Quelle OG_Syntax.thy Sprache: Isabelle

theory OG_Syntax
imports OG_Tactics Quote_Antiquote
begin

text\<open>Syntax for commands and for assertions and boolean expressions in
commands \<open>com\<close> and annotated commands \<open>ann_com\<close>.\<close>

abbreviation Skip :: "'a com"  (\<open>SKIP\<close> 63)
  where "SKIP \ Basic id"

abbreviation AnnSkip :: "'a assn \ 'a ann_com" (\_//SKIP\ [90] 63)
  where "r SKIP \ AnnBasic r id"

notation
  Seq  (\<open>_,,/ _\<close> [55, 56] 55) and
  AnnSeq  (\<open>_;;/ _\<close> [60,61] 60)

syntax
  "_Assign"      :: "idt \ 'b \ 'a com" (\(\_ :=/ _)\ [70, 65] 61)
  "_AnnAssign"   :: "'a assn \ idt \ 'b \ 'a com" (\(_ \_ :=/ _)\ [90,70,65] 61)

translations
  "\x := a" \ "CONST Basic \\(_update_name x (\_. a))\"
  "r \x := a" \ "CONST AnnBasic r \\(_update_name x (\_. a))\"

syntax
  "_AnnCond1"    :: "'a assn \ 'a bexp \ 'a ann_com \ 'a ann_com \ 'a ann_com"
                    (\<open>_ //IF _ /THEN _ /ELSE _ /FI\<close>  [90,0,0,0] 61)
  "_AnnCond2"    :: "'a assn \ 'a bexp \ 'a ann_com \ 'a ann_com"
                    (\<open>_ //IF _ /THEN _ /FI\<close>  [90,0,0] 61)
  "_AnnWhile"    :: "'a assn \ 'a bexp \ 'a assn \ 'a ann_com \ 'a ann_com"
                    (\<open>_ //WHILE _ /INV _ //DO _//OD\<close>  [90,0,0,0] 61)
  "_AnnAwait"    :: "'a assn \ 'a bexp \ 'a com \ 'a ann_com"
                    (\<open>_ //AWAIT _ /THEN /_ /END\<close>  [90,0,0] 61)
  "_AnnAtom"     :: "'a assn \ 'a com \ 'a ann_com" (\_//\_\\ [90,0] 61)
  "_AnnWait"     :: "'a assn \ 'a bexp \ 'a ann_com" (\_//WAIT _ END\ [90,0] 61)

  "_Cond"        :: "'a bexp \ 'a com \ 'a com \ 'a com"
                                  (\<open>(0IF _/ THEN _/ ELSE _/ FI)\<close> [0, 0, 0] 61)
  "_Cond2"       :: "'a bexp \ 'a com \ 'a com" (\IF _ THEN _ FI\ [0,0] 56)
  "_While_inv"   :: "'a bexp \ 'a assn \ 'a com \ 'a com"
                    (\<open>(0WHILE _/ INV _ //DO _ /OD)\<close>  [0, 0, 0] 61)
  "_While"       :: "'a bexp \ 'a com \ 'a com"
                    (\<open>(0WHILE _ //DO _ /OD)\<close>  [0, 0] 61)

translations
  "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 INV i DO c OD" \<rightharpoonup> "CONST While \<lbrace>b\<rbrace> i c"
  "WHILE b DO c OD" \<rightleftharpoons> "WHILE b INV CONST undefined DO c OD"

  "r IF b THEN c1 ELSE c2 FI" \<rightharpoonup> "CONST AnnCond1 r \<lbrace>b\<rbrace> c1 c2"
  "r IF b THEN c FI" \<rightharpoonup> "CONST AnnCond2 r \<lbrace>b\<rbrace> c"
  "r WHILE b INV i DO c OD" \<rightharpoonup> "CONST AnnWhile r \<lbrace>b\<rbrace> i c"
  "r AWAIT b THEN c END" \<rightharpoonup> "CONST AnnAwait r \<lbrace>b\<rbrace> c"
  "r \c\" \ "r AWAIT CONST True THEN c END"
  "r WAIT b END" \<rightleftharpoons> "r AWAIT b THEN SKIP END"

nonterminal prgs

syntax
  "_PAR" :: "prgs \ 'a" (\COBEGIN//_//COEND\ [57] 56)
  "_prg" :: "['a, 'a] \ prgs" (\_//_\ [60, 90] 57)
  "_prgs" :: "['a, 'a, prgs] \ prgs" (\_//_//\//_\ [60,90,57] 57)

  "_prg_scheme" :: "['a, 'a, 'a, 'a, 'a] \ prgs"
                  (\<open>SCHEME [_ \<le> _ < _] _// _\<close> [0,0,0,60, 90] 57)

translations
  "_prg c q" \<rightleftharpoons> "[(CONST Some c, q)]"
  "_prgs c q ps" \<rightleftharpoons> "(CONST Some c, q) # ps"
  "_PAR ps" \<rightleftharpoons> "CONST Parallel ps"

  "_prg_scheme j i k c q" \<rightleftharpoons> "CONST map (\<lambda>i. (CONST Some c, q)) [j..<k]"

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;

    fun annquote_tr' f (r :: t :: ts) =
          Term.list_comb (f $ r $ Syntax_Trans.quote_tr' \<^syntax_const>\_antiquote\ t, ts)
      | annquote_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 annbexp_tr' name (r :: (Const (\<^const_syntax>\Collect\, _) $ t) :: ts) =
          annquote_tr' (Syntax.const name) (r :: t :: ts)
      | annbexp_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;

    fun annassign_tr' (r :: Abs (x, _, f $ k $ Bound 0) :: ts) =
          quote_tr' (Syntax.const \<^syntax_const>\_AnnAssign\ $ r $ Syntax_Trans.update_name_tr' f)
            (Abs (x, dummyT, Syntax_Trans.const_abs_tr' k) :: ts)
      | annassign_tr' _ = raise Match;

    fun Parallel_PAR [(Const (\<^const_syntax>\<open>Cons\<close>, _) $
            (Const (\<^const_syntax>\<open>Pair\<close>, _) $ (Const (\<^const_syntax>\<open>Some\<close>,_) $ t1 ) $ t2) $
            Const (\<^const_syntax>\<open>Nil\<close>, _))] = Syntax.const \<^syntax_const>\<open>_prg\<close> $ t1 $ t2
      | Parallel_PAR [(Const (\<^const_syntax>\<open>Cons\<close>, _) $
            (Const (\<^const_syntax>\<open>Pair\<close>, _) $ (Const (\<^const_syntax>\<open>Some\<close>, _) $ t1) $ t2) $ ts)] =
          Syntax.const \<^syntax_const>\<open>_prgs\<close> $ t1 $ t2 $ Parallel_PAR [ts]
      | Parallel_PAR _ = raise Match;

    fun Parallel_tr' ts = Syntax.const \<^syntax_const>\_PAR\ $ Parallel_PAR ts;
  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_inv\<close>)),
    (\<^const_syntax>\<open>AnnBasic\<close>, K annassign_tr'),
    (\<^const_syntax>\<open>AnnWhile\<close>, K (annbexp_tr' \<^syntax_const>\<open>_AnnWhile\<close>)),
    (\<^const_syntax>\<open>AnnAwait\<close>, K (annbexp_tr' \<^syntax_const>\<open>_AnnAwait\<close>)),
    (\<^const_syntax>\<open>AnnCond1\<close>, K (annbexp_tr' \<^syntax_const>\<open>_AnnCond1\<close>)),
    (\<^const_syntax>\<open>AnnCond2\<close>, K (annbexp_tr' \<^syntax_const>\<open>_AnnCond2\<close>))]
  end
\<close>

end

quality69%

¤ Dauer der Verarbeitung: 0.11 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.