src/Pure/Syntax/syn_trans.ML

+(*  Title:      Pure/Syntax/syn_trans.ML
+    ID:         $Id$
+    Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen
+
+Syntax translation functions.
+*)
+
+signature SYN_TRANS0 =
+sig
+  val eta_contract: bool ref
+  val mk_binder_tr: string * string -> string * (term list -> term)
+  val mk_binder_tr': string * string -> string * (term list -> term)
+  val dependent_tr': string * string -> term list -> term
+end;
+
+signature SYN_TRANS1 =
+sig
+  include SYN_TRANS0
+  structure Parser: PARSER
+  local open Parser.SynExt.Ast in
+    val constrainAbsC: string
+    val pure_trfuns:
+      (string * (ast list -> ast)) list *
+      (string * (term list -> term)) list *
+      (string * (term list -> term)) list *
+      (string * (ast list -> ast)) list
+  end
+end;
+
+signature SYN_TRANS =
+sig
+  include SYN_TRANS1
+  local open Parser Parser.SynExt Parser.SynExt.Ast in
+    val abs_tr': term -> term
+    val prop_tr': bool -> term -> term
+    val appl_ast_tr': ast * ast list -> ast
+    val pt_to_ast: (string -> (ast list -> ast) option) -> parsetree -> ast
+    val ast_to_term: (string -> (term list -> term) option) -> ast -> term
+  end
+end;
+
+functor SynTransFun(structure TypeExt: TYPE_EXT and Parser: PARSER
+  sharing TypeExt.SynExt = Parser.SynExt): SYN_TRANS =
+struct
+
+structure Parser = Parser;
+open TypeExt Parser.Lexicon Parser.SynExt.Ast Parser.SynExt Parser;
+
+
+(** parse (ast) translations **)
+
+(* application *)
+
+fun appl_ast_tr (*"_appl"*) [f, args] = Appl (f :: unfold_ast "_args" args)
+  | appl_ast_tr (*"_appl"*) asts = raise_ast "appl_ast_tr" asts;
+
+
+(* abstraction *)
+
+fun idtyp_ast_tr (*"_idtyp"*) [x, ty] = Appl [Constant constrainC, x, ty]
+  | idtyp_ast_tr (*"_idtyp"*) asts = raise_ast "idtyp_ast_tr" asts;
+
+fun lambda_ast_tr (*"_lambda"*) [idts, body] =
+      fold_ast_p "_abs" (unfold_ast "_idts" idts, body)
+  | lambda_ast_tr (*"_lambda"*) asts = raise_ast "lambda_ast_tr" asts;
+
+val constrainAbsC = "_constrainAbs";
+
+fun abs_tr (*"_abs"*) [Free (x, T), body] = absfree (x, T, body)
+  | abs_tr (*"_abs"*) (ts as [Const (c, _) $ Free (x, T) $ tT, body]) =
+      if c = constrainC
+        then const constrainAbsC $ absfree (x, T, body) $ tT
+      else raise_term "abs_tr" ts
+  | abs_tr (*"_abs"*) ts = raise_term "abs_tr" ts;
+
+
+(* nondependent abstraction *)
+
+fun k_tr (*"_K"*) [t] = Abs ("uu", dummyT, incr_boundvars 1 t)
+  | k_tr (*"_K"*) ts = raise_term "k_tr" ts;
+
+
+(* binder *)
+
+fun mk_binder_tr (sy, name) =
+  let
+    fun tr (Free (x, T), t) = const name $ absfree (x, T, t)
+      | tr (Const ("_idts", _) $ idt $ idts, t) = tr (idt, tr (idts, t))
+      | tr (t1 as Const (c, _) $ Free (x, T) $ tT, t) =
+          if c = constrainC then
+            const name $ (const constrainAbsC $ absfree (x, T, t) $ tT)
+          else raise_term "binder_tr" [t1, t]
+      | tr (t1, t2) = raise_term "binder_tr" [t1, t2];
+
+    fun binder_tr (*sy*) [idts, body] = tr (idts, body)
+      | binder_tr (*sy*) ts = raise_term "binder_tr" ts;
+  in
+    (sy, binder_tr)
+  end;
+
+
+(* meta propositions *)
+
+fun aprop_tr (*"_aprop"*) [t] = const constrainC $ t $ const "prop"
+  | aprop_tr (*"_aprop"*) ts = raise_term "aprop_tr" ts;
+
+fun ofclass_tr (*"_ofclass"*) [ty, cls] =
+      cls $ (const constrainC $ const "TYPE" $ (const "itself" $ ty))
+  | ofclass_tr (*"_ofclass"*) ts = raise_term "ofclass_tr" ts;
+
+
+(* meta implication *)
+
+fun bigimpl_ast_tr (*"_bigimpl"*) [asms, concl] =
+      fold_ast_p "==>" (unfold_ast "_asms" asms, concl)
+  | bigimpl_ast_tr (*"_bigimpl"*) asts = raise_ast "bigimpl_ast_tr" asts;
+
+
+(* explode atoms *)
+
+fun explode_tr (*"_explode"*) (ts as [consC, nilC, bit0, bit1, txt]) =
+      let
+        fun mk_list [] = nilC
+          | mk_list (t :: ts) = consC $ t $ mk_list ts;
+
+        fun encode_bit 0 = bit0
+          | encode_bit 1 = bit1
+          | encode_bit _ = sys_error "encode_bit";
+
+        fun encode_char c =   (* FIXME leading 0s (?) *)
+          mk_list (map encode_bit (radixpand (2, (ord c))));
+
+        val str =
+          (case txt of
+            Free (s, _) => s
+          | Const (s, _) => s
+          | _ => raise_term "explode_tr" ts);
+      in
+        mk_list (map encode_char (explode str))
+      end
+  | explode_tr (*"_explode"*) ts = raise_term "explode_tr" ts;
+
+
+
+(** print (ast) translations **)
+
+(* application *)
+
+fun appl_ast_tr' (f, []) = raise_ast "appl_ast_tr'" [f]
+  | appl_ast_tr' (f, args) = Appl [Constant "_appl", f, fold_ast "_args" args];
+
+
+(* abstraction *)
+
+fun strip_abss vars_of body_of tm =
+  let
+    val vars = vars_of tm;
+    val body = body_of tm;
+    val rev_new_vars = rename_wrt_term body vars;
+  in
+    (map Free (rev rev_new_vars),
+      subst_bounds (map (free o #1) rev_new_vars, body))
+  end;
+
+(*do (partial) eta-contraction before printing*)
+
+val eta_contract = ref false;
+
+fun eta_contr tm =
+  let
+    fun eta_abs (Abs (a, T, t)) =
+          (case eta_abs t of
+            t' as f $ u =>
+              (case eta_abs u of
+                Bound 0 =>
+                  if not (0 mem loose_bnos f) then incr_boundvars ~1 f
+                  else Abs (a, T, t')
+              | _ => Abs (a, T, t'))
+          | t' => Abs (a, T, t'))
+      | eta_abs t = t;
+  in
+    if ! eta_contract then eta_abs tm else tm
+  end;
+
+
+fun abs_tr' tm =
+  foldr (fn (x, t) => const "_abs" $ x $ t)
+    (strip_abss strip_abs_vars strip_abs_body (eta_contr tm));
+
+
+fun abs_ast_tr' (*"_abs"*) asts =
+  (case unfold_ast_p "_abs" (Appl (Constant "_abs" :: asts)) of
+    ([], _) => raise_ast "abs_ast_tr'" asts
+  | (xs, body) => Appl [Constant "_lambda", fold_ast "_idts" xs, body]);
+
+
+(* binder *)
+
+fun mk_binder_tr' (name, sy) =
+  let
+    fun mk_idts [] = raise Match    (*abort translation*)
+      | mk_idts [idt] = idt
+      | mk_idts (idt :: idts) = const "_idts" $ idt $ mk_idts idts;
+
+    fun tr' t =
+      let
+        val (xs, bd) = strip_abss (strip_qnt_vars name) (strip_qnt_body name) t;
+      in
+        const sy $ mk_idts xs $ bd
+      end;
+
+    fun binder_tr' (*name*) (t :: ts) =
+          list_comb (tr' (const name $ t), ts)
+      | binder_tr' (*name*) [] = raise Match;
+  in
+    (name, binder_tr')
+  end;
+
+
+(* idts *)
+
+fun idts_ast_tr' (*"_idts"*) [Appl [Constant c, x, ty], xs] =
+      if c = constrainC then
+        Appl [Constant "_idts", Appl [Constant "_idtyp", x, ty], xs]
+      else raise Match
+  | idts_ast_tr' (*"_idts"*) _ = raise Match;
+
+
+(* meta propositions *)
+
+fun prop_tr' show_sorts tm =
+  let
+    fun aprop t = const "_aprop" $ t;
+
+    fun is_prop tys t =
+      fastype_of1 (tys, t) = propT handle TERM _ => false;
+
+    fun tr' _ (t as Const _) = t
+      | tr' _ (t as Free (x, ty)) =
+          if ty = propT then aprop (free x) else t
+      | tr' _ (t as Var (xi, ty)) =
+          if ty = propT then aprop (var xi) else t
+      | tr' tys (t as Bound _) =
+          if is_prop tys t then aprop t else t
+      | tr' tys (Abs (x, ty, t)) = Abs (x, ty, tr' (ty :: tys) t)
+      | tr' tys (t as t1 $ (t2 as Const ("TYPE", Type ("itself", [ty])))) =
+          if is_prop tys t then
+            const "_ofclass" $ term_of_typ show_sorts ty $ tr' tys t1
+          else tr' tys t1 $ tr' tys t2
+      | tr' tys (t as t1 $ t2) =
+          (if is_Const (head_of t) orelse not (is_prop tys t)
+            then I else aprop) (tr' tys t1 $ tr' tys t2);
+  in
+    tr' [] tm
+  end;
+
+
+(* meta implication *)
+
+fun impl_ast_tr' (*"==>"*) asts =
+  (case unfold_ast_p "==>" (Appl (Constant "==>" :: asts)) of
+    (asms as _ :: _ :: _, concl)
+      => Appl [Constant "_bigimpl", fold_ast "_asms" asms, concl]
+  | _ => raise Match);
+
+
+(* dependent / nondependent quantifiers *)
+
+fun dependent_tr' (q, r) (A :: Abs (x, T, B) :: ts) =
+      if 0 mem (loose_bnos B) then
+        let val (x', B') = variant_abs (x, dummyT, B);
+        in list_comb (const q $ Free (x', T) $ A $ B', ts) end
+      else list_comb (const r $ A $ B, ts)
+  | dependent_tr' _ _ = raise Match;
+
+
+(* implode atoms *)
+
+fun implode_ast_tr' (*"_implode"*) (asts as [Constant cons_name, nilC,
+    bit0, bit1, bitss]) =
+      let
+        fun err () = raise_ast "implode_ast_tr'" asts;
+
+        fun strip_list lst =
+          let val (xs, y) = unfold_ast_p cons_name lst
+          in if y = nilC then xs else err ()
+          end;
+
+        fun decode_bit bit =
+          if bit = bit0 then "0"
+          else if bit = bit1 then "1"
+          else err ();
+
+        fun decode_char bits =
+          chr (#1 (scan_radixint (2, map decode_bit (strip_list bits))));
+      in
+        Variable (implode (map decode_char (strip_list bitss)))
+      end
+  | implode_ast_tr' (*"_implode"*) asts = raise_ast "implode_ast_tr'" asts;
+
+
+
+(** pure_trfuns **)
+
+val pure_trfuns =
+ ([(applC, appl_ast_tr), ("_lambda", lambda_ast_tr), ("_idtyp", idtyp_ast_tr),
+    ("_bigimpl", bigimpl_ast_tr)],
+  [("_abs", abs_tr), ("_aprop", aprop_tr), ("_ofclass", ofclass_tr),
+    ("_K", k_tr), ("_explode", explode_tr)],
+  [],
+  [("_abs", abs_ast_tr'), ("_idts", idts_ast_tr'), ("==>", impl_ast_tr'),
+    ("_implode", implode_ast_tr')]);
+
+
+
+(** pt_to_ast **)
+
+fun pt_to_ast trf pt =
+  let
+    fun trans a args =
+      (case trf a of
+        None => mk_appl (Constant a) args
+      | Some f => f args handle exn
+          => (writeln ("Error in parse ast translation for " ^ quote a); raise exn));
+
+    fun ast_of (Node (a, pts)) = trans a (map ast_of pts)
+      | ast_of (Tip tok) = Variable (str_of_token tok);
+  in
+    ast_of pt
+  end;
+
+
+
+(** ast_to_term **)
+
+fun ast_to_term trf ast =
+  let
+    fun trans a args =
+      (case trf a of
+        None => list_comb (const a, args)
+      | Some f => f args handle exn
+          => (writeln ("Error in parse translation for " ^ quote a); raise exn));
+
+    fun term_of (Constant a) = trans a []
+      | term_of (Variable x) = scan_var x
+      | term_of (Appl (Constant a :: (asts as _ :: _))) =
+          trans a (map term_of asts)
+      | term_of (Appl (ast :: (asts as _ :: _))) =
+          list_comb (term_of ast, map term_of asts)
+      | term_of (ast as Appl _) = raise_ast "ast_to_term: malformed ast" [ast];
+  in
+    term_of ast
+  end;
+
+
+end;
+