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subsection "Collecting Semantics Examples"
theory Collecting_Examples
imports Collecting Vars
begin
subsubsection "Pretty printing state sets"
text\<open>Tweak code generation to work with sets of non-equality types:\<close>
declare insert_code[code del] union_coset_filter[code del]
lemma insert_code [code]: "insert x (set xs) = set (x#xs)"
by simp
text\<open>Compensate for the fact that sets may now have duplicates:\<close>
definition compact :: "'a set \ 'a set" where
"compact X = X"
lemma [code]: "compact(set xs) = set(remdups xs)"
by(simp add: compact_def)
definition "vars_acom = compact o vars o strip"
text\<open>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:\<close>
definition show_acom :: "state set acom \ (vname*val)set set acom" where
"show_acom C =
annotate (\<lambda>p. (\<lambda>s. (\<lambda>x. (x, s x)) ` (vars_acom C)) ` anno C p) (strip C)"
subsubsection "Examples"
definition "c0 = WHILE Less (V ''x'') (N 3)
DO ''x'' ::= Plus (V ''x'') (N 2)"
definition C0 :: "state set acom" where "C0 = annotate (\p. {}) c0"
text\<open>Collecting semantics:\<close>
value "show_acom (((step {<>}) ^^ 0) 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\<open>Small-step semantics:\<close>
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
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