1 (* Title: Pure/Syntax/syn_trans.ML
3 Author: Tobias Nipkow and Markus Wenzel, TU Muenchen
5 Syntax translation functions.
10 val eta_contract: bool ref
11 val atomic_abs_tr': string * typ * term -> term * term
12 val mk_binder_tr: string * string -> string * (term list -> term)
13 val mk_binder_tr': string * string -> string * (term list -> term)
14 val dependent_tr': string * string -> term list -> term
15 val antiquote_tr: string -> term -> term
16 val quote_tr: string -> term -> term
17 val quote_antiquote_tr: string -> string -> string -> string * (term list -> term)
18 val antiquote_tr': string -> term -> term
19 val quote_tr': string -> term -> term
20 val quote_antiquote_tr': string -> string -> string -> string * (term list -> term)
21 val mark_bound: string -> term
22 val mark_boundT: string * typ -> term
23 val bound_vars: (string * typ) list -> term -> term
24 val variant_abs: string * typ * term -> string * term
25 val variant_abs': string * typ * term -> string * term
28 signature SYN_TRANS1 =
31 val non_typed_tr': (term list -> term) -> bool -> typ -> term list -> term
32 val non_typed_tr'': ('a -> term list -> term) -> 'a -> bool -> typ -> term list -> term
33 val constrainAbsC: string
35 (string * (Ast.ast list -> Ast.ast)) list *
36 (string * (term list -> term)) list *
37 (string * (term list -> term)) list *
38 (string * (Ast.ast list -> Ast.ast)) list
39 val pure_trfunsT: (string * (bool -> typ -> term list -> term)) list
40 val struct_trfuns: string list ->
41 (string * (Ast.ast list -> Ast.ast)) list *
42 (string * (term list -> term)) list *
43 (string * (bool -> typ -> term list -> term)) list *
44 (string * (Ast.ast list -> Ast.ast)) list
50 val abs_tr': term -> term
51 val prop_tr': term -> term
52 val appl_ast_tr': Ast.ast * Ast.ast list -> Ast.ast
53 val applC_ast_tr': Ast.ast * Ast.ast list -> Ast.ast
54 val pts_to_asts: Proof.context ->
55 (string -> (Proof.context -> Ast.ast list -> Ast.ast) option) ->
56 Parser.parsetree list -> Ast.ast list
57 val asts_to_terms: Proof.context ->
58 (string -> (Proof.context -> term list -> term) option) -> Ast.ast list -> term list
61 structure SynTrans: SYN_TRANS =
65 (** parse (ast) translations **)
69 fun constify_ast_tr [Ast.Variable c] = Ast.Constant c
70 | constify_ast_tr asts = raise Ast.AST ("constify_ast_tr", asts);
75 fun appl_ast_tr [f, args] = Ast.Appl (f :: Ast.unfold_ast "_args" args)
76 | appl_ast_tr asts = raise Ast.AST ("appl_ast_tr", asts);
78 fun applC_ast_tr [f, args] = Ast.Appl (f :: Ast.unfold_ast "_cargs" args)
79 | applC_ast_tr asts = raise Ast.AST ("applC_ast_tr", asts);
84 fun idtyp_ast_tr (*"_idtyp"*) [x, ty] = Ast.Appl [Ast.Constant "_constrain", x, ty]
85 | idtyp_ast_tr (*"_idtyp"*) asts = raise Ast.AST ("idtyp_ast_tr", asts);
87 fun idtypdummy_ast_tr (*"_idtypdummy"*) [ty] =
88 Ast.Appl [Ast.Constant "_constrain", Ast.Constant "_idtdummy", ty]
89 | idtypdummy_ast_tr (*"_idtypdummy"*) asts = raise Ast.AST ("idtyp_ast_tr", asts);
91 fun lambda_ast_tr (*"_lambda"*) [pats, body] =
92 Ast.fold_ast_p "_abs" (Ast.unfold_ast "_pttrns" pats, body)
93 | lambda_ast_tr (*"_lambda"*) asts = raise Ast.AST ("lambda_ast_tr", asts);
95 val constrainAbsC = "_constrainAbs";
97 fun absfree_proper (x, T, t) =
98 if can Name.dest_internal x then error ("Illegal internal variable in abstraction: " ^ quote x)
99 else Term.absfree (x, T, t);
101 fun abs_tr (*"_abs"*) [Free (x, T), t] = absfree_proper (x, T, t)
102 | abs_tr (*"_abs"*) [Const ("_idtdummy", T), t] = Term.absdummy (T, t)
103 | abs_tr (*"_abs"*) [Const ("_constrain", _) $ Free (x, T) $ tT, t] =
104 Lexicon.const constrainAbsC $ absfree_proper (x, T, t) $ tT
105 | abs_tr (*"_abs"*) [Const ("_constrain", _) $ Const ("_idtdummy", T) $ tT, t] =
106 Lexicon.const constrainAbsC $ Term.absdummy (T, t) $ tT
107 | abs_tr (*"_abs"*) ts = raise TERM ("abs_tr", ts);
112 fun mk_binder_tr (syn, name) =
114 fun tr (Free (x, T), t) = Lexicon.const name $ absfree_proper (x, T, t)
115 | tr (Const ("_idtdummy", T), t) = Lexicon.const name $ Term.absdummy (T, t)
116 | tr (Const ("_constrain", _) $ Free (x, T) $ tT, t) =
117 Lexicon.const name $ (Lexicon.const constrainAbsC $ absfree_proper (x, T, t) $ tT)
118 | tr (Const ("_constrain", _) $ Const ("_idtdummy", T) $ tT, t) =
119 Lexicon.const name $ (Lexicon.const constrainAbsC $ Term.absdummy (T, t) $ tT)
120 | tr (Const ("_idts", _) $ idt $ idts, t) = tr (idt, tr (idts, t))
121 | tr (t1, t2) = raise TERM ("binder_tr", [t1, t2]);
123 fun binder_tr [idts, body] = tr (idts, body)
124 | binder_tr ts = raise TERM ("binder_tr", ts);
125 in (syn, binder_tr) end;
128 (* meta propositions *)
130 fun aprop_tr (*"_aprop"*) [t] = Lexicon.const "_constrain" $ t $ Lexicon.const "prop"
131 | aprop_tr (*"_aprop"*) ts = raise TERM ("aprop_tr", ts);
133 fun ofclass_tr (*"_ofclass"*) [ty, cls] =
134 cls $ (Lexicon.const "_constrain" $ Lexicon.const "TYPE" $
135 (Lexicon.const "itself" $ ty))
136 | ofclass_tr (*"_ofclass"*) ts = raise TERM ("ofclass_tr", ts);
139 (* meta implication *)
141 fun bigimpl_ast_tr (*"_bigimpl"*) (asts as [asms, concl]) =
143 (case Ast.unfold_ast_p "_asms" asms of
144 (asms', Ast.Appl [Ast.Constant "_asm", asm']) => asms' @ [asm']
145 | _ => raise Ast.AST ("bigimpl_ast_tr", asts))
146 in Ast.fold_ast_p "==>" (prems, concl) end
147 | bigimpl_ast_tr (*"_bigimpl"*) asts = raise Ast.AST ("bigimpl_ast_tr", asts);
150 (* meta conjunction *)
152 fun conjunction_tr [t, u] = Lexicon.const "ProtoPure.conjunction" $ t $ u
153 | conjunction_tr ts = raise TERM ("conjunction_tr", ts);
156 (* type/term reflection *)
158 fun type_tr (*"_TYPE"*) [ty] =
159 Lexicon.const "_constrain" $ Lexicon.const "TYPE" $ (Lexicon.const "itself" $ ty)
160 | type_tr (*"_TYPE"*) ts = raise TERM ("type_tr", ts);
162 fun term_tr [t] = Lexicon.const "ProtoPure.term" $ t
163 | term_tr ts = raise TERM ("term_tr", ts);
168 fun dddot_tr (*"_DDDOT"*) ts = Term.list_comb (Lexicon.var SynExt.dddot_indexname, ts);
171 (* quote / antiquote *)
173 fun antiquote_tr name =
175 fun tr i ((t as Const (c, _)) $ u) =
176 if c = name then tr i u $ Bound i
178 | tr i (t $ u) = tr i t $ tr i u
179 | tr i (Abs (x, T, t)) = Abs (x, T, tr (i + 1) t)
183 fun quote_tr name t = Abs ("s", dummyT, antiquote_tr name (Term.incr_boundvars 1 t));
185 fun quote_antiquote_tr quoteN antiquoteN name =
187 fun tr [t] = Lexicon.const name $ quote_tr antiquoteN t
188 | tr ts = raise TERM ("quote_tr", ts);
194 fun struct_ast_tr (*"_struct"*) [Ast.Appl [Ast.Constant "_index", ast]] = ast
195 | struct_ast_tr (*"_struct"*) asts = Ast.mk_appl (Ast.Constant "_struct") asts;
197 fun index_ast_tr ast =
198 Ast.mk_appl (Ast.Constant "_index") [Ast.mk_appl (Ast.Constant "_struct") [ast]];
200 fun indexdefault_ast_tr (*"_indexdefault"*) [] =
201 index_ast_tr (Ast.Constant "_indexdefault")
202 | indexdefault_ast_tr (*"_indexdefault"*) asts =
203 raise Ast.AST ("indexdefault_ast_tr", asts);
205 fun indexnum_ast_tr (*"_indexnum"*) [ast] =
206 index_ast_tr (Ast.mk_appl (Ast.Constant "_indexnum") [ast])
207 | indexnum_ast_tr (*"_indexnum"*) asts = raise Ast.AST ("indexnum_ast_tr", asts);
209 fun indexvar_ast_tr (*"_indexvar"*) [] =
210 Ast.mk_appl (Ast.Constant "_index") [Ast.Variable "some_index"]
211 | indexvar_ast_tr (*"_indexvar"*) asts = raise Ast.AST ("indexvar_ast_tr", asts);
213 fun index_tr (*"_index"*) [t] = t
214 | index_tr (*"_index"*) ts = raise TERM ("index_tr", ts);
217 (* implicit structures *)
219 fun the_struct structs i =
220 if 1 <= i andalso i <= length structs then List.nth (structs, i - 1)
221 else raise error ("Illegal reference to implicit structure #" ^ string_of_int i);
223 fun struct_tr structs (*"_struct"*) [Const ("_indexdefault", _)] =
224 Lexicon.free (the_struct structs 1)
225 | struct_tr structs (*"_struct"*) [t as (Const ("_indexnum", _) $ Const (s, _))] =
226 Lexicon.free (the_struct structs
227 (case Lexicon.read_nat s of SOME n => n | NONE => raise TERM ("struct_tr", [t])))
228 | struct_tr _ (*"_struct"*) ts = raise TERM ("struct_tr", ts);
232 (** print (ast) translations **)
236 fun non_typed_tr' f _ _ ts = f ts;
237 fun non_typed_tr'' f x _ _ ts = f x ts;
242 fun appl_ast_tr' (f, []) = raise Ast.AST ("appl_ast_tr'", [f])
243 | appl_ast_tr' (f, args) = Ast.Appl [Ast.Constant "_appl", f, Ast.fold_ast "_args" args];
245 fun applC_ast_tr' (f, []) = raise Ast.AST ("applC_ast_tr'", [f])
246 | applC_ast_tr' (f, args) = Ast.Appl [Ast.Constant "_applC", f, Ast.fold_ast "_cargs" args];
251 fun mark_boundT (x, T) = Const ("_bound", T --> T) $ Free (x, T);
252 fun mark_bound x = mark_boundT (x, dummyT);
254 fun bound_vars vars body =
255 subst_bounds (map mark_boundT (Term.rename_wrt_term body vars), body);
257 fun strip_abss vars_of body_of tm =
259 val vars = vars_of tm;
260 val body = body_of tm;
261 val rev_new_vars = rename_wrt_term body vars;
263 if can Name.dest_internal x andalso not (Term.loose_bvar1 (b, 0))
264 then (Const ("_idtdummy", T), incr_boundvars ~1 b)
265 else (mark_boundT (x, T), Term.subst_bound (mark_bound x, b));
266 val (rev_vars', body') = fold_map subst rev_new_vars body;
267 in (rev rev_vars', body') end;
270 (*do (partial) eta-contraction before printing*)
272 val eta_contract = ref true;
276 fun is_aprop (Const ("_aprop", _)) = true
277 | is_aprop _ = false;
279 fun eta_abs (Abs (a, T, t)) =
284 if Term.loose_bvar1 (f, 0) orelse is_aprop f then Abs (a, T, t')
285 else incr_boundvars ~1 f
286 | _ => Abs (a, T, t'))
287 | t' => Abs (a, T, t'))
290 if ! eta_contract then eta_abs tm else tm
295 uncurry (fold_rev (fn x => fn t => Lexicon.const "_abs" $ x $ t))
296 (strip_abss strip_abs_vars strip_abs_body (eta_contr tm));
298 fun atomic_abs_tr' (x, T, t) =
299 let val [xT] = rename_wrt_term t [(x, T)]
300 in (mark_boundT xT, subst_bound (mark_bound (fst xT), t)) end;
302 fun abs_ast_tr' (*"_abs"*) asts =
303 (case Ast.unfold_ast_p "_abs" (Ast.Appl (Ast.Constant "_abs" :: asts)) of
304 ([], _) => raise Ast.AST ("abs_ast_tr'", asts)
305 | (xs, body) => Ast.Appl [Ast.Constant "_lambda", Ast.fold_ast "_pttrns" xs, body]);
310 fun mk_binder_tr' (name, syn) =
312 fun mk_idts [] = raise Match (*abort translation*)
313 | mk_idts [idt] = idt
314 | mk_idts (idt :: idts) = Lexicon.const "_idts" $ idt $ mk_idts idts;
318 val (xs, bd) = strip_abss (strip_qnt_vars name) (strip_qnt_body name) t;
319 in Lexicon.const syn $ mk_idts xs $ bd end;
321 fun binder_tr' (t :: ts) = Term.list_comb (tr' (Lexicon.const name $ t), ts)
322 | binder_tr' [] = raise Match;
323 in (name, binder_tr') end;
326 (* idtyp constraints *)
328 fun idtyp_ast_tr' a [Ast.Appl [Ast.Constant c, x, ty], xs] =
329 if c = "_constrain" then
330 Ast.Appl [ Ast.Constant a, Ast.Appl [Ast.Constant "_idtyp", x, ty], xs]
332 | idtyp_ast_tr' _ _ = raise Match;
335 (* meta propositions *)
339 fun aprop t = Lexicon.const "_aprop" $ t;
342 fastype_of1 (Ts, t) = propT handle TERM _ => false;
344 fun is_term (Const ("ProtoPure.term", _) $ _) = true
347 fun tr' _ (t as Const _) = t
348 | tr' Ts (t as Const ("_bound", _) $ u) =
349 if is_prop Ts u then aprop t else t
350 | tr' _ (t as Free (x, T)) =
351 if T = propT then aprop (Lexicon.free x) else t
352 | tr' _ (t as Var (xi, T)) =
353 if T = propT then aprop (Lexicon.var xi) else t
354 | tr' Ts (t as Bound _) =
355 if is_prop Ts t then aprop t else t
356 | tr' Ts (Abs (x, T, t)) = Abs (x, T, tr' (T :: Ts) t)
357 | tr' Ts (t as t1 $ (t2 as Const ("TYPE", Type ("itself", [T])))) =
358 if is_prop Ts t andalso not (is_term t) then Const ("_mk_ofclass", T) $ tr' Ts t1
359 else tr' Ts t1 $ tr' Ts t2
360 | tr' Ts (t as t1 $ t2) =
361 (if is_Const (Term.head_of t) orelse not (is_prop Ts t)
362 then I else aprop) (tr' Ts t1 $ tr' Ts t2);
365 fun mk_ofclass_tr' show_sorts (*"_mk_ofclass"*) T [t] =
366 Lexicon.const "_ofclass" $ TypeExt.term_of_typ show_sorts T $ t
367 | mk_ofclass_tr' _ (*"_mk_ofclass"*) T ts = raise TYPE ("mk_ofclass_tr'", [T], ts);
370 (* meta implication *)
372 fun impl_ast_tr' (*"==>"*) asts =
373 if TypeExt.no_brackets () then raise Match
375 (case Ast.unfold_ast_p "==>" (Ast.Appl (Ast.Constant "==>" :: asts)) of
376 (prems as _ :: _ :: _, concl) =>
378 val (asms, asm) = split_last prems;
379 val asms' = Ast.fold_ast_p "_asms" (asms, Ast.Appl [Ast.Constant "_asm", asm]);
380 in Ast.Appl [Ast.Constant "_bigimpl", asms', concl] end
384 (* type reflection *)
386 fun type_tr' show_sorts (*"TYPE"*) (Type ("itself", [T])) ts =
387 Term.list_comb (Lexicon.const "_TYPE" $ TypeExt.term_of_typ show_sorts T, ts)
388 | type_tr' _ _ _ = raise Match;
391 (* type constraints *)
393 fun type_constraint_tr' show_sorts (*"_type_constraint_"*) (Type ("fun", [T, _])) (t :: ts) =
394 Term.list_comb (Lexicon.const SynExt.constrainC $ t $ TypeExt.term_of_typ show_sorts T, ts)
395 | type_constraint_tr' _ _ _ = raise Match;
398 (* dependent / nondependent quantifiers *)
400 fun var_abs mark (x, T, b) =
401 let val ([x'], _) = Name.variants [x] (Term.declare_term_names b Name.context)
402 in (x', subst_bound (mark (x', T), b)) end;
404 val variant_abs = var_abs Free;
405 val variant_abs' = var_abs mark_boundT;
407 fun dependent_tr' (q, r) (A :: Abs (x, T, B) :: ts) =
408 if Term.loose_bvar1 (B, 0) then
409 let val (x', B') = variant_abs' (x, dummyT, B);
410 in Term.list_comb (Lexicon.const q $ mark_boundT (x', T) $ A $ B', ts) end
411 else Term.list_comb (Lexicon.const r $ A $ B, ts)
412 | dependent_tr' _ _ = raise Match;
415 (* quote / antiquote *)
417 fun antiquote_tr' name =
420 if u aconv Bound i then Lexicon.const name $ tr' i t
421 else tr' i t $ tr' i u
422 | tr' i (Abs (x, T, t)) = Abs (x, T, tr' (i + 1) t)
423 | tr' i a = if a aconv Bound i then raise Match else a;
426 fun quote_tr' name (Abs (_, _, t)) = Term.incr_boundvars ~1 (antiquote_tr' name t)
427 | quote_tr' _ _ = raise Match;
429 fun quote_antiquote_tr' quoteN antiquoteN name =
431 fun tr' (t :: ts) = Term.list_comb (Lexicon.const quoteN $ quote_tr' antiquoteN t, ts)
432 | tr' _ = raise Match;
438 fun index_ast_tr' (*"_index"*) [Ast.Appl [Ast.Constant "_struct", ast]] = ast
439 | index_ast_tr' _ = raise Match;
442 (* implicit structures *)
444 fun the_struct' structs s =
445 [(case Lexicon.read_nat s of
446 SOME i => Ast.Variable (the_struct structs i handle ERROR _ => raise Match)
447 | NONE => raise Match)] |> Ast.mk_appl (Ast.Constant "_free");
449 fun struct_ast_tr' structs (*"_struct"*) [Ast.Constant "_indexdefault"] =
450 the_struct' structs "1"
451 | struct_ast_tr' structs (*"_struct"*) [Ast.Appl [Ast.Constant "_indexnum", Ast.Constant s]] =
452 the_struct' structs s
453 | struct_ast_tr' _ _ = raise Match;
457 (** Pure translations **)
460 ([("_constify", constify_ast_tr), ("_appl", appl_ast_tr), ("_applC", applC_ast_tr),
461 ("_lambda", lambda_ast_tr), ("_idtyp", idtyp_ast_tr), ("_idtypdummy", idtypdummy_ast_tr),
462 ("_bigimpl", bigimpl_ast_tr), ("_indexdefault", indexdefault_ast_tr),
463 ("_indexnum", indexnum_ast_tr), ("_indexvar", indexvar_ast_tr), ("_struct", struct_ast_tr)],
464 [("_abs", abs_tr), ("_aprop", aprop_tr), ("_ofclass", ofclass_tr),
465 ("\\<^fixed>meta_conjunction", conjunction_tr), ("_TYPE", type_tr),
466 ("\\<^fixed>meta_term", term_tr), ("_DDDOT", dddot_tr), ("_index", index_tr)],
467 ([]: (string * (term list -> term)) list),
468 [("_abs", abs_ast_tr'), ("_idts", idtyp_ast_tr' "_idts"),
469 ("_pttrns", idtyp_ast_tr' "_pttrns"), ("==>", impl_ast_tr'),
470 ("_index", index_ast_tr')]);
473 [("_mk_ofclass", mk_ofclass_tr'), ("TYPE", type_tr'),
474 ("_type_constraint_", type_constraint_tr')];
476 fun struct_trfuns structs =
477 ([], [("_struct", struct_tr structs)], [], [("_struct", struct_ast_tr' structs)]);
483 fun pts_to_asts ctxt trf pts =
487 NONE => Ast.mk_appl (Ast.Constant a) args
488 | SOME f => transform_failure (fn exn =>
489 EXCEPTION (exn, "Error in parse ast translation for " ^ quote a))
490 (fn () => f ctxt args) ());
492 (*translate pt bottom-up*)
493 fun ast_of (Parser.Node (a, pts)) = trans a (map ast_of pts)
494 | ast_of (Parser.Tip tok) = Ast.Variable (Lexicon.str_of_token tok);
496 val exn_results = map (capture ast_of) pts;
497 val exns = map_filter get_exn exn_results;
498 val results = map_filter get_result exn_results
499 in (case (results, exns) of ([], exn :: _) => raise exn | _ => results) end;
503 (** asts_to_terms **)
505 fun asts_to_terms ctxt trf asts =
509 NONE => Term.list_comb (Lexicon.const a, args)
510 | SOME f => transform_failure (fn exn =>
511 EXCEPTION (exn, "Error in parse translation for " ^ quote a))
512 (fn () => f ctxt args) ());
514 fun term_of (Ast.Constant a) = trans a []
515 | term_of (Ast.Variable x) = Lexicon.read_var x
516 | term_of (Ast.Appl (Ast.Constant a :: (asts as _ :: _))) =
517 trans a (map term_of asts)
518 | term_of (Ast.Appl (ast :: (asts as _ :: _))) =
519 Term.list_comb (term_of ast, map term_of asts)
520 | term_of (ast as Ast.Appl _) = raise Ast.AST ("ast_to_term: malformed ast", [ast]);
522 val free_fixed = Term.map_aterms
523 (fn t as Const (c, T) =>
524 (case try (unprefix Lexicon.fixedN) c of
526 | SOME x => Free (x, T))
529 val exn_results = map (capture (term_of #> free_fixed)) asts;
530 val exns = map_filter get_exn exn_results;
531 val results = map_filter get_result exn_results
532 in (case (results, exns) of ([], exn :: _) => raise exn | _ => results) end;