(* Title: HOL/Tools/choice_specification.ML
Author: Sebastian Skalberg, TU Muenchen
Package for defining constants by specification.
*)
signature CHOICE_SPECIFICATION =
sig
val close_form : term -> term
val add_specification: string option -> (bstring * xstring * bool) list ->
theory * thm -> theory * thm
end
structure Choice_Specification: CHOICE_SPECIFICATION =
struct
(* actual code *)
fun close_form t =
fold_rev (fn (s, T) => fn t => HOLogic.mk_all (s, T, t))
(map dest_Free (Misc_Legacy.term_frees t)) t
fun add_final overloaded (c, T) thy =
let
val ctxt = Syntax.init_pretty_global thy;
val _ = Theory.check_overloading ctxt overloaded (c, T);
in Theory.add_deps ctxt "" (c, T) [] thy end;
local
fun mk_definitional [] arg = arg
| mk_definitional ((thname,cname,covld)::cos) (thy,thm) =
case HOLogic.dest_Trueprop (concl_of thm) of
Const(@{const_name Ex},_) $ P =>
let
val ctype = domain_type (type_of P)
val cname_full = Sign.intern_const thy cname
val cdefname = if thname = ""
then Thm.def_name (Long_Name.base_name cname)
else thname
val def_eq = Logic.mk_equals (Const(cname_full,ctype),
HOLogic.choice_const ctype $ P)
val (thms, thy') = Global_Theory.add_defs covld [((Binding.name cdefname, def_eq),[])] thy
val thm' = [thm,hd thms] MRS @{thm exE_some}
in
mk_definitional cos (thy',thm')
end
| _ => raise THM ("Internal error: Bad specification theorem",0,[thm])
fun mk_axiomatic axname cos arg =
let
fun process [] (thy,tm) =
let
val (thm, thy') =
Specification.axiom ((Binding.name axname, []), HOLogic.mk_Trueprop tm) thy
in
(thy', Drule.export_without_context thm)
end
| process ((thname,cname,covld)::cos) (thy,tm) =
case tm of
Const(@{const_name Ex},_) $ P =>
let
val ctype = domain_type (type_of P)
val cname_full = Sign.intern_const thy cname
val cdefname = if thname = ""
then Thm.def_name (Long_Name.base_name cname)
else thname
val thy' = add_final covld (cname_full,ctype) thy
val co = Const (cname_full,ctype)
val tm' = case P of
Abs(_, _, bodt) => subst_bound (co, bodt)
| _ => P $ co
in
process cos (thy',tm')
end
| _ => raise TERM ("Internal error: Bad specification theorem",[tm])
in
process cos arg
end
in
fun proc_exprop axiomatic cos arg =
case axiomatic of
SOME axname => mk_axiomatic axname cos (apsnd (HOLogic.dest_Trueprop o concl_of) arg)
| NONE => mk_definitional cos arg
end
fun add_specification axiomatic cos =
proc_exprop axiomatic cos
#> apsnd Drule.export_without_context
(* Collect all intances of constants in term *)
fun collect_consts ( t $ u,tms) = collect_consts (u,collect_consts (t,tms))
| collect_consts ( Abs(_,_,t),tms) = collect_consts (t,tms)
| collect_consts (tm as Const _,tms) = insert (op aconv) tm tms
| collect_consts ( _,tms) = tms
(* Complementing Type.varify_global... *)
fun unvarify_global t fmap =
let
val fmap' = map Library.swap fmap
fun unthaw (f as (a, S)) =
(case AList.lookup (op =) fmap' a of
NONE => TVar f
| SOME (b, _) => TFree (b, S))
in
map_types (map_type_tvar unthaw) t
end
(* The syntactic meddling needed to setup add_specification for work *)
fun process_spec axiomatic cos alt_props thy =
let
fun zip3 [] [] [] = []
| zip3 (x::xs) (y::ys) (z::zs) = (x,y,z)::zip3 xs ys zs
| zip3 _ _ _ = error "Choice_Specification.process_spec internal error"
fun myfoldr f [x] = x
| myfoldr f (x::xs) = f (x,myfoldr f xs)
| myfoldr f [] = error "Choice_Specification.process_spec internal error"
val rew_imps = alt_props |>
map (Object_Logic.atomize o Thm.cterm_of thy o Syntax.read_prop_global thy o snd)
val props' = rew_imps |>
map (HOLogic.dest_Trueprop o term_of o snd o Thm.dest_equals o cprop_of)
fun proc_single prop =
let
val frees = Misc_Legacy.term_frees prop
val _ = forall (fn v => Sign.of_sort thy (type_of v,HOLogic.typeS)) frees
orelse error "Specificaton: Only free variables of sort 'type' allowed"
val prop_closed = close_form prop
in
(prop_closed,frees)
end
val props'' = map proc_single props'
val frees = map snd props''
val prop = myfoldr HOLogic.mk_conj (map fst props'')
val cprop = cterm_of thy (HOLogic.mk_Trueprop prop)
val (vmap, prop_thawed) = Type.varify_global [] prop
val thawed_prop_consts = collect_consts (prop_thawed,[])
val (altcos,overloaded) = Library.split_list cos
val (names,sconsts) = Library.split_list altcos
val consts = map (Syntax.read_term_global thy) sconsts
val _ = not (Library.exists (not o Term.is_Const) consts)
orelse error "Specification: Non-constant found as parameter"
fun proc_const c =
let
val (_, c') = Type.varify_global [] c
val (cname,ctyp) = dest_Const c'
in
case filter (fn t => let val (name,typ) = dest_Const t
in name = cname andalso Sign.typ_equiv thy (typ, ctyp)
end) thawed_prop_consts of
[] => error ("Specification: No suitable instances of constant \"" ^ Syntax.string_of_term_global thy c ^ "\" found")
| [cf] => unvarify_global cf vmap
| _ => error ("Specification: Several variations of \"" ^ Syntax.string_of_term_global thy c ^ "\" found (try applying explicit type constraints)")
end
val proc_consts = map proc_const consts
fun mk_exist c prop =
let
val T = type_of c
val cname = Long_Name.base_name (fst (dest_Const c))
val vname = if Lexicon.is_identifier cname
then cname
else "x"
in
HOLogic.exists_const T $ Abs(vname,T,Term.abstract_over (c,prop))
end
val ex_prop = fold_rev mk_exist proc_consts prop
val cnames = map (fst o dest_Const) proc_consts
fun post_process (arg as (thy,thm)) =
let
fun inst_all thy v thm =
let
val cv = cterm_of thy v
val cT = ctyp_of_term cv
val spec' = instantiate' [SOME cT] [NONE,SOME cv] spec
in
thm RS spec'
end
fun remove_alls frees thm =
fold (inst_all (Thm.theory_of_thm thm)) frees thm
fun process_single ((name,atts),rew_imp,frees) args =
let
fun undo_imps thm =
Thm.equal_elim (Thm.symmetric rew_imp) thm
fun add_final (thm, thy) =
if name = ""
then (thm, thy)
else (writeln (" " ^ name ^ ": " ^ Display.string_of_thm_global thy thm);
Global_Theory.store_thm (Binding.name name, thm) thy)
in
swap args
|> apfst (remove_alls frees)
|> apfst undo_imps
|> apfst Drule.export_without_context
|-> Thm.theory_attributes
(map (Attrib.attribute_cmd_global thy)
(@{attributes [nitpick_choice_spec]} @ atts))
|> add_final
|> swap
end
fun process_all [proc_arg] args =
process_single proc_arg args
| process_all (proc_arg::rest) (thy,thm) =
let
val single_th = thm RS conjunct1
val rest_th = thm RS conjunct2
val (thy',_) = process_single proc_arg (thy,single_th)
in
process_all rest (thy',rest_th)
end
| process_all [] _ = error "Choice_Specification.process_spec internal error"
val alt_names = map fst alt_props
val _ = if exists (fn(name,_) => not (name = "")) alt_names
then writeln "specification"
else ()
in
arg |> apsnd Thm.unvarify_global
|> process_all (zip3 alt_names rew_imps frees)
end
fun after_qed [[thm]] = Proof_Context.background_theory (fn thy =>
#1 (post_process (add_specification axiomatic (zip3 names cnames overloaded) (thy, thm))));
in
thy
|> Proof_Context.init_global
|> Variable.declare_term ex_prop
|> Proof.theorem NONE after_qed [[(HOLogic.mk_Trueprop ex_prop, [])]]
end;
(* outer syntax *)
val opt_name = Scan.optional (Parse.name --| @{keyword ":"}) ""
val opt_overloaded = Parse.opt_keyword "overloaded"
val _ =
Outer_Syntax.command @{command_spec "specification"} "define constants by specification"
(@{keyword "("} |-- Scan.repeat1 (opt_name -- Parse.term -- opt_overloaded) --| @{keyword ")"} --
Scan.repeat1 ((Parse_Spec.opt_thm_name ":" >> apfst Binding.name_of) -- Parse.prop)
>> (fn (cos, alt_props) => Toplevel.print o
(Toplevel.theory_to_proof (process_spec NONE cos alt_props))))
val _ =
Outer_Syntax.command @{command_spec "ax_specification"} "define constants by specification"
(Parse.name --
(@{keyword "("} |-- Scan.repeat1 (opt_name -- Parse.term -- opt_overloaded) --| @{keyword ")"} --
Scan.repeat1 ((Parse_Spec.opt_thm_name ":" >> apfst Binding.name_of) -- Parse.prop))
>> (fn (axname, (cos, alt_props)) =>
Toplevel.print o (Toplevel.theory_to_proof (process_spec (SOME axname) cos alt_props))))
end