src/Pure/Syntax/syn_trans.ML
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Object logic specific operations.
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(*  Title:      Pure/Syntax/syn_trans.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen
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Syntax translation functions.
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*)
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signature SYN_TRANS0 =
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sig
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  val eta_contract: bool ref
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  val mk_binder_tr: string * string -> string * (term list -> term)
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  val mk_binder_tr': string * string -> string * (term list -> term)
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  val dependent_tr': string * string -> term list -> term
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  val quote_antiquote_tr: string -> string -> string -> string * (term list -> term)
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  val quote_antiquote_tr': string -> string -> string -> string * (term list -> term)
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  val mark_bound: string -> term
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  val mark_boundT: string * typ -> term
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  val variant_abs': string * typ * term -> string * term
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end;
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signature SYN_TRANS1 =
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sig
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  include SYN_TRANS0
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  val constrainAbsC: string
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  val pure_trfuns:
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      (string * (Ast.ast list -> Ast.ast)) list *
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      (string * (term list -> term)) list *
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      (string * (term list -> term)) list *
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      (string * (Ast.ast list -> Ast.ast)) list
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  val pure_trfunsT: (string * (bool -> typ -> term list -> term)) list
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end;
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signature SYN_TRANS =
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sig
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  include SYN_TRANS1
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  val abs_tr': term -> term
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  val prop_tr': term -> term
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  val appl_ast_tr': Ast.ast * Ast.ast list -> Ast.ast
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  val applC_ast_tr': Ast.ast * Ast.ast list -> Ast.ast
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  val pt_to_ast: (string -> (Ast.ast list -> Ast.ast) option) -> Parser.parsetree -> Ast.ast
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  val ast_to_term: (string -> (term list -> term) option) -> Ast.ast -> term
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end;
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structure SynTrans: SYN_TRANS =
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struct
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(** parse (ast) translations **)
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(* application *)
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fun appl_ast_tr [f, args] = Ast.Appl (f :: Ast.unfold_ast "_args" args)
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  | appl_ast_tr asts = raise Ast.AST ("appl_ast_tr", asts);
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fun applC_ast_tr [f, args] = Ast.Appl (f :: Ast.unfold_ast "_cargs" args)
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  | applC_ast_tr asts = raise Ast.AST ("applC_ast_tr", asts);
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(* abstraction *)
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fun idtyp_ast_tr (*"_idtyp"*) [x, ty] = Ast.Appl [Ast.Constant SynExt.constrainC, x, ty]
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  | idtyp_ast_tr (*"_idtyp"*) asts = raise Ast.AST ("idtyp_ast_tr", asts);
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fun lambda_ast_tr (*"_lambda"*) [pats, body] =
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      Ast.fold_ast_p "_abs" (Ast.unfold_ast "_pttrns" pats, body)
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  | lambda_ast_tr (*"_lambda"*) asts = raise Ast.AST ("lambda_ast_tr", asts);
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val constrainAbsC = "_constrainAbs";
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fun abs_tr (*"_abs"*) [Free (x, T), body] = Term.absfree (x, T, body)
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  | abs_tr (*"_abs"*) (ts as [Const (c, _) $ Free (x, T) $ tT, body]) =
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      if c = SynExt.constrainC
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        then Lexicon.const constrainAbsC $ Term.absfree (x, T, body) $ tT
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      else raise TERM ("abs_tr", ts)
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  | abs_tr (*"_abs"*) ts = raise TERM ("abs_tr", ts);
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(* nondependent abstraction *)
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fun k_tr (*"_K"*) [t] = Abs ("uu", dummyT, Term.incr_boundvars 1 t)
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  | k_tr (*"_K"*) ts = raise TERM ("k_tr", ts);
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(* binder *)
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fun mk_binder_tr (sy, name) =
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  let
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    fun tr (Free (x, T), t) = Lexicon.const name $ Term.absfree (x, T, t)
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      | tr (Const ("_idts", _) $ idt $ idts, t) = tr (idt, tr (idts, t))
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      | tr (t1 as Const (c, _) $ Free (x, T) $ tT, t) =
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          if c = SynExt.constrainC then
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            Lexicon.const name $ (Lexicon.const constrainAbsC $ Term.absfree (x, T, t) $ tT)
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          else raise TERM ("binder_tr", [t1, t])
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      | tr (t1, t2) = raise TERM ("binder_tr", [t1, t2]);
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    fun binder_tr (*sy*) [idts, body] = tr (idts, body)
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      | binder_tr (*sy*) ts = raise TERM ("binder_tr", ts);
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  in
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    (sy, binder_tr)
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  end;
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(* meta propositions *)
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fun aprop_tr (*"_aprop"*) [t] = Lexicon.const SynExt.constrainC $ t $ Lexicon.const "prop"
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  | aprop_tr (*"_aprop"*) ts = raise TERM ("aprop_tr", ts);
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fun ofclass_tr (*"_ofclass"*) [ty, cls] =
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      cls $ (Lexicon.const SynExt.constrainC $ Lexicon.const "TYPE" $
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        (Lexicon.const "itself" $ ty))
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  | ofclass_tr (*"_ofclass"*) ts = raise TERM ("ofclass_tr", ts);
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(* meta implication *)
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fun bigimpl_ast_tr (*"_bigimpl"*) [asms, concl] =
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      Ast.fold_ast_p "==>" (Ast.unfold_ast "_asms" asms, concl)
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  | bigimpl_ast_tr (*"_bigimpl"*) asts = raise Ast.AST ("bigimpl_ast_tr", asts);
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(* type reflection *)
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fun type_tr (*"_TYPE"*) [ty] =
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      Lexicon.const SynExt.constrainC $ Lexicon.const "TYPE" $ (Lexicon.const "itself" $ ty)
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  | type_tr (*"_TYPE"*) ts = raise TERM ("type_tr", ts);
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(* binds *)
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fun bind_ast_tr (*"_BIND"*) [Ast.Variable x] =
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      Ast.Variable (Lexicon.string_of_vname (Lexicon.binding x, 0))
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  | bind_ast_tr (*"_BIND"*) asts = raise Ast.AST ("bind_ast_tr", asts);
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(* quote / antiquote *)
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fun quote_antiquote_tr quoteN antiquoteN name =
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  let
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    fun antiquote_tr i ((a as Const (c, _)) $ t) =
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          if c = antiquoteN then t $ Bound i
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          else a $ antiquote_tr i t
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      | antiquote_tr i (t $ u) = antiquote_tr i t $ antiquote_tr i u
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      | antiquote_tr i (Abs (x, T, t)) = Abs (x, T, antiquote_tr (i + 1) t)
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      | antiquote_tr _ a = a;
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    fun quote_tr [t] = Lexicon.const name $
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          Abs ("uu", dummyT, antiquote_tr 0 (Term.incr_boundvars 1 t))
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      | quote_tr ts = raise TERM ("quote_tr", ts);
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  in (quoteN, quote_tr) end;
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(** print (ast) translations **)
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(* application *)
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fun appl_ast_tr' (f, []) = raise Ast.AST ("appl_ast_tr'", [f])
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  | appl_ast_tr' (f, args) = Ast.Appl [Ast.Constant "_appl", f, Ast.fold_ast "_args" args];
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fun applC_ast_tr' (f, []) = raise Ast.AST ("applC_ast_tr'", [f])
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  | applC_ast_tr' (f, args) = Ast.Appl [Ast.Constant "_applC", f, Ast.fold_ast "_cargs" args];
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(* abstraction *)
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fun mark_boundT x_T = Lexicon.const "_bound" $ Free x_T;
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fun mark_bound x = mark_boundT (x, dummyT);
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fun strip_abss vars_of body_of tm =
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  let
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    val vars = vars_of tm;
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    val body = body_of tm;
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    val rev_new_vars = rename_wrt_term body vars;
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  in
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    (map mark_boundT (rev rev_new_vars),
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      subst_bounds (map (mark_bound o #1) rev_new_vars, body))
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  end;
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(*do (partial) eta-contraction before printing*)
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val eta_contract = ref true;
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fun eta_contr tm =
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  let
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    fun is_aprop (Const ("_aprop", _)) = true
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      | is_aprop _ = false;
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    fun eta_abs (Abs (a, T, t)) =
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          (case eta_abs t of
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            t' as f $ u =>
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              (case eta_abs u of
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                Bound 0 =>
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                  if Term.loose_bvar1 (f, 0) orelse is_aprop f then Abs (a, T, t')
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                  else  incr_boundvars ~1 f
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              | _ => Abs (a, T, t'))
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          | t' => Abs (a, T, t'))
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      | eta_abs t = t;
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  in
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    if ! eta_contract then eta_abs tm else tm
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  end;
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fun abs_tr' tm =
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  foldr (fn (x, t) => Lexicon.const "_abs" $ x $ t)
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    (strip_abss strip_abs_vars strip_abs_body (eta_contr tm));
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fun abs_ast_tr' (*"_abs"*) asts =
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  (case Ast.unfold_ast_p "_abs" (Ast.Appl (Ast.Constant "_abs" :: asts)) of
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    ([], _) => raise Ast.AST ("abs_ast_tr'", asts)
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  | (xs, body) => Ast.Appl [Ast.Constant "_lambda", Ast.fold_ast "_pttrns" xs, body]);
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(* binder *)
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fun mk_binder_tr' (name, sy) =
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  let
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    fun mk_idts [] = raise Match    (*abort translation*)
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      | mk_idts [idt] = idt
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      | mk_idts (idt :: idts) = Lexicon.const "_idts" $ idt $ mk_idts idts;
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    fun tr' t =
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      let
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        val (xs, bd) = strip_abss (strip_qnt_vars name) (strip_qnt_body name) t;
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      in Lexicon.const sy $ mk_idts xs $ bd end;
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    fun binder_tr' (*name*) (t :: ts) = Term.list_comb (tr' (Lexicon.const name $ t), ts)
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      | binder_tr' (*name*) [] = raise Match;
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  in
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    (name, binder_tr')
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  end;
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(* idtyp constraints *)
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fun idtyp_ast_tr' a [Ast.Appl [Ast.Constant c, x, ty], xs] =
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      if c = SynExt.constrainC then
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        Ast.Appl [ Ast.Constant a,  Ast.Appl [Ast.Constant "_idtyp", x, ty], xs]
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      else raise Match
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  | idtyp_ast_tr' _ _ = raise Match;
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(* meta propositions *)
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fun prop_tr' tm =
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  let
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    fun aprop t = Lexicon.const "_aprop" $ t;
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    fun is_prop Ts t =
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      fastype_of1 (Ts, t) = propT handle TERM _ => false;
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    fun tr' _ (t as Const _) = t
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      | tr' _ (t as Free (x, T)) =
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          if T = propT then aprop (Lexicon.free x) else t
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      | tr' _ (t as Var (xi, T)) =
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          if T = propT then aprop (Lexicon.var xi) else t
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      | tr' Ts (t as Bound _) =
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          if is_prop Ts t then aprop t else t
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      | tr' Ts (Abs (x, T, t)) = Abs (x, T, tr' (T :: Ts) t)
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      | tr' Ts (t as t1 $ (t2 as Const ("TYPE", Type ("itself", [T])))) =
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          if is_prop Ts t then Const ("_mk_ofclass", T) $ tr' Ts t1
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          else tr' Ts t1 $ tr' Ts t2
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      | tr' Ts (t as t1 $ t2) =
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          (if is_Const (Term.head_of t) orelse not (is_prop Ts t)
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            then I else aprop) (tr' Ts t1 $ tr' Ts t2);
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  in
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    tr' [] tm
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  end;
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fun mk_ofclass_tr' show_sorts (*"_mk_ofclass"*) T [t] =
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      Lexicon.const "_ofclass" $ TypeExt.term_of_typ show_sorts T $ t
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  | mk_ofclass_tr' _ (*"_mk_ofclass"*) T ts = raise TYPE ("mk_ofclass_tr'", [T], ts);
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(* meta implication *)
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fun impl_ast_tr' (*"==>"*) asts =
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  (case Ast.unfold_ast_p "==>" (Ast.Appl (Ast.Constant "==>" :: asts)) of
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    (asms as _ :: _ :: _, concl)
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      => Ast.Appl [Ast.Constant "_bigimpl", Ast.fold_ast "_asms" asms, concl]
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  | _ => raise Match);
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(* type reflection *)
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fun type_tr' show_sorts (*"TYPE"*) (Type ("itself", [T])) ts =
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      Term.list_comb (Lexicon.const "_TYPE" $ TypeExt.term_of_typ show_sorts T, ts)
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  | type_tr' _ _ _ = raise Match;
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(* dependent / nondependent quantifiers *)
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fun variant_abs' (x, T, B) =
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  let val x' = variant (add_term_names (B, [])) x in
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    (x', subst_bound (mark_boundT (x', T), B))
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  end;
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fun dependent_tr' (q, r) (A :: Abs (x, T, B) :: ts) =
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      if Term.loose_bvar1 (B, 0) then
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        let val (x', B') = variant_abs' (x, dummyT, B);
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        in Term.list_comb (Lexicon.const q $ mark_boundT (x', T) $ A $ B', ts) end
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      else Term.list_comb (Lexicon.const r $ A $ B, ts)
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  | dependent_tr' _ _ = raise Match;
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(* quote / antiquote *)
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fun no_loose_bvar i t =
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  if Term.loose_bvar1 (t, i) then raise Match else t;
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fun quote_antiquote_tr' quoteN antiquoteN name =
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  let
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    fun antiquote_tr' i (t $ u) =
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          if u = Bound i then Lexicon.const antiquoteN $ no_loose_bvar i t
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          else antiquote_tr' i t $ antiquote_tr' i u
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      | antiquote_tr' i (Abs (x, T, t)) = Abs (x, T, antiquote_tr' (i + 1) t)
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      | antiquote_tr' i a = no_loose_bvar i a;
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    fun quote_tr' (Abs (x, T, t) :: ts) =
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          Term.list_comb ( Lexicon.const quoteN $ Term.incr_boundvars ~1 (antiquote_tr' 0 t), ts)
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      | quote_tr' _ = raise Match;
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  in (name, quote_tr') end;
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(** pure_trfuns **)
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val pure_trfuns =
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 ([("_appl", appl_ast_tr), ("_applC", applC_ast_tr),
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   ("_lambda", lambda_ast_tr), ("_idtyp", idtyp_ast_tr),
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   ("_bigimpl", bigimpl_ast_tr), ("_BIND", bind_ast_tr)],
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  [("_abs", abs_tr), ("_aprop", aprop_tr), ("_ofclass", ofclass_tr),
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   ("_TYPE", type_tr), ("_K", k_tr)],
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  []: (string * (term list -> term)) list,
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  [("_abs", abs_ast_tr'), ("_idts", idtyp_ast_tr' "_idts"),
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   ("_pttrns", idtyp_ast_tr' "_pttrns"), ("==>", impl_ast_tr')]);
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val pure_trfunsT =
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  [("_mk_ofclass", mk_ofclass_tr'), ("TYPE", type_tr')];
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(** pt_to_ast **)
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fun pt_to_ast trf pt =
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  let
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    fun trans a args =
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      (case trf a of
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        None => Ast.mk_appl (Ast.Constant a) args
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      | Some f => f args handle exn
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          => (writeln ("Error in parse ast translation for " ^ quote a);
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              raise exn));
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    (*translate pt bottom-up*)
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    fun ast_of (Parser.Node (a, pts)) = trans a (map ast_of pts)
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      | ast_of (Parser.Tip tok) = Ast.Variable (Lexicon.str_of_token tok);
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  in
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    ast_of pt
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  end;
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(** ast_to_term **)
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fun ast_to_term trf ast =
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  let
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    fun trans a args =
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      (case trf a of
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        None => Term.list_comb (Lexicon.const a, args)
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      | Some f => f args handle exn
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          => (writeln ("Error in parse translation for " ^ quote a);
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              raise exn));
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    fun term_of (Ast.Constant a) = trans a []
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      | term_of (Ast.Variable x) = Lexicon.read_var x
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      | term_of (Ast.Appl (Ast.Constant a :: (asts as _ :: _))) =
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          trans a (map term_of asts)
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      | term_of (Ast.Appl (ast :: (asts as _ :: _))) =
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          Term.list_comb (term_of ast, map term_of asts)
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      | term_of (ast as Ast.Appl _) = raise Ast.AST ("ast_to_term: malformed ast", [ast]);
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  in
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    term_of ast
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  end;
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end;