1 (* Title: HOL/Tools/primrec_package.ML
2 Author: Stefan Berghofer, TU Muenchen; Norbert Voelker, FernUni Hagen;
3 Florian Haftmann, TU Muenchen
5 Package for defining functions on datatypes by primitive recursion.
8 signature PRIMREC_PACKAGE =
10 val add_primrec: (binding * typ option * mixfix) list ->
11 (Attrib.binding * term) list -> local_theory -> thm list * local_theory
12 val add_primrec_cmd: (binding * string option * mixfix) list ->
13 (Attrib.binding * string) list -> local_theory -> thm list * local_theory
14 val add_primrec_global: (binding * typ option * mixfix) list ->
15 (Attrib.binding * term) list -> theory -> thm list * theory
16 val add_primrec_overloaded: (string * (string * typ) * bool) list ->
17 (binding * typ option * mixfix) list ->
18 (Attrib.binding * term) list -> theory -> thm list * theory
19 val add_primrec_simple: ((binding * typ) * mixfix) list -> term list ->
20 local_theory -> (string * thm list list) * local_theory
23 structure PrimrecPackage : PRIMREC_PACKAGE =
28 exception PrimrecError of string * term option;
30 fun primrec_error msg = raise PrimrecError (msg, NONE);
31 fun primrec_error_eqn msg eqn = raise PrimrecError (msg, SOME eqn);
33 fun message s = if ! Toplevel.debug then tracing s else ();
36 (* preprocessing of equations *)
38 fun process_eqn is_fixed spec rec_fns =
40 val (vs, Ts) = split_list (strip_qnt_vars "all" spec);
41 val body = strip_qnt_body "all" spec;
42 val (vs', _) = Name.variants vs (Name.make_context (fold_aterms
43 (fn Free (v, _) => insert (op =) v | _ => I) body []));
44 val eqn = curry subst_bounds (map2 (curry Free) vs' Ts |> rev) body;
45 val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eqn)
46 handle TERM _ => primrec_error "not a proper equation";
47 val (recfun, args) = strip_comb lhs;
48 val fname = case recfun of Free (v, _) => if is_fixed v then v
49 else primrec_error "illegal head of function equation"
50 | _ => primrec_error "illegal head of function equation";
52 val (ls', rest) = take_prefix is_Free args;
53 val (middle, rs') = take_suffix is_Free rest;
54 val rpos = length ls';
56 val (constr, cargs') = if null middle then primrec_error "constructor missing"
57 else strip_comb (hd middle);
58 val (cname, T) = dest_Const constr
59 handle TERM _ => primrec_error "ill-formed constructor";
60 val (tname, _) = dest_Type (body_type T) handle TYPE _ =>
61 primrec_error "cannot determine datatype associated with function"
64 (map dest_Free ls', map dest_Free cargs', map dest_Free rs')
65 handle TERM _ => primrec_error "illegal argument in pattern";
66 val lfrees = ls @ rs @ cargs;
68 fun check_vars _ [] = ()
69 | check_vars s vars = primrec_error (s ^ commas_quote (map fst vars)) eqn;
71 if length middle > 1 then
72 primrec_error "more than one non-variable in pattern"
74 (check_vars "repeated variable names in pattern: " (duplicates (op =) lfrees);
75 check_vars "extra variables on rhs: "
76 (map dest_Free (OldTerm.term_frees rhs) |> subtract (op =) lfrees
77 |> filter_out (is_fixed o fst));
78 case AList.lookup (op =) rec_fns fname of
80 (fname, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eqn))]))::rec_fns
81 | SOME (_, rpos', eqns) =>
82 if AList.defined (op =) eqns cname then
83 primrec_error "constructor already occurred as pattern"
84 else if rpos <> rpos' then
85 primrec_error "position of recursive argument inconsistent"
88 (fname, (tname, rpos, (cname, (ls, cargs, rs, rhs, eqn))::eqns))
90 end handle PrimrecError (msg, NONE) => primrec_error_eqn msg spec;
92 fun process_fun descr eqns (i, fname) (fnames, fnss) =
94 val (_, (tname, _, constrs)) = nth descr i;
96 (* substitute "fname ls x rs" by "y ls rs" for (x, (_, y)) in subs *)
98 fun subst [] t fs = (t, fs)
99 | subst subs (Abs (a, T, t)) fs =
102 |-> (fn t' => pair (Abs (a, T, t')))
103 | subst subs (t as (_ $ _)) fs =
105 val (f, ts) = strip_comb t;
108 andalso member (fn ((v, _), (w, _)) => v = w) eqns (dest_Free f) then
110 val (fname', _) = dest_Free f;
111 val (_, rpos, _) = the (AList.lookup (op =) eqns fname');
112 val (ls, rs) = chop rpos ts
113 val (x', rs') = case rs
114 of x' :: rs => (x', rs)
115 | [] => primrec_error ("not enough arguments in recursive application\n"
116 ^ "of function " ^ quote fname' ^ " on rhs");
117 val (x, xs) = strip_comb x';
118 in case AList.lookup (op =) subs x
121 |> fold_map (subst subs) ts
122 |-> (fn ts' => pair (list_comb (f, ts')))
125 |> fold_map (subst subs) (xs @ ls @ rs')
126 ||> process_fun descr eqns (i', fname')
127 |-> (fn ts' => pair (list_comb (y, ts')))
131 |> fold_map (subst subs) (f :: ts)
132 |-> (fn (f'::ts') => pair (list_comb (f', ts')))
134 | subst _ t fs = (t, fs);
136 (* translate rec equations into function arguments suitable for rec comb *)
138 fun trans eqns (cname, cargs) (fnames', fnss', fns) =
139 (case AList.lookup (op =) eqns cname of
140 NONE => (warning ("No equation for constructor " ^ quote cname ^
141 "\nin definition of function " ^ quote fname);
142 (fnames', fnss', (Const ("HOL.undefined", dummyT))::fns))
143 | SOME (ls, cargs', rs, rhs, eq) =>
145 val recs = filter (is_rec_type o snd) (cargs' ~~ cargs);
146 val rargs = map fst recs;
147 val subs = map (rpair dummyT o fst)
148 (rev (Term.rename_wrt_term rhs rargs));
149 val (rhs', (fnames'', fnss'')) = subst (map2 (fn (x, y) => fn z =>
150 (Free x, (body_index y, Free z))) recs subs) rhs (fnames', fnss')
151 handle PrimrecError (s, NONE) => primrec_error_eqn s eq
152 in (fnames'', fnss'',
153 (list_abs_free (cargs' @ subs @ ls @ rs, rhs'))::fns)
156 in (case AList.lookup (op =) fnames i of
158 if exists (fn (_, v) => fname = v) fnames then
159 primrec_error ("inconsistent functions for datatype " ^ quote tname)
162 val (_, _, eqns) = the (AList.lookup (op =) eqns fname);
163 val (fnames', fnss', fns) = fold_rev (trans eqns) constrs
164 ((i, fname)::fnames, fnss, [])
166 (fnames', (i, (fname, #1 (snd (hd eqns)), fns))::fnss')
169 if fname = fname' then (fnames, fnss)
170 else primrec_error ("inconsistent functions for datatype " ^ quote tname))
174 (* prepare functions needed for definitions *)
176 fun get_fns fns ((i : int, (tname, _, constrs)), rec_name) (fs, defs) =
177 case AList.lookup (op =) fns i of
180 val dummy_fns = map (fn (_, cargs) => Const ("HOL.undefined",
181 replicate ((length cargs) + (length (List.filter is_rec_type cargs)))
182 dummyT ---> HOLogic.unitT)) constrs;
183 val _ = warning ("No function definition for datatype " ^ quote tname)
185 (dummy_fns @ fs, defs)
187 | SOME (fname, ls, fs') => (fs' @ fs, (fname, ls, rec_name, tname) :: defs);
190 (* make definition *)
192 fun make_def ctxt fixes fs (fname, ls, rec_name, tname) =
194 val SOME (var, varT) = get_first (fn ((b, T), mx) =>
195 if Binding.name_of b = fname then SOME ((b, mx), T) else NONE) fixes;
196 val def_name = Thm.def_name (Long_Name.base_name fname);
197 val raw_rhs = fold_rev (fn T => fn t => Abs ("", T, t)) (map snd ls @ [dummyT])
198 (list_comb (Const (rec_name, dummyT), fs @ map Bound (0 :: (length ls downto 1))))
199 val rhs = singleton (Syntax.check_terms ctxt)
200 (TypeInfer.constrain varT raw_rhs);
201 in (var, ((Binding.name def_name, []), rhs)) end;
204 (* find datatypes which contain all datatypes in tnames' *)
206 fun find_dts (dt_info : datatype_info Symtab.table) _ [] = []
207 | find_dts dt_info tnames' (tname::tnames) =
208 (case Symtab.lookup dt_info tname of
209 NONE => primrec_error (quote tname ^ " is not a datatype")
211 if tnames' subset (map (#1 o snd) (#descr dt)) then
212 (tname, dt)::(find_dts dt_info tnames' tnames)
213 else find_dts dt_info tnames' tnames);
216 (* distill primitive definition(s) from primrec specification *)
218 fun distill lthy fixes eqs =
220 val eqns = fold_rev (process_eqn (fn v => Variable.is_fixed lthy v
221 orelse exists (fn ((w, _), _) => v = Binding.name_of w) fixes)) eqs [];
222 val tnames = distinct (op =) (map (#1 o snd) eqns);
223 val dts = find_dts (DatatypePackage.get_datatypes (ProofContext.theory_of lthy)) tnames tnames;
224 val main_fns = map (fn (tname, {index, ...}) =>
225 (index, (fst o the o find_first (fn (_, x) => #1 x = tname)) eqns)) dts;
226 val {descr, rec_names, rec_rewrites, ...} =
227 if null dts then primrec_error
228 ("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive")
230 val (fnames, fnss) = fold_rev (process_fun descr eqns) main_fns ([], []);
231 val (fs, raw_defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []);
232 val defs = map (make_def lthy fixes fs) raw_defs;
233 val names = map snd fnames;
234 val names_eqns = map fst eqns;
235 val _ = if gen_eq_set (op =) (names, names_eqns) then ()
236 else primrec_error ("functions " ^ commas_quote names_eqns ^
237 "\nare not mutually recursive");
238 val rec_rewrites' = map mk_meta_eq rec_rewrites;
239 val prefix = space_implode "_" (map (Long_Name.base_name o #1) raw_defs);
240 fun prove lthy defs =
242 val rewrites = rec_rewrites' @ map (snd o snd) defs;
243 fun tac _ = EVERY [rewrite_goals_tac rewrites, rtac refl 1];
244 val _ = message ("Proving equations for primrec function(s) " ^ commas_quote names);
245 in map (fn eq => [Goal.prove lthy [] [] eq tac]) eqs end;
246 in ((prefix, (fs, defs)), prove) end
247 handle PrimrecError (msg, some_eqn) =>
248 error ("Primrec definition error:\n" ^ msg ^ (case some_eqn
249 of SOME eqn => "\nin\n" ^ quote (Syntax.string_of_term lthy eqn)
253 (* primrec definition *)
255 fun add_primrec_simple fixes ts lthy =
257 val ((prefix, (fs, defs)), prove) = distill lthy fixes ts;
260 |> fold_map (LocalTheory.define Thm.definitionK) defs
261 |-> (fn defs => `(fn lthy => (prefix, prove lthy defs)))
266 fun gen_primrec set_group prep_spec raw_fixes raw_spec lthy =
268 val (fixes, spec) = fst (prep_spec raw_fixes raw_spec lthy);
269 fun attr_bindings prefix = map (fn ((b, attrs), _) =>
270 (Binding.qualify false prefix b, Code.add_default_eqn_attrib :: attrs)) spec;
271 fun simp_attr_binding prefix = (Binding.qualify true prefix (Binding.name "simps"),
272 map (Attrib.internal o K)
273 [Simplifier.simp_add, Nitpick_Const_Simp_Thms.add, Quickcheck_RecFun_Simp_Thms.add]);
276 |> set_group ? LocalTheory.set_group (serial_string ())
277 |> add_primrec_simple fixes (map snd spec)
278 |-> (fn (prefix, simps) => fold_map (LocalTheory.note Thm.generatedK)
279 (attr_bindings prefix ~~ simps)
280 #-> (fn simps' => LocalTheory.note Thm.generatedK
281 (simp_attr_binding prefix, maps snd simps')))
287 val add_primrec = gen_primrec false Specification.check_spec;
288 val add_primrec_cmd = gen_primrec true Specification.read_spec;
292 fun add_primrec_global fixes specs thy =
294 val lthy = TheoryTarget.init NONE thy;
295 val (simps, lthy') = add_primrec fixes specs lthy;
296 val simps' = ProofContext.export lthy' lthy simps;
297 in (simps', LocalTheory.exit_global lthy') end;
299 fun add_primrec_overloaded ops fixes specs thy =
301 val lthy = TheoryTarget.overloading ops thy;
302 val (simps, lthy') = add_primrec fixes specs lthy;
303 val simps' = ProofContext.export lthy' lthy simps;
304 in (simps', LocalTheory.exit_global lthy') end;
309 local structure P = OuterParse and K = OuterKeyword in
311 val opt_unchecked_name =
312 Scan.optional (P.$$$ "(" |-- P.!!!
313 (((P.$$$ "unchecked" >> K true) -- Scan.optional P.name "" ||
314 P.name >> pair false) --| P.$$$ ")")) (false, "");
316 val old_primrec_decl =
317 opt_unchecked_name -- Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Binding.name_of) -- P.prop);
319 val primrec_decl = P.opt_target -- P.fixes -- SpecParse.where_alt_specs;
322 OuterSyntax.command "primrec" "define primitive recursive functions on datatypes" K.thy_decl
323 ((primrec_decl >> (fn ((opt_target, fixes), specs) =>
324 Toplevel.local_theory opt_target (add_primrec_cmd fixes specs #> snd)))
325 || (old_primrec_decl >> (fn ((unchecked, alt_name), eqns) =>
326 Toplevel.theory (snd o
327 (if unchecked then OldPrimrecPackage.add_primrec_unchecked else OldPrimrecPackage.add_primrec)
328 alt_name (map P.triple_swap eqns)))));