section \<open>Concrete Syntax\<close>
theory RG_Syntax
imports RG_Hoare Quote_Antiquote
begin
abbreviation Skip :: "'a com" (\<open>SKIP\<close>)
where "SKIP \<equiv> Basic id"
notation Seq (\<open>(_;;/ _)\<close> [60,61] 60)
syntax
"_Assign" :: "idt \<Rightarrow> 'b \<Rightarrow> 'a com" (\<open>(\<acute>_ :=/ _)\<close> [70, 65] 61)
"_Cond" :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a com \<Rightarrow> 'a com" (\<open>(0IF _/ THEN _/ ELSE _/FI)\<close> [0, 0, 0] 61)
"_Cond2" :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a com" (\<open>(0IF _ THEN _ FI)\<close> [0,0] 56)
"_While" :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a com" (\<open>(0WHILE _ /DO _ /OD)\<close> [0, 0] 61)
"_Await" :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a com" (\<open>(0AWAIT _ /THEN /_ /END)\<close> [0,0] 61)
"_Atom" :: "'a com \<Rightarrow> 'a com" (\<open>(\<langle>_\<rangle>)\<close> 61)
"_Wait" :: "'a bexp \<Rightarrow> 'a com" (\<open>(0WAIT _ END)\<close> 61)
translations
"\<acute>x := a" \<rightharpoonup> "CONST Basic \<guillemotleft>\<acute>(_update_name x (\<lambda>_. a))\<guillemotright>"
"IF b THEN c1 ELSE c2 FI" \<rightharpoonup> "CONST Cond \<lbrace>b\<rbrace> c1 c2"
"IF b THEN c FI" \<rightleftharpoons> "IF b THEN c ELSE SKIP FI"
"WHILE b DO c OD" \<rightharpoonup> "CONST While \<lbrace>b\<rbrace> c"
"AWAIT b THEN c END" \<rightleftharpoons> "CONST Await \<lbrace>b\<rbrace> c"
"\<langle>c\<rangle>" \<rightleftharpoons> "AWAIT CONST True THEN c END"
"WAIT b END" \<rightleftharpoons> "AWAIT b THEN SKIP END"
nonterminal prgs
syntax
"_PAR" :: "prgs \<Rightarrow> 'a" (\<open>COBEGIN//_//COEND\<close> 60)
"_prg" :: "'a \<Rightarrow> prgs" (\<open>_\<close> 57)
"_prgs" :: "['a, prgs] \<Rightarrow> prgs" (\<open>_//\<parallel>//_\<close> [60,57] 57)
translations
"_prg a" \<rightharpoonup> "[a]"
"_prgs a ps" \<rightharpoonup> "a # ps"
"_PAR ps" \<rightharpoonup> "ps"
syntax
"_prg_scheme" :: "['a, 'a, 'a, 'a] \<Rightarrow> prgs" (\<open>SCHEME [_ \<le> _ < _] _\<close> [0,0,0,60] 57)
translations
"_prg_scheme j i k c" \<rightleftharpoons> "(CONST map (\<lambda>i. c) [j..<k])"
text \<open>Translations for variables before and after a transition:\<close>
syntax
"_before" :: "id \<Rightarrow> 'a" (\<open>\<ordmasculine>_\<close>)
"_after" :: "id \<Rightarrow> 'a" (\<open>\<ordfeminine>_\<close>)
translations
"\<ordmasculine>x" \<rightleftharpoons> "x \<acute>CONST fst"
"\<ordfeminine>x" \<rightleftharpoons> "x \<acute>CONST snd"
print_translation \<open>
let
fun quote_tr' f (t :: ts) =
Term.list_comb (f $ Syntax_Trans.quote_tr' \<^syntax_const>\<open>_antiquote\<close> t, ts)
| quote_tr' _ _ = raise Match;
val assert_tr' = quote_tr' (Syntax.const \<^syntax_const>\<open>_Assert\<close>);
fun bexp_tr' name ((Const (\<^const_syntax>\<open>Collect\<close>, _) $ t) :: ts) =
quote_tr' (Syntax.const name) (t :: ts)
| bexp_tr' _ _ = raise Match;
fun assign_tr' (Abs (x, _, f $ k $ Bound 0) :: ts) =
quote_tr' (Syntax.const \<^syntax_const>\<open>_Assign\<close> $ Syntax_Trans.update_name_tr' f)
(Abs (x, dummyT, Syntax_Trans.const_abs_tr' k) :: ts)
| assign_tr' _ = raise Match;
in
[(\<^const_syntax>\<open>Collect\<close>, K assert_tr'),
(\<^const_syntax>\<open>Basic\<close>, K assign_tr'),
(\<^const_syntax>\<open>Cond\<close>, K (bexp_tr' \<^syntax_const>\<open>_Cond\<close>)),
(\<^const_syntax>\<open>While\<close>, K (bexp_tr' \<^syntax_const>\<open>_While\<close>))]
end
\<close>
end