supports gradual skolemization (cf. Z3) by threading context through correctly
(* Title: HOL/Tools/Sledgehammer/sledgehammer_isar.ML
Author: Jasmin Blanchette, TU Muenchen
Author: Steffen Juilf Smolka, TU Muenchen
Isar proof reconstruction from ATP proofs.
*)
signature SLEDGEHAMMER_ISAR =
sig
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
type stature = ATP_Problem_Generate.stature
type one_line_params = Sledgehammer_Proof_Methods.one_line_params
val trace : bool Config.T
type isar_params =
bool * (string option * string option) * Time.time * real * bool * bool
* (term, string) atp_step list * thm
val proof_text : Proof.context -> bool -> bool option -> bool option -> (unit -> isar_params) ->
int -> one_line_params -> string
end;
structure Sledgehammer_Isar : SLEDGEHAMMER_ISAR =
struct
open ATP_Util
open ATP_Problem
open ATP_Proof
open ATP_Proof_Reconstruct
open Sledgehammer_Util
open Sledgehammer_Proof_Methods
open Sledgehammer_Isar_Proof
open Sledgehammer_Isar_Preplay
open Sledgehammer_Isar_Compress
open Sledgehammer_Isar_Minimize
structure String_Redirect = ATP_Proof_Redirect(
type key = atp_step_name
val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s')
val string_of = fst)
open String_Redirect
val trace = Attrib.setup_config_bool @{binding sledgehammer_isar_trace} (K false)
val e_skolemize_rules = ["skolemize", "shift_quantors"]
val spass_pirate_datatype_rule = "DT"
val vampire_skolemisation_rule = "skolemisation"
(* TODO: Use "Z3_Proof.string_of_rule" once it is moved to Isabelle *)
val z3_skolemize_rule = "sk"
val z3_th_lemma_rule = "th-lemma"
val skolemize_rules =
e_skolemize_rules @ [spass_skolemize_rule, vampire_skolemisation_rule, z3_skolemize_rule]
val is_skolemize_rule = member (op =) skolemize_rules
val is_arith_rule = String.isPrefix z3_th_lemma_rule
val is_datatype_rule = String.isPrefix spass_pirate_datatype_rule
fun raw_label_of_num num = (num, 0)
fun label_of_clause [(num, _)] = raw_label_of_num num
| label_of_clause c = (space_implode "___" (map (fst o raw_label_of_num o fst) c), 0)
fun add_fact_of_dependencies [(_, ss as _ :: _)] = apsnd (union (op =) ss)
| add_fact_of_dependencies names = apfst (insert (op =) (label_of_clause names))
fun is_True_prop t = t aconv @{prop True}
fun add_line_pass1 (line as (name, role, t, rule, [])) lines =
(* No dependencies: lemma (for Z3), fact, conjecture, or (for Vampire) internal facts or
definitions. *)
if role = Conjecture orelse role = Negated_Conjecture then line :: lines
else if is_True_prop t then map (replace_dependencies_in_line (name, [])) lines
else if role = Lemma orelse role = Hypothesis orelse is_arith_rule rule then line :: lines
else if role = Axiom then lines (* axioms (facts) need no proof lines *)
else map (replace_dependencies_in_line (name, [])) lines
| add_line_pass1 line lines = line :: lines
fun add_lines_pass2 res _ [] = rev res
| add_lines_pass2 res prev_t ((line as (name, role, t, rule, deps)) :: lines) =
let
val is_last_line = null lines
fun looks_interesting () =
not (is_True_prop t) andalso not (t aconv prev_t) andalso null (Term.add_tvars t []) andalso
length deps >= 2 andalso not (can the_single lines)
fun is_skolemizing_line (_, _, _, rule', deps') =
is_skolemize_rule rule' andalso member (op =) deps' name
fun is_before_skolemize_rule () = exists is_skolemizing_line lines
in
if role <> Plain orelse is_skolemize_rule rule orelse is_arith_rule rule orelse
is_datatype_rule rule orelse is_last_line orelse looks_interesting () orelse
is_before_skolemize_rule () then
add_lines_pass2 (line :: res) t lines
else
add_lines_pass2 res t (map (replace_dependencies_in_line (name, deps)) lines)
end
type isar_params =
bool * (string option * string option) * Time.time * real * bool * bool
* (term, string) atp_step list * thm
val basic_systematic_methods = [Metis_Method (NONE, NONE), Meson_Method, Blast_Method, SATx_Method]
val simp_based_methods = [Auto_Method, Simp_Method, Fastforce_Method, Force_Method]
val basic_arith_methods = [Linarith_Method, Presburger_Method, Algebra_Method]
val arith_methods = basic_arith_methods @ simp_based_methods @ basic_systematic_methods
val datatype_methods = [Simp_Method, Simp_Size_Method]
val systematic_methods0 = basic_systematic_methods @ basic_arith_methods @ simp_based_methods @
[Metis_Method (SOME no_typesN, NONE)]
val rewrite_methods = simp_based_methods @ basic_systematic_methods @ basic_arith_methods
val skolem_methods = basic_systematic_methods
fun isar_proof_text ctxt debug isar_proofs smt_proofs isar_params
(one_line_params as ((_, one_line_play), banner, used_facts, minimize_command, subgoal,
subgoal_count)) =
let
val _ = if debug then Output.urgent_message "Constructing Isar proof..." else ()
fun generate_proof_text () =
let
val (verbose, alt_metis_args, preplay_timeout, compress, try0, minimize, atp_proof, goal) =
isar_params ()
val systematic_methods = insert (op =) (Metis_Method alt_metis_args) systematic_methods0
fun massage_methods (meths as meth :: _) =
if not try0 then [meth]
else if smt_proofs = SOME true then SMT2_Method :: meths
else meths
val (params, _, concl_t) = strip_subgoal goal subgoal ctxt
val fixes = map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) params
val ctxt = ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes |> snd
val do_preplay = preplay_timeout <> Time.zeroTime
val compress = if isar_proofs = NONE andalso do_preplay then 1000.0 else compress
fun is_fixed ctxt = Variable.is_declared ctxt orf Name.is_skolem
fun skolems_of ctxt t = Term.add_frees t [] |> filter_out (is_fixed ctxt o fst) |> rev
fun get_role keep_role ((num, _), role, t, rule, _) =
if keep_role role then SOME ((raw_label_of_num num, t), rule) else NONE
val atp_proof =
atp_proof
|> rpair [] |-> fold_rev add_line_pass1
|> add_lines_pass2 [] Term.dummy
val conjs =
map_filter (fn (name, role, _, _, _) =>
if member (op =) [Conjecture, Negated_Conjecture] role then SOME name else NONE)
atp_proof
val assms = map_filter (Option.map fst o get_role (curry (op =) Hypothesis)) atp_proof
fun add_lemma ((l, t), rule) ctxt =
let
val (skos, meths) =
(if is_skolemize_rule rule then (skolems_of ctxt t, skolem_methods)
else if is_arith_rule rule then ([], arith_methods)
else ([], rewrite_methods))
||> massage_methods
in
(Prove ([], skos, l, t, [], ([], []), meths, ""),
ctxt |> not (null skos) ? (Variable.add_fixes (map fst skos) #> snd))
end
val (lems, _) =
fold_map add_lemma (map_filter (get_role (curry (op =) Lemma)) atp_proof) ctxt
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
HOLogic.dest_Trueprop
#> role <> Conjecture ? s_not
#> fold exists_of (map Var (Term.add_vars t []))
#> HOLogic.mk_Trueprop
else
I))))
atp_proof
val rule_of_clause_id = fst o the o Symtab.lookup steps o fst
fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> close_form
| prop_of_clause names =
let
val lits = map (HOLogic.dest_Trueprop o 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 maybe_show outer c = (outer andalso eq_set (op =) (c, conjs)) ? cons Show
fun isar_steps outer predecessor accum [] =
accum
|> (if tainted = [] then
cons (Prove (if outer then [Show] else [], [], no_label, concl_t, [],
(the_list predecessor, []), massage_methods systematic_methods, ""))
else
I)
|> rev
| isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) =
let
val l = label_of_clause c
val t = prop_of_clause c
val rule = rule_of_clause_id id
val skolem = is_skolemize_rule rule
val deps = fold add_fact_of_dependencies gamma ([], [])
val meths =
(if skolem then skolem_methods
else if is_arith_rule rule then arith_methods
else if is_datatype_rule rule then datatype_methods
else systematic_methods)
|> massage_methods
fun prove sub facts = Prove (maybe_show outer c [], [], l, t, sub, facts, meths, "")
fun steps_of_rest step = isar_steps outer (SOME l) (step :: accum) infs
in
if is_clause_tainted c then
(case gamma of
[g] =>
if skolem andalso is_clause_tainted g then
let val subproof = Proof (skolems_of ctxt (prop_of_clause g), [], rev accum) in
isar_steps outer (SOME l) [prove [subproof] ([], [])] infs
end
else
steps_of_rest (prove [] deps)
| _ => steps_of_rest (prove [] deps))
else
steps_of_rest
(if skolem then Prove ([], skolems_of ctxt t, l, t, [], deps, meths, "")
else prove [] deps)
end
| isar_steps outer predecessor accum (Cases cases :: infs) =
let
fun isar_case (c, subinfs) =
isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] subinfs
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,
map isar_case (filter_out (null o snd) cases),
(the_list predecessor, []), massage_methods systematic_methods, "")
in
isar_steps outer (SOME l) (step :: accum) infs
end
and isar_proof outer fix assms lems infs =
Proof (fix, assms, lems @ isar_steps outer NONE [] infs)
val trace = Config.get ctxt trace
val canonical_isar_proof =
refute_graph
|> trace ? tap (tracing o prefix "Refute graph: " o string_of_refute_graph)
|> redirect_graph axioms tainted bot
|> trace ? tap (tracing o prefix "Direct proof: " o string_of_direct_proof)
|> isar_proof true params assms lems
|> postprocess_isar_proof_remove_unreferenced_steps I
|> relabel_isar_proof_canonically
val ctxt = ctxt |> enrich_context_with_local_facts canonical_isar_proof
val preplay_data = Unsynchronized.ref Canonical_Label_Tab.empty
val _ = fold_isar_steps (fn meth =>
K (set_preplay_outcomes_of_isar_step ctxt preplay_timeout preplay_data meth []))
(steps_of_isar_proof canonical_isar_proof) ()
fun str_of_preplay_outcome outcome =
if Lazy.is_finished outcome then string_of_play_outcome (Lazy.force outcome) else "?"
fun str_of_meth l meth =
string_of_proof_method ctxt [] meth ^ " " ^
str_of_preplay_outcome (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)
fun comment_of l = map (str_of_meth l) #> commas
fun trace_isar_proof label proof =
if trace then
tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^
string_of_isar_proof ctxt subgoal subgoal_count
(comment_isar_proof comment_of proof) ^ "\n")
else
()
fun comment_of l (meth :: _) =
(case (verbose,
Lazy.force (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)) of
(false, Played _) => ""
| (_, outcome) => string_of_play_outcome outcome)
val (play_outcome, isar_proof) =
canonical_isar_proof
|> tap (trace_isar_proof "Original")
|> compress_isar_proof ctxt compress preplay_timeout preplay_data
|> tap (trace_isar_proof "Compressed")
|> postprocess_isar_proof_remove_unreferenced_steps
(keep_fastest_method_of_isar_step (!preplay_data)
#> minimize ? minimize_isar_step_dependencies ctxt preplay_data)
|> tap (trace_isar_proof "Minimized")
(* It's not clear whether this is worth the trouble (and if so, "compress" has an
unnatural semantics): *)
(*
|> minimize
? (compress_isar_proof ctxt compress preplay_timeout preplay_data
#> tap (trace_isar_proof "Compressed again"))
*)
|> `(preplay_outcome_of_isar_proof (!preplay_data))
||> (comment_isar_proof comment_of
#> chain_isar_proof
#> kill_useless_labels_in_isar_proof
#> relabel_isar_proof_nicely)
in
(case add_isar_steps (steps_of_isar_proof isar_proof) 0 of
1 =>
one_line_proof_text ctxt 0
(if play_outcome_ord (play_outcome, one_line_play) = LESS then
(case isar_proof of
Proof (_, _, [Prove (_, _, _, _, _, (_, gfs), meth :: _, _)]) =>
let val used_facts' = filter (member (op =) gfs o fst) used_facts in
((meth, play_outcome), banner, used_facts', minimize_command, subgoal,
subgoal_count)
end)
else
one_line_params) ^
(if isar_proofs = SOME true then "\n(No structured proof available -- proof too simple.)"
else "")
| num_steps =>
let
val msg =
(if verbose then [string_of_int num_steps ^ " step" ^ plural_s num_steps] else []) @
(if do_preplay then [string_of_play_outcome play_outcome] else [])
in
one_line_proof_text ctxt 0 one_line_params ^
"\n\nStructured proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^
Active.sendback_markup [Markup.padding_command]
(string_of_isar_proof ctxt subgoal subgoal_count isar_proof)
end)
end
in
if debug then
generate_proof_text ()
else
(case try generate_proof_text () of
SOME s => s
| NONE =>
one_line_proof_text ctxt 0 one_line_params ^
(if isar_proofs = SOME true then "\nWarning: Isar proof construction failed." else ""))
end
fun isar_proof_would_be_a_good_idea smt_proofs (meth, play) =
(case play of
Played _ => meth = SMT2_Method andalso smt_proofs <> SOME true
| Play_Timed_Out time => Time.> (time, Time.zeroTime)
| Play_Failed => true)
fun proof_text ctxt debug isar_proofs smt_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 smt_proofs preplay) then
isar_proof_text ctxt debug isar_proofs smt_proofs isar_params
else
one_line_proof_text ctxt num_chained) one_line_params
end;