(* Title: HOL/Tools/SMT/smt_solver.ML
Author: Sascha Boehme, TU Muenchen
SMT solvers registry and SMT tactic.
*)
signature SMT_SOLVER =
sig
(*configuration*)
type interface = {
extra_norm: SMT_Normalize.extra_norm,
translate: SMT_Translate.config }
datatype outcome = Unsat | Sat | Unknown
type solver_config = {
name: string,
env_var: string,
is_remote: bool,
options: Proof.context -> string list,
interface: interface,
outcome: string -> string list -> outcome * string list,
cex_parser: (Proof.context -> SMT_Translate.recon -> string list ->
term list) option,
reconstruct: (Proof.context -> SMT_Translate.recon -> string list ->
(int list * thm) * Proof.context) option }
(*registry*)
type solver = bool option -> Proof.context -> (int * thm) list ->
int list * thm
val add_solver: solver_config -> theory -> theory
val solver_of: Proof.context -> solver
val is_locally_installed: Proof.context -> bool
(*filter*)
val smt_filter: bool -> Time.time -> Proof.state -> ('a * thm) list -> int ->
{outcome: SMT_Failure.failure option, used_facts: 'a list,
run_time_in_msecs: int option}
(*tactic*)
val smt_tac': bool -> Proof.context -> thm list -> int -> Tactical.tactic
val smt_tac: Proof.context -> thm list -> int -> Tactical.tactic
(*setup*)
val setup: theory -> theory
end
structure SMT_Solver: SMT_SOLVER =
struct
structure C = SMT_Config
(* configuration *)
type interface = {
extra_norm: SMT_Normalize.extra_norm,
translate: SMT_Translate.config }
datatype outcome = Unsat | Sat | Unknown
type solver_config = {
name: string,
env_var: string,
is_remote: bool,
options: Proof.context -> string list,
interface: interface,
outcome: string -> string list -> outcome * string list,
cex_parser: (Proof.context -> SMT_Translate.recon -> string list ->
term list) option,
reconstruct: (Proof.context -> SMT_Translate.recon -> string list ->
(int list * thm) * Proof.context) option }
(* interface to external solvers *)
fun get_local_solver env_var =
let val local_solver = getenv env_var
in if local_solver <> "" then SOME local_solver else NONE end
local
fun choose (rm, env_var, is_remote, name) =
let
val force_local = (case rm of SOME false => true | _ => false)
val force_remote = (case rm of SOME true => true | _ => false)
val lsolver = get_local_solver env_var
val remote_url = getenv "REMOTE_SMT_URL"
val trace = if is_some rm then K () else tracing
in
if not force_remote andalso is_some lsolver
then
(trace ("Invoking local SMT solver " ^ quote (the lsolver) ^ " ...");
[the lsolver])
else if not force_local andalso is_remote
then
(trace ("Invoking remote SMT solver " ^ quote name ^ " at " ^
quote remote_url ^ " ...");
[getenv "REMOTE_SMT", name])
else if force_remote
then error ("The SMT solver " ^ quote name ^ " is not remotely available.")
else error ("The SMT solver " ^ quote name ^ " has not been found " ^
"on this computer. Please set the Isabelle environment variable " ^
quote env_var ^ ".")
end
fun make_cmd solver args problem_path proof_path = space_implode " " (
map File.shell_quote (solver @ args) @
[File.shell_path problem_path, "2>&1", ">", File.shell_path proof_path])
fun run ctxt cmd args input =
(case C.certificates_of ctxt of
NONE =>
let
val {output, redirected_output, ...} =
Cache_IO.run (make_cmd (choose cmd) args) input
in (redirected_output, output) end
| SOME certs =>
(case Cache_IO.lookup certs input of
(NONE, key) =>
if Config.get ctxt C.fixed
then error ("Bad certificates cache: missing certificate")
else Cache_IO.run_and_cache certs key (make_cmd (choose cmd) args)
input
| (SOME output, _) =>
(tracing ("Using cached certificate from " ^
File.shell_path (Cache_IO.cache_path_of certs) ^ " ...");
output)))
in
fun run_solver ctxt cmd args input =
let
fun pretty tag ls = Pretty.string_of (Pretty.big_list tag
(map Pretty.str ls))
val _ = C.trace_msg ctxt (pretty "Problem:" o split_lines) input
val (res, err) = C.with_timeout ctxt (run ctxt cmd args) input
val _ = C.trace_msg ctxt (pretty "Solver:") err
val ls = rev (snd (chop_while (equal "") (rev res)))
val _ = C.trace_msg ctxt (pretty "Result:") ls
in ls end
end
fun trace_assms ctxt = C.trace_msg ctxt (Pretty.string_of o
Pretty.big_list "Assertions:" o map (Display.pretty_thm ctxt o snd))
fun trace_recon_data ctxt ({typs, terms, ...} : SMT_Translate.recon) =
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
C.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
fun invoke translate_config name cmd options irules ctxt =
let
val args = C.solver_options_of ctxt @ options ctxt
val comments = ("solver: " ^ name) ::
("timeout: " ^ Time.toString (seconds (Config.get ctxt C.timeout))) ::
"arguments:" :: args
in
irules
|> tap (trace_assms ctxt)
|> SMT_Translate.translate translate_config ctxt comments
||> tap (trace_recon_data ctxt)
|>> run_solver ctxt cmd args
|> rpair ctxt
end
fun discharge_definitions thm =
if Thm.nprems_of thm = 0 then thm
else discharge_definitions (@{thm reflexive} RS thm)
fun set_has_datatypes with_datatypes translate =
let
val {prefixes, header, strict, builtins, serialize} = translate
val {builtin_typ, builtin_num, builtin_fun, has_datatypes} = builtins
val with_datatypes' = has_datatypes andalso with_datatypes
val builtins' = {builtin_typ=builtin_typ, builtin_num=builtin_num,
builtin_fun=builtin_fun, has_datatypes=with_datatypes}
val translate' = {prefixes=prefixes, header=header, strict=strict,
builtins=builtins', serialize=serialize}
in (with_datatypes', translate') end
fun trace_assumptions ctxt irules idxs =
let
val thms = filter (fn i => i >= 0) idxs
|> map_filter (AList.lookup (op =) irules)
in
if Config.get ctxt C.trace_used_facts andalso length thms > 0
then
tracing (Pretty.string_of (Pretty.big_list "SMT used facts:"
(map (Display.pretty_thm ctxt) thms)))
else ()
end
fun gen_solver name info rm ctxt irules =
let
val {env_var, is_remote, options, interface, reconstruct} = info
val {extra_norm, translate} = interface
val (with_datatypes, translate') =
set_has_datatypes (Config.get ctxt C.datatypes) translate
val cmd = (rm, env_var, is_remote, name)
in
(irules, ctxt)
|-> SMT_Normalize.normalize extra_norm with_datatypes
|-> invoke translate' name cmd options
|-> reconstruct
|-> (fn (idxs, thm) => fn ctxt' => thm
|> singleton (ProofContext.export ctxt' ctxt)
|> discharge_definitions
|> tap (fn _ => trace_assumptions ctxt irules idxs)
|> pair idxs)
end
(* registry *)
type solver = bool option -> Proof.context -> (int * thm) list -> int list * thm
type solver_info = {
env_var: string,
is_remote: bool,
options: Proof.context -> string list,
interface: interface,
reconstruct: string list * SMT_Translate.recon -> Proof.context ->
(int list * thm) * Proof.context }
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
handle Symtab.DUP name => error ("Duplicate SMT solver: " ^ quote name)
)
local
fun finish outcome cex_parser reconstruct ocl (output, recon) ctxt =
(case outcome output of
(Unsat, ls) =>
if not (Config.get ctxt C.oracle) andalso is_some reconstruct
then the reconstruct ctxt recon ls
else (([], ocl ()), ctxt)
| (result, ls) =>
let val ts = (case cex_parser of SOME f => f ctxt recon ls | _ => [])
in
raise SMT_Failure.SMT (SMT_Failure.Counterexample (result = Sat, ts))
end)
in
fun add_solver cfg =
let
val {name, env_var, is_remote, options, interface, outcome, cex_parser,
reconstruct} = cfg
fun core_oracle () = @{cprop False}
fun solver ocl = { env_var=env_var, is_remote=is_remote, options=options,
interface=interface,
reconstruct=finish (outcome name) cex_parser reconstruct ocl }
in
Thm.add_oracle (Binding.name name, core_oracle) #-> (fn (_, ocl) =>
Context.theory_map (Solvers.map (Symtab.update_new (name, solver ocl)))) #>
Context.theory_map (C.add_solver name)
end
end
fun name_and_solver_of ctxt =
let val name = C.solver_of ctxt
in (name, the (Symtab.lookup (Solvers.get (Context.Proof ctxt)) name)) end
fun solver_of ctxt =
let val (name, raw_solver) = name_and_solver_of ctxt
in gen_solver name raw_solver end
fun is_locally_installed ctxt =
let val (_, {env_var, ...}) = name_and_solver_of ctxt
in is_some (get_local_solver env_var) end
(* filter *)
val has_topsort = Term.exists_type (Term.exists_subtype (fn
TFree (_, []) => true
| TVar (_, []) => true
| _ => false))
fun smt_solver rm ctxt irules =
(* without this test, we would run into problems when atomizing the rules: *)
if exists (has_topsort o Thm.prop_of o snd) irules then
raise SMT_Failure.SMT (SMT_Failure.Other_Failure ("proof state " ^
"contains the universal sort {}"))
else solver_of ctxt rm ctxt irules
fun smt_filter run_remote time_limit st xrules i =
let
val {facts, goal, ...} = Proof.goal st
val ctxt =
Proof.context_of st
|> Config.put C.oracle false
|> Config.put C.timeout (Real.fromInt (Time.toSeconds time_limit))
|> Config.put C.drop_bad_facts true
|> Config.put C.filter_only_facts true
val ({context=ctxt', prems, concl, ...}, _) = Subgoal.focus ctxt i goal
val cprop =
concl
|> Thm.rhs_of o SMT_Normalize.atomize_conv ctxt'
|> Thm.capply @{cterm Trueprop} o Thm.capply @{cterm Not} o Thm.dest_arg
val irs = map (pair ~1) (Thm.assume cprop :: prems @ facts)
val rm = SOME run_remote
in
split_list xrules
||> distinct (op =) o fst o smt_solver rm ctxt' o append irs o map_index I
|-> map_filter o try o nth
|> (fn xs => {outcome=NONE, used_facts=xs, run_time_in_msecs=NONE})
end
handle SMT_Failure.SMT fail => {outcome=SOME fail, used_facts=[],
run_time_in_msecs=NONE}
(* FIXME: measure runtime *)
(* SMT tactic *)
fun smt_tac' pass_exns ctxt rules =
CONVERSION (SMT_Normalize.atomize_conv ctxt)
THEN' Tactic.rtac @{thm ccontr}
THEN' SUBPROOF (fn {context=ctxt', prems, ...} =>
let
fun solve irules = snd (smt_solver NONE ctxt' irules)
val tag = "Solver " ^ C.solver_of ctxt' ^ ": "
val str_of = SMT_Failure.string_of_failure ctxt'
fun safe_solve irules =
if pass_exns then SOME (solve irules)
else (SOME (solve irules) handle SMT_Failure.SMT fail =>
(C.trace_msg ctxt' (prefix tag o str_of) fail; NONE))
in
safe_solve (map (pair ~1) (rules @ prems))
|> (fn SOME thm => Tactic.rtac thm 1 | _ => Tactical.no_tac)
end) ctxt
val smt_tac = smt_tac' false
val smt_method =
Scan.optional Attrib.thms [] >>
(fn thms => fn ctxt => METHOD (fn facts =>
HEADGOAL (smt_tac ctxt (thms @ facts))))
(* setup *)
val setup =
Method.setup @{binding smt} smt_method
"Applies an SMT solver to the current goal."
end