code] "list (AI_const test3_const Top)"
-value [code] "list (AI_const test4_const Top)"
-value [code] "list (AI_const test5_const Top)"
-value [code] "list (AI_const test6_const Top)"
-value [code] "list (AI_const test7_const Top)"
-
-end