1 (* Title: HOL/Tools/specification_package.ML
3 Author: Sebastian Skalberg, TU Muenchen
5 Package for defining constants by specification.
8 signature SPECIFICATION_PACKAGE =
10 val quiet_mode: bool ref
11 val add_specification: string option -> (bstring * xstring * bool) list ->
12 theory * thm -> theory * thm
15 structure SpecificationPackage: SPECIFICATION_PACKAGE =
20 val quiet_mode = ref false
21 fun message s = if ! quiet_mode then () else writeln s
27 val exE_some = thm "exE_some";
29 fun mk_definitional [] arg = arg
30 | mk_definitional ((thname,cname,covld)::cos) (thy,thm) =
31 case HOLogic.dest_Trueprop (concl_of thm) of
34 val ctype = domain_type (type_of P)
35 val cname_full = Sign.intern_const thy cname
36 val cdefname = if thname = ""
37 then Thm.def_name (Sign.base_name cname)
39 val def_eq = Logic.mk_equals (Const(cname_full,ctype),
40 HOLogic.choice_const ctype $ P)
41 val (thms, thy') = PureThy.add_defs_i covld [((cdefname,def_eq),[])] thy
42 val thm' = [thm,hd thms] MRS exE_some
44 mk_definitional cos (thy',thm')
46 | _ => raise THM ("Internal error: Bad specification theorem",0,[thm])
48 fun mk_axiomatic axname cos arg =
50 fun process [] (thy,tm) =
52 val (thms, thy') = PureThy.add_axioms_i [((axname,HOLogic.mk_Trueprop tm),[])] thy
56 | process ((thname,cname,covld)::cos) (thy,tm) =
60 val ctype = domain_type (type_of P)
61 val cname_full = Sign.intern_const thy cname
62 val cdefname = if thname = ""
63 then Thm.def_name (Sign.base_name cname)
65 val co = Const(cname_full,ctype)
66 val thy' = Theory.add_finals_i covld [co] thy
68 Abs(_, _, bodt) => subst_bound (co, bodt)
71 process cos (thy',tm')
73 | _ => raise TERM ("Internal error: Bad specification theorem",[tm])
79 fun proc_exprop axiomatic cos arg =
81 SOME axname => mk_axiomatic axname cos (apsnd (HOLogic.dest_Trueprop o concl_of) arg)
82 | NONE => mk_definitional cos arg
85 fun add_specification axiomatic cos arg =
86 arg |> apsnd Thm.freezeT
87 |> proc_exprop axiomatic cos
91 (* Collect all intances of constants in term *)
93 fun collect_consts ( t $ u,tms) = collect_consts (u,collect_consts (t,tms))
94 | collect_consts ( Abs(_,_,t),tms) = collect_consts (t,tms)
95 | collect_consts (tm as Const _,tms) = insert (op aconv) tm tms
96 | collect_consts ( _,tms) = tms
98 (* Complementing Type.varify... *)
100 fun unvarify t fmap =
102 val fmap' = map Library.swap fmap
103 fun unthaw (f as (a, S)) =
104 (case AList.lookup (op =) fmap' a of
106 | SOME (b, _) => TFree (b, S))
108 map_types (map_type_tvar unthaw) t
111 (* The syntactic meddling needed to setup add_specification for work *)
113 fun process_spec axiomatic cos alt_props thy =
115 fun zip3 [] [] [] = []
116 | zip3 (x::xs) (y::ys) (z::zs) = (x,y,z)::zip3 xs ys zs
117 | zip3 _ _ _ = error "SpecificationPackage.process_spec internal error"
119 fun myfoldr f [x] = x
120 | myfoldr f (x::xs) = f (x,myfoldr f xs)
121 | myfoldr f [] = error "SpecificationPackage.process_spec internal error"
123 val rew_imps = alt_props |>
124 map (ObjectLogic.atomize o Thm.cterm_of thy o Syntax.read_prop_global thy o snd)
125 val props' = rew_imps |>
126 map (HOLogic.dest_Trueprop o term_of o snd o Thm.dest_equals o cprop_of)
128 fun proc_single prop =
130 val frees = Term.term_frees prop
131 val _ = forall (fn v => Sign.of_sort thy (type_of v,HOLogic.typeS)) frees
132 orelse error "Specificaton: Only free variables of sort 'type' allowed"
133 val prop_closed = foldr (fn ((vname,T),prop) => HOLogic.mk_all (vname,T,prop)) prop (map dest_Free frees)
138 val props'' = map proc_single props'
139 val frees = map snd props''
140 val prop = myfoldr HOLogic.mk_conj (map fst props'')
141 val cprop = cterm_of thy (HOLogic.mk_Trueprop prop)
143 val (vmap, prop_thawed) = Type.varify [] prop
144 val thawed_prop_consts = collect_consts (prop_thawed,[])
145 val (altcos,overloaded) = Library.split_list cos
146 val (names,sconsts) = Library.split_list altcos
147 val consts = map (Syntax.read_term_global thy) sconsts
148 val _ = not (Library.exists (not o Term.is_Const) consts)
149 orelse error "Specification: Non-constant found as parameter"
153 val (_, c') = Type.varify [] c
154 val (cname,ctyp) = dest_Const c'
156 case List.filter (fn t => let val (name,typ) = dest_Const t
157 in name = cname andalso Sign.typ_equiv thy (typ, ctyp)
158 end) thawed_prop_consts of
159 [] => error ("Specification: No suitable instances of constant \"" ^ (Sign.string_of_term thy c) ^ "\" found")
160 | [cf] => unvarify cf vmap
161 | _ => error ("Specification: Several variations of \"" ^ (Sign.string_of_term thy c) ^ "\" found (try applying explicit type constraints)")
163 val proc_consts = map proc_const consts
164 fun mk_exist (c,prop) =
167 val cname = Sign.base_name (fst (dest_Const c))
168 val vname = if Syntax.is_identifier cname
172 HOLogic.exists_const T $ Abs(vname,T,Term.abstract_over (c,prop))
174 val ex_prop = foldr mk_exist prop proc_consts
175 val cnames = map (fst o dest_Const) proc_consts
176 fun post_process (arg as (thy,thm)) =
178 fun inst_all thy (thm,v) =
180 val cv = cterm_of thy v
181 val cT = ctyp_of_term cv
182 val spec' = instantiate' [SOME cT] [NONE,SOME cv] spec
186 fun remove_alls frees thm =
187 Library.foldl (inst_all (Thm.theory_of_thm thm)) (thm,frees)
188 fun process_single ((name,atts),rew_imp,frees) args =
191 equal_elim (symmetric rew_imp) thm
193 fun add_final (arg as (thy, thm)) =
195 then arg |> Library.swap
196 else (writeln (" " ^ name ^ ": " ^ (string_of_thm thm));
197 PureThy.store_thm ((name, thm), []) thy)
199 args |> apsnd (remove_alls frees)
202 |> Thm.theory_attributes (map (Attrib.attribute thy) atts)
207 fun process_all [proc_arg] args =
208 process_single proc_arg args
209 | process_all (proc_arg::rest) (thy,thm) =
211 val single_th = thm RS conjunct1
212 val rest_th = thm RS conjunct2
213 val (thy',_) = process_single proc_arg (thy,single_th)
215 process_all rest (thy',rest_th)
217 | process_all [] _ = error "SpecificationPackage.process_spec internal error"
218 val alt_names = map fst alt_props
219 val _ = if exists (fn(name,_) => not (name = "")) alt_names
220 then writeln "specification"
223 arg |> apsnd Thm.freezeT
224 |> process_all (zip3 alt_names rew_imps frees)
227 fun after_qed [[thm]] = ProofContext.theory (fn thy =>
228 #1 (post_process (add_specification axiomatic (zip3 names cnames overloaded) (thy, thm))));
232 |> Proof.theorem_i NONE after_qed [[(HOLogic.mk_Trueprop ex_prop, [])]]
238 local structure P = OuterParse and K = OuterKeyword in
240 val opt_name = Scan.optional (P.name --| P.$$$ ":") ""
241 val opt_overloaded = P.opt_keyword "overloaded";
243 val specification_decl =
244 P.$$$ "(" |-- Scan.repeat1 (opt_name -- P.term -- opt_overloaded) --| P.$$$ ")" --
245 Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop)
248 OuterSyntax.command "specification" "define constants by specification" K.thy_goal
249 (specification_decl >> (fn (cos,alt_props) =>
250 Toplevel.print o (Toplevel.theory_to_proof
251 (process_spec NONE cos alt_props))))
253 val ax_specification_decl =
255 (P.$$$ "(" |-- Scan.repeat1 (opt_name -- P.term -- opt_overloaded) --| P.$$$ ")" --
256 Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop))
259 OuterSyntax.command "ax_specification" "define constants by specification" K.thy_goal
260 (ax_specification_decl >> (fn (axname,(cos,alt_props)) =>
261 Toplevel.print o (Toplevel.theory_to_proof
262 (process_spec (SOME axname) cos alt_props))))