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Datei: RG_Syntax.thy Sprache: Isabelle

Original von: Isabelle^©

section \<open>Concrete Syntax\<close>

theory RG_Syntax
imports RG_Hoare Quote_Antiquote
begin

abbreviation Skip :: "'a com"  ("SKIP")
  where "SKIP \ Basic id"

notation Seq  ("(_;;/ _)" [60,61] 60)

syntax
  "_Assign"    :: "idt \ 'b \ 'a com" ("(\_ :=/ _)" [70, 65] 61)
  "_Cond"      :: "'a bexp \ 'a com \ 'a com \ 'a com" ("(0IF _/ THEN _/ ELSE _/FI)" [0, 0, 0] 61)
  "_Cond2"     :: "'a bexp \ 'a com \ 'a com" ("(0IF _ THEN _ FI)" [0,0] 56)
  "_While"     :: "'a bexp \ 'a com \ 'a com" ("(0WHILE _ /DO _ /OD)" [0, 0] 61)
  "_Await"     :: "'a bexp \ 'a com \ 'a com" ("(0AWAIT _ /THEN /_ /END)" [0,0] 61)
  "_Atom"      :: "'a com \ 'a com" ("(\_\)" 61)
  "_Wait"      :: "'a bexp \ 'a com" ("(0WAIT _ END)" 61)

translations
  "\x := a" \ "CONST Basic \\(_update_name x (\_. a))\"
  "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"
  "\c\" \ "AWAIT CONST True THEN c END"
  "WAIT b END" \<rightleftharpoons> "AWAIT b THEN SKIP END"

nonterminal prgs

syntax
  "_PAR"        :: "prgs \ 'a" ("COBEGIN//_//COEND" 60)
  "_prg"        :: "'a \ prgs" ("_" 57)
  "_prgs"       :: "['a, prgs] \ prgs" ("_//\//_" [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] \ prgs" ("SCHEME [_ \ _ < _] _" [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 \ 'a" ("\_")
  "_after"  :: "id \ 'a" ("\_")

translations
  "\x" \ "x \CONST fst"
  "\x" \ "x \CONST snd"

print_translation \<open>
  let
    fun quote_tr' f (t :: ts) =
          Term.list_comb (f $ Syntax_Trans.quote_tr' \<^syntax_const>\_antiquote\ 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>\Collect\, _) $ 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>\_Assign\ $ 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

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