(* Title: HOL/Tools/Nitpick/nitpick.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2008, 2009, 2010
Finite model generation for HOL formulas using Kodkod.
*)
signature NITPICK =
sig
type styp = Nitpick_Util.styp
type term_postprocessor = Nitpick_Model.term_postprocessor
datatype mode = Auto_Try | Try | Normal | TPTP
type params =
{cards_assigns: (typ option * int list) list,
maxes_assigns: (styp option * int list) list,
iters_assigns: (styp option * int list) list,
bitss: int list,
bisim_depths: int list,
boxes: (typ option * bool option) list,
finitizes: (typ option * bool option) list,
monos: (typ option * bool option) list,
stds: (typ option * bool) list,
wfs: (styp option * bool option) list,
sat_solver: string,
blocking: bool,
falsify: bool,
debug: bool,
verbose: bool,
overlord: bool,
user_axioms: bool option,
assms: bool,
whacks: term list,
merge_type_vars: bool,
binary_ints: bool option,
destroy_constrs: bool,
specialize: bool,
star_linear_preds: bool,
total_consts: bool option,
needs: term list option,
peephole_optim: bool,
datatype_sym_break: int,
kodkod_sym_break: int,
timeout: Time.time option,
tac_timeout: Time.time option,
max_threads: int,
show_datatypes: bool,
show_skolems: bool,
show_consts: bool,
evals: term list,
formats: (term option * int list) list,
atomss: (typ option * string list) list,
max_potential: int,
max_genuine: int,
check_potential: bool,
check_genuine: bool,
batch_size: int,
expect: string}
val genuineN : string
val quasi_genuineN : string
val potentialN : string
val noneN : string
val unknownN : string
val register_frac_type : string -> (string * string) list -> theory -> theory
val unregister_frac_type : string -> theory -> theory
val register_codatatype : typ -> string -> styp list -> theory -> theory
val unregister_codatatype : typ -> theory -> theory
val register_term_postprocessor :
typ -> term_postprocessor -> theory -> theory
val unregister_term_postprocessor : typ -> theory -> theory
val pick_nits_in_term :
Proof.state -> params -> mode -> int -> int -> int -> (term * term) list
-> term list -> term list -> term -> string * Proof.state
val pick_nits_in_subgoal :
Proof.state -> params -> mode -> int -> int -> string * Proof.state
end;
structure Nitpick : NITPICK =
struct
open Nitpick_Util
open Nitpick_HOL
open Nitpick_Preproc
open Nitpick_Mono
open Nitpick_Scope
open Nitpick_Peephole
open Nitpick_Rep
open Nitpick_Nut
open Nitpick_Kodkod
open Nitpick_Model
structure KK = Kodkod
datatype mode = Auto_Try | Try | Normal | TPTP
fun is_mode_nt mode = (mode = Normal orelse mode = TPTP)
type params =
{cards_assigns: (typ option * int list) list,
maxes_assigns: (styp option * int list) list,
iters_assigns: (styp option * int list) list,
bitss: int list,
bisim_depths: int list,
boxes: (typ option * bool option) list,
finitizes: (typ option * bool option) list,
monos: (typ option * bool option) list,
stds: (typ option * bool) list,
wfs: (styp option * bool option) list,
sat_solver: string,
blocking: bool,
falsify: bool,
debug: bool,
verbose: bool,
overlord: bool,
user_axioms: bool option,
assms: bool,
whacks: term list,
merge_type_vars: bool,
binary_ints: bool option,
destroy_constrs: bool,
specialize: bool,
star_linear_preds: bool,
total_consts: bool option,
needs: term list option,
peephole_optim: bool,
datatype_sym_break: int,
kodkod_sym_break: int,
timeout: Time.time option,
tac_timeout: Time.time option,
max_threads: int,
show_datatypes: bool,
show_skolems: bool,
show_consts: bool,
evals: term list,
formats: (term option * int list) list,
atomss: (typ option * string list) list,
max_potential: int,
max_genuine: int,
check_potential: bool,
check_genuine: bool,
batch_size: int,
expect: string}
val genuineN = "genuine"
val quasi_genuineN = "quasi_genuine"
val potentialN = "potential"
val noneN = "none"
val unknownN = "unknown"
(* TODO: eliminate these historical aliases *)
val register_frac_type = Nitpick_HOL.register_frac_type_global
val unregister_frac_type = Nitpick_HOL.unregister_frac_type_global
val register_codatatype = Nitpick_HOL.register_codatatype_global
val unregister_codatatype = Nitpick_HOL.unregister_codatatype_global
val register_term_postprocessor =
Nitpick_Model.register_term_postprocessor_global
val unregister_term_postprocessor =
Nitpick_Model.unregister_term_postprocessor_global
type problem_extension =
{free_names: nut list,
sel_names: nut list,
nonsel_names: nut list,
rel_table: nut NameTable.table,
unsound: bool,
scope: scope}
type rich_problem = KK.problem * problem_extension
fun pretties_for_formulas _ _ [] = []
| pretties_for_formulas ctxt s ts =
[Pretty.str (s ^ plural_s_for_list ts ^ ":"),
Pretty.indent indent_size (Pretty.chunks
(map2 (fn j => fn t =>
Pretty.block [t |> shorten_names_in_term
|> Syntax.pretty_term ctxt,
Pretty.str (if j = 1 then "." else ";")])
(length ts downto 1) ts))]
val isabelle_wrong_message =
"Something appears to be wrong with your Isabelle installation."
fun java_not_found_message () =
"Java could not be launched. " ^ isabelle_wrong_message
fun java_too_old_message () =
"The Java version is too old. " ^ isabelle_wrong_message
fun kodkodi_not_installed_message () =
"Nitpick requires the external Java program Kodkodi."
fun kodkodi_too_old_message () = "The installed Kodkodi version is too old."
val max_unsound_delay_ms = 200
val max_unsound_delay_percent = 2
fun unsound_delay_for_timeout NONE = max_unsound_delay_ms
| unsound_delay_for_timeout (SOME timeout) =
Int.max (0, Int.min (max_unsound_delay_ms,
Time.toMilliseconds timeout
* max_unsound_delay_percent div 100))
fun passed_deadline NONE = false
| passed_deadline (SOME time) = Time.compare (Time.now (), time) <> LESS
fun none_true assigns = forall (not_equal (SOME true) o snd) assigns
fun has_lonely_bool_var (@{const Pure.conjunction}
$ (@{const Trueprop} $ Free _) $ _) = true
| has_lonely_bool_var _ = false
val syntactic_sorts =
@{sort "{default,zero,one,plus,minus,uminus,times,inverse,abs,sgn,ord,equal}"} @
@{sort numeral}
fun has_tfree_syntactic_sort (TFree (_, S as _ :: _)) =
subset (op =) (S, syntactic_sorts)
| has_tfree_syntactic_sort _ = false
val has_syntactic_sorts = exists_type (exists_subtype has_tfree_syntactic_sort)
fun plazy f = Pretty.blk (0, pstrs (f ()))
fun pick_them_nits_in_term deadline state (params : params) mode i n step
subst def_assm_ts nondef_assm_ts orig_t =
let
val timer = Timer.startRealTimer ()
val thy = Proof.theory_of state
val ctxt = Proof.context_of state
(* FIXME: reintroduce code before new release:
val nitpick_thy = Thy_Info.get_theory "Nitpick"
val _ = Theory.subthy (nitpick_thy, thy) orelse
error "You must import the theory \"Nitpick\" to use Nitpick"
*)
val {cards_assigns, maxes_assigns, iters_assigns, bitss, bisim_depths,
boxes, finitizes, monos, stds, wfs, sat_solver, falsify, debug,
verbose, overlord, user_axioms, assms, whacks, merge_type_vars,
binary_ints, destroy_constrs, specialize, star_linear_preds,
total_consts, needs, peephole_optim, datatype_sym_break,
kodkod_sym_break, tac_timeout, max_threads, show_datatypes,
show_skolems, show_consts, evals, formats, atomss, max_potential,
max_genuine, check_potential, check_genuine, batch_size, ...} = params
val state_ref = Unsynchronized.ref state
fun pprint print =
if mode = Auto_Try then
Unsynchronized.change state_ref o Proof.goal_message o K
o Pretty.chunks o cons (Pretty.str "") o single
o Pretty.mark Markup.intensify
else
print o Pretty.string_of
val pprint_a = pprint Output.urgent_message
fun pprint_nt f = () |> is_mode_nt mode ? pprint Output.urgent_message o f
fun pprint_v f = () |> verbose ? pprint Output.urgent_message o f
fun pprint_d f = () |> debug ? pprint tracing o f
val print = pprint Output.urgent_message o curry Pretty.blk 0 o pstrs
fun print_t f = () |> mode = TPTP ? print o f
(*
val print_g = pprint tracing o Pretty.str
*)
val print_nt = pprint_nt o K o plazy
val print_v = pprint_v o K o plazy
fun check_deadline () =
if passed_deadline deadline then raise TimeLimit.TimeOut else ()
val (def_assm_ts, nondef_assm_ts) =
if assms orelse mode <> Normal then (def_assm_ts, nondef_assm_ts)
else ([], [])
val _ =
if step = 0 then
print_nt (fn () => "Nitpicking formula...")
else
pprint_nt (fn () => Pretty.chunks (
pretties_for_formulas ctxt ("Nitpicking " ^
(if i <> 1 orelse n <> 1 then
"subgoal " ^ string_of_int i ^ " of " ^ string_of_int n
else
"goal")) [Logic.list_implies (nondef_assm_ts, orig_t)]))
val _ = print_v (enclose "Timestamp: " "." o Date.fmt "%H:%M:%S"
o Date.fromTimeLocal o Time.now)
val neg_t = if falsify then Logic.mk_implies (orig_t, @{prop False})
else orig_t
val conj_ts = neg_t :: def_assm_ts @ nondef_assm_ts @ evals @ these needs
val tfree_table =
if merge_type_vars then merged_type_var_table_for_terms thy conj_ts
else []
val merge_tfrees = merge_type_vars_in_term thy merge_type_vars tfree_table
val neg_t = neg_t |> merge_tfrees
val def_assm_ts = def_assm_ts |> map merge_tfrees
val nondef_assm_ts = nondef_assm_ts |> map merge_tfrees
val evals = evals |> map merge_tfrees
val needs = needs |> Option.map (map merge_tfrees)
val conj_ts = neg_t :: def_assm_ts @ nondef_assm_ts @ evals @ these needs
val original_max_potential = max_potential
val original_max_genuine = max_genuine
val max_bisim_depth = fold Integer.max bisim_depths ~1
val case_names = case_const_names ctxt stds
val defs = def_assm_ts @ all_defs_of thy subst
val nondefs = all_nondefs_of ctxt subst
val def_tables = const_def_tables ctxt subst defs
val nondef_table = const_nondef_table nondefs
val simp_table = Unsynchronized.ref (const_simp_table ctxt subst)
val psimp_table = const_psimp_table ctxt subst
val choice_spec_table = const_choice_spec_table ctxt subst
val nondefs =
nondefs |> filter_out (is_choice_spec_axiom thy choice_spec_table)
val intro_table = inductive_intro_table ctxt subst def_tables
val ground_thm_table = ground_theorem_table thy
val ersatz_table = ersatz_table ctxt
val hol_ctxt as {wf_cache, ...} =
{thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
whacks = whacks, binary_ints = binary_ints,
destroy_constrs = destroy_constrs, specialize = specialize,
star_linear_preds = star_linear_preds, total_consts = total_consts,
needs = needs, tac_timeout = tac_timeout, evals = evals,
case_names = case_names, def_tables = def_tables,
nondef_table = nondef_table, nondefs = nondefs, simp_table = simp_table,
psimp_table = psimp_table, choice_spec_table = choice_spec_table,
intro_table = intro_table, ground_thm_table = ground_thm_table,
ersatz_table = ersatz_table, skolems = Unsynchronized.ref [],
special_funs = Unsynchronized.ref [],
unrolled_preds = Unsynchronized.ref [], wf_cache = Unsynchronized.ref [],
constr_cache = Unsynchronized.ref []}
val pseudo_frees = []
val real_frees = fold Term.add_frees conj_ts []
val _ = null (fold Term.add_tvars conj_ts []) orelse
error "Nitpick cannot handle goals with schematic type variables."
val (nondef_ts, def_ts, need_ts, got_all_mono_user_axioms,
no_poly_user_axioms, binarize) =
preprocess_formulas hol_ctxt nondef_assm_ts neg_t
val got_all_user_axioms =
got_all_mono_user_axioms andalso no_poly_user_axioms
fun print_wf (x, (gfp, wf)) =
pprint_nt (fn () => Pretty.blk (0,
pstrs ("The " ^ (if gfp then "co" else "") ^ "inductive predicate \"")
@ Syntax.pretty_term ctxt (Const x) ::
pstrs (if wf then
"\" was proved well-founded. Nitpick can compute it \
\efficiently."
else
"\" could not be proved well-founded. Nitpick might need to \
\unroll it.")))
val _ = if verbose then List.app print_wf (!wf_cache) else ()
val das_wort_formula = if falsify then "Negated conjecture" else "Formula"
val _ =
pprint_d (fn () => Pretty.chunks
(pretties_for_formulas ctxt das_wort_formula [hd nondef_ts] @
pretties_for_formulas ctxt "Relevant definitional axiom" def_ts @
pretties_for_formulas ctxt "Relevant nondefinitional axiom"
(tl nondef_ts)))
val _ = List.app (ignore o Term.type_of) (nondef_ts @ def_ts)
handle TYPE (_, Ts, ts) =>
raise TYPE ("Nitpick.pick_them_nits_in_term", Ts, ts)
val nondef_us = nondef_ts |> map (nut_from_term hol_ctxt Eq)
val def_us = def_ts |> map (nut_from_term hol_ctxt DefEq)
val need_us = need_ts |> map (nut_from_term hol_ctxt Eq)
val (free_names, const_names) =
fold add_free_and_const_names (nondef_us @ def_us @ need_us) ([], [])
val (sel_names, nonsel_names) =
List.partition (is_sel o nickname_of) const_names
val sound_finitizes = none_true finitizes
val standard = forall snd stds
(*
val _ =
List.app (print_g o string_for_nut ctxt) (nondef_us @ def_us @ need_us)
*)
val unique_scope = forall (curry (op =) 1 o length o snd) cards_assigns
fun monotonicity_message Ts extra =
let val pretties = map (pretty_maybe_quote o pretty_for_type ctxt) Ts in
Pretty.blk (0,
pstrs ("The type" ^ plural_s_for_list pretties ^ " ") @
pretty_serial_commas "and" pretties @
pstrs (" " ^
(if none_true monos then
"passed the monotonicity test"
else
(if length pretties = 1 then "is" else "are") ^
" considered monotonic") ^
". " ^ extra))
end
fun is_type_fundamentally_monotonic T =
(is_datatype ctxt stds T andalso not (is_quot_type ctxt T) andalso
(not (is_pure_typedef ctxt T) orelse is_univ_typedef ctxt T)) orelse
is_number_type ctxt T orelse is_bit_type T
fun is_type_actually_monotonic T =
time_limit tac_timeout (formulas_monotonic hol_ctxt binarize T)
(nondef_ts, def_ts)
handle TimeLimit.TimeOut => false
fun is_type_kind_of_monotonic T =
case triple_lookup (type_match thy) monos T of
SOME (SOME false) => false
| _ => is_type_actually_monotonic T
fun is_type_monotonic T =
unique_scope orelse
case triple_lookup (type_match thy) monos T of
SOME (SOME b) => b
| _ => is_type_fundamentally_monotonic T orelse
is_type_actually_monotonic T
fun is_deep_datatype_finitizable T =
triple_lookup (type_match thy) finitizes T = SOME (SOME true)
fun is_shallow_datatype_finitizable (T as Type (@{type_name fun_box}, _)) =
is_type_kind_of_monotonic T
| is_shallow_datatype_finitizable T =
case triple_lookup (type_match thy) finitizes T of
SOME (SOME b) => b
| _ => is_type_kind_of_monotonic T
fun is_datatype_deep T =
not standard orelse T = @{typ unit} orelse T = nat_T orelse
is_word_type T orelse
exists (curry (op =) T o domain_type o type_of) sel_names
val all_Ts = ground_types_in_terms hol_ctxt binarize (nondef_ts @ def_ts)
|> sort Term_Ord.typ_ord
val _ =
if verbose andalso binary_ints = SOME true andalso
exists (member (op =) [nat_T, int_T]) all_Ts then
print_v (K "The option \"binary_ints\" will be ignored because of the \
\presence of rationals, reals, \"Suc\", \"gcd\", or \"lcm\" \
\in the problem or because of the \"non_std\" option.")
else
()
val _ =
if mode = Normal andalso
exists (fn Type (@{type_name Datatype.node}, _) => true | _ => false)
all_Ts then
print_nt (K ("Warning: The problem involves directly or indirectly the \
\internal type " ^ quote @{type_name Datatype.node} ^
". This type is very Nitpick-unfriendly, and its presence \
\usually indicates either a failure of abstraction or a \
\quirk in Nitpick."))
else
()
val (mono_Ts, nonmono_Ts) = List.partition is_type_monotonic all_Ts
val _ =
if verbose andalso not unique_scope then
case filter_out is_type_fundamentally_monotonic mono_Ts of
[] => ()
| interesting_mono_Ts =>
pprint_v (K (monotonicity_message interesting_mono_Ts
"Nitpick might be able to skip some scopes."))
else
()
val (deep_dataTs, shallow_dataTs) =
all_Ts |> filter (is_datatype ctxt stds)
|> List.partition is_datatype_deep
val finitizable_dataTs =
(deep_dataTs |> filter_out (is_finite_type hol_ctxt)
|> filter is_deep_datatype_finitizable) @
(shallow_dataTs |> filter_out (is_finite_type hol_ctxt)
|> filter is_shallow_datatype_finitizable)
val _ =
if verbose andalso not (null finitizable_dataTs) then
pprint_v (K (monotonicity_message finitizable_dataTs
"Nitpick can use a more precise finite encoding."))
else
()
(* This detection code is an ugly hack. Fortunately, it is used only to
provide a hint to the user. *)
fun is_struct_induct_step (name, (Rule_Cases.Case {fixes, assumes, ...}, _)) =
not (null fixes) andalso
exists (String.isSuffix ".hyps" o fst) assumes andalso
exists (exists (curry (op =) name o shortest_name o fst)
o datatype_constrs hol_ctxt) deep_dataTs
val likely_in_struct_induct_step =
exists is_struct_induct_step (Proof_Context.cases_of ctxt)
val _ = if standard andalso likely_in_struct_induct_step then
pprint_nt (fn () => Pretty.blk (0,
pstrs "Hint: To check that the induction hypothesis is \
\general enough, try this command: " @
[Pretty.mark
(Active.make_markup Markup.sendbackN {implicit = false, properties = []})
(Pretty.blk (0,
pstrs ("nitpick [non_std, show_all]")))] @ pstrs "."))
else
()
(*
val _ = print_g "Monotonic types:"
val _ = List.app (print_g o string_for_type ctxt) mono_Ts
val _ = print_g "Nonmonotonic types:"
val _ = List.app (print_g o string_for_type ctxt) nonmono_Ts
*)
val incremental = Int.max (max_potential, max_genuine) >= 2
val actual_sat_solver =
if sat_solver <> "smart" then
if incremental andalso
not (member (op =) (Kodkod_SAT.configured_sat_solvers true)
sat_solver) then
(print_nt (K ("An incremental SAT solver is required: \"SAT4J\" will \
\be used instead of " ^ quote sat_solver ^ "."));
"SAT4J")
else
sat_solver
else
Kodkod_SAT.smart_sat_solver_name incremental
val _ =
if sat_solver = "smart" then
print_v (fn () =>
"Using SAT solver " ^ quote actual_sat_solver ^ ". The following" ^
(if incremental then " incremental " else " ") ^
"solvers are configured: " ^
commas_quote (Kodkod_SAT.configured_sat_solvers incremental) ^ ".")
else
()
val too_big_scopes = Unsynchronized.ref []
fun problem_for_scope unsound
(scope as {card_assigns, bits, bisim_depth, datatypes, ofs, ...}) =
let
val _ = not (exists (fn other => scope_less_eq other scope)
(!too_big_scopes)) orelse
raise TOO_LARGE ("Nitpick.pick_them_nits_in_term.\
\problem_for_scope", "too large scope")
(*
val _ = print_g "Offsets:"
val _ = List.app (fn (T, j0) =>
print_g (string_for_type ctxt T ^ " = " ^
string_of_int j0))
(Typtab.dest ofs)
*)
val effective_total_consts =
case total_consts of
SOME b => b
| NONE => forall (is_exact_type datatypes true) all_Ts
val main_j0 = offset_of_type ofs bool_T
val (nat_card, nat_j0) = spec_of_type scope nat_T
val (int_card, int_j0) = spec_of_type scope int_T
val _ = (nat_j0 = main_j0 andalso int_j0 = main_j0) orelse
raise BAD ("Nitpick.pick_them_nits_in_term.problem_for_scope",
"bad offsets")
val kk = kodkod_constrs peephole_optim nat_card int_card main_j0
val (free_names, rep_table) =
choose_reps_for_free_vars scope pseudo_frees free_names
NameTable.empty
val (sel_names, rep_table) = choose_reps_for_all_sels scope rep_table
val (nonsel_names, rep_table) =
choose_reps_for_consts scope effective_total_consts nonsel_names
rep_table
val (guiltiest_party, min_highest_arity) =
NameTable.fold (fn (name, R) => fn (s, n) =>
let val n' = arity_of_rep R in
if n' > n then (nickname_of name, n') else (s, n)
end) rep_table ("", 1)
val min_univ_card =
NameTable.fold (Integer.max o min_univ_card_of_rep o snd) rep_table
(univ_card nat_card int_card main_j0 [] KK.True)
val _ = if debug then ()
else check_arity guiltiest_party min_univ_card min_highest_arity
val def_us =
def_us |> map (choose_reps_in_nut scope unsound rep_table true)
val nondef_us =
nondef_us |> map (choose_reps_in_nut scope unsound rep_table false)
val need_us =
need_us |> map (choose_reps_in_nut scope unsound rep_table false)
(*
val _ = List.app (print_g o string_for_nut ctxt)
(free_names @ sel_names @ nonsel_names @
nondef_us @ def_us @ need_us)
*)
val (free_rels, pool, rel_table) =
rename_free_vars free_names initial_pool NameTable.empty
val (sel_rels, pool, rel_table) =
rename_free_vars sel_names pool rel_table
val (other_rels, pool, rel_table) =
rename_free_vars nonsel_names pool rel_table
val nondef_us = nondef_us |> map (rename_vars_in_nut pool rel_table)
val def_us = def_us |> map (rename_vars_in_nut pool rel_table)
val need_us = need_us |> map (rename_vars_in_nut pool rel_table)
val nondef_fs = map (kodkod_formula_from_nut ofs kk) nondef_us
val def_fs = map (kodkod_formula_from_nut ofs kk) def_us
val formula = fold (fold s_and) [def_fs, nondef_fs] KK.True
val comment = (if unsound then "unsound" else "sound") ^ "\n" ^
Print_Mode.setmp [] multiline_string_for_scope scope
val kodkod_sat_solver =
Kodkod_SAT.sat_solver_spec actual_sat_solver |> snd
val bit_width = if bits = 0 then 16 else bits + 1
val delay =
if unsound then
Option.map (fn time => Time.- (time, Time.now ())) deadline
|> unsound_delay_for_timeout
else
0
val settings = [("solver", commas_quote kodkod_sat_solver),
("bit_width", string_of_int bit_width),
("symmetry_breaking", string_of_int kodkod_sym_break),
("sharing", "3"),
("flatten", "false"),
("delay", signed_string_of_int delay)]
val plain_rels = free_rels @ other_rels
val plain_bounds = map (bound_for_plain_rel ctxt debug) plain_rels
val plain_axioms = map (declarative_axiom_for_plain_rel kk) plain_rels
val need_vals =
map (fn dtype as {typ, ...} =>
(typ, needed_values_for_datatype need_us ofs dtype)) datatypes
val sel_bounds =
map (bound_for_sel_rel ctxt debug need_vals datatypes) sel_rels
val dtype_axioms =
declarative_axioms_for_datatypes hol_ctxt binarize need_us need_vals
datatype_sym_break bits ofs kk rel_table datatypes
val declarative_axioms = plain_axioms @ dtype_axioms
val univ_card = Int.max (univ_card nat_card int_card main_j0
(plain_bounds @ sel_bounds) formula,
main_j0 |> bits > 0 ? Integer.add (bits + 1))
val (built_in_bounds, built_in_axioms) =
bounds_and_axioms_for_built_in_rels_in_formulas debug univ_card
nat_card int_card main_j0 (formula :: declarative_axioms)
val bounds = built_in_bounds @ plain_bounds @ sel_bounds
|> not debug ? merge_bounds
val axioms = built_in_axioms @ declarative_axioms
val highest_arity =
fold Integer.max (map (fst o fst) (maps fst bounds)) 0
val formula = fold_rev s_and axioms formula
val _ = if bits = 0 then () else check_bits bits formula
val _ = if debug orelse formula = KK.False then ()
else check_arity "" univ_card highest_arity
in
SOME ({comment = comment, settings = settings, univ_card = univ_card,
tuple_assigns = [], bounds = bounds,
int_bounds = if bits = 0 then sequential_int_bounds univ_card
else pow_of_two_int_bounds bits main_j0,
expr_assigns = [], formula = formula},
{free_names = free_names, sel_names = sel_names,
nonsel_names = nonsel_names, rel_table = rel_table,
unsound = unsound, scope = scope})
end
handle TOO_LARGE (loc, msg) =>
if loc = "Nitpick_Kodkod.check_arity" andalso
not (Typtab.is_empty ofs) then
problem_for_scope unsound
{hol_ctxt = hol_ctxt, binarize = binarize,
card_assigns = card_assigns, bits = bits,
bisim_depth = bisim_depth, datatypes = datatypes,
ofs = Typtab.empty}
else if loc = "Nitpick.pick_them_nits_in_term.\
\problem_for_scope" then
NONE
else
(Unsynchronized.change too_big_scopes (cons scope);
print_v (fn () =>
"Limit reached: " ^ msg ^ ". Skipping " ^
(if unsound then "potential component of " else "") ^
"scope.");
NONE)
| TOO_SMALL (_, msg) =>
(print_v (fn () =>
"Limit reached: " ^ msg ^ ". Skipping " ^
(if unsound then "potential component of " else "") ^
"scope.");
NONE)
val das_wort_model =
(if falsify then "counterexample" else "model")
|> not standard ? prefix "nonstandard "
val scopes = Unsynchronized.ref []
val generated_scopes = Unsynchronized.ref []
val generated_problems = Unsynchronized.ref ([] : rich_problem list)
val checked_problems = Unsynchronized.ref (SOME [])
val met_potential = Unsynchronized.ref 0
fun update_checked_problems problems =
List.app (Unsynchronized.change checked_problems o Option.map o cons
o nth problems)
fun show_kodkod_warning "" = ()
| show_kodkod_warning s = print_nt (fn () => "Kodkod warning: " ^ s ^ ".")
fun print_and_check_model genuine bounds
({free_names, sel_names, nonsel_names, rel_table, scope, ...}
: problem_extension) =
let
val _ =
print_t (fn () =>
"% SZS status " ^
(if genuine then
if falsify then "CounterSatisfiable" else "Satisfiable"
else
"Unknown") ^ "\n" ^
"% SZS output start FiniteModel")
val (reconstructed_model, codatatypes_ok) =
reconstruct_hol_model
{show_datatypes = show_datatypes, show_skolems = show_skolems,
show_consts = show_consts}
scope formats atomss real_frees pseudo_frees free_names sel_names
nonsel_names rel_table bounds
val genuine_means_genuine =
got_all_user_axioms andalso none_true wfs andalso
sound_finitizes andalso total_consts <> SOME true andalso
codatatypes_ok
fun assms_prop () =
Logic.mk_conjunction_list (neg_t :: def_assm_ts @ nondef_assm_ts)
in
(pprint_a (Pretty.chunks
[Pretty.blk (0,
(pstrs ((if mode = Auto_Try then "Auto " else "") ^
"Nitpick found a" ^
(if not genuine then " potentially spurious "
else if genuine_means_genuine then " "
else " quasi genuine ") ^ das_wort_model) @
(case pretties_for_scope scope verbose of
[] => []
| pretties => pstrs " for " @ pretties) @
[Pretty.str ":\n"])),
Pretty.indent indent_size reconstructed_model]);
print_t (K "% SZS output end FiniteModel");
if genuine then
(if check_genuine andalso standard then
case prove_hol_model scope tac_timeout free_names sel_names
rel_table bounds (assms_prop ()) of
SOME true =>
print ("Confirmation by \"auto\": The above " ^
das_wort_model ^ " is really genuine.")
| SOME false =>
if genuine_means_genuine then
error ("A supposedly genuine " ^ das_wort_model ^ " was \
\shown to be spurious by \"auto\".\nThis should never \
\happen.\nPlease send a bug report to blanchet\
\te@in.tum.de.")
else
print ("Refutation by \"auto\": The above " ^
das_wort_model ^ " is spurious.")
| NONE => print "No confirmation by \"auto\"."
else
();
if not standard andalso likely_in_struct_induct_step then
print "The existence of a nonstandard model suggests that the \
\induction hypothesis is not general enough or may even be \
\wrong. See the Nitpick manual's \"Inductive Properties\" \
\section for details (\"isabelle doc nitpick\")."
else
();
if has_lonely_bool_var orig_t then
print "Hint: Maybe you forgot a colon after the lemma's name?"
else if has_syntactic_sorts orig_t then
print "Hint: Maybe you forgot a type constraint?"
else
();
if not genuine_means_genuine then
if no_poly_user_axioms then
let
val options =
[] |> not got_all_mono_user_axioms
? cons ("user_axioms", "\"true\"")
|> not (none_true wfs)
? cons ("wf", "\"smart\" or \"false\"")
|> not sound_finitizes
? cons ("finitize", "\"smart\" or \"false\"")
|> total_consts = SOME true
? cons ("total_consts", "\"smart\" or \"false\"")
|> not codatatypes_ok
? cons ("bisim_depth", "a nonnegative value")
val ss =
map (fn (name, value) => quote name ^ " set to " ^ value)
options
in
print ("Try again with " ^
space_implode " " (serial_commas "and" ss) ^
" to confirm that the " ^ das_wort_model ^
" is genuine.")
end
else
print ("Nitpick is unable to guarantee the authenticity of \
\the " ^ das_wort_model ^ " in the presence of \
\polymorphic axioms.")
else
();
NONE)
else
if not genuine then
(Unsynchronized.inc met_potential;
if check_potential then
let
val status = prove_hol_model scope tac_timeout free_names
sel_names rel_table bounds
(assms_prop ())
in
(case status of
SOME true => print ("Confirmation by \"auto\": The \
\above " ^ das_wort_model ^
" is genuine.")
| SOME false => print ("Refutation by \"auto\": The above " ^
das_wort_model ^ " is spurious.")
| NONE => print "No confirmation by \"auto\".");
status
end
else
NONE)
else
NONE)
|> pair genuine_means_genuine
end
fun solve_any_problem (found_really_genuine, max_potential, max_genuine,
donno) first_time problems =
let
val max_potential = Int.max (0, max_potential)
val max_genuine = Int.max (0, max_genuine)
fun print_and_check genuine (j, bounds) =
print_and_check_model genuine bounds (snd (nth problems j))
val max_solutions = max_potential + max_genuine
|> not incremental ? Integer.min 1
in
if max_solutions <= 0 then
(found_really_genuine, 0, 0, donno)
else
case KK.solve_any_problem debug overlord deadline max_threads
max_solutions (map fst problems) of
KK.JavaNotFound =>
(print_nt java_not_found_message;
(found_really_genuine, max_potential, max_genuine, donno + 1))
| KK.JavaTooOld =>
(print_nt java_too_old_message;
(found_really_genuine, max_potential, max_genuine, donno + 1))
| KK.KodkodiNotInstalled =>
(print_nt kodkodi_not_installed_message;
(found_really_genuine, max_potential, max_genuine, donno + 1))
| KK.KodkodiTooOld =>
(print_nt kodkodi_too_old_message;
(found_really_genuine, max_potential, max_genuine, donno + 1))
| KK.Normal ([], unsat_js, s) =>
(update_checked_problems problems unsat_js; show_kodkod_warning s;
(found_really_genuine, max_potential, max_genuine, donno))
| KK.Normal (sat_ps, unsat_js, s) =>
let
val (lib_ps, con_ps) =
List.partition (#unsound o snd o nth problems o fst) sat_ps
in
update_checked_problems problems (unsat_js @ map fst lib_ps);
show_kodkod_warning s;
if null con_ps then
let
val genuine_codes =
lib_ps |> take max_potential
|> map (print_and_check false)
|> filter (curry (op =) (SOME true) o snd)
val found_really_genuine =
found_really_genuine orelse exists fst genuine_codes
val num_genuine = length genuine_codes
val max_genuine = max_genuine - num_genuine
val max_potential = max_potential
- (length lib_ps - num_genuine)
in
if max_genuine <= 0 then
(found_really_genuine, 0, 0, donno)
else
let
(* "co_js" is the list of sound problems whose unsound
pendants couldn't be satisfied and hence that most
probably can't be satisfied themselves. *)
val co_js =
map (fn j => j - 1) unsat_js
|> filter (fn j =>
j >= 0 andalso
scopes_equivalent
(#scope (snd (nth problems j)),
#scope (snd (nth problems (j + 1)))))
val bye_js = sort_distinct int_ord (map fst sat_ps @
unsat_js @ co_js)
val problems =
problems |> filter_out_indices bye_js
|> max_potential <= 0
? filter_out (#unsound o snd)
in
solve_any_problem (found_really_genuine, max_potential,
max_genuine, donno) false problems
end
end
else
let
val genuine_codes =
con_ps |> take max_genuine
|> map (print_and_check true)
val max_genuine = max_genuine - length genuine_codes
val found_really_genuine =
found_really_genuine orelse exists fst genuine_codes
in
if max_genuine <= 0 orelse not first_time then
(found_really_genuine, 0, max_genuine, donno)
else
let
val bye_js = sort_distinct int_ord
(map fst sat_ps @ unsat_js)
val problems =
problems |> filter_out_indices bye_js
|> filter_out (#unsound o snd)
in
solve_any_problem (found_really_genuine, 0, max_genuine,
donno) false problems
end
end
end
| KK.TimedOut unsat_js =>
(update_checked_problems problems unsat_js; raise TimeLimit.TimeOut)
| KK.Error (s, unsat_js) =>
(update_checked_problems problems unsat_js;
print_v (K ("Kodkod error: " ^ s ^ "."));
(found_really_genuine, max_potential, max_genuine, donno + 1))
end
fun run_batch j n scopes (found_really_genuine, max_potential, max_genuine,
donno) =
let
val _ =
if null scopes then
print_nt (K "The scope specification is inconsistent.")
else if verbose then
pprint_nt (fn () => Pretty.chunks
[Pretty.blk (0,
pstrs ((if n > 1 then
"Batch " ^ string_of_int (j + 1) ^ " of " ^
signed_string_of_int n ^ ": "
else
"") ^
"Trying " ^ string_of_int (length scopes) ^
" scope" ^ plural_s_for_list scopes ^ ":")),
Pretty.indent indent_size
(Pretty.chunks (map2
(fn j => fn scope =>
Pretty.block (
(case pretties_for_scope scope true of
[] => [Pretty.str "Empty"]
| pretties => pretties) @
[Pretty.str (if j = 1 then "." else ";")]))
(length scopes downto 1) scopes))])
else
()
fun add_problem_for_scope (scope, unsound) (problems, donno) =
(check_deadline ();
case problem_for_scope unsound scope of
SOME problem =>
(problems
|> (null problems orelse
not (KK.problems_equivalent (fst problem, fst (hd problems))))
? cons problem, donno)
| NONE => (problems, donno + 1))
val (problems, donno) =
fold add_problem_for_scope
(map_product pair scopes
((if max_genuine > 0 then [false] else []) @
(if max_potential > 0 then [true] else [])))
([], donno)
val _ = Unsynchronized.change generated_problems (append problems)
val _ = Unsynchronized.change generated_scopes (append scopes)
val _ =
if j + 1 = n then
let
val (unsound_problems, sound_problems) =
List.partition (#unsound o snd) (!generated_problems)
in
if not (null sound_problems) andalso
forall (KK.is_problem_trivially_false o fst)
sound_problems then
print_nt (fn () =>
"Warning: The conjecture " ^
(if falsify then "either trivially holds"
else "is either trivially unsatisfiable") ^
" for the given scopes or lies outside Nitpick's supported \
\fragment." ^
(if exists (not o KK.is_problem_trivially_false o fst)
unsound_problems then
" Only potentially spurious " ^ das_wort_model ^
"s may be found."
else
""))
else
()
end
else
()
in
solve_any_problem (found_really_genuine, max_potential, max_genuine,
donno) true (rev problems)
end
fun scope_count (problems : rich_problem list) scope =
length (filter (curry scopes_equivalent scope o #scope o snd) problems)
fun excipit did_so_and_so =
let
val do_filter =
if !met_potential = max_potential then filter_out (#unsound o snd)
else I
val total = length (!scopes)
val unsat =
fold (fn scope =>
case scope_count (do_filter (!generated_problems)) scope of
0 => I
| n =>
scope_count (do_filter (these (!checked_problems)))
scope = n
? Integer.add 1) (!generated_scopes) 0
in
(if mode = TPTP then "% SZS status Unknown\n" else "") ^
"Nitpick " ^ did_so_and_so ^
(if is_some (!checked_problems) andalso total > 0 then
" " ^ string_of_int unsat ^ " of " ^ string_of_int total ^ " scope"
^ plural_s total
else
"") ^ "."
end
val (skipped, the_scopes) =
all_scopes hol_ctxt binarize cards_assigns maxes_assigns iters_assigns
bitss bisim_depths mono_Ts nonmono_Ts deep_dataTs
finitizable_dataTs
val _ = if skipped > 0 then
print_nt (fn () => "Too many scopes. Skipping " ^
string_of_int skipped ^ " scope" ^
plural_s skipped ^
". (Consider using \"mono\" or \
\\"merge_type_vars\" to prevent this.)")
else
()
val _ = scopes := the_scopes
fun run_batches _ _ []
(found_really_genuine, max_potential, max_genuine, donno) =
if donno > 0 andalso max_genuine > 0 then
(print_nt (fn () => excipit "checked"); unknownN)
else if max_genuine = original_max_genuine then
if max_potential = original_max_potential then
(print_t (K "% SZS status Unknown");
print_nt (fn () =>
"Nitpick found no " ^ das_wort_model ^ "." ^
(if not standard andalso likely_in_struct_induct_step then
" This suggests that the induction hypothesis might be \
\general enough to prove this subgoal."
else
"")); if skipped > 0 then unknownN else noneN)
else
(print_nt (fn () =>
excipit ("could not find a" ^
(if max_genuine = 1 then
" better " ^ das_wort_model ^ "."
else
"ny better " ^ das_wort_model ^ "s.") ^
" It checked"));
potentialN)
else if found_really_genuine then
genuineN
else
quasi_genuineN
| run_batches j n (batch :: batches) z =
let val (z as (_, _, max_genuine, _)) = run_batch j n batch z in
run_batches (j + 1) n (if max_genuine > 0 then batches else []) z
end
val batches = chunk_list batch_size (!scopes)
val outcome_code =
run_batches 0 (length batches) batches
(false, max_potential, max_genuine, 0)
handle TimeLimit.TimeOut =>
(print_nt (fn () => excipit "ran out of time after checking");
if !met_potential > 0 then potentialN else unknownN)
val _ = print_v (fn () =>
"Total time: " ^ string_of_time (Timer.checkRealTimer timer) ^
".")
in (outcome_code, !state_ref) end
(* Give the inner timeout a chance. *)
val timeout_bonus = seconds 1.0
fun pick_nits_in_term state (params as {debug, timeout, expect, ...}) mode i n
step subst def_assm_ts nondef_assm_ts orig_t =
let
val print_nt = if is_mode_nt mode then Output.urgent_message else K ()
val print_t = if mode = TPTP then Output.urgent_message else K ()
in
if getenv "KODKODI" = "" then
(* The "expect" argument is deliberately ignored if Kodkodi is missing so
that the "Nitpick_Examples" can be processed on any machine. *)
(print_nt (Pretty.string_of (plazy kodkodi_not_installed_message));
("no_kodkodi", state))
else
let
val unknown_outcome = (unknownN, state)
val deadline = Option.map (curry Time.+ (Time.now ())) timeout
val outcome as (outcome_code, _) =
time_limit (if debug orelse is_none timeout then NONE
else SOME (Time.+ (the timeout, timeout_bonus)))
(pick_them_nits_in_term deadline state params mode i n step subst
def_assm_ts nondef_assm_ts) orig_t
handle TOO_LARGE (_, details) =>
(print_t "% SZS status Unknown";
print_nt ("Limit reached: " ^ details ^ "."); unknown_outcome)
| TOO_SMALL (_, details) =>
(print_t "% SZS status Unknown";
print_nt ("Limit reached: " ^ details ^ "."); unknown_outcome)
| Kodkod.SYNTAX (_, details) =>
(print_t "% SZS status Unknown";
print_nt ("Malformed Kodkodi output: " ^ details ^ ".");
unknown_outcome)
| TimeLimit.TimeOut =>
(print_t "% SZS status TimedOut";
print_nt "Nitpick ran out of time."; unknown_outcome)
in
if expect = "" orelse outcome_code = expect then outcome
else error ("Unexpected outcome: " ^ quote outcome_code ^ ".")
end
end
fun is_fixed_equation ctxt
(Const (@{const_name "=="}, _) $ Free (s, _) $ Const _) =
Variable.is_fixed ctxt s
| is_fixed_equation _ _ = false
fun extract_fixed_frees ctxt (assms, t) =
let
val (subst, other_assms) =
List.partition (is_fixed_equation ctxt) assms
|>> map Logic.dest_equals
in (subst, other_assms, subst_atomic subst t) end
fun pick_nits_in_subgoal state params mode i step =
let
val ctxt = Proof.context_of state
val t = state |> Proof.raw_goal |> #goal |> prop_of
in
case Logic.count_prems t of
0 => (Output.urgent_message "No subgoal!"; (noneN, state))
| n =>
let
val t = Logic.goal_params t i |> fst
val assms = map term_of (Assumption.all_assms_of ctxt)
val (subst, assms, t) = extract_fixed_frees ctxt (assms, t)
in pick_nits_in_term state params mode i n step subst [] assms t end
end
end;