src/HOL/IMP/Collecting_list.thy

 imports ACom
 begin
 
 subsection "Executable Collecting Semantics on lists"
 
-fun step_cs :: "state list \<Rightarrow> state list acom \<Rightarrow> state list acom" where
-"step_cs S (SKIP {P}) = (SKIP {S})" |
-"step_cs S (x ::= e {P}) =
+fun step :: "state list \<Rightarrow> state list acom \<Rightarrow> state list acom" where
+"step S (SKIP {P}) = (SKIP {S})" |
+"step S (x ::= e {P}) =
   (x ::= e {[s(x := aval e s). s \<leftarrow> S]})" |
-"step_cs S (c1; c2) = step_cs S c1; step_cs (post c1) c2" |
-"step_cs S (IF b THEN c1 ELSE c2 {P}) =
-   IF b THEN step_cs [s \<leftarrow> S. bval b s] c1 ELSE step_cs [s\<leftarrow>S. \<not> bval b s] c2
+"step S (c1; c2) = step S c1; step (post c1) c2" |
+"step S (IF b THEN c1 ELSE c2 {P}) =
+   IF b THEN step [s \<leftarrow> S. bval b s] c1 ELSE step [s\<leftarrow>S. \<not> bval b s] c2
    {post c1 @ post c2}" |
-"step_cs S ({Inv} WHILE b DO c {P}) =
-  {S @ post c} WHILE b DO (step_cs [s\<leftarrow>Inv. bval b s] c) {[s\<leftarrow>Inv. \<not> bval b s]}"
+"step S ({Inv} WHILE b DO c {P}) =
+  {S @ post c} WHILE b DO (step [s\<leftarrow>Inv. bval b s] c) {[s\<leftarrow>Inv. \<not> bval b s]}"
 
 definition "c = WHILE Less (V ''x'') (N 2) DO ''x'' ::= Plus (V ''x'') (N 1)"
 definition "c0 = anno [] c"
 
 definition "show_acom xs = map_acom (map (show_state xs))"
 
-value "show_acom [''x''] (((step_cs [<>]) ^^ 6) c0)"
+text{* Collecting semantics: *}
+
+value "show_acom [''x''] (((step [<>]) ^^ 6) c0)"
+
+text{* Small step semantics: *}
+
+value "show_acom [''x''] (((step []) ^^ 5) (step [<>] c0))"
 
 end