do not embed 'nat' into 'int's in 'smt2' method -- this is highly inefficient and decreases the Sledgehammer success rate significantly
(* 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 parsed_proof =
{outcome: SMT2_Failure.failure option,
fact_ids: (int * ((string * ATP_Problem_Generate.stature) * thm)) list,
atp_proof: unit -> (term, string) ATP_Proof.atp_step list}
type solver_config =
{name: string,
class: Proof.context -> SMT2_Util.class,
avail: unit -> bool,
command: unit -> string list,
options: Proof.context -> string list,
smt_options: (string * string) list,
default_max_relevant: int,
outcome: string -> string list -> outcome * string list,
parse_proof: (Proof.context -> SMT2_Translate.replay_data ->
((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
parsed_proof) option,
replay: (Proof.context -> SMT2_Translate.replay_data -> string 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 -> ((string * ATP_Problem_Generate.stature) * thm) list ->
int -> Time.time -> parsed_proof
(*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 lines = Pretty.string_of (Pretty.big_list tag (map Pretty.str lines))
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 smt_options 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 smt_options 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 parsed_proof =
{outcome: SMT2_Failure.failure option,
fact_ids: (int * ((string * ATP_Problem_Generate.stature) * thm)) list,
atp_proof: unit -> (term, string) ATP_Proof.atp_step list}
type solver_config =
{name: string,
class: Proof.context -> SMT2_Util.class,
avail: unit -> bool,
command: unit -> string list,
options: Proof.context -> string list,
smt_options: (string * string) list,
default_max_relevant: int,
outcome: string -> string list -> outcome * string list,
parse_proof: (Proof.context -> SMT2_Translate.replay_data ->
((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
parsed_proof) option,
replay: (Proof.context -> SMT2_Translate.replay_data -> string 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,
smt_options: (string * string) list,
default_max_relevant: int,
parse_proof: Proof.context -> SMT2_Translate.replay_data ->
((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
parsed_proof,
replay: Proof.context -> SMT2_Translate.replay_data -> string 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 parse_proof outcome parse_proof0 outer_ctxt replay_data xfacts prems concl output =
(case outcome output of
(Unsat, lines) =>
(case parse_proof0 of
SOME pp => pp outer_ctxt replay_data xfacts prems concl lines
| NONE => {outcome = NONE, fact_ids = [], atp_proof = K []})
| (result, _) => raise SMT2_Failure.SMT (SMT2_Failure.Counterexample (result = Sat)))
fun replay outcome replay0 oracle outer_ctxt
(replay_data as {context = ctxt, ...} : SMT2_Translate.replay_data) output =
(case outcome output of
(Unsat, lines) =>
if not (Config.get ctxt SMT2_Config.oracle) andalso is_some replay0
then the replay0 outer_ctxt replay_data lines
else oracle ()
| (result, _) => raise SMT2_Failure.SMT (SMT2_Failure.Counterexample (result = Sat)))
val cfalse = Thm.cterm_of @{theory} @{prop False}
in
fun add_solver ({name, class, avail, command, options, smt_options, default_max_relevant, outcome,
parse_proof = parse_proof0, replay = replay0} : solver_config) =
let
fun solver oracle = {
command = command,
smt_options = smt_options,
default_max_relevant = default_max_relevant,
parse_proof = parse_proof (outcome name) parse_proof0,
replay = replay (outcome name) replay0 oracle}
val info = {name = name, class = class, avail = avail, options = options}
in
Thm.add_oracle (Binding.name name, K cfalse) #-> (fn (_, oracle) =>
Context.theory_map (Solvers.map (Symtab.update_new (name, solver oracle)))) #>
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
val default_max_relevant = #default_max_relevant oo get_info
fun apply_solver_and_replay ctxt thms0 =
let
val thms = map (check_topsort ctxt) thms0
val (name, {command, smt_options, replay, ...}) = name_and_info_of ctxt
val (output, replay_data) =
invoke name command smt_options (SMT2_Normalize.normalize ctxt thms) ctxt
in replay ctxt replay_data output end
(* filter *)
fun smt2_filter ctxt0 goal xfacts i time_limit =
let
val ctxt = ctxt0 |> 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 conjecture = Thm.assume cprop
val facts = map snd xfacts
val thms = conjecture :: prems @ facts
val thms' = map (check_topsort ctxt) thms
val (name, {command, smt_options, parse_proof, ...}) = name_and_info_of ctxt
val (output, replay_data) =
invoke name command smt_options (SMT2_Normalize.normalize ctxt thms') ctxt
in
parse_proof ctxt replay_data xfacts (map Thm.prop_of prems) (Thm.term_of concl) output
end
handle SMT2_Failure.SMT fail => {outcome = SOME fail, fact_ids = [], atp_proof = K []}
(* SMT tactic *)
local
fun str_of ctxt fail =
"Solver " ^ SMT2_Config.solver_of ctxt ^ ": " ^ SMT2_Failure.string_of_failure fail
fun safe_solve ctxt facts = SOME (apply_solver_and_replay ctxt facts)
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 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 (rules @ prems))) ctxt
in
val smt2_tac = tac safe_solve
val smt2_tac' = tac (SOME oo apply_solver_and_replay)
end
end;