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
27 signature SYN_TRANS1 =
30 val non_typed_tr': (term list -> term) -> bool -> typ -> term list -> term
31 val non_typed_tr'': ('a -> term list -> term) -> 'a -> bool -> typ -> term list -> term
32 val constrainAbsC: string
34 (string * (Ast.ast list -> Ast.ast)) list *
35 (string * (term list -> term)) list *
36 (string * (term list -> term)) list *
37 (string * (Ast.ast list -> Ast.ast)) list
38 val pure_trfunsT: (string * (bool -> typ -> term list -> term)) list
39 val struct_trfuns: string list ->
40 (string * (Ast.ast list -> Ast.ast)) list *
41 (string * (term list -> term)) list *
42 (string * (bool -> typ -> term list -> term)) list *
43 (string * (Ast.ast list -> Ast.ast)) list
49 val abs_tr': term -> term
50 val prop_tr': term -> term
51 val appl_ast_tr': Ast.ast * Ast.ast list -> Ast.ast
52 val applC_ast_tr': Ast.ast * Ast.ast list -> Ast.ast
53 val pts_to_asts: Context.generic ->
54 (string -> (Context.generic -> Ast.ast list -> Ast.ast) option) ->
55 Parser.parsetree list -> Ast.ast list
56 val asts_to_terms: Context.generic ->
57 (string -> (Context.generic -> term list -> term) option) -> Ast.ast list -> term list
60 structure SynTrans: SYN_TRANS =
64 (** parse (ast) translations **)
68 fun constify_ast_tr [Ast.Variable c] = Ast.Constant c
69 | constify_ast_tr asts = raise Ast.AST ("constify_ast_tr", asts);
74 fun appl_ast_tr [f, args] = Ast.Appl (f :: Ast.unfold_ast "_args" args)
75 | appl_ast_tr asts = raise Ast.AST ("appl_ast_tr", asts);
77 fun applC_ast_tr [f, args] = Ast.Appl (f :: Ast.unfold_ast "_cargs" args)
78 | applC_ast_tr asts = raise Ast.AST ("applC_ast_tr", asts);
83 fun idtyp_ast_tr (*"_idtyp"*) [x, ty] = Ast.Appl [Ast.Constant "_constrain", x, ty]
84 | idtyp_ast_tr (*"_idtyp"*) asts = raise Ast.AST ("idtyp_ast_tr", asts);
86 fun idtypdummy_ast_tr (*"_idtypdummy"*) [ty] =
87 Ast.Appl [Ast.Constant "_constrain", Ast.Constant "_idtdummy", ty]
88 | idtypdummy_ast_tr (*"_idtypdummy"*) asts = raise Ast.AST ("idtyp_ast_tr", asts);
90 fun lambda_ast_tr (*"_lambda"*) [pats, body] =
91 Ast.fold_ast_p "_abs" (Ast.unfold_ast "_pttrns" pats, body)
92 | lambda_ast_tr (*"_lambda"*) asts = raise Ast.AST ("lambda_ast_tr", asts);
94 val constrainAbsC = "_constrainAbs";
96 fun abs_tr (*"_abs"*) [Free (x, T), t] = Term.absfree (x, T, t)
97 | abs_tr (*"_abs"*) [Const ("_idtdummy", T), t] = Term.absdummy (T, t)
98 | abs_tr (*"_abs"*) [Const ("_constrain", _) $ Free (x, T) $ tT, t] =
99 Lexicon.const constrainAbsC $ Term.absfree (x, T, t) $ tT
100 | abs_tr (*"_abs"*) [Const ("_constrain", _) $ Const ("_idtdummy", T) $ tT, t] =
101 Lexicon.const constrainAbsC $ Term.absdummy (T, t) $ tT
102 | abs_tr (*"_abs"*) ts = raise TERM ("abs_tr", ts);
107 fun mk_binder_tr (sy, name) =
109 fun tr (Free (x, T), t) = Lexicon.const name $ Term.absfree (x, T, t)
110 | tr (Const ("_idtdummy", T), t) = Lexicon.const name $ Term.absdummy (T, t)
111 | tr (Const ("_constrain", _) $ Free (x, T) $ tT, t) =
112 Lexicon.const name $ (Lexicon.const constrainAbsC $ Term.absfree (x, T, t) $ tT)
113 | tr (Const ("_constrain", _) $ Const ("_idtdummy", T) $ tT, t) =
114 Lexicon.const name $ (Lexicon.const constrainAbsC $ Term.absdummy (T, t) $ tT)
115 | tr (Const ("_idts", _) $ idt $ idts, t) = tr (idt, tr (idts, t))
116 | tr (t1, t2) = raise TERM ("binder_tr", [t1, t2]);
118 fun binder_tr (*sy*) [idts, body] = tr (idts, body)
119 | binder_tr (*sy*) ts = raise TERM ("binder_tr", ts);
120 in (sy, binder_tr) end;
123 (* meta propositions *)
125 fun aprop_tr (*"_aprop"*) [t] = Lexicon.const "_constrain" $ t $ Lexicon.const "prop"
126 | aprop_tr (*"_aprop"*) ts = raise TERM ("aprop_tr", ts);
128 fun ofclass_tr (*"_ofclass"*) [ty, cls] =
129 cls $ (Lexicon.const "_constrain" $ Lexicon.const "TYPE" $
130 (Lexicon.const "itself" $ ty))
131 | ofclass_tr (*"_ofclass"*) ts = raise TERM ("ofclass_tr", ts);
134 (* meta implication *)
136 fun bigimpl_ast_tr (*"_bigimpl"*) (asts as [asms, concl]) =
138 (case Ast.unfold_ast_p "_asms" asms of
139 (asms', Ast.Appl [Ast.Constant "_asm", asm']) => asms' @ [asm']
140 | _ => raise Ast.AST ("bigimpl_ast_tr", asts))
141 in Ast.fold_ast_p "==>" (prems, concl) end
142 | bigimpl_ast_tr (*"_bigimpl"*) asts = raise Ast.AST ("bigimpl_ast_tr", asts);
145 (* type reflection *)
147 fun type_tr (*"_TYPE"*) [ty] =
148 Lexicon.const "_constrain" $ Lexicon.const "TYPE" $ (Lexicon.const "itself" $ ty)
149 | type_tr (*"_TYPE"*) ts = raise TERM ("type_tr", ts);
154 fun dddot_tr (*"_DDDOT"*) ts = Term.list_comb (Lexicon.var SynExt.dddot_indexname, ts);
157 (* quote / antiquote *)
159 fun antiquote_tr name =
161 fun tr i ((t as Const (c, _)) $ u) =
162 if c = name then tr i u $ Bound i
164 | tr i (t $ u) = tr i t $ tr i u
165 | tr i (Abs (x, T, t)) = Abs (x, T, tr (i + 1) t)
169 fun quote_tr name t = Abs ("s", dummyT, antiquote_tr name (Term.incr_boundvars 1 t));
171 fun quote_antiquote_tr quoteN antiquoteN name =
173 fun tr [t] = Lexicon.const name $ quote_tr antiquoteN t
174 | tr ts = raise TERM ("quote_tr", ts);
180 fun struct_ast_tr (*"_struct"*) [Ast.Appl [Ast.Constant "_index", ast]] = ast
181 | struct_ast_tr (*"_struct"*) asts = Ast.mk_appl (Ast.Constant "_struct") asts;
183 fun index_ast_tr ast =
184 Ast.mk_appl (Ast.Constant "_index") [Ast.mk_appl (Ast.Constant "_struct") [ast]];
186 fun indexdefault_ast_tr (*"_indexdefault"*) [] =
187 index_ast_tr (Ast.Constant "_indexdefault")
188 | indexdefault_ast_tr (*"_indexdefault"*) asts =
189 raise Ast.AST ("indexdefault_ast_tr", asts);
191 fun indexnum_ast_tr (*"_indexnum"*) [ast] =
192 index_ast_tr (Ast.mk_appl (Ast.Constant "_indexnum") [ast])
193 | indexnum_ast_tr (*"_indexnum"*) asts = raise Ast.AST ("indexnum_ast_tr", asts);
195 fun indexvar_ast_tr (*"_indexvar"*) [] =
196 Ast.mk_appl (Ast.Constant "_index") [Ast.Variable "some_index"]
197 | indexvar_ast_tr (*"_indexvar"*) asts = raise Ast.AST ("indexvar_ast_tr", asts);
199 fun index_tr (*"_index"*) [t] = t
200 | index_tr (*"_index"*) ts = raise TERM ("index_tr", ts);
203 (* implicit structures *)
205 fun the_struct structs i =
206 if 1 <= i andalso i <= length structs then List.nth (structs, i - 1)
207 else raise error ("Illegal reference to implicit structure #" ^ string_of_int i);
209 fun struct_tr structs (*"_struct"*) [Const ("_indexdefault", _)] =
210 Lexicon.free (the_struct structs 1)
211 | struct_tr structs (*"_struct"*) [t as (Const ("_indexnum", _) $ Const (s, _))] =
212 Lexicon.free (the_struct structs
213 (case Lexicon.read_nat s of SOME n => n | NONE => raise TERM ("struct_tr", [t])))
214 | struct_tr _ (*"_struct"*) ts = raise TERM ("struct_tr", ts);
218 (** print (ast) translations **)
222 fun non_typed_tr' f _ _ ts = f ts;
223 fun non_typed_tr'' f x _ _ ts = f x ts;
228 fun appl_ast_tr' (f, []) = raise Ast.AST ("appl_ast_tr'", [f])
229 | appl_ast_tr' (f, args) = Ast.Appl [Ast.Constant "_appl", f, Ast.fold_ast "_args" args];
231 fun applC_ast_tr' (f, []) = raise Ast.AST ("applC_ast_tr'", [f])
232 | applC_ast_tr' (f, args) = Ast.Appl [Ast.Constant "_applC", f, Ast.fold_ast "_cargs" args];
237 fun mark_boundT x_T = Lexicon.const "_bound" $ Free x_T;
238 fun mark_bound x = mark_boundT (x, dummyT);
240 fun bound_vars vars body =
241 subst_bounds (map mark_boundT (Term.rename_wrt_term body vars), body);
243 fun strip_abss vars_of body_of tm =
245 val vars = vars_of tm;
246 val body = body_of tm;
247 val rev_new_vars = rename_wrt_term body vars;
249 (map mark_boundT (rev rev_new_vars),
250 subst_bounds (map (mark_bound o #1) rev_new_vars, body))
254 (*do (partial) eta-contraction before printing*)
256 val eta_contract = ref true;
260 fun is_aprop (Const ("_aprop", _)) = true
261 | is_aprop _ = false;
263 fun eta_abs (Abs (a, T, t)) =
268 if Term.loose_bvar1 (f, 0) orelse is_aprop f then Abs (a, T, t')
269 else incr_boundvars ~1 f
270 | _ => Abs (a, T, t'))
271 | t' => Abs (a, T, t'))
274 if ! eta_contract then eta_abs tm else tm
279 Library.foldr (fn (x, t) => Lexicon.const "_abs" $ x $ t)
280 (strip_abss strip_abs_vars strip_abs_body (eta_contr tm));
282 fun atomic_abs_tr' (x, T, t) =
283 let val [xT] = rename_wrt_term t [(x, T)]
284 in (mark_boundT xT, subst_bound (mark_bound (fst xT), t)) end;
286 fun abs_ast_tr' (*"_abs"*) asts =
287 (case Ast.unfold_ast_p "_abs" (Ast.Appl (Ast.Constant "_abs" :: asts)) of
288 ([], _) => raise Ast.AST ("abs_ast_tr'", asts)
289 | (xs, body) => Ast.Appl [Ast.Constant "_lambda", Ast.fold_ast "_pttrns" xs, body]);
294 fun mk_binder_tr' (name, sy) =
296 fun mk_idts [] = raise Match (*abort translation*)
297 | mk_idts [idt] = idt
298 | mk_idts (idt :: idts) = Lexicon.const "_idts" $ idt $ mk_idts idts;
302 val (xs, bd) = strip_abss (strip_qnt_vars name) (strip_qnt_body name) t;
303 in Lexicon.const sy $ mk_idts xs $ bd end;
305 fun binder_tr' (*name*) (t :: ts) = Term.list_comb (tr' (Lexicon.const name $ t), ts)
306 | binder_tr' (*name*) [] = raise Match;
312 (* idtyp constraints *)
314 fun idtyp_ast_tr' a [Ast.Appl [Ast.Constant c, x, ty], xs] =
315 if c = "_constrain" then
316 Ast.Appl [ Ast.Constant a, Ast.Appl [Ast.Constant "_idtyp", x, ty], xs]
318 | idtyp_ast_tr' _ _ = raise Match;
321 (* meta propositions *)
325 fun aprop t = Lexicon.const "_aprop" $ t;
328 fastype_of1 (Ts, t) = propT handle TERM _ => false;
330 fun tr' _ (t as Const _) = t
331 | tr' Ts (t as Const ("_bound", _) $ u) =
332 if is_prop Ts u then aprop t else t
333 | tr' _ (t as Free (x, T)) =
334 if T = propT then aprop (Lexicon.free x) else t
335 | tr' _ (t as Var (xi, T)) =
336 if T = propT then aprop (Lexicon.var xi) else t
337 | tr' Ts (t as Bound _) =
338 if is_prop Ts t then aprop t else t
339 | tr' Ts (Abs (x, T, t)) = Abs (x, T, tr' (T :: Ts) t)
340 | tr' Ts (t as t1 $ (t2 as Const ("TYPE", Type ("itself", [T])))) =
341 if is_prop Ts t then Const ("_mk_ofclass", T) $ tr' Ts t1
342 else tr' Ts t1 $ tr' Ts t2
343 | tr' Ts (t as t1 $ t2) =
344 (if is_Const (Term.head_of t) orelse not (is_prop Ts t)
345 then I else aprop) (tr' Ts t1 $ tr' Ts t2);
348 fun mk_ofclass_tr' show_sorts (*"_mk_ofclass"*) T [t] =
349 Lexicon.const "_ofclass" $ TypeExt.term_of_typ show_sorts T $ t
350 | mk_ofclass_tr' _ (*"_mk_ofclass"*) T ts = raise TYPE ("mk_ofclass_tr'", [T], ts);
353 (* meta implication *)
355 fun impl_ast_tr' (*"==>"*) asts =
356 if TypeExt.no_brackets () then raise Match
358 (case Ast.unfold_ast_p "==>" (Ast.Appl (Ast.Constant "==>" :: asts)) of
359 (prems as _ :: _ :: _, concl) =>
361 val (asms, asm) = split_last prems;
362 val asms' = Ast.fold_ast_p "_asms" (asms, Ast.Appl [Ast.Constant "_asm", asm]);
363 in Ast.Appl [Ast.Constant "_bigimpl", asms', concl] end
367 (* type reflection *)
369 fun type_tr' show_sorts (*"TYPE"*) (Type ("itself", [T])) ts =
370 Term.list_comb (Lexicon.const "_TYPE" $ TypeExt.term_of_typ show_sorts T, ts)
371 | type_tr' _ _ _ = raise Match;
374 (* dependent / nondependent quantifiers *)
376 fun variant_abs' (x, T, B) =
377 let val x' = variant (add_term_names (B, [])) x in
378 (x', subst_bound (mark_boundT (x', T), B))
381 fun dependent_tr' (q, r) (A :: Abs (x, T, B) :: ts) =
382 if Term.loose_bvar1 (B, 0) then
383 let val (x', B') = variant_abs' (x, dummyT, B);
384 in Term.list_comb (Lexicon.const q $ mark_boundT (x', T) $ A $ B', ts) end
385 else Term.list_comb (Lexicon.const r $ A $ B, ts)
386 | dependent_tr' _ _ = raise Match;
389 (* quote / antiquote *)
391 fun antiquote_tr' name =
394 if u aconv Bound i then Lexicon.const name $ tr' i t
395 else tr' i t $ tr' i u
396 | tr' i (Abs (x, T, t)) = Abs (x, T, tr' (i + 1) t)
397 | tr' i a = if a aconv Bound i then raise Match else a;
400 fun quote_tr' name (Abs (_, _, t)) = Term.incr_boundvars ~1 (antiquote_tr' name t)
401 | quote_tr' _ _ = raise Match;
403 fun quote_antiquote_tr' quoteN antiquoteN name =
405 fun tr' (t :: ts) = Term.list_comb (Lexicon.const quoteN $ quote_tr' antiquoteN t, ts)
406 | tr' _ = raise Match;
412 fun index_ast_tr' (*"_index"*) [Ast.Appl [Ast.Constant "_struct", ast]] = ast
413 | index_ast_tr' _ = raise Match;
416 (* implicit structures *)
418 fun the_struct' structs s =
419 [(case Lexicon.read_nat s of
420 SOME i => Ast.Variable (the_struct structs i handle ERROR _ => raise Match)
421 | NONE => raise Match)] |> Ast.mk_appl (Ast.Constant "_free");
423 fun struct_ast_tr' structs (*"_struct"*) [Ast.Constant "_indexdefault"] =
424 the_struct' structs "1"
425 | struct_ast_tr' structs (*"_struct"*) [Ast.Appl [Ast.Constant "_indexnum", Ast.Constant s]] =
426 the_struct' structs s
427 | struct_ast_tr' _ _ = raise Match;
431 (** Pure translations **)
434 ([("_constify", constify_ast_tr), ("_appl", appl_ast_tr), ("_applC", applC_ast_tr),
435 ("_lambda", lambda_ast_tr), ("_idtyp", idtyp_ast_tr), ("_idtypdummy", idtypdummy_ast_tr),
436 ("_bigimpl", bigimpl_ast_tr), ("_indexdefault", indexdefault_ast_tr),
437 ("_indexnum", indexnum_ast_tr), ("_indexvar", indexvar_ast_tr), ("_struct", struct_ast_tr)],
438 [("_abs", abs_tr), ("_aprop", aprop_tr), ("_ofclass", ofclass_tr),
439 ("_TYPE", type_tr), ("_DDDOT", dddot_tr),
440 ("_index", index_tr)],
441 ([]: (string * (term list -> term)) list),
442 [("_abs", abs_ast_tr'), ("_idts", idtyp_ast_tr' "_idts"),
443 ("_pttrns", idtyp_ast_tr' "_pttrns"), ("==>", impl_ast_tr'),
444 ("_index", index_ast_tr')]);
447 [("_mk_ofclass", mk_ofclass_tr'), ("TYPE", type_tr')];
449 fun struct_trfuns structs =
450 ([], [("_struct", struct_tr structs)], [], [("_struct", struct_ast_tr' structs)]);
456 fun pts_to_asts context trf pts =
460 NONE => Ast.mk_appl (Ast.Constant a) args
461 | SOME f => transform_failure (fn exn =>
462 EXCEPTION (exn, "Error in parse ast translation for " ^ quote a))
463 (fn () => f context args) ());
465 (*translate pt bottom-up*)
466 fun ast_of (Parser.Node (a, pts)) = trans a (map ast_of pts)
467 | ast_of (Parser.Tip tok) = Ast.Variable (Lexicon.str_of_token tok);
469 val exn_results = map (capture ast_of) pts;
470 val exns = List.mapPartial get_exn exn_results;
471 val results = List.mapPartial get_result exn_results
472 in (case (results, exns) of ([], exn :: _) => raise exn | _ => results) end;
476 (** asts_to_terms **)
478 fun asts_to_terms context trf asts =
482 NONE => Term.list_comb (Lexicon.const a, args)
483 | SOME f => transform_failure (fn exn =>
484 EXCEPTION (exn, "Error in parse translation for " ^ quote a))
485 (fn () => f context args) ());
487 fun term_of (Ast.Constant a) = trans a []
488 | term_of (Ast.Variable x) = Lexicon.read_var x
489 | term_of (Ast.Appl (Ast.Constant a :: (asts as _ :: _))) =
490 trans a (map term_of asts)
491 | term_of (Ast.Appl (ast :: (asts as _ :: _))) =
492 Term.list_comb (term_of ast, map term_of asts)
493 | term_of (ast as Ast.Appl _) = raise Ast.AST ("ast_to_term: malformed ast", [ast]);
495 val free_fixed = Term.map_aterms
496 (fn t as Const (c, T) =>
497 (case try (unprefix Lexicon.fixedN) c of
499 | SOME x => Free (x, T))
502 val exn_results = map (capture (term_of #> free_fixed)) asts;
503 val exns = List.mapPartial get_exn exn_results;
504 val results = List.mapPartial get_result exn_results
505 in (case (results, exns) of ([], exn :: _) => raise exn | _ => results) end;