section ‹Concrete Syntax›

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 (λ_. a))¬"
  "IF b THEN c1 ELSE c2 FI" ⇀ "CONST Cond {b} c1 c2"
  "IF b THEN c FI" ⇌ "IF b THEN c ELSE SKIP FI"
  "WHILE b DO c OD" ⇀ "CONST While {b} c"
  "AWAIT b THEN c END" ⇌ "CONST Await {b} c"
  "⟨c⟩" ⇌ "AWAIT CONST True THEN c END"
  "WAIT b END" ⇌ "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" ⇀ "[a]"
  "_prgs a ps" ⇀ "a # ps"
  "_PAR ps" ⇀ "ps"

syntax
  "_prg_scheme" :: "['a, 'a, 'a, 'a] → prgs"  (‹SCHEME [_ ≤ _ < _] _› [0,0,0,60] 57)

translations
  "_prg_scheme j i k c" ⇌ "(CONST map (λi. c) [j..<k])"

text ‹Translations for variables before and after a transition:›

syntax
  "_before" :: "id → 'a" (‹♂_›)
  "_after"  :: "id → 'a" (‹♀_›)

translations
  "♂x" ⇌ "x 🚫CONST fst"
  "♀x" ⇌ "x 🚫CONST snd"

print_translation ‹
 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‹_Assert›);

 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‹Collect›, K assert_tr'),
 (const_syntax‹Basic›, K assign_tr'),
 (const_syntax‹Cond›, K (bexp_tr' syntax_const‹_Cond›)),
 (const_syntax‹While›, K (bexp_tr' syntax_const‹_While›))]
 end
 ›

end