1 (* Title: HOL/Tools/datatype_aux.ML |
|
2 Author: Stefan Berghofer, TU Muenchen |
|
3 |
|
4 Auxiliary functions for defining datatypes. |
|
5 *) |
|
6 |
|
7 signature DATATYPE_AUX = |
|
8 sig |
|
9 val quiet_mode : bool ref |
|
10 val message : string -> unit |
|
11 |
|
12 val add_path : bool -> string -> theory -> theory |
|
13 val parent_path : bool -> theory -> theory |
|
14 |
|
15 val store_thmss_atts : string -> string list -> attribute list list -> thm list list |
|
16 -> theory -> thm list list * theory |
|
17 val store_thmss : string -> string list -> thm list list -> theory -> thm list list * theory |
|
18 val store_thms_atts : string -> string list -> attribute list list -> thm list |
|
19 -> theory -> thm list * theory |
|
20 val store_thms : string -> string list -> thm list -> theory -> thm list * theory |
|
21 |
|
22 val split_conj_thm : thm -> thm list |
|
23 val mk_conj : term list -> term |
|
24 val mk_disj : term list -> term |
|
25 |
|
26 val app_bnds : term -> int -> term |
|
27 |
|
28 val cong_tac : int -> tactic |
|
29 val indtac : thm -> string list -> int -> tactic |
|
30 val exh_tac : (string -> thm) -> int -> tactic |
|
31 |
|
32 datatype simproc_dist = FewConstrs of thm list |
|
33 | ManyConstrs of thm * simpset; |
|
34 |
|
35 datatype dtyp = |
|
36 DtTFree of string |
|
37 | DtType of string * (dtyp list) |
|
38 | DtRec of int; |
|
39 type descr |
|
40 type datatype_info |
|
41 |
|
42 exception Datatype |
|
43 exception Datatype_Empty of string |
|
44 val name_of_typ : typ -> string |
|
45 val dtyp_of_typ : (string * string list) list -> typ -> dtyp |
|
46 val mk_Free : string -> typ -> int -> term |
|
47 val is_rec_type : dtyp -> bool |
|
48 val typ_of_dtyp : descr -> (string * sort) list -> dtyp -> typ |
|
49 val dest_DtTFree : dtyp -> string |
|
50 val dest_DtRec : dtyp -> int |
|
51 val strip_dtyp : dtyp -> dtyp list * dtyp |
|
52 val body_index : dtyp -> int |
|
53 val mk_fun_dtyp : dtyp list -> dtyp -> dtyp |
|
54 val get_nonrec_types : descr -> (string * sort) list -> typ list |
|
55 val get_branching_types : descr -> (string * sort) list -> typ list |
|
56 val get_arities : descr -> int list |
|
57 val get_rec_types : descr -> (string * sort) list -> typ list |
|
58 val check_nonempty : descr list -> unit |
|
59 val unfold_datatypes : |
|
60 theory -> descr -> (string * sort) list -> datatype_info Symtab.table -> |
|
61 descr -> int -> descr list * int |
|
62 end; |
|
63 |
|
64 structure DatatypeAux : DATATYPE_AUX = |
|
65 struct |
|
66 |
|
67 val quiet_mode = ref false; |
|
68 fun message s = if !quiet_mode then () else writeln s; |
|
69 |
|
70 fun add_path flat_names s = if flat_names then I else Sign.add_path s; |
|
71 fun parent_path flat_names = if flat_names then I else Sign.parent_path; |
|
72 |
|
73 |
|
74 (* store theorems in theory *) |
|
75 |
|
76 fun store_thmss_atts label tnames attss thmss = |
|
77 fold_map (fn ((tname, atts), thms) => |
|
78 Sign.add_path tname |
|
79 #> PureThy.add_thmss [((Binding.name label, thms), atts)] |
|
80 #-> (fn thm::_ => Sign.parent_path #> pair thm)) (tnames ~~ attss ~~ thmss) |
|
81 ##> Theory.checkpoint; |
|
82 |
|
83 fun store_thmss label tnames = store_thmss_atts label tnames (replicate (length tnames) []); |
|
84 |
|
85 fun store_thms_atts label tnames attss thmss = |
|
86 fold_map (fn ((tname, atts), thms) => |
|
87 Sign.add_path tname |
|
88 #> PureThy.add_thms [((Binding.name label, thms), atts)] |
|
89 #-> (fn thm::_ => Sign.parent_path #> pair thm)) (tnames ~~ attss ~~ thmss) |
|
90 ##> Theory.checkpoint; |
|
91 |
|
92 fun store_thms label tnames = store_thms_atts label tnames (replicate (length tnames) []); |
|
93 |
|
94 |
|
95 (* split theorem thm_1 & ... & thm_n into n theorems *) |
|
96 |
|
97 fun split_conj_thm th = |
|
98 ((th RS conjunct1)::(split_conj_thm (th RS conjunct2))) handle THM _ => [th]; |
|
99 |
|
100 val mk_conj = foldr1 (HOLogic.mk_binop "op &"); |
|
101 val mk_disj = foldr1 (HOLogic.mk_binop "op |"); |
|
102 |
|
103 fun app_bnds t i = list_comb (t, map Bound (i - 1 downto 0)); |
|
104 |
|
105 |
|
106 fun cong_tac i st = (case Logic.strip_assums_concl |
|
107 (List.nth (prems_of st, i - 1)) of |
|
108 _ $ (_ $ (f $ x) $ (g $ y)) => |
|
109 let |
|
110 val cong' = Thm.lift_rule (Thm.cprem_of st i) cong; |
|
111 val _ $ (_ $ (f' $ x') $ (g' $ y')) = |
|
112 Logic.strip_assums_concl (prop_of cong'); |
|
113 val insts = map (pairself (cterm_of (Thm.theory_of_thm st)) o |
|
114 apsnd (curry list_abs (Logic.strip_params (concl_of cong'))) o |
|
115 apfst head_of) [(f', f), (g', g), (x', x), (y', y)] |
|
116 in compose_tac (false, cterm_instantiate insts cong', 2) i st |
|
117 handle THM _ => no_tac st |
|
118 end |
|
119 | _ => no_tac st); |
|
120 |
|
121 (* instantiate induction rule *) |
|
122 |
|
123 fun indtac indrule indnames i st = |
|
124 let |
|
125 val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule)); |
|
126 val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop |
|
127 (Logic.strip_imp_concl (List.nth (prems_of st, i - 1)))); |
|
128 val getP = if can HOLogic.dest_imp (hd ts) then |
|
129 (apfst SOME) o HOLogic.dest_imp else pair NONE; |
|
130 val flt = if null indnames then I else |
|
131 filter (fn Free (s, _) => s mem indnames | _ => false); |
|
132 fun abstr (t1, t2) = (case t1 of |
|
133 NONE => (case flt (OldTerm.term_frees t2) of |
|
134 [Free (s, T)] => SOME (absfree (s, T, t2)) |
|
135 | _ => NONE) |
|
136 | SOME (_ $ t') => SOME (Abs ("x", fastype_of t', abstract_over (t', t2)))) |
|
137 val cert = cterm_of (Thm.theory_of_thm st); |
|
138 val insts = List.mapPartial (fn (t, u) => case abstr (getP u) of |
|
139 NONE => NONE |
|
140 | SOME u' => SOME (t |> getP |> snd |> head_of |> cert, cert u')) (ts ~~ ts'); |
|
141 val indrule' = cterm_instantiate insts indrule |
|
142 in |
|
143 rtac indrule' i st |
|
144 end; |
|
145 |
|
146 (* perform exhaustive case analysis on last parameter of subgoal i *) |
|
147 |
|
148 fun exh_tac exh_thm_of i state = |
|
149 let |
|
150 val thy = Thm.theory_of_thm state; |
|
151 val prem = nth (prems_of state) (i - 1); |
|
152 val params = Logic.strip_params prem; |
|
153 val (_, Type (tname, _)) = hd (rev params); |
|
154 val exhaustion = Thm.lift_rule (Thm.cprem_of state i) (exh_thm_of tname); |
|
155 val prem' = hd (prems_of exhaustion); |
|
156 val _ $ (_ $ lhs $ _) = hd (rev (Logic.strip_assums_hyp prem')); |
|
157 val exhaustion' = cterm_instantiate [(cterm_of thy (head_of lhs), |
|
158 cterm_of thy (List.foldr (fn ((_, T), t) => Abs ("z", T, t)) |
|
159 (Bound 0) params))] exhaustion |
|
160 in compose_tac (false, exhaustion', nprems_of exhaustion) i state |
|
161 end; |
|
162 |
|
163 (* handling of distinctness theorems *) |
|
164 |
|
165 datatype simproc_dist = FewConstrs of thm list |
|
166 | ManyConstrs of thm * simpset; |
|
167 |
|
168 (********************** Internal description of datatypes *********************) |
|
169 |
|
170 datatype dtyp = |
|
171 DtTFree of string |
|
172 | DtType of string * (dtyp list) |
|
173 | DtRec of int; |
|
174 |
|
175 (* information about datatypes *) |
|
176 |
|
177 (* index, datatype name, type arguments, constructor name, types of constructor's arguments *) |
|
178 type descr = (int * (string * dtyp list * (string * dtyp list) list)) list; |
|
179 |
|
180 type datatype_info = |
|
181 {index : int, |
|
182 alt_names : string list option, |
|
183 descr : descr, |
|
184 sorts : (string * sort) list, |
|
185 rec_names : string list, |
|
186 rec_rewrites : thm list, |
|
187 case_name : string, |
|
188 case_rewrites : thm list, |
|
189 induction : thm, |
|
190 exhaustion : thm, |
|
191 distinct : simproc_dist, |
|
192 inject : thm list, |
|
193 nchotomy : thm, |
|
194 case_cong : thm, |
|
195 weak_case_cong : thm}; |
|
196 |
|
197 fun mk_Free s T i = Free (s ^ (string_of_int i), T); |
|
198 |
|
199 fun subst_DtTFree _ substs (T as (DtTFree name)) = |
|
200 AList.lookup (op =) substs name |> the_default T |
|
201 | subst_DtTFree i substs (DtType (name, ts)) = |
|
202 DtType (name, map (subst_DtTFree i substs) ts) |
|
203 | subst_DtTFree i _ (DtRec j) = DtRec (i + j); |
|
204 |
|
205 exception Datatype; |
|
206 exception Datatype_Empty of string; |
|
207 |
|
208 fun dest_DtTFree (DtTFree a) = a |
|
209 | dest_DtTFree _ = raise Datatype; |
|
210 |
|
211 fun dest_DtRec (DtRec i) = i |
|
212 | dest_DtRec _ = raise Datatype; |
|
213 |
|
214 fun is_rec_type (DtType (_, dts)) = exists is_rec_type dts |
|
215 | is_rec_type (DtRec _) = true |
|
216 | is_rec_type _ = false; |
|
217 |
|
218 fun strip_dtyp (DtType ("fun", [T, U])) = apfst (cons T) (strip_dtyp U) |
|
219 | strip_dtyp T = ([], T); |
|
220 |
|
221 val body_index = dest_DtRec o snd o strip_dtyp; |
|
222 |
|
223 fun mk_fun_dtyp [] U = U |
|
224 | mk_fun_dtyp (T :: Ts) U = DtType ("fun", [T, mk_fun_dtyp Ts U]); |
|
225 |
|
226 fun name_of_typ (Type (s, Ts)) = |
|
227 let val s' = Long_Name.base_name s |
|
228 in space_implode "_" (List.filter (not o equal "") (map name_of_typ Ts) @ |
|
229 [if Syntax.is_identifier s' then s' else "x"]) |
|
230 end |
|
231 | name_of_typ _ = ""; |
|
232 |
|
233 fun dtyp_of_typ _ (TFree (n, _)) = DtTFree n |
|
234 | dtyp_of_typ _ (TVar _) = error "Illegal schematic type variable(s)" |
|
235 | dtyp_of_typ new_dts (Type (tname, Ts)) = |
|
236 (case AList.lookup (op =) new_dts tname of |
|
237 NONE => DtType (tname, map (dtyp_of_typ new_dts) Ts) |
|
238 | SOME vs => if map (try (fst o dest_TFree)) Ts = map SOME vs then |
|
239 DtRec (find_index (curry op = tname o fst) new_dts) |
|
240 else error ("Illegal occurrence of recursive type " ^ tname)); |
|
241 |
|
242 fun typ_of_dtyp descr sorts (DtTFree a) = TFree (a, (the o AList.lookup (op =) sorts) a) |
|
243 | typ_of_dtyp descr sorts (DtRec i) = |
|
244 let val (s, ds, _) = (the o AList.lookup (op =) descr) i |
|
245 in Type (s, map (typ_of_dtyp descr sorts) ds) end |
|
246 | typ_of_dtyp descr sorts (DtType (s, ds)) = |
|
247 Type (s, map (typ_of_dtyp descr sorts) ds); |
|
248 |
|
249 (* find all non-recursive types in datatype description *) |
|
250 |
|
251 fun get_nonrec_types descr sorts = |
|
252 map (typ_of_dtyp descr sorts) (Library.foldl (fn (Ts, (_, (_, _, constrs))) => |
|
253 Library.foldl (fn (Ts', (_, cargs)) => |
|
254 filter_out is_rec_type cargs union Ts') (Ts, constrs)) ([], descr)); |
|
255 |
|
256 (* get all recursive types in datatype description *) |
|
257 |
|
258 fun get_rec_types descr sorts = map (fn (_ , (s, ds, _)) => |
|
259 Type (s, map (typ_of_dtyp descr sorts) ds)) descr; |
|
260 |
|
261 (* get all branching types *) |
|
262 |
|
263 fun get_branching_types descr sorts = |
|
264 map (typ_of_dtyp descr sorts) (fold (fn (_, (_, _, constrs)) => |
|
265 fold (fn (_, cargs) => fold (strip_dtyp #> fst #> fold (insert op =)) cargs) |
|
266 constrs) descr []); |
|
267 |
|
268 fun get_arities descr = fold (fn (_, (_, _, constrs)) => |
|
269 fold (fn (_, cargs) => fold (insert op =) (map (length o fst o strip_dtyp) |
|
270 (List.filter is_rec_type cargs))) constrs) descr []; |
|
271 |
|
272 (* nonemptiness check for datatypes *) |
|
273 |
|
274 fun check_nonempty descr = |
|
275 let |
|
276 val descr' = List.concat descr; |
|
277 fun is_nonempty_dt is i = |
|
278 let |
|
279 val (_, _, constrs) = (the o AList.lookup (op =) descr') i; |
|
280 fun arg_nonempty (_, DtRec i) = if i mem is then false |
|
281 else is_nonempty_dt (i::is) i |
|
282 | arg_nonempty _ = true; |
|
283 in exists ((forall (arg_nonempty o strip_dtyp)) o snd) constrs |
|
284 end |
|
285 in assert_all (fn (i, _) => is_nonempty_dt [i] i) (hd descr) |
|
286 (fn (_, (s, _, _)) => raise Datatype_Empty s) |
|
287 end; |
|
288 |
|
289 (* unfold a list of mutually recursive datatype specifications *) |
|
290 (* all types of the form DtType (dt_name, [..., DtRec _, ...]) *) |
|
291 (* need to be unfolded *) |
|
292 |
|
293 fun unfold_datatypes sign orig_descr sorts (dt_info : datatype_info Symtab.table) descr i = |
|
294 let |
|
295 fun typ_error T msg = error ("Non-admissible type expression\n" ^ |
|
296 Syntax.string_of_typ_global sign (typ_of_dtyp (orig_descr @ descr) sorts T) ^ "\n" ^ msg); |
|
297 |
|
298 fun get_dt_descr T i tname dts = |
|
299 (case Symtab.lookup dt_info tname of |
|
300 NONE => typ_error T (tname ^ " is not a datatype - can't use it in\ |
|
301 \ nested recursion") |
|
302 | (SOME {index, descr, ...}) => |
|
303 let val (_, vars, _) = (the o AList.lookup (op =) descr) index; |
|
304 val subst = ((map dest_DtTFree vars) ~~ dts) handle Library.UnequalLengths => |
|
305 typ_error T ("Type constructor " ^ tname ^ " used with wrong\ |
|
306 \ number of arguments") |
|
307 in (i + index, map (fn (j, (tn, args, cs)) => (i + j, |
|
308 (tn, map (subst_DtTFree i subst) args, |
|
309 map (apsnd (map (subst_DtTFree i subst))) cs))) descr) |
|
310 end); |
|
311 |
|
312 (* unfold a single constructor argument *) |
|
313 |
|
314 fun unfold_arg ((i, Ts, descrs), T) = |
|
315 if is_rec_type T then |
|
316 let val (Us, U) = strip_dtyp T |
|
317 in if exists is_rec_type Us then |
|
318 typ_error T "Non-strictly positive recursive occurrence of type" |
|
319 else (case U of |
|
320 DtType (tname, dts) => |
|
321 let |
|
322 val (index, descr) = get_dt_descr T i tname dts; |
|
323 val (descr', i') = unfold_datatypes sign orig_descr sorts |
|
324 dt_info descr (i + length descr) |
|
325 in (i', Ts @ [mk_fun_dtyp Us (DtRec index)], descrs @ descr') end |
|
326 | _ => (i, Ts @ [T], descrs)) |
|
327 end |
|
328 else (i, Ts @ [T], descrs); |
|
329 |
|
330 (* unfold a constructor *) |
|
331 |
|
332 fun unfold_constr ((i, constrs, descrs), (cname, cargs)) = |
|
333 let val (i', cargs', descrs') = Library.foldl unfold_arg ((i, [], descrs), cargs) |
|
334 in (i', constrs @ [(cname, cargs')], descrs') end; |
|
335 |
|
336 (* unfold a single datatype *) |
|
337 |
|
338 fun unfold_datatype ((i, dtypes, descrs), (j, (tname, tvars, constrs))) = |
|
339 let val (i', constrs', descrs') = |
|
340 Library.foldl unfold_constr ((i, [], descrs), constrs) |
|
341 in (i', dtypes @ [(j, (tname, tvars, constrs'))], descrs') |
|
342 end; |
|
343 |
|
344 val (i', descr', descrs) = Library.foldl unfold_datatype ((i, [],[]), descr); |
|
345 |
|
346 in (descr' :: descrs, i') end; |
|
347 |
|
348 end; |
|