--- a/src/HOL/IMP/Collecting_Examples.thy Wed Mar 27 22:36:03 2013 +0100
+++ b/src/HOL/IMP/Collecting_Examples.thy Thu Mar 28 15:45:08 2013 +0100
@@ -1,46 +1,66 @@
theory Collecting_Examples
-imports Collecting
+imports Collecting Vars
begin
+subsection "Pretty printing state sets"
+
text{* Tweak code generation to work with sets of non-equality types: *}
declare insert_code[code del] union_coset_filter[code del]
lemma insert_code [code]: "insert x (set xs) = set (x#xs)"
by simp
-text{* In order to display commands annotated with state sets,
-states must be translated into a printable format as sets of pairs,
-for a given set of variable names. This is what @{text show_acom} does: *}
+text{* Collect variables in acom: *}
+fun cvars :: "'a acom \<Rightarrow> vname set" where
+"cvars (SKIP {P})= {}" |
+"cvars (x::=e {P}) = {x} \<union> vars e" |
+"cvars (c1;c2) = cvars c1 \<union> cvars c2" |
+"cvars (IF b THEN {P1} c1 ELSE {P2} c2 {Q}) = vars b \<union> cvars c1 \<union> cvars c2" |
+"cvars ({I} WHILE b DO {P} c {Q}) = vars b \<union> cvars c"
+
+text{* Compensate for the fact that sets may now have duplicates: *}
+definition compact :: "'a set \<Rightarrow> 'a set" where
+"compact X = X"
+
+lemma [code]: "compact(set xs) = set(remdups xs)"
+by(simp add: compact_def)
+
+definition "vars_acom = compact o cvars"
+
+text{* In order to display commands annotated with state sets, states must be
+translated into a printable format as sets of variable-state pairs, for the
+variables in the command: *}
definition show_acom ::
- "vname set \<Rightarrow> state set acom \<Rightarrow> (vname*val)set set acom" where
-"show_acom X = map_acom (\<lambda>S. (\<lambda>s. (\<lambda>x. (x, s x)) ` X) ` S)"
+ "state set acom \<Rightarrow> (vname*val)set set acom" where
+"show_acom C = map_acom (\<lambda>S. (\<lambda>s. (\<lambda>x. (x, s x)) ` (vars_acom C)) ` S) C"
-text{* The example: *}
-definition "c = WHILE Less (V ''x'') (N 3)
+subsection "Examples"
+
+definition "c0 = WHILE Less (V ''x'') (N 3)
DO ''x'' ::= Plus (V ''x'') (N 2)"
-definition C0 :: "state set acom" where "C0 = anno {} c"
+definition C0 :: "state set acom" where "C0 = anno {} c0"
text{* Collecting semantics: *}
-value "show_acom {''x''} (((step {<>}) ^^ 1) C0)"
-value "show_acom {''x''} (((step {<>}) ^^ 2) C0)"
-value "show_acom {''x''} (((step {<>}) ^^ 3) C0)"
-value "show_acom {''x''} (((step {<>}) ^^ 4) C0)"
-value "show_acom {''x''} (((step {<>}) ^^ 5) C0)"
-value "show_acom {''x''} (((step {<>}) ^^ 6) C0)"
-value "show_acom {''x''} (((step {<>}) ^^ 7) C0)"
-value "show_acom {''x''} (((step {<>}) ^^ 8) C0)"
+value "show_acom (((step {<>}) ^^ 1) C0)"
+value "show_acom (((step {<>}) ^^ 2) C0)"
+value "show_acom (((step {<>}) ^^ 3) C0)"
+value "show_acom (((step {<>}) ^^ 4) C0)"
+value "show_acom (((step {<>}) ^^ 5) C0)"
+value "show_acom (((step {<>}) ^^ 6) C0)"
+value "show_acom (((step {<>}) ^^ 7) C0)"
+value "show_acom (((step {<>}) ^^ 8) C0)"
text{* Small-step semantics: *}
-value "show_acom {''x''} (((step {}) ^^ 0) (step {<>} C0))"
-value "show_acom {''x''} (((step {}) ^^ 1) (step {<>} C0))"
-value "show_acom {''x''} (((step {}) ^^ 2) (step {<>} C0))"
-value "show_acom {''x''} (((step {}) ^^ 3) (step {<>} C0))"
-value "show_acom {''x''} (((step {}) ^^ 4) (step {<>} C0))"
-value "show_acom {''x''} (((step {}) ^^ 5) (step {<>} C0))"
-value "show_acom {''x''} (((step {}) ^^ 6) (step {<>} C0))"
-value "show_acom {''x''} (((step {}) ^^ 7) (step {<>} C0))"
-value "show_acom {''x''} (((step {}) ^^ 8) (step {<>} C0))"
+value "show_acom (((step {}) ^^ 0) (step {<>} C0))"
+value "show_acom (((step {}) ^^ 1) (step {<>} C0))"
+value "show_acom (((step {}) ^^ 2) (step {<>} C0))"
+value "show_acom (((step {}) ^^ 3) (step {<>} C0))"
+value "show_acom (((step {}) ^^ 4) (step {<>} C0))"
+value "show_acom (((step {}) ^^ 5) (step {<>} C0))"
+value "show_acom (((step {}) ^^ 6) (step {<>} C0))"
+value "show_acom (((step {}) ^^ 7) (step {<>} C0))"
+value "show_acom (((step {}) ^^ 8) (step {<>} C0))"
end