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(* Title: HOL/Import/import_rule.ML
Author: Cezary Kaliszyk, University of Innsbruck
Author: Alexander Krauss, QAware GmbH
Importer proof rules and processing of lines and files.
Based on earlier code by Steven Obua and Sebastian Skalberg.
*)
signature IMPORT_RULE =
sig
val beta : cterm -> thm
val eq_mp : thm -> thm -> thm
val comb : thm -> thm -> thm
val trans : thm -> thm -> thm
val deduct : thm -> thm -> thm
val conj1 : thm -> thm
val conj2 : thm -> thm
val refl : cterm -> thm
val abs : cterm -> thm -> thm
val mdef : string -> theory -> thm
val def : string -> cterm -> theory -> thm * theory
val mtydef : string -> theory -> thm
val tydef :
string -> string -> string -> cterm -> cterm -> thm -> theory -> thm * theory
val inst_type : (ctyp * ctyp) list -> thm -> theory -> thm
val inst : (cterm * cterm) list -> thm -> thm
type state
val init_state : state
val process_line : string -> (theory * state) -> (theory * state)
val process_file : Path.T -> theory -> theory
end
structure Import_Rule: IMPORT_RULE =
struct
val init_state = ((Inttab.empty, 0), (Inttab.empty, 0), (Inttab.empty, 0))
type state = (ctyp Inttab.table * int) * (cterm Inttab.table * int) * (thm Inttab.table * int)
fun implies_elim_all th = implies_elim_list th (map Thm.assume (cprems_of th))
fun meta_mp th1 th2 =
let
val th1a = implies_elim_all th1
val th1b = Thm.implies_intr (strip_imp_concl (Thm.cprop_of th2)) th1a
val th2a = implies_elim_all th2
val th3 = Thm.implies_elim th1b th2a
in
implies_intr_hyps th3
end
fun meta_eq_to_obj_eq th =
let
val (tml, tmr) = Thm.dest_binop (strip_imp_concl (Thm.cprop_of th))
val cty = Thm.ctyp_of_cterm tml
val i = Thm.instantiate' [SOME cty] [SOME tml, SOME tmr]
@{thm meta_eq_to_obj_eq}
in
Thm.implies_elim i th
end
fun beta ct = meta_eq_to_obj_eq (Thm.beta_conversion false ct)
fun eq_mp th1 th2 =
let
val (tm1l, tm1r) = Thm.dest_binop (Thm.dest_arg (strip_imp_concl (Thm.cprop_of th1)))
val i1 = Thm.instantiate' [] [SOME tm1l, SOME tm1r] @{thm iffD1}
val i2 = meta_mp i1 th1
in
meta_mp i2 th2
end
fun comb th1 th2 =
let
val t1c = Thm.dest_arg (strip_imp_concl (Thm.cprop_of th1))
val t2c = Thm.dest_arg (strip_imp_concl (Thm.cprop_of th2))
val (cf, cg) = Thm.dest_binop t1c
val (cx, cy) = Thm.dest_binop t2c
val [fd, fr] = Thm.dest_ctyp (Thm.ctyp_of_cterm cf)
val i1 = Thm.instantiate' [SOME fd, SOME fr]
[SOME cf, SOME cg, SOME cx, SOME cy] @{thm cong}
val i2 = meta_mp i1 th1
in
meta_mp i2 th2
end
fun trans th1 th2 =
let
val t1c = Thm.dest_arg (strip_imp_concl (Thm.cprop_of th1))
val t2c = Thm.dest_arg (strip_imp_concl (Thm.cprop_of th2))
val (r, s) = Thm.dest_binop t1c
val (_, t) = Thm.dest_binop t2c
val ty = Thm.ctyp_of_cterm r
val i1 = Thm.instantiate' [SOME ty] [SOME r, SOME s, SOME t] @{thm trans}
val i2 = meta_mp i1 th1
in
meta_mp i2 th2
end
fun deduct th1 th2 =
let
val th1c = strip_imp_concl (Thm.cprop_of th1)
val th2c = strip_imp_concl (Thm.cprop_of th2)
val th1a = implies_elim_all th1
val th2a = implies_elim_all th2
val th1b = Thm.implies_intr th2c th1a
val th2b = Thm.implies_intr th1c th2a
val i = Thm.instantiate' []
[SOME (Thm.dest_arg th1c), SOME (Thm.dest_arg th2c)] @{thm iffI}
val i1 = Thm.implies_elim i (Thm.assume (Thm.cprop_of th2b))
val i2 = Thm.implies_elim i1 th1b
val i3 = Thm.implies_intr (Thm.cprop_of th2b) i2
val i4 = Thm.implies_elim i3 th2b
in
implies_intr_hyps i4
end
fun conj1 th =
let
val (tml, tmr) = Thm.dest_binop (Thm.dest_arg (strip_imp_concl (Thm.cprop_of th)))
val i = Thm.instantiate' [] [SOME tml, SOME tmr] @{thm conjunct1}
in
meta_mp i th
end
fun conj2 th =
let
val (tml, tmr) = Thm.dest_binop (Thm.dest_arg (strip_imp_concl (Thm.cprop_of th)))
val i = Thm.instantiate' [] [SOME tml, SOME tmr] @{thm conjunct2}
in
meta_mp i th
end
fun refl ctm =
let
val cty = Thm.ctyp_of_cterm ctm
in
Thm.instantiate' [SOME cty] [SOME ctm] @{thm refl}
end
fun abs cv th =
let
val th1 = implies_elim_all th
val (tl, tr) = Thm.dest_binop (Thm.dest_arg (strip_imp_concl (Thm.cprop_of th1)))
val (ll, lr) = (Thm.lambda cv tl, Thm.lambda cv tr)
val (al, ar) = (Thm.apply ll cv, Thm.apply lr cv)
val bl = beta al
val br = meta_eq_to_obj_eq (Thm.symmetric (Thm.beta_conversion false ar))
val th2 = trans (trans bl th1) br
val th3 = implies_elim_all th2
val th4 = Thm.forall_intr cv th3
val i = Thm.instantiate' [SOME (Thm.ctyp_of_cterm cv), SOME (Thm.ctyp_of_cterm tl)]
[SOME ll, SOME lr] @{thm ext2}
in
meta_mp i th4
end
fun freezeT thy thm =
let
val tvars = Term.add_tvars (Thm.prop_of thm) []
val tfrees = map (fn ((t, _), s) => TFree (t, s)) tvars
in
Thm.instantiate ((tvars ~~ map (Thm.global_ctyp_of thy) tfrees), []) thm
end
fun def' constname rhs thy =
let
val rhs = Thm.term_of rhs
val typ = type_of rhs
val constbinding = Binding.name constname
val thy1 = Sign.add_consts [(constbinding, typ, NoSyn)] thy
val eq = Logic.mk_equals (Const (Sign.full_name thy1 constbinding, typ), rhs)
val (thms, thy2) = Global_Theory.add_defs false
[((Binding.suffix_name "_hldef" constbinding, eq), [])] thy1
val def_thm = freezeT thy1 (hd thms)
in
(meta_eq_to_obj_eq def_thm, thy2)
end
fun mdef name thy =
case Import_Data.get_const_def name thy of
SOME th => th
| NONE => error ("constant mapped but no definition: " ^ name)
fun def constname rhs thy =
case Import_Data.get_const_def constname thy of
SOME _ =>
let
val () = warning ("Const mapped but def provided: " ^ constname)
in
(mdef constname thy, thy)
end
| NONE => def' constname rhs thy
fun typedef_hollight th thy =
let
val (th_s, cn) = Thm.dest_comb (Thm.dest_arg (Thm.cprop_of th))
val (th_s, abst) = Thm.dest_comb th_s
val rept = Thm.dest_arg th_s
val P = Thm.dest_arg cn
val [nty, oty] = Thm.dest_ctyp (Thm.ctyp_of_cterm rept)
in
Thm.instantiate' [SOME nty, SOME oty] [SOME rept, SOME abst, SOME P,
SOME (Thm.global_cterm_of thy (Free ("a", Thm.typ_of nty))),
SOME (Thm.global_cterm_of thy (Free ("r", Thm.typ_of oty)))] @{thm typedef_hol2hollight}
end
fun tydef' tycname abs_name rep_name cP ct td_th thy =
let
val ctT = Thm.ctyp_of_cterm ct
val nonempty = Thm.instantiate' [SOME ctT] [SOME cP, SOME ct] @{thm light_ex_imp_nonempty}
val th2 = meta_mp nonempty td_th
val c =
case Thm.concl_of th2 of
_ $ (Const(\<^const_name>\<open>Ex\<close>,_) $ Abs(_,_,Const(\<^const_name>\<open>Set.member\<close>,_) $ _ $ c)) => c
| _ => error "type_introduction: bad type definition theorem"
val tfrees = Term.add_tfrees c []
val tnames = sort_strings (map fst tfrees)
val typedef_bindings =
{Rep_name = Binding.name rep_name,
Abs_name = Binding.name abs_name,
type_definition_name = Binding.name ("type_definition_" ^ tycname)}
val ((_, typedef_info), thy') =
Named_Target.theory_map_result (apsnd o Typedef.transform_info)
(Typedef.add_typedef {overloaded = false}
(Binding.name tycname, map (rpair dummyS) tnames, NoSyn) c
(SOME typedef_bindings) (fn ctxt => resolve_tac ctxt [th2] 1)) thy
val aty = #abs_type (#1 typedef_info)
val th = freezeT thy' (#type_definition (#2 typedef_info))
val (th_s, _) = Thm.dest_comb (Thm.dest_arg (Thm.cprop_of th))
val (th_s, abst) = Thm.dest_comb th_s
val rept = Thm.dest_arg th_s
val [nty, oty] = Thm.dest_ctyp (Thm.ctyp_of_cterm rept)
val typedef_th =
Thm.instantiate'
[SOME nty, SOME oty]
[SOME rept, SOME abst, SOME cP, SOME (Thm.global_cterm_of thy' (Free ("a", aty))),
SOME (Thm.global_cterm_of thy' (Free ("r", Thm.typ_of ctT)))]
@{thm typedef_hol2hollight}
val th4 = typedef_th OF [#type_definition (#2 typedef_info)]
in
(th4, thy')
end
fun mtydef name thy =
case Import_Data.get_typ_def name thy of
SOME thn => meta_mp (typedef_hollight thn thy) thn
| NONE => error ("type mapped but no tydef thm registered: " ^ name)
fun tydef tycname abs_name rep_name P t td_th thy =
case Import_Data.get_typ_def tycname thy of
SOME _ =>
let
val () = warning ("Type mapped but proofs provided: " ^ tycname)
in
(mtydef tycname thy, thy)
end
| NONE => tydef' tycname abs_name rep_name P t td_th thy
fun inst_type lambda th thy =
let
fun assoc _ [] = error "assoc"
| assoc x ((x',y)::rest) = if x = x' then y else assoc x rest
val lambda = map (fn (a, b) => (Thm.typ_of a, b)) lambda
val tys_before = Term.add_tfrees (Thm.prop_of th) []
val th1 = Thm.varifyT_global th
val tys_after = Term.add_tvars (Thm.prop_of th1) []
val tyinst =
map2 (fn bef => fn iS =>
(case try (assoc (TFree bef)) lambda of
SOME cty => (iS, cty)
| NONE => (iS, Thm.global_ctyp_of thy (TFree bef))))
tys_before tys_after
in
Thm.instantiate (tyinst,[]) th1
end
fun inst sigma th =
let
val (dom, rng) = ListPair.unzip (rev sigma)
in
th |> forall_intr_list dom
|> forall_elim_list rng
end
fun transl_dotc #"." = "dot"
| transl_dotc c = Char.toString c
val transl_dot = String.translate transl_dotc
fun transl_qmc #"?" = "t"
| transl_qmc c = Char.toString c
val transl_qm = String.translate transl_qmc
fun getconstname s thy =
case Import_Data.get_const_map s thy of
SOME s => s
| NONE => Sign.full_name thy (Binding.name (transl_dot s))
fun gettyname s thy =
case Import_Data.get_typ_map s thy of
SOME s => s
| NONE => Sign.full_name thy (Binding.name s)
fun get (map, no) s =
case Int.fromString s of
NONE => error "Import_Rule.get: not a number"
| SOME i => (case Inttab.lookup map (Int.abs i) of
NONE => error "Import_Rule.get: lookup failed"
| SOME res => (res, (if i < 0 then Inttab.delete (Int.abs i) map else map, no)))
fun getty i (thy, (tyi, tmi, thi)) = let val (i, tyi) = (get tyi i) in (i, (thy, (tyi, tmi, thi))) end
fun gettm i (thy, (tyi, tmi, thi)) = let val (i, tmi) = (get tmi i) in (i, (thy, (tyi, tmi, thi))) end
fun getth i (thy, (tyi, tmi, thi)) = let val (i, thi) = (get thi i) in (i, (thy, (tyi, tmi, thi))) end
fun set (map, no) v = (Inttab.update_new (no + 1, v) map, no + 1)
fun setty v (thy, (tyi, tmi, thi)) = (thy, (set tyi v, tmi, thi))
fun settm v (thy, (tyi, tmi, thi)) = (thy, (tyi, set tmi v, thi))
fun setth v (thy, (tyi, tmi, thi)) = (thy, (tyi, tmi, set thi v))
fun last_thm (_, _, (map, no)) =
case Inttab.lookup map no of
NONE => error "Import_Rule.last_thm: lookup failed"
| SOME thm => thm
fun listLast (h1 :: (h2 :: t)) = apfst (fn t => h1 :: h2 :: t) (listLast t)
| listLast [p] = ([], p)
| listLast [] = error "listLast: empty"
fun pairList (h1 :: (h2 :: t)) = ((h1, h2) :: pairList t)
| pairList [] = []
| pairList _ = error "pairList: odd list length"
fun store_thm binding thm thy =
let
val ctxt = Proof_Context.init_global thy
val thm = Drule.export_without_context_open thm
val tvs = Term.add_tvars (Thm.prop_of thm) []
val tns = map (fn (_, _) => "'") tvs
val nms = fst (fold_map Name.variant tns (Variable.names_of ctxt))
val vs = map TVar ((nms ~~ (map (snd o fst) tvs)) ~~ (map snd tvs))
val thm' = Thm.instantiate ((tvs ~~ map (Thm.ctyp_of ctxt) vs), []) thm
in
snd (Global_Theory.add_thm ((binding, thm'), []) thy)
end
fun log_timestamp () =
let
val time = Time.now ()
val millis = nth (space_explode "." (Time.fmt 3 time)) 1
in
Date.fmt "%d.%m.%Y %H:%M:%S." (Date.fromTimeLocal time) ^ millis
end
fun process_line str tstate =
let
fun process tstate (#"R", [t]) = gettm t tstate |>> refl |-> setth
| process tstate (#"B", [t]) = gettm t tstate |>> beta |-> setth
| process tstate (#"1", [th]) = getth th tstate |>> conj1 |-> setth
| process tstate (#"2", [th]) = getth th tstate |>> conj2 |-> setth
| process tstate (#"H", [t]) =
gettm t tstate |>> Thm.apply \<^cterm>\<open>Trueprop\<close> |>> Thm.trivial |-> setth
| process tstate (#"A", [_, t]) =
gettm t tstate |>> Thm.apply \<^cterm>\<open>Trueprop\<close> |>> Skip_Proof.make_thm_cterm |-> setth
| process tstate (#"C", [th1, th2]) =
getth th1 tstate ||>> getth th2 |>> (fn (t1, t2) => comb t1 t2) |-> setth
| process tstate (#"T", [th1, th2]) =
getth th1 tstate ||>> getth th2 |>> (fn (t1, t2) => trans t1 t2) |-> setth
| process tstate (#"E", [th1, th2]) =
getth th1 tstate ||>> getth th2 |>> (fn (t1, t2) => eq_mp t1 t2) |-> setth
| process tstate (#"D", [th1, th2]) =
getth th1 tstate ||>> getth th2 |>> (fn (t1, t2) => deduct t1 t2) |-> setth
| process tstate (#"L", [t, th]) =
gettm t tstate ||>> (fn ti => getth th ti) |>> (fn (tm, th) => abs tm th) |-> setth
| process (thy, state) (#"M", [s]) =
let
val ctxt = Proof_Context.init_global thy
val thm = freezeT thy (Global_Theory.get_thm thy s)
val ((_, [th']), _) = Variable.import true [thm] ctxt
in
setth th' (thy, state)
end
| process (thy, state) (#"Q", l) =
let
val (tys, th) = listLast l
val (th, tstate) = getth th (thy, state)
val (tys, tstate) = fold_map getty tys tstate
in
setth (inst_type (pairList tys) th thy) tstate
end
| process tstate (#"S", l) =
let
val (tms, th) = listLast l
val (th, tstate) = getth th tstate
val (tms, tstate) = fold_map gettm tms tstate
in
setth (inst (pairList tms) th) tstate
end
| process tstate (#"F", [name, t]) =
let
val (tm, (thy, state)) = gettm t tstate
val (th, thy) = def (transl_dot name) tm thy
in
setth th (thy, state)
end
| process (thy, state) (#"F", [name]) = setth (mdef name thy) (thy, state)
| process tstate (#"Y", [name, absname, repname, t1, t2, th]) =
let
val (th, tstate) = getth th tstate
val (t1, tstate) = gettm t1 tstate
val (t2, (thy, state)) = gettm t2 tstate
val (th, thy) = tydef name absname repname t1 t2 th thy
in
setth th (thy, state)
end
| process (thy, state) (#"Y", [name, _, _]) = setth (mtydef name thy) (thy, state)
| process (thy, state) (#"t", [n]) =
setty (Thm.global_ctyp_of thy (TFree ("'" ^ (transl_qm n), \<^sort>\<open>type\<close>))) (thy, state)
| process (thy, state) (#"a", n :: l) =
fold_map getty l (thy, state) |>>
(fn tys => Thm.global_ctyp_of thy (Type (gettyname n thy, map Thm.typ_of tys))) |-> setty
| process (thy, state) (#"v", [n, ty]) =
getty ty (thy, state) |>> (fn ty => Thm.global_cterm_of thy (Free (transl_dot n, Thm.typ_of ty))) |-> settm
| process (thy, state) (#"c", [n, ty]) =
getty ty (thy, state) |>> (fn ty => Thm.global_cterm_of thy (Const (getconstname n thy, Thm.typ_of ty))) |-> settm
| process tstate (#"f", [t1, t2]) =
gettm t1 tstate ||>> gettm t2 |>> (fn (t1, t2) => Thm.apply t1 t2) |-> settm
| process tstate (#"l", [t1, t2]) =
gettm t1 tstate ||>> gettm t2 |>> (fn (t1, t2) => Thm.lambda t1 t2) |-> settm
| process (thy, state) (#"+", [s]) =
(store_thm (Binding.name (transl_dot s)) (last_thm state) thy, state)
| process _ (c, _) = error ("process: unknown command: " ^ String.implode [c])
fun parse_line s =
case String.tokens (fn x => (x = #"\n" orelse x = #" ")) s of
[] => error "parse_line: empty"
| h :: t => (case String.explode h of
[] => error "parse_line: empty command"
| sh :: st => (sh, (String.implode st) :: t))
in
process tstate (parse_line str)
end
fun process_file path thy =
(thy, init_state) |> File.fold_lines process_line path |> fst
val _ = Outer_Syntax.command \<^command_keyword>\<open>import_file\<close>
"import a recorded proof file"
(Parse.path >> (fn name => Toplevel.theory (fn thy => process_file (Path.explode name) thy)))
end
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