(* Title: HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML
Author: Jasmin Blanchette, TU Muenchen
Author: Steffen Juilf Smolka, TU Muenchen
Isar proof reconstruction from ATP proofs.
*)
signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
sig
type 'a proof = 'a ATP_Proof.proof
type stature = ATP_Problem_Generate.stature
datatype reconstructor =
Metis of string * string |
SMT
datatype play =
Played of reconstructor * Time.time |
Trust_Playable of reconstructor * Time.time option |
Failed_to_Play of reconstructor
type minimize_command = string list -> string
type one_line_params =
play * string * (string * stature) list * minimize_command * int * int
type isar_params =
bool * bool * Time.time option * bool * real * string Symtab.table
* (string * stature) list vector * (string * term) list * int Symtab.table
* string proof * thm
val smtN : string
val string_of_reconstructor : reconstructor -> string
val lam_trans_of_atp_proof : string proof -> string -> string
val is_typed_helper_used_in_atp_proof : string proof -> bool
val used_facts_in_atp_proof :
Proof.context -> (string * stature) list vector -> string proof ->
(string * stature) list
val used_facts_in_unsound_atp_proof :
Proof.context -> (string * stature) list vector -> 'a proof ->
string list option
val one_line_proof_text : int -> one_line_params -> string
val isar_proof_text :
Proof.context -> bool option -> isar_params -> one_line_params -> string
val proof_text :
Proof.context -> bool option -> isar_params -> int -> one_line_params
-> string
end;
structure Sledgehammer_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
struct
open ATP_Util
open ATP_Problem
open ATP_Proof
open ATP_Problem_Generate
open ATP_Proof_Reconstruct
open Sledgehammer_Util
open Sledgehammer_Proof
open Sledgehammer_Annotate
open Sledgehammer_Compress
structure String_Redirect = ATP_Proof_Redirect(
type key = step_name
val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s')
val string_of = fst)
open String_Redirect
(** reconstructors **)
datatype reconstructor =
Metis of string * string |
SMT
datatype play =
Played of reconstructor * Time.time |
Trust_Playable of reconstructor * Time.time option |
Failed_to_Play of reconstructor
val smtN = "smt"
fun string_of_reconstructor (Metis (type_enc, lam_trans)) =
metis_call type_enc lam_trans
| string_of_reconstructor SMT = smtN
(** fact extraction from ATP proofs **)
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 is_fact fact_names = not o null o resolve_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
val is_conjecture = not o null o resolve_conjecture
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 is_axiom_used_in_proof pred =
exists (fn ((_, ss), _, _, _, []) => exists pred ss | _ => false)
fun lam_trans_of_atp_proof atp_proof default =
case (is_axiom_used_in_proof is_combinator_def atp_proof,
is_axiom_used_in_proof is_lam_lifted atp_proof) of
(false, false) => default
| (false, true) => liftingN
(* | (true, true) => combs_and_liftingN -- not supported by "metis" *)
| (true, _) => combsN
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 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_coreN orelse rule = satallax_coreN 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 (is_conjecture o single) atp_proof) then
SOME (map fst used_facts)
else
NONE
end
(** one-liner reconstructor proofs **)
fun show_time NONE = ""
| show_time (SOME ext_time) = " (" ^ string_of_ext_time ext_time ^ ")"
(* FIXME: Various bugs, esp. with "unfolding"
fun unusing_chained_facts _ 0 = ""
| unusing_chained_facts used_chaineds num_chained =
if length used_chaineds = num_chained then ""
else if null used_chaineds then "(* using no facts *) "
else "(* using only " ^ space_implode " " used_chaineds ^ " *) "
*)
fun apply_on_subgoal _ 1 = "by "
| apply_on_subgoal 1 _ = "apply "
| apply_on_subgoal i n =
"prefer " ^ string_of_int i ^ " " ^ apply_on_subgoal 1 n
fun using_labels [] = ""
| using_labels ls =
"using " ^ space_implode " " (map string_of_label ls) ^ " "
fun command_call name [] =
name |> not (Symbol_Pos.is_identifier name) ? enclose "(" ")"
| command_call name args = "(" ^ name ^ " " ^ space_implode " " args ^ ")"
fun reconstructor_command reconstr i n used_chaineds num_chained (ls, ss) =
(* unusing_chained_facts used_chaineds num_chained ^ *)
using_labels ls ^ apply_on_subgoal i n ^
command_call (string_of_reconstructor reconstr) ss
fun try_command_line banner time command =
banner ^ ": " ^ Active.sendback_markup command ^ show_time time ^ "."
fun minimize_line _ [] = ""
| minimize_line minimize_command ss =
case minimize_command ss of
"" => ""
| command =>
"\nTo minimize: " ^ Active.sendback_markup command ^ "."
fun split_used_facts facts =
facts |> List.partition (fn (_, (sc, _)) => sc = Chained)
|> pairself (sort_distinct (string_ord o pairself fst))
type minimize_command = string list -> string
type one_line_params =
play * string * (string * stature) list * minimize_command * int * int
fun one_line_proof_text num_chained
(preplay, banner, used_facts, minimize_command, subgoal,
subgoal_count) =
let
val (chained, extra) = split_used_facts used_facts
val (failed, reconstr, ext_time) =
case preplay of
Played (reconstr, time) => (false, reconstr, (SOME (false, time)))
| Trust_Playable (reconstr, time) =>
(false, reconstr,
case time of
NONE => NONE
| SOME time =>
if time = Time.zeroTime then NONE else SOME (true, time))
| Failed_to_Play reconstr => (true, reconstr, NONE)
val try_line =
([], map fst extra)
|> reconstructor_command reconstr subgoal subgoal_count (map fst chained)
num_chained
|> (if failed then
enclose "One-line proof reconstruction failed: "
".\n(Invoking \"sledgehammer\" with \"[strict]\" might \
\solve this.)"
else
try_command_line banner ext_time)
in try_line ^ minimize_line minimize_command (map fst (extra @ chained)) end
(** Isar proof construction and manipulation **)
val assume_prefix = "a"
val have_prefix = "f"
val raw_prefix = "x"
fun raw_label_of_name (num, ss) =
case resolve_conjecture ss of
[j] => (conjecture_prefix, j)
| _ => (raw_prefix ^ ascii_of num, 0)
fun label_of_clause [name] = raw_label_of_name name
| label_of_clause c =
(space_implode "___" (map (fst o raw_label_of_name) c), 0)
fun add_fact_of_dependencies fact_names (names as [(_, ss)]) =
if is_fact fact_names ss then
apsnd (union (op =) (map fst (resolve_fact fact_names ss)))
else
apfst (insert (op =) (label_of_clause names))
| add_fact_of_dependencies _ names =
apfst (insert (op =) (label_of_clause names))
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
case AList.lookup (op =) lifted s of
SOME t =>
(* FIXME: do something about the types *)
unlift_term lifted t
| NONE => t
else
t
| t => t)
fun decode_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
in (name, role, t, rule, deps) end
fun replace_one_dependency (old, new) dep =
if is_same_atp_step dep old then new else [dep]
fun replace_dependencies_in_line p (name, role, t, rule, deps) =
(name, role, t, rule, fold (union (op =) o replace_one_dependency p) deps [])
(* No "real" literals means only type information (tfree_tcs, clsrel, or
clsarity). *)
fun is_only_type_information t = t aconv @{term True}
fun s_maybe_not role = role <> Conjecture ? s_not
fun is_same_inference (role, t) (_, role', t', _, _) =
s_maybe_not role t aconv s_maybe_not role' t'
(* Discard facts; consolidate adjacent lines that prove the same formula, since
they differ only in type information.*)
fun add_line fact_names (name as (_, ss), role, t, rule, []) lines =
(* No dependencies: fact, conjecture, or (for Vampire) internal facts or
definitions. *)
if is_conjecture ss then
(name, role, t, rule, []) :: lines
else if is_fact fact_names ss then
(* Facts are not proof lines. *)
if is_only_type_information t then
map (replace_dependencies_in_line (name, [])) lines
else
lines
else
map (replace_dependencies_in_line (name, [])) lines
| add_line _ (line as (name, role, t, _, _)) lines =
(* Type information will be deleted later; skip repetition test. *)
if is_only_type_information t then
line :: lines
(* Is there a repetition? If so, replace later line by earlier one. *)
else case take_prefix (not o is_same_inference (role, t)) lines of
(_, []) => line :: lines
| (pre, (name', _, _, _, _) :: post) =>
line :: pre @ map (replace_dependencies_in_line (name', [name])) post
val waldmeister_conjecture_num = "1.0.0.0"
fun repair_waldmeister_endgame arg =
let
fun do_tail (name, _, t, rule, deps) =
(name, Negated_Conjecture, s_not t, rule, deps)
fun do_body [] = []
| do_body ((line as ((num, _), _, _, _, _)) :: lines) =
if num = waldmeister_conjecture_num then map do_tail (line :: lines)
else line :: do_body lines
in do_body arg end
(* Recursively delete empty lines (type information) from the proof. *)
fun add_nontrivial_line (line as (name, _, t, _, [])) lines =
if is_only_type_information t then delete_dependency name lines
else line :: lines
| add_nontrivial_line line lines = line :: lines
and delete_dependency name lines =
fold_rev add_nontrivial_line
(map (replace_dependencies_in_line (name, [])) lines) []
val e_skolemize_rule = "skolemize"
val vampire_skolemisation_rule = "skolemisation"
val is_skolemize_rule =
member (op =) [e_skolemize_rule, vampire_skolemisation_rule]
fun add_desired_line fact_names (name as (_, ss), role, t, rule, deps)
(j, lines) =
(j + 1,
if is_fact fact_names ss orelse
is_conjecture ss orelse
is_skolemize_rule rule orelse
(* the last line must be kept *)
j = 0 orelse
(not (is_only_type_information t) andalso
null (Term.add_tvars t []) andalso
length deps >= 2 andalso
(* kill next to last line, which usually results in a trivial step *)
j <> 1) then
(name, role, t, rule, deps) :: lines (* keep line *)
else
map (replace_dependencies_in_line (name, deps)) lines) (* drop line *)
val indent_size = 2
fun string_of_proof ctxt type_enc lam_trans i n proof =
let
val ctxt =
(* make sure type constraint are actually printed *)
ctxt |> Config.put show_markup false
(* make sure only type constraints inserted by sh_annotate are printed *)
|> Config.put Printer.show_type_emphasis false
|> Config.put show_types false
|> Config.put show_sorts false
|> Config.put show_consts false
val register_fixes = map Free #> fold Variable.auto_fixes
fun add_suffix suffix (s, ctxt) = (s ^ suffix, ctxt)
fun of_indent ind = replicate_string (ind * indent_size) " "
fun of_moreover ind = of_indent ind ^ "moreover\n"
fun of_label l = if l = no_label then "" else string_of_label l ^ ": "
fun of_obtain qs nr =
(if nr > 1 orelse (nr = 1 andalso member (op =) qs Then) then
"ultimately "
else if nr=1 orelse member (op =) qs Then then
"then "
else
"") ^ "obtain"
fun of_show_have qs = if member (op =) qs Show then "show" else "have"
fun of_thus_hence qs = if member (op =) qs Show then "thus" else "hence"
fun of_prove qs nr =
if nr > 1 orelse (nr = 1 andalso member (op =) qs Then) then
"ultimately " ^ of_show_have qs
else if nr=1 orelse member (op =) qs Then then
of_thus_hence qs
else
of_show_have qs
fun add_term term (s, ctxt) =
(s ^ (term
|> singleton (Syntax.uncheck_terms ctxt)
|> annotate_types ctxt
|> with_vanilla_print_mode (Syntax.unparse_term ctxt #> Pretty.string_of)
|> simplify_spaces
|> maybe_quote),
ctxt |> Variable.auto_fixes term)
val reconstr = Metis (type_enc, lam_trans)
fun of_metis ind options (ls, ss) =
"\n" ^ of_indent (ind + 1) ^ options ^
reconstructor_command reconstr 1 1 [] 0
(ls |> sort_distinct (prod_ord string_ord int_ord),
ss |> sort_distinct string_ord)
fun of_free (s, T) =
maybe_quote s ^ " :: " ^
maybe_quote (simplify_spaces (with_vanilla_print_mode
(Syntax.string_of_typ ctxt) T))
fun add_frees xs (s, ctxt) =
(s ^ space_implode " and " (map of_free xs), ctxt |> register_fixes xs)
fun add_fix _ [] = I
| add_fix ind xs = add_suffix (of_indent ind ^ "fix ")
#> add_frees xs
#> add_suffix "\n"
fun add_assm ind (l, t) =
add_suffix (of_indent ind ^ "assume " ^ of_label l)
#> add_term t
#> add_suffix "\n"
fun add_assms ind assms = fold (add_assm ind) assms
fun add_step_post ind l t facts options =
add_suffix (of_label l)
#> add_term t
#> add_suffix (of_metis ind options facts ^ "\n")
fun of_subproof ind ctxt proof =
let
val ind = ind + 1
val s = of_proof ind ctxt proof
val prefix = "{ "
val suffix = " }"
in
replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
String.extract (s, ind * indent_size,
SOME (size s - ind * indent_size - 1)) ^
suffix ^ "\n"
end
and of_subproofs _ _ _ [] = ""
| of_subproofs ind ctxt qs subproofs =
(if member (op =) qs Then then of_moreover ind else "") ^
space_implode (of_moreover ind) (map (of_subproof ind ctxt) subproofs)
and add_step_pre ind qs subproofs (s, ctxt) =
(s ^ of_subproofs ind ctxt qs subproofs ^ of_indent ind, ctxt)
and add_step ind (Let (t1, t2)) =
add_suffix (of_indent ind ^ "let ")
#> add_term t1
#> add_suffix " = "
#> add_term t2
#> add_suffix "\n"
| add_step ind (Prove (qs, l, t, By_Metis (subproofs, facts))) =
add_step_pre ind qs subproofs
#> add_suffix (of_prove qs (length subproofs) ^ " ")
#> add_step_post ind l t facts ""
| add_step ind (Obtain (qs, Fix xs, l, t, By_Metis (subproofs, facts))) =
add_step_pre ind qs subproofs
#> add_suffix (of_obtain qs (length subproofs) ^ " ")
#> add_frees xs
#> add_suffix " where "
(* The new skolemizer puts the arguments in the same order as the ATPs
(E and Vampire -- but see also "atp_proof_reconstruct.ML" regarding
Vampire). *)
#> add_step_post ind l t facts
(if exists (fn (_, T) => length (binder_types T) > 1) xs then
"using [[metis_new_skolem]] "
else
"")
and add_steps ind = fold (add_step ind)
and of_proof ind ctxt (Proof (Fix xs, Assume assms, steps)) =
("", ctxt)
|> add_fix ind xs
|> add_assms ind assms
|> add_steps ind steps
|> fst
in
(* One-step proofs are pointless; better use the Metis one-liner
directly. *)
case proof of
Proof (Fix [], Assume [], [Prove (_, _, _, By_Metis ([], _))]) => ""
| _ => (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
of_indent 0 ^ "proof -\n" ^ of_proof 1 ctxt proof ^
of_indent 0 ^ (if n <> 1 then "next" else "qed")
end
fun add_labels_of_step step =
case byline_of_step step of
NONE => I
| SOME (By_Metis (subproofs, (ls, _))) =>
union (op =) ls #> fold add_labels_of_proof subproofs
and add_labels_of_proof proof = fold add_labels_of_step (steps_of_proof proof)
fun kill_useless_labels_in_proof proof =
let
val used_ls = add_labels_of_proof proof []
fun do_label l = if member (op =) used_ls l then l else no_label
fun do_assms (Assume assms) = Assume (map (apfst do_label) assms)
fun do_step (Obtain (qs, xs, l, t, By_Metis (subproofs, facts))) =
Obtain (qs, xs, do_label l, t, By_Metis (map do_proof subproofs, facts))
| do_step (Prove (qs, l, t, By_Metis (subproofs, facts))) =
Prove (qs, do_label l, t, By_Metis (map do_proof subproofs, facts))
| do_step step = step
and do_proof (Proof (fix, assms, steps)) =
Proof (fix, do_assms assms, map do_step steps)
in do_proof proof end
fun prefix_of_depth n = replicate_string (n + 1)
val relabel_proof =
let
fun fresh_label depth prefix (old as (l, subst, next)) =
if l = no_label then
old
else
let val l' = (prefix_of_depth depth prefix, next) in
(l', (l, l') :: subst, next + 1)
end
fun do_facts subst =
apfst (maps (the_list o AList.lookup (op =) subst))
fun do_assm depth (l, t) (subst, next) =
let
val (l, subst, next) =
(l, subst, next) |> fresh_label depth assume_prefix
in
((l, t), (subst, next))
end
fun do_assms subst depth (Assume assms) =
fold_map (do_assm depth) assms (subst, 1)
|> apfst Assume
|> apsnd fst
fun do_steps _ _ _ [] = []
| do_steps subst depth next (Obtain (qs, xs, l, t, by) :: steps) =
let
val (l, subst, next) =
(l, subst, next) |> fresh_label depth have_prefix
val by = by |> do_byline subst depth
in Obtain (qs, xs, l, t, by) :: do_steps subst depth next steps end
| do_steps subst depth next (Prove (qs, l, t, by) :: steps) =
let
val (l, subst, next) =
(l, subst, next) |> fresh_label depth have_prefix
val by = by |> do_byline subst depth
in Prove (qs, l, t, by) :: do_steps subst depth next steps end
| do_steps subst depth next (step :: steps) =
step :: do_steps subst depth next steps
and do_proof subst depth (Proof (fix, assms, steps)) =
let val (assms, subst) = do_assms subst depth assms in
Proof (fix, assms, do_steps subst depth 1 steps)
end
and do_byline subst depth (By_Metis (subproofs, facts)) =
By_Metis (do_proofs subst depth subproofs, do_facts subst facts)
and do_proofs subst depth = map (do_proof subst (depth + 1))
in do_proof [] 0 end
val chain_direct_proof =
let
fun do_qs_lfs NONE lfs = ([], lfs)
| do_qs_lfs (SOME l0) lfs =
if member (op =) lfs l0 then ([Then], lfs |> remove (op =) l0)
else ([], lfs)
fun chain_step lbl (Obtain (qs, xs, l, t,
By_Metis (subproofs, (lfs, gfs)))) =
let val (qs', lfs) = do_qs_lfs lbl lfs in
Obtain (qs' @ qs, xs, l, t,
By_Metis (chain_proofs subproofs, (lfs, gfs)))
end
| chain_step lbl (Prove (qs, l, t, By_Metis (subproofs, (lfs, gfs)))) =
let val (qs', lfs) = do_qs_lfs lbl lfs in
Prove (qs' @ qs, l, t, By_Metis (chain_proofs subproofs, (lfs, gfs)))
end
| chain_step _ step = step
and chain_steps _ [] = []
| chain_steps (prev as SOME _) (i :: is) =
chain_step prev i :: chain_steps (label_of_step i) is
| chain_steps _ (i :: is) = i :: chain_steps (label_of_step i) is
and chain_proof (Proof (fix, Assume assms, steps)) =
Proof (fix, Assume assms,
chain_steps (try (List.last #> fst) assms) steps)
and chain_proofs proofs = map (chain_proof) proofs
in chain_proof end
type isar_params =
bool * bool * Time.time option * bool * real * string Symtab.table
* (string * stature) list vector * (string * term) list * int Symtab.table
* string proof * thm
fun isar_proof_text ctxt isar_proofs
(debug, verbose, preplay_timeout, preplay_trace, isar_compress, pool,
fact_names, lifted, sym_tab, atp_proof, goal)
(one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
let
val (params, hyp_ts, concl_t) = strip_subgoal goal subgoal ctxt
val (_, ctxt) =
params
|> map (fn (s, T) => (Binding.name s, SOME T, NoSyn))
|> (fn fixes =>
ctxt |> Variable.set_body false
|> Proof_Context.add_fixes fixes)
val one_line_proof = one_line_proof_text 0 one_line_params
val type_enc =
if is_typed_helper_used_in_atp_proof atp_proof then full_typesN
else partial_typesN
val lam_trans = lam_trans_of_atp_proof atp_proof metis_default_lam_trans
val preplay = preplay_timeout <> SOME Time.zeroTime
fun isar_proof_of () =
let
val atp_proof =
atp_proof
|> clean_up_atp_proof_dependencies
|> nasty_atp_proof pool
|> map_term_names_in_atp_proof repair_name
|> map (decode_line ctxt lifted sym_tab)
|> repair_waldmeister_endgame
|> rpair [] |-> fold_rev (add_line fact_names)
|> rpair [] |-> fold_rev add_nontrivial_line
|> rpair (0, [])
|-> fold_rev (add_desired_line fact_names)
|> snd
val conj_name = conjecture_prefix ^ string_of_int (length hyp_ts)
val conjs =
atp_proof |> map_filter
(fn (name as (_, ss), _, _, _, []) =>
if member (op =) ss conj_name then SOME name else NONE
| _ => NONE)
val assms =
atp_proof |> map_filter
(fn (name as (_, ss), _, _, _, []) =>
(case resolve_conjecture ss of
[j] =>
if j = length hyp_ts then NONE
else SOME (raw_label_of_name name, nth hyp_ts j)
| _ => NONE)
| _ => NONE)
val bot = atp_proof |> List.last |> #1
val refute_graph =
atp_proof
|> map (fn (name, _, _, _, from) => (from, name))
|> make_refute_graph bot
|> fold (Atom_Graph.default_node o rpair ()) conjs
val axioms = axioms_of_refute_graph refute_graph conjs
val tainted = tainted_atoms_of_refute_graph refute_graph conjs
val is_clause_tainted = exists (member (op =) tainted)
val steps =
Symtab.empty
|> fold (fn (name as (s, _), role, t, rule, _) =>
Symtab.update_new (s, (rule,
t |> (if is_clause_tainted [name] then
s_maybe_not role
#> fold exists_of (map Var (Term.add_vars t []))
else
I))))
atp_proof
fun is_clause_skolemize_rule [(s, _)] =
Option.map (is_skolemize_rule o fst) (Symtab.lookup steps s) =
SOME true
| is_clause_skolemize_rule _ = false
(* The assumptions and conjecture are "prop"s; the other formulas are
"bool"s. *)
fun prop_of_clause [(s, ss)] =
(case resolve_conjecture ss of
[j] => if j = length hyp_ts then concl_t else nth hyp_ts j
| _ => the_default ("", @{term False}) (Symtab.lookup steps s)
|> snd |> HOLogic.mk_Trueprop |> close_form)
| prop_of_clause names =
let
val lits = map snd (map_filter (Symtab.lookup steps o fst) names)
in
case List.partition (can HOLogic.dest_not) lits of
(negs as _ :: _, pos as _ :: _) =>
s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs),
Library.foldr1 s_disj pos)
| _ => fold (curry s_disj) lits @{term False}
end
|> HOLogic.mk_Trueprop |> close_form
fun isar_proof_of_direct_proof infs =
let
fun maybe_show outer c =
(outer andalso length c = 1 andalso subset (op =) (c, conjs))
? cons Show
val is_fixed = Variable.is_declared ctxt orf can Name.dest_skolem
fun skolems_of t =
Term.add_frees t [] |> filter_out (is_fixed o fst) |> rev
fun do_steps outer predecessor accum [] =
accum
|> (if tainted = [] then
cons (Prove (if outer then [Show] else [], no_label,
concl_t,
By_Metis ([], ([the predecessor], []))))
else
I)
|> rev
| do_steps outer _ accum (Have (gamma, c) :: infs) =
let
val l = label_of_clause c
val t = prop_of_clause c
val by =
By_Metis ([],
(fold (add_fact_of_dependencies fact_names)
gamma no_facts))
fun prove by = Prove (maybe_show outer c [], l, t, by)
fun do_rest l step =
do_steps outer (SOME l) (step :: accum) infs
in
if is_clause_tainted c then
case gamma of
[g] =>
if is_clause_skolemize_rule g andalso
is_clause_tainted g then
let
val subproof =
Proof (Fix (skolems_of (prop_of_clause g)),
Assume [], rev accum)
in
do_steps outer (SOME l)
[prove (By_Metis ([subproof], no_facts))] []
end
else
do_rest l (prove by)
| _ => do_rest l (prove by)
else
if is_clause_skolemize_rule c then
do_rest l (Obtain ([], Fix (skolems_of t), l, t, by))
else
do_rest l (prove by)
end
| do_steps outer predecessor accum (Cases cases :: infs) =
let
fun do_case (c, infs) =
do_proof false [] [(label_of_clause c, prop_of_clause c)]
infs
val c = succedent_of_cases cases
val l = label_of_clause c
val t = prop_of_clause c
val step =
Prove (maybe_show outer c [], l, t,
By_Metis (map do_case cases, (the_list predecessor, [])))
in
do_steps outer (SOME l) (step :: accum) infs
end
and do_proof outer fix assms infs =
Proof (Fix fix, Assume assms, do_steps outer NONE [] infs)
in
do_proof true params assms infs
end
val clean_up_labels_in_proof =
chain_direct_proof
#> kill_useless_labels_in_proof
#> relabel_proof
val (isar_proof, (preplay_fail, preplay_time)) =
refute_graph
|> redirect_graph axioms tainted bot
|> isar_proof_of_direct_proof
|> (if not preplay andalso isar_compress <= 1.0 then
rpair (false, (true, seconds 0.0))
else
compress_and_preplay_proof debug ctxt type_enc lam_trans preplay
preplay_timeout preplay_trace
(if isar_proofs = SOME true then isar_compress else 1000.0))
|>> clean_up_labels_in_proof
val isar_text =
string_of_proof ctxt type_enc lam_trans subgoal subgoal_count
isar_proof
in
case isar_text of
"" =>
if isar_proofs = SOME true then
"\nNo structured proof available (proof too simple)."
else
""
| _ =>
let
val msg =
(if verbose then
let
val num_steps = add_metis_steps (steps_of_proof isar_proof) 0
in [string_of_int num_steps ^ " step" ^ plural_s num_steps] end
else
[]) @
(if preplay then
[(if preplay_fail then "may fail, " else "") ^
Sledgehammer_Preplay.string_of_preplay_time preplay_time]
else
[])
in
"\n\nStructured proof"
^ (commas msg |> not (null msg) ? enclose " (" ")")
^ ":\n" ^ Active.sendback_markup isar_text
end
end
val isar_proof =
if debug then
isar_proof_of ()
else case try isar_proof_of () of
SOME s => s
| NONE => if isar_proofs = SOME true then
"\nWarning: The Isar proof construction failed."
else
""
in one_line_proof ^ isar_proof end
fun isar_proof_would_be_a_good_idea preplay =
case preplay of
Played (reconstr, _) => reconstr = SMT
| Trust_Playable _ => true
| Failed_to_Play _ => true
fun proof_text ctxt isar_proofs isar_params num_chained
(one_line_params as (preplay, _, _, _, _, _)) =
(if isar_proofs = SOME true orelse
(isar_proofs = NONE andalso isar_proof_would_be_a_good_idea preplay) then
isar_proof_text ctxt isar_proofs isar_params
else
one_line_proof_text num_chained) one_line_params
end;