(* Title: HOL/Tools/ATP/atp_proof_reconstruct.ML
Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
Author: Claire Quigley, Cambridge University Computer Laboratory
Author: Jasmin Blanchette, TU Muenchen
Basic proof reconstruction from ATP proofs.
*)
signature ATP_PROOF_RECONSTRUCT =
sig
type 'a atp_type = 'a ATP_Problem.atp_type
type ('a, 'b) atp_term = ('a, 'b) ATP_Problem.atp_term
type ('a, 'b, 'c, 'd) atp_formula = ('a, 'b, 'c, 'd) ATP_Problem.atp_formula
type stature = ATP_Problem_Generate.stature
type atp_step_name = ATP_Proof.atp_step_name
type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
type 'a atp_proof = 'a ATP_Proof.atp_proof
val metisN : string
val full_typesN : string
val partial_typesN : string
val no_typesN : string
val really_full_type_enc : string
val full_type_enc : string
val partial_type_enc : string
val no_type_enc : string
val full_type_encs : string list
val partial_type_encs : string list
val default_metis_lam_trans : string
val metis_call : string -> string -> string
val forall_of : term -> term -> term
val exists_of : term -> term -> term
val unalias_type_enc : string -> string list
val term_of_atp : Proof.context -> bool -> int Symtab.table -> typ option ->
(string, string atp_type) atp_term -> term
val prop_of_atp : Proof.context -> bool -> int Symtab.table ->
(string, string, (string, string atp_type) atp_term, string) atp_formula -> term
val used_facts_in_atp_proof :
Proof.context -> (string * stature) list vector -> string atp_proof -> (string * stature) list
val used_facts_in_unsound_atp_proof : Proof.context -> (string * stature) list vector ->
'a atp_proof -> string list option
val atp_proof_prefers_lifting : string atp_proof -> bool
val is_typed_helper_used_in_atp_proof : string atp_proof -> bool
val replace_dependencies_in_line : atp_step_name * atp_step_name list -> ('a, 'b) atp_step ->
('a, 'b) atp_step
val termify_atp_proof : Proof.context -> string Symtab.table -> (string * term) list ->
int Symtab.table -> string atp_proof -> (term, string) atp_step list
val introduce_spass_skolem : (term, string) atp_step list -> (term, string) atp_step list
val factify_atp_proof : (string * 'a) list vector -> term list -> term ->
(term, string) atp_step list -> (term, string) atp_step list
end;
structure ATP_Proof_Reconstruct : ATP_PROOF_RECONSTRUCT =
struct
open ATP_Util
open ATP_Problem
open ATP_Proof
open ATP_Problem_Generate
val metisN = "metis"
val full_typesN = "full_types"
val partial_typesN = "partial_types"
val no_typesN = "no_types"
val really_full_type_enc = "mono_tags"
val full_type_enc = "poly_guards_query"
val partial_type_enc = "poly_args"
val no_type_enc = "erased"
val full_type_encs = [full_type_enc, really_full_type_enc]
val partial_type_encs = partial_type_enc :: full_type_encs
val type_enc_aliases =
[(full_typesN, full_type_encs),
(partial_typesN, partial_type_encs),
(no_typesN, [no_type_enc])]
fun unalias_type_enc s =
AList.lookup (op =) type_enc_aliases s |> the_default [s]
val default_metis_lam_trans = combsN
fun metis_call type_enc lam_trans =
let
val type_enc =
(case AList.find (fn (enc, encs) => enc = hd encs) type_enc_aliases type_enc of
[alias] => alias
| _ => type_enc)
val opts =
[] |> type_enc <> partial_typesN ? cons type_enc
|> lam_trans <> default_metis_lam_trans ? cons lam_trans
in metisN ^ (if null opts then "" else " (" ^ commas opts ^ ")") end
fun term_name' (Var ((s, _), _)) = perhaps (try Name.dest_skolem) s
| term_name' _ = ""
fun lambda' v = Term.lambda_name (term_name' v, v)
fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda' v t
fun exists_of v t = HOLogic.exists_const (fastype_of v) $ lambda' v t
fun make_tfree ctxt w =
let val ww = "'" ^ w in
TFree (ww, the_default HOLogic.typeS (Variable.def_sort ctxt (ww, ~1)))
end
exception ATP_CLASS of string list
exception ATP_TYPE of string atp_type list
exception ATP_TERM of (string, string atp_type) atp_term list
exception ATP_FORMULA of
(string, string, (string, string atp_type) atp_term, string) atp_formula list
exception SAME of unit
fun class_of_atp_class cls =
(case unprefix_and_unascii class_prefix cls of
SOME s => s
| NONE => raise ATP_CLASS [cls])
(* Type variables are given the basic sort "HOL.type". Some will later be constrained by information
from type literals, or by type inference. *)
fun typ_of_atp_type ctxt (ty as AType ((a, clss), tys)) =
let val Ts = map (typ_of_atp_type ctxt) tys in
(case unprefix_and_unascii type_const_prefix a of
SOME b => Type (invert_const b, Ts)
| NONE =>
if not (null tys) then
raise ATP_TYPE [ty] (* only "tconst"s have type arguments *)
else
(case unprefix_and_unascii tfree_prefix a of
SOME b => make_tfree ctxt b
| NONE =>
(* The term could be an Isabelle variable or a variable from the ATP, say "X1" or "_5018".
Sometimes variables from the ATP are indistinguishable from Isabelle variables, which
forces us to use a type parameter in all cases. *)
Type_Infer.param 0 ("'" ^ perhaps (unprefix_and_unascii tvar_prefix) a,
(if null clss then HOLogic.typeS else map class_of_atp_class clss))))
end
fun atp_type_of_atp_term (ATerm ((s, _), us)) = AType ((s, []), map atp_type_of_atp_term us)
fun typ_of_atp_term ctxt = typ_of_atp_type ctxt o atp_type_of_atp_term
(* Type class literal applied to a type. Returns triple of polarity, class, type. *)
fun type_constraint_of_term ctxt (u as ATerm ((a, _), us)) =
(case (unprefix_and_unascii class_prefix a, map (typ_of_atp_term ctxt) us) of
(SOME b, [T]) => (b, T)
| _ => raise ATP_TERM [u])
(* Accumulate type constraints in a formula: negative type literals. *)
fun add_var (key, z) = Vartab.map_default (key, []) (cons z)
fun add_type_constraint false (cl, TFree (a ,_)) = add_var ((a, ~1), cl)
| add_type_constraint false (cl, TVar (ix, _)) = add_var (ix, cl)
| add_type_constraint _ _ = I
fun repair_var_name_raw s =
let
fun subscript_name s n = s ^ nat_subscript n
val s = s |> String.map Char.toLower
in
(case space_explode "_" s of
[_] =>
(case take_suffix Char.isDigit (String.explode s) of
(cs1 as _ :: _, cs2 as _ :: _) =>
subscript_name (String.implode cs1) (the (Int.fromString (String.implode cs2)))
| (_, _) => s)
| [s1, s2] => (case Int.fromString s2 of SOME n => subscript_name s1 n | NONE => s)
| _ => s)
end
fun repair_var_name textual s =
(case unprefix_and_unascii schematic_var_prefix s of
SOME s => s
| NONE => s |> textual ? repair_var_name_raw)
(* The number of type arguments of a constant, zero if it's monomorphic. For (instances of) Skolem
pseudoconstants, this information is encoded in the constant name. *)
fun robust_const_num_type_args thy s =
if String.isPrefix skolem_const_prefix s then
s |> Long_Name.explode |> List.last |> Int.fromString |> the
else if String.isPrefix lam_lifted_prefix s then
if String.isPrefix lam_lifted_poly_prefix s then 2 else 0
else
(s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
fun slack_fastype_of t = fastype_of t handle TERM _ => HOLogic.typeT
(* Cope with "tt(X) = X" atoms, where "X" is existentially quantified. *)
fun loose_aconv (Free (s, _), Free (s', _)) = s = s'
| loose_aconv (t, t') = t aconv t'
val spass_skolem_prefix = "sk" (* "skc" or "skf" *)
val vampire_skolem_prefix = "sK"
(* First-order translation. No types are known for variables. "HOLogic.typeT" should allow them to
be inferred. *)
fun term_of_atp ctxt textual sym_tab =
let
val thy = Proof_Context.theory_of ctxt
(* For Metis, we use 1 rather than 0 because variable references in clauses may otherwise
conflict with variable constraints in the goal. At least, type inference often fails
otherwise. See also "axiom_inference" in "Metis_Reconstruct". *)
val var_index = if textual then 0 else 1
fun do_term extra_ts opt_T u =
(case u of
ATerm ((s, tys), us) =>
if s = ""
then error "Isar proof reconstruction failed because the ATP proof \
\contains unparsable material."
else if String.isPrefix native_type_prefix s then
@{const True} (* ignore TPTP type information *)
else if s = tptp_equal then
let val ts = map (do_term [] NONE) us in
if textual andalso length ts = 2 andalso loose_aconv (hd ts, List.last ts) then
@{const True}
else
list_comb (Const (@{const_name HOL.eq}, HOLogic.typeT), ts)
end
else
(case unprefix_and_unascii const_prefix s of
SOME s' =>
let val ((s', s''), mangled_us) = s' |> unmangled_const |>> `invert_const in
if s' = type_tag_name then
(case mangled_us @ us of
[typ_u, term_u] => do_term extra_ts (SOME (typ_of_atp_term ctxt typ_u)) term_u
| _ => raise ATP_TERM us)
else if s' = predicator_name then
do_term [] (SOME @{typ bool}) (hd us)
else if s' = app_op_name then
let val extra_t = do_term [] NONE (List.last us) in
do_term (extra_t :: extra_ts)
(case opt_T of
SOME T => SOME (slack_fastype_of extra_t --> T)
| NONE => NONE)
(nth us (length us - 2))
end
else if s' = type_guard_name then
@{const True} (* ignore type predicates *)
else
let
val new_skolem = String.isPrefix new_skolem_const_prefix s''
val num_ty_args = length us - the_default 0 (Symtab.lookup sym_tab s)
val (type_us, term_us) = chop num_ty_args us |>> append mangled_us
val term_ts = map (do_term [] NONE) term_us
val Ts = map (typ_of_atp_type ctxt) tys @ map (typ_of_atp_term ctxt) type_us
val T =
(if not (null Ts) andalso robust_const_num_type_args thy s' = length Ts then
if new_skolem then
SOME (Type_Infer.paramify_vars (tl Ts ---> hd Ts))
else if textual then
try (Sign.const_instance thy) (s', Ts)
else
NONE
else
NONE)
|> (fn SOME T => T
| NONE =>
map slack_fastype_of term_ts ---> the_default HOLogic.typeT opt_T)
val t =
if new_skolem then Var ((new_skolem_var_name_of_const s'', var_index), T)
else Const (unproxify_const s', T)
in list_comb (t, term_ts @ extra_ts) end
end
| NONE => (* a free or schematic variable *)
let
(* This assumes that distinct names are mapped to distinct names by
"Variable.variant_frees". This does not hold in general but should hold for
ATP-generated Skolem function names, since these end with a digit and
"variant_frees" appends letters. *)
fun fresh_up s =
[(s, ())] |> Variable.variant_frees ctxt [] |> hd |> fst
val term_ts =
map (do_term [] NONE) us
(* SPASS (3.8ds) and Vampire (2.6) pass arguments to Skolem functions in reverse
order, which is incompatible with the new Metis skolemizer. *)
|> exists (fn pre => String.isPrefix pre s)
[spass_skolem_prefix, vampire_skolem_prefix] ? rev
val ts = term_ts @ extra_ts
val T =
(case opt_T of
SOME T => map slack_fastype_of term_ts ---> T
| NONE =>
map slack_fastype_of ts --->
(case tys of [ty] => typ_of_atp_type ctxt ty | _ => HOLogic.typeT))
val t =
(case unprefix_and_unascii fixed_var_prefix s of
SOME s => Free (s, T)
| NONE =>
if textual andalso not (is_tptp_variable s) then
Free (s |> textual ? (repair_var_name_raw #> fresh_up), T)
else
Var ((repair_var_name textual s, var_index), T))
in list_comb (t, ts) end))
in do_term [] end
fun term_of_atom ctxt textual sym_tab pos (u as ATerm ((s, _), _)) =
if String.isPrefix class_prefix s then
add_type_constraint pos (type_constraint_of_term ctxt u)
#> pair @{const True}
else
pair (term_of_atp ctxt textual sym_tab (SOME @{typ bool}) u)
(* Update schematic type variables with detected sort constraints. It's not
totally clear whether this code is necessary. *)
fun repair_tvar_sorts (t, tvar_tab) =
let
fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
| do_type (TVar (xi, s)) =
TVar (xi, the_default s (Vartab.lookup tvar_tab xi))
| do_type (TFree z) = TFree z
fun do_term (Const (a, T)) = Const (a, do_type T)
| do_term (Free (a, T)) = Free (a, do_type T)
| do_term (Var (xi, T)) = Var (xi, do_type T)
| do_term (t as Bound _) = t
| do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
| do_term (t1 $ t2) = do_term t1 $ do_term t2
in t |> not (Vartab.is_empty tvar_tab) ? do_term end
fun quantify_over_var quant_of var_s t =
let
val vars = filter (fn ((s, _), _) => s = var_s) (Term.add_vars t [])
val normTs = vars |> AList.group (op =) |> map (apsnd hd)
fun norm_var_types (Var (x, T)) =
Var (x, (case AList.lookup (op =) normTs x of NONE => T | SOME T' => T'))
| norm_var_types t = t
in t |> map_aterms norm_var_types |> fold_rev quant_of (map Var normTs) end
(* Interpret an ATP formula as a HOL term, extracting sort constraints as they appear in the
formula. *)
fun prop_of_atp ctxt textual sym_tab phi =
let
fun do_formula pos phi =
(case phi of
AQuant (_, [], phi) => do_formula pos phi
| AQuant (q, (s, _) :: xs, phi') =>
do_formula pos (AQuant (q, xs, phi'))
(* FIXME: TFF *)
#>> quantify_over_var (case q of AForall => forall_of | AExists => exists_of)
(repair_var_name textual s)
| AConn (ANot, [phi']) => do_formula (not pos) phi' #>> s_not
| AConn (c, [phi1, phi2]) =>
do_formula (pos |> c = AImplies ? not) phi1
##>> do_formula pos phi2
#>> (case c of
AAnd => s_conj
| AOr => s_disj
| AImplies => s_imp
| AIff => s_iff
| ANot => raise Fail "impossible connective")
| AAtom tm => term_of_atom ctxt textual sym_tab pos tm
| _ => raise ATP_FORMULA [phi])
in
repair_tvar_sorts (do_formula true phi Vartab.empty)
end
fun find_first_in_list_vector vec key =
Vector.foldl (fn (ps, NONE) => AList.lookup (op =) ps key
| (_, value) => value) NONE vec
val unprefix_fact_number = space_implode "_" o tl o space_explode "_"
fun resolve_one_named_fact fact_names s =
(case try (unprefix fact_prefix) s of
SOME s' =>
let val s' = s' |> unprefix_fact_number |> unascii_of in
s' |> find_first_in_list_vector fact_names |> Option.map (pair s')
end
| NONE => NONE)
fun resolve_fact fact_names = map_filter (resolve_one_named_fact fact_names)
fun resolve_one_named_conjecture s =
(case try (unprefix conjecture_prefix) s of
SOME s' => Int.fromString s'
| NONE => NONE)
val resolve_conjecture = map_filter resolve_one_named_conjecture
fun is_axiom_used_in_proof pred =
exists (fn ((_, ss), _, _, _, []) => exists pred ss | _ => false)
fun add_non_rec_defs fact_names accum =
Vector.foldl (fn (facts, facts') =>
union (op =) (filter (fn (_, (_, status)) => status = Non_Rec_Def) facts) facts')
accum fact_names
val isa_ext = Thm.get_name_hint @{thm ext}
val isa_short_ext = Long_Name.base_name isa_ext
fun ext_name ctxt =
if Thm.eq_thm_prop (@{thm ext},
singleton (Attrib.eval_thms ctxt) (Facts.named isa_short_ext, [])) then
isa_short_ext
else
isa_ext
val leo2_extcnf_equal_neg_rule = "extcnf_equal_neg"
val leo2_unfold_def_rule = "unfold_def"
fun add_fact ctxt fact_names ((_, ss), _, _, rule, deps) =
(if rule = leo2_extcnf_equal_neg_rule then
insert (op =) (ext_name ctxt, (Global, General))
else if rule = leo2_unfold_def_rule then
(* LEO 1.3.3 does not record definitions properly, leading to missing dependencies in the TSTP
proof. Remove the next line once this is fixed. *)
add_non_rec_defs fact_names
else if rule = agsyhol_core_rule orelse rule = satallax_core_rule then
(fn [] =>
(* agsyHOL and Satallax don't include definitions in their unsatisfiable cores, so we
assume the worst and include them all here. *)
[(ext_name ctxt, (Global, General))] |> add_non_rec_defs fact_names
| facts => facts)
else
I)
#> (if null deps then union (op =) (resolve_fact fact_names ss) else I)
fun used_facts_in_atp_proof ctxt fact_names atp_proof =
if null atp_proof then Vector.foldl (uncurry (union (op =))) [] fact_names
else fold (add_fact ctxt fact_names) atp_proof []
fun used_facts_in_unsound_atp_proof _ _ [] = NONE
| used_facts_in_unsound_atp_proof ctxt fact_names atp_proof =
let val used_facts = used_facts_in_atp_proof ctxt fact_names atp_proof in
if forall (fn (_, (sc, _)) => sc = Global) used_facts andalso
not (is_axiom_used_in_proof (not o null o resolve_conjecture o single) atp_proof) then
SOME (map fst used_facts)
else
NONE
end
val ascii_of_lam_fact_prefix = ascii_of lam_fact_prefix
(* overapproximation (good enough) *)
fun is_lam_lifted s =
String.isPrefix fact_prefix s andalso
String.isSubstring ascii_of_lam_fact_prefix s
val is_combinator_def = String.isPrefix (helper_prefix ^ combinator_prefix)
fun atp_proof_prefers_lifting atp_proof =
(is_axiom_used_in_proof is_combinator_def atp_proof,
is_axiom_used_in_proof is_lam_lifted atp_proof) = (false, true)
val is_typed_helper_name =
String.isPrefix helper_prefix andf String.isSuffix typed_helper_suffix
fun is_typed_helper_used_in_atp_proof atp_proof =
is_axiom_used_in_proof is_typed_helper_name atp_proof
fun replace_one_dependency (old, new) dep = if is_same_atp_step dep old then new else [dep]
fun replace_dependencies_in_line old_new (name, role, t, rule, deps) =
(name, role, t, rule, fold (union (op =) o replace_one_dependency old_new) deps [])
fun repair_name "$true" = "c_True"
| repair_name "$false" = "c_False"
| repair_name "$$e" = tptp_equal (* seen in Vampire proofs *)
| repair_name s =
if is_tptp_equal s orelse
(* seen in Vampire proofs *)
(String.isPrefix "sQ" s andalso String.isSuffix "_eqProxy" s) then
tptp_equal
else
s
fun infer_formula_types ctxt =
Type.constraint HOLogic.boolT
#> Syntax.check_term (Proof_Context.set_mode Proof_Context.mode_schematic ctxt)
val combinator_table =
[(@{const_name Meson.COMBI}, @{thm Meson.COMBI_def [abs_def]}),
(@{const_name Meson.COMBK}, @{thm Meson.COMBK_def [abs_def]}),
(@{const_name Meson.COMBB}, @{thm Meson.COMBB_def [abs_def]}),
(@{const_name Meson.COMBC}, @{thm Meson.COMBC_def [abs_def]}),
(@{const_name Meson.COMBS}, @{thm Meson.COMBS_def [abs_def]})]
fun uncombine_term thy =
let
fun aux (t1 $ t2) = betapply (pairself aux (t1, t2))
| aux (Abs (s, T, t')) = Abs (s, T, aux t')
| aux (t as Const (x as (s, _))) =
(case AList.lookup (op =) combinator_table s of
SOME thm => thm |> prop_of |> specialize_type thy x |> Logic.dest_equals |> snd
| NONE => t)
| aux t = t
in aux end
fun unlift_term lifted =
map_aterms (fn t as Const (s, _) =>
if String.isPrefix lam_lifted_prefix s then
(* FIXME: do something about the types *)
(case AList.lookup (op =) lifted s of
SOME t => unlift_term lifted t
| NONE => t)
else
t
| t => t)
fun termify_line ctxt lifted sym_tab (name, role, u, rule, deps) =
let
val thy = Proof_Context.theory_of ctxt
val t = u
|> prop_of_atp ctxt true sym_tab
|> uncombine_term thy
|> unlift_term lifted
|> infer_formula_types ctxt
|> HOLogic.mk_Trueprop
in
(name, role, t, rule, deps)
end
val waldmeister_conjecture_num = "1.0.0.0"
fun repair_waldmeister_endgame proof =
let
fun repair_tail (name, _, t, rule, deps) = (name, Negated_Conjecture, s_not t, rule, deps)
fun repair_body [] = []
| repair_body ((line as ((num, _), _, _, _, _)) :: lines) =
if num = waldmeister_conjecture_num then map repair_tail (line :: lines)
else line :: repair_body lines
in
repair_body proof
end
fun termify_atp_proof ctxt pool lifted sym_tab =
clean_up_atp_proof_dependencies
#> nasty_atp_proof pool
#> map_term_names_in_atp_proof repair_name
#> map (termify_line ctxt lifted sym_tab)
#> repair_waldmeister_endgame
fun take_distinct_vars seen ((t as Var _) :: ts) =
if member (op aconv) seen t then rev seen else take_distinct_vars (t :: seen) ts
| take_distinct_vars seen _ = rev seen
fun unskolemize_term skos t =
let
val is_sko = member (op =) skos
fun find_args args (t $ u) = find_args (u :: args) t #> find_args [] u
| find_args _ (Abs (_, _, t)) = find_args [] t
| find_args args (Free (s, _)) =
if is_sko s then
let val new = take_distinct_vars [] args in
(fn [] => new | old => if length new < length old then new else old)
end
else
I
| find_args _ _ = I
val alls = find_args [] t []
val num_alls = length alls
fun fix_skos args (t $ u) = fix_skos (fix_skos [] u :: args) t
| fix_skos args (t as Free (s, T)) =
if is_sko s then list_comb (Free (s, funpow num_alls body_type T), drop num_alls args)
else list_comb (t, args)
| fix_skos [] (Abs (s, T, t)) = Abs (s, T, fix_skos [] t)
| fix_skos [] t = t
| fix_skos args t = list_comb (fix_skos [] t, args)
val t' = fix_skos [] t
fun add_sko (t as Free (s, _)) = is_sko s ? insert (op aconv) t
| add_sko _ = I
val exs = Term.fold_aterms add_sko t' []
in
t'
|> HOLogic.dest_Trueprop
|> fold exists_of exs |> Term.map_abs_vars (K Name.uu)
|> fold_rev forall_of alls
|> HOLogic.mk_Trueprop
end
fun introduce_spass_skolem [] = []
| introduce_spass_skolem (proof as (_, _, _, rule1, _) :: _) =
if rule1 = spass_input_rule then
let
fun add_sko (Free (s, _)) = String.isPrefix spass_skolem_prefix s ? insert (op =) s
| add_sko _ = I
(* union-find would be faster *)
fun add_cycle [] = I
| add_cycle ss =
fold (fn s => Graph.default_node (s, ())) ss
#> fold Graph.add_edge (ss ~~ tl ss @ [hd ss])
val (input_steps, other_steps) = List.partition (null o #5) proof
val skoss = map (fn (_, _, t, _, _) => Term.fold_aterms add_sko t []) input_steps
val skoss_input_steps = filter_out (null o fst) (skoss ~~ input_steps)
val groups = Graph.strong_conn (fold add_cycle skoss Graph.empty)
fun step_name_of_group skos = (implode skos, [])
fun in_group group = member (op =) group o hd
fun group_of sko = the (find_first (fn group => in_group group sko) groups)
fun new_steps (skoss_steps : (string list * (term, 'a) atp_step) list) group =
let
val name = step_name_of_group group
val name0 = name |>> prefix "0"
val t =
skoss_steps
|> map (snd #> #3 #> HOLogic.dest_Trueprop)
|> Library.foldr1 s_conj
|> HOLogic.mk_Trueprop
val skos = fold (union (op =) o fst) skoss_steps []
val deps = map (snd #> #1) skoss_steps
in
[(name0, Unknown, unskolemize_term skos t, spass_pre_skolemize_rule, deps),
(name, Unknown, t, spass_skolemize_rule, [name0])]
end
val sko_steps =
maps (fn group => new_steps (filter (in_group group o fst) skoss_input_steps) group)
groups
val old_news =
map (fn (skos, (name, _, _, _, _)) => (name, [step_name_of_group (group_of skos)]))
skoss_input_steps
val repair_deps = fold replace_dependencies_in_line old_news
in
input_steps @ sko_steps @ map repair_deps other_steps
end
else
proof
fun factify_atp_proof fact_names hyp_ts concl_t atp_proof =
let
fun factify_step ((num, ss), _, t, rule, deps) =
let
val (ss', role', t') =
(case resolve_conjecture ss of
[j] =>
if j = length hyp_ts then ([], Conjecture, concl_t) else ([], Hypothesis, nth hyp_ts j)
| _ =>
(case resolve_fact fact_names ss of
[] => (ss, Plain, t)
| facts => (map fst facts, Axiom, t)))
in
((num, ss'), role', t', rule, deps)
end
val atp_proof = map factify_step atp_proof
val names = map #1 atp_proof
fun repair_dep (num, ss) = (num, the_default ss (AList.lookup (op =) names num))
fun repair_deps (name, role, t, rule, deps) = (name, role, t, rule, map repair_dep deps)
in
map repair_deps atp_proof
end
end;