(* Title: HOL/Tools/SMT2/smt2_solver.ML
Author: Sascha Boehme, TU Muenchen
SMT solvers registry and SMT tactic.
*)
signature SMT2_SOLVER =
sig
(*configuration*)
datatype outcome = Unsat | Sat | Unknown
type solver_config = {
name: string,
class: Proof.context -> SMT2_Util.class,
avail: unit -> bool,
command: unit -> string list,
options: Proof.context -> string list,
default_max_relevant: int,
can_filter: bool,
outcome: string -> string list -> outcome * string list,
replay: (Proof.context -> SMT2_Translate.replay_data -> string list ->
((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm) option}
(*registry*)
val add_solver: solver_config -> theory -> theory
val default_max_relevant: Proof.context -> string -> int
(*filter*)
val smt2_filter: Proof.context -> thm -> ('a * (int option * thm)) list -> int -> Time.time ->
{outcome: SMT2_Failure.failure option, rewrite_rules: thm list, conjecture_id: int,
prem_ids: int list, helper_ids: (int * thm) list, fact_ids: (int * ('a * thm)) list,
z3_proof: Z3_New_Proof.z3_step list}
(*tactic*)
val smt2_tac: Proof.context -> thm list -> int -> tactic
val smt2_tac': Proof.context -> thm list -> int -> tactic
end
structure SMT2_Solver: SMT2_SOLVER =
struct
(* interface to external solvers *)
local
fun make_command command options problem_path proof_path =
"(exec 2>&1;" :: map File.shell_quote (command () @ options) @
[File.shell_path problem_path, ")", ">", File.shell_path proof_path]
|> space_implode " "
fun with_trace ctxt msg f x =
let val _ = SMT2_Config.trace_msg ctxt (fn () => msg) ()
in f x end
fun run ctxt name mk_cmd input =
(case SMT2_Config.certificates_of ctxt of
NONE =>
if not (SMT2_Config.is_available ctxt name) then
error ("The SMT solver " ^ quote name ^ " is not installed")
else if Config.get ctxt SMT2_Config.debug_files = "" then
with_trace ctxt ("Invoking SMT solver " ^ quote name ^ " ...") (Cache_IO.run mk_cmd) input
else
let
val base_path = Path.explode (Config.get ctxt SMT2_Config.debug_files)
val in_path = Path.ext "smt2_in" base_path
val out_path = Path.ext "smt2_out" base_path
in Cache_IO.raw_run mk_cmd input in_path out_path end
| SOME certs =>
(case Cache_IO.lookup certs input of
(NONE, key) =>
if Config.get ctxt SMT2_Config.read_only_certificates then
error ("Bad certificate cache: missing certificate")
else
Cache_IO.run_and_cache certs key mk_cmd input
| (SOME output, _) =>
with_trace ctxt ("Using cached certificate from " ^
File.shell_path (Cache_IO.cache_path_of certs) ^ " ...") I output))
(* Z3 returns 1 if "get-model" or "get-model" fails *)
val normal_return_codes = [0, 1]
fun run_solver ctxt name mk_cmd input =
let
fun pretty tag ls = Pretty.string_of (Pretty.big_list tag (map Pretty.str ls))
val _ = SMT2_Config.trace_msg ctxt (pretty "Problem:" o split_lines) input
val {redirected_output = res, output = err, return_code} =
SMT2_Config.with_timeout ctxt (run ctxt name mk_cmd) input
val _ = SMT2_Config.trace_msg ctxt (pretty "Solver:") err
val output = fst (take_suffix (equal "") res)
val _ = SMT2_Config.trace_msg ctxt (pretty "Result:") output
val _ = member (op =) normal_return_codes return_code orelse
raise SMT2_Failure.SMT (SMT2_Failure.Abnormal_Termination return_code)
in output end
fun trace_assms ctxt =
SMT2_Config.trace_msg ctxt (Pretty.string_of o
Pretty.big_list "Assertions:" o map (Display.pretty_thm ctxt o snd))
fun trace_replay_data ({context = ctxt, typs, terms, ...} : SMT2_Translate.replay_data) =
let
fun pretty_eq n p = Pretty.block [Pretty.str n, Pretty.str " = ", p]
fun p_typ (n, T) = pretty_eq n (Syntax.pretty_typ ctxt T)
fun p_term (n, t) = pretty_eq n (Syntax.pretty_term ctxt t)
in
SMT2_Config.trace_msg ctxt (fn () =>
Pretty.string_of (Pretty.big_list "Names:" [
Pretty.big_list "sorts:" (map p_typ (Symtab.dest typs)),
Pretty.big_list "functions:" (map p_term (Symtab.dest terms))])) ()
end
in
fun invoke name command ithms ctxt =
let
val options = SMT2_Config.solver_options_of ctxt
val comments = [space_implode " " options]
val (str, replay_data as {context = ctxt', ...}) =
ithms
|> tap (trace_assms ctxt)
|> SMT2_Translate.translate ctxt comments
||> tap trace_replay_data
in (run_solver ctxt' name (make_command command options) str, replay_data) end
end
(* configuration *)
datatype outcome = Unsat | Sat | Unknown
type solver_config = {
name: string,
class: Proof.context -> SMT2_Util.class,
avail: unit -> bool,
command: unit -> string list,
options: Proof.context -> string list,
default_max_relevant: int,
can_filter: bool,
outcome: string -> string list -> outcome * string list,
replay: (Proof.context -> SMT2_Translate.replay_data -> string list ->
((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm) option}
(* check well-sortedness *)
val has_topsort = Term.exists_type (Term.exists_subtype (fn
TFree (_, []) => true
| TVar (_, []) => true
| _ => false))
(* top sorts cause problems with atomization *)
fun check_topsort ctxt thm =
if has_topsort (Thm.prop_of thm) then (SMT2_Normalize.drop_fact_warning ctxt thm; TrueI) else thm
(* registry *)
type solver_info = {
command: unit -> string list,
default_max_relevant: int,
can_filter: bool,
finish: Proof.context -> SMT2_Translate.replay_data -> string list ->
((int * (int * thm)) list * Z3_New_Proof.z3_step list) * thm}
structure Solvers = Generic_Data
(
type T = solver_info Symtab.table
val empty = Symtab.empty
val extend = I
fun merge data = Symtab.merge (K true) data
)
local
fun finish outcome replay ocl outer_ctxt
(replay_data as {context = ctxt, ...} : SMT2_Translate.replay_data) output =
(case outcome output of
(Unsat, ls) =>
if not (Config.get ctxt SMT2_Config.oracle) andalso is_some replay
then the replay outer_ctxt replay_data ls
else (([], []), ocl ())
| (result, ls) =>
raise SMT2_Failure.SMT (SMT2_Failure.Counterexample {
is_real_cex = (result = Sat),
free_constraints = [],
const_defs = []}))
val cfalse = Thm.cterm_of @{theory} (@{const Trueprop} $ @{const False})
in
fun add_solver ({name, class, avail, command, options, default_max_relevant, can_filter,
outcome, replay} : solver_config) =
let
fun solver ocl = {
command = command,
default_max_relevant = default_max_relevant,
can_filter = can_filter,
finish = finish (outcome name) replay ocl}
val info = {name = name, class = class, avail = avail, options = options}
in
Thm.add_oracle (Binding.name name, K cfalse) #-> (fn (_, ocl) =>
Context.theory_map (Solvers.map (Symtab.update_new (name, solver ocl)))) #>
Context.theory_map (SMT2_Config.add_solver info)
end
end
fun get_info ctxt name = the (Symtab.lookup (Solvers.get (Context.Proof ctxt)) name)
fun name_and_info_of ctxt =
let val name = SMT2_Config.solver_of ctxt
in (name, get_info ctxt name) end
fun apply_solver ctxt wthms0 =
let
val wthms = map (apsnd (check_topsort ctxt)) wthms0
val (name, {command, finish, ...}) = name_and_info_of ctxt
val (output, replay_data) = invoke name command (SMT2_Normalize.normalize ctxt wthms) ctxt
in (finish ctxt replay_data output, replay_data) end
val default_max_relevant = #default_max_relevant oo get_info
val can_filter = #can_filter o snd o name_and_info_of
(* filter *)
val no_id = ~1
fun smt2_filter ctxt goal xwfacts i time_limit =
let
val ctxt =
ctxt
|> Config.put SMT2_Config.oracle false
|> Config.put SMT2_Config.filter_only_facts true
|> Config.put SMT2_Config.timeout (Time.toReal time_limit)
val ({context = ctxt, prems, concl, ...}, _) = Subgoal.focus ctxt i goal
fun negate ct = Thm.dest_comb ct ||> Thm.apply @{cterm Not} |-> Thm.apply
val cprop =
(case try negate (Thm.rhs_of (SMT2_Normalize.atomize_conv ctxt concl)) of
SOME ct => ct
| NONE => raise SMT2_Failure.SMT (SMT2_Failure.Other_Failure "goal is not a HOL term"))
val wconjecture = (NONE, Thm.assume cprop)
val wprems = map (pair NONE) prems
val wfacts = map snd xwfacts
val wthms = wconjecture :: wprems @ wfacts
val iwthms = map_index I wthms
val conjecture_i = 0
val prems_i = 1
val facts_i = prems_i + length wprems
in
wthms
|> apply_solver ctxt
|> (fn (((iidths0, z3_proof), _), {rewrite_rules, ...}) =>
let
val iidths = if can_filter ctxt then iidths0 else map (apsnd (apfst (K no_id))) iwthms
fun id_of_index i = the_default no_id (Option.map fst (AList.lookup (op =) iidths i))
in
{outcome = NONE,
rewrite_rules = rewrite_rules,
conjecture_id = id_of_index conjecture_i,
prem_ids = map id_of_index (prems_i upto facts_i - 1),
helper_ids = map_filter (try (fn (~1, idth) => idth)) iidths,
fact_ids = map_filter (fn (i, (id, _)) =>
try (apsnd (apsnd snd o nth xwfacts)) (id, i - facts_i)) iidths,
z3_proof = z3_proof}
end)
end
handle SMT2_Failure.SMT fail => {outcome = SOME fail, rewrite_rules = [], conjecture_id = no_id,
prem_ids = [], helper_ids = [], fact_ids = [], z3_proof = []}
(* SMT tactic *)
local
fun trace_assumptions ctxt wfacts iidths =
let val used = map_filter (try (snd o nth wfacts) o fst) iidths in
if Config.get ctxt SMT2_Config.trace_used_facts andalso length wfacts > 0 then
tracing (Pretty.string_of (Pretty.big_list "SMT used facts:"
(map (Display.pretty_thm ctxt) used)))
else ()
end
fun solve ctxt wfacts =
wfacts
|> apply_solver ctxt
|> fst
|>> apfst (trace_assumptions ctxt wfacts)
|> snd
fun str_of ctxt fail =
"Solver " ^ SMT2_Config.solver_of ctxt ^ ": " ^ SMT2_Failure.string_of_failure ctxt fail
fun safe_solve ctxt wfacts = SOME (solve ctxt wfacts)
handle
SMT2_Failure.SMT (fail as SMT2_Failure.Counterexample _) =>
(SMT2_Config.verbose_msg ctxt (str_of ctxt) fail; NONE)
| SMT2_Failure.SMT (fail as SMT2_Failure.Time_Out) =>
error ("SMT: Solver " ^ quote (SMT2_Config.solver_of ctxt) ^ ": " ^
SMT2_Failure.string_of_failure ctxt fail ^ " (setting the " ^
"configuration option " ^ quote (Config.name_of SMT2_Config.timeout) ^ " might help)")
| SMT2_Failure.SMT fail => error (str_of ctxt fail)
fun resolve (SOME thm) = rtac thm 1
| resolve NONE = no_tac
fun tac prove ctxt rules =
CONVERSION (SMT2_Normalize.atomize_conv ctxt)
THEN' rtac @{thm ccontr}
THEN' SUBPROOF (fn {context = ctxt, prems, ...} =>
resolve (prove ctxt (map (pair NONE) (rules @ prems)))) ctxt
in
val smt2_tac = tac safe_solve
val smt2_tac' = tac (SOME oo solve)
end
end