1(* Title: HOL/Tools/SMT/smt_solver.ML 2 Author: Sascha Boehme, TU Muenchen 3 4SMT solvers registry and SMT tactic. 5*) 6 7signature SMT_SOLVER = 8sig 9 (*configuration*) 10 datatype outcome = Unsat | Sat | Unknown | Time_Out 11 12 type parsed_proof = 13 {outcome: SMT_Failure.failure option, 14 fact_ids: (int * ((string * ATP_Problem_Generate.stature) * thm)) list option, 15 atp_proof: unit -> (term, string) ATP_Proof.atp_step list} 16 17 type solver_config = 18 {name: string, 19 class: Proof.context -> SMT_Util.class, 20 avail: unit -> bool, 21 command: unit -> string list, 22 options: Proof.context -> string list, 23 smt_options: (string * string) list, 24 default_max_relevant: int, 25 outcome: string -> string list -> outcome * string list, 26 parse_proof: (Proof.context -> SMT_Translate.replay_data -> 27 ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list -> 28 parsed_proof) option, 29 replay: (Proof.context -> SMT_Translate.replay_data -> string list -> thm) option} 30 31 (*registry*) 32 val add_solver: solver_config -> theory -> theory 33 val default_max_relevant: Proof.context -> string -> int 34 35 (*filter*) 36 val smt_filter: Proof.context -> thm -> ((string * ATP_Problem_Generate.stature) * thm) list -> 37 int -> Time.time -> parsed_proof 38 39 (*tactic*) 40 val smt_tac: Proof.context -> thm list -> int -> tactic 41 val smt_tac': Proof.context -> thm list -> int -> tactic 42end; 43 44structure SMT_Solver: SMT_SOLVER = 45struct 46 47(* interface to external solvers *) 48 49local 50 51fun make_command command options problem_path proof_path = 52 Bash.strings (command () @ options) ^ " " ^ 53 Bash.string (File.platform_path problem_path) ^ 54 " > " ^ File.bash_path proof_path ^ " 2>&1" 55 56fun with_trace ctxt msg f x = 57 let val _ = SMT_Config.trace_msg ctxt (fn () => msg) () 58 in f x end 59 60fun run ctxt name mk_cmd input = 61 (case SMT_Config.certificates_of ctxt of 62 NONE => 63 if not (SMT_Config.is_available ctxt name) then 64 error ("The SMT solver " ^ quote name ^ " is not installed") 65 else if Config.get ctxt SMT_Config.debug_files = "" then 66 with_trace ctxt ("Invoking SMT solver " ^ quote name ^ " ...") (Cache_IO.run mk_cmd) input 67 else 68 let 69 val base_path = Path.explode (Config.get ctxt SMT_Config.debug_files) 70 val in_path = Path.ext "smt_in" base_path 71 val out_path = Path.ext "smt_out" base_path 72 in Cache_IO.raw_run mk_cmd input in_path out_path end 73 | SOME certs => 74 (case Cache_IO.lookup certs input of 75 (NONE, key) => 76 if Config.get ctxt SMT_Config.read_only_certificates then 77 error ("Bad certificate cache: missing certificate") 78 else 79 Cache_IO.run_and_cache certs key mk_cmd input 80 | (SOME output, _) => 81 with_trace ctxt ("Using cached certificate from " ^ 82 Path.print (Cache_IO.cache_path_of certs) ^ " ...") I output)) 83 84(* Z3 returns 1 if "get-proof" or "get-model" fails. veriT returns 255. *) 85val normal_return_codes = [0, 1, 255] 86 87fun run_solver ctxt name mk_cmd input = 88 let 89 fun pretty tag lines = Pretty.string_of (Pretty.big_list tag (map Pretty.str lines)) 90 91 val _ = SMT_Config.trace_msg ctxt (pretty "Problem:" o split_lines) input 92 93 val ({elapsed, ...}, {redirected_output = res, output = err, return_code}) = 94 Timing.timing (SMT_Config.with_timeout ctxt (run ctxt name mk_cmd)) input 95 val _ = SMT_Config.trace_msg ctxt (pretty "Solver:") err 96 97 val output = drop_suffix (equal "") res 98 val _ = SMT_Config.trace_msg ctxt (pretty "Result:") output 99 val _ = SMT_Config.trace_msg ctxt (pretty "Time (ms):") [\<^make_string> (Time.toMilliseconds elapsed)] 100 val _ = SMT_Config.statistics_msg ctxt (pretty "Time (ms):") [\<^make_string> (Time.toMilliseconds elapsed)] 101 102 val _ = member (op =) normal_return_codes return_code orelse 103 raise SMT_Failure.SMT (SMT_Failure.Abnormal_Termination return_code) 104 in output end 105 106fun trace_assms ctxt = 107 SMT_Config.trace_msg ctxt (Pretty.string_of o 108 Pretty.big_list "Assertions:" o map (Thm.pretty_thm ctxt o snd)) 109 110fun trace_replay_data ({context = ctxt, typs, terms, ...} : SMT_Translate.replay_data) = 111 let 112 fun pretty_eq n p = Pretty.block [Pretty.str n, Pretty.str " = ", p] 113 fun p_typ (n, T) = pretty_eq n (Syntax.pretty_typ ctxt T) 114 fun p_term (n, t) = pretty_eq n (Syntax.pretty_term ctxt t) 115 in 116 SMT_Config.trace_msg ctxt (fn () => 117 Pretty.string_of (Pretty.big_list "Names:" [ 118 Pretty.big_list "sorts:" (map p_typ (Symtab.dest typs)), 119 Pretty.big_list "functions:" (map p_term (Symtab.dest terms))])) () 120 end 121 122in 123 124fun invoke name command smt_options ithms ctxt = 125 let 126 val options = SMT_Config.solver_options_of ctxt 127 val comments = [space_implode " " options] 128 129 val (str, replay_data as {context = ctxt', ...}) = 130 ithms 131 |> tap (trace_assms ctxt) 132 |> SMT_Translate.translate ctxt smt_options comments 133 ||> tap trace_replay_data 134 in (run_solver ctxt' name (make_command command options) str, replay_data) end 135 136end 137 138 139(* configuration *) 140 141datatype outcome = Unsat | Sat | Unknown | Time_Out 142 143type parsed_proof = 144 {outcome: SMT_Failure.failure option, 145 fact_ids: (int * ((string * ATP_Problem_Generate.stature) * thm)) list option, 146 atp_proof: unit -> (term, string) ATP_Proof.atp_step list} 147 148type solver_config = 149 {name: string, 150 class: Proof.context -> SMT_Util.class, 151 avail: unit -> bool, 152 command: unit -> string list, 153 options: Proof.context -> string list, 154 smt_options: (string * string) list, 155 default_max_relevant: int, 156 outcome: string -> string list -> outcome * string list, 157 parse_proof: (Proof.context -> SMT_Translate.replay_data -> 158 ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list -> 159 parsed_proof) option, 160 replay: (Proof.context -> SMT_Translate.replay_data -> string list -> thm) option} 161 162 163(* check well-sortedness *) 164 165val has_topsort = Term.exists_type (Term.exists_subtype (fn 166 TFree (_, []) => true 167 | TVar (_, []) => true 168 | _ => false)) 169 170(* top sorts cause problems with atomization *) 171fun check_topsort ctxt thm = 172 if has_topsort (Thm.prop_of thm) then (SMT_Normalize.drop_fact_warning ctxt thm; TrueI) else thm 173 174 175(* registry *) 176 177type solver_info = { 178 command: unit -> string list, 179 smt_options: (string * string) list, 180 default_max_relevant: int, 181 parse_proof: Proof.context -> SMT_Translate.replay_data -> 182 ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list -> 183 parsed_proof, 184 replay: Proof.context -> SMT_Translate.replay_data -> string list -> thm} 185 186structure Solvers = Generic_Data 187( 188 type T = solver_info Symtab.table 189 val empty = Symtab.empty 190 val extend = I 191 fun merge data = Symtab.merge (K true) data 192) 193 194local 195 fun parse_proof outcome parse_proof0 outer_ctxt replay_data xfacts prems concl output = 196 (case outcome output of 197 (Unsat, lines) => 198 (case parse_proof0 of 199 SOME pp => pp outer_ctxt replay_data xfacts prems concl lines 200 | NONE => {outcome = NONE, fact_ids = NONE, atp_proof = K []}) 201 | (Time_Out, _) => raise SMT_Failure.SMT (SMT_Failure.Time_Out) 202 | (result, _) => raise SMT_Failure.SMT (SMT_Failure.Counterexample (result = Sat))) 203 204 fun replay outcome replay0 oracle outer_ctxt 205 (replay_data as {context = ctxt, ...} : SMT_Translate.replay_data) output = 206 (case outcome output of 207 (Unsat, lines) => 208 if Config.get ctxt SMT_Config.oracle then 209 oracle () 210 else 211 (case replay0 of 212 SOME replay => replay outer_ctxt replay_data lines 213 | NONE => error "No proof reconstruction for solver -- \ 214 \declare [[smt_oracle]] to allow oracle") 215 | (Time_Out, _) => raise SMT_Failure.SMT (SMT_Failure.Time_Out) 216 | (result, _) => raise SMT_Failure.SMT (SMT_Failure.Counterexample (result = Sat))) 217 218 val cfalse = Thm.cterm_of \<^context> \<^prop>\<open>False\<close> 219in 220 221fun add_solver ({name, class, avail, command, options, smt_options, default_max_relevant, outcome, 222 parse_proof = parse_proof0, replay = replay0} : solver_config) = 223 let 224 fun solver oracle = { 225 command = command, 226 smt_options = smt_options, 227 default_max_relevant = default_max_relevant, 228 parse_proof = parse_proof (outcome name) parse_proof0, 229 replay = replay (outcome name) replay0 oracle} 230 231 val info = {name = name, class = class, avail = avail, options = options} 232 in 233 Thm.add_oracle (Binding.name name, K cfalse) #-> (fn (_, oracle) => 234 Context.theory_map (Solvers.map (Symtab.update_new (name, solver oracle)))) #> 235 Context.theory_map (SMT_Config.add_solver info) 236 end 237 238end 239 240fun get_info ctxt name = the (Symtab.lookup (Solvers.get (Context.Proof ctxt)) name) 241 242fun name_and_info_of ctxt = 243 let val name = SMT_Config.solver_of ctxt 244 in (name, get_info ctxt name) end 245 246val default_max_relevant = #default_max_relevant oo get_info 247 248fun apply_solver_and_replay ctxt thms0 = 249 let 250 val thms = map (check_topsort ctxt) thms0 251 val (name, {command, smt_options, replay, ...}) = name_and_info_of ctxt 252 val (output, replay_data) = 253 invoke name command smt_options (SMT_Normalize.normalize ctxt thms) ctxt 254 in replay ctxt replay_data output end 255 256 257(* filter *) 258 259fun smt_filter ctxt0 goal xfacts i time_limit = 260 let 261 val ctxt = ctxt0 |> Config.put SMT_Config.timeout (Time.toReal time_limit) 262 263 val ({context = ctxt, prems, concl, ...}, _) = Subgoal.focus ctxt i NONE goal 264 fun negate ct = Thm.dest_comb ct ||> Thm.apply \<^cterm>\<open>Not\<close> |-> Thm.apply 265 val cprop = 266 (case try negate (Thm.rhs_of (SMT_Normalize.atomize_conv ctxt concl)) of 267 SOME ct => ct 268 | NONE => raise SMT_Failure.SMT (SMT_Failure.Other_Failure "cannot atomize goal")) 269 270 val conjecture = Thm.assume cprop 271 val facts = map snd xfacts 272 val thms = conjecture :: prems @ facts 273 val thms' = map (check_topsort ctxt) thms 274 275 val (name, {command, smt_options, parse_proof, ...}) = name_and_info_of ctxt 276 val (output, replay_data) = 277 invoke name command smt_options (SMT_Normalize.normalize ctxt thms') ctxt 278 in 279 parse_proof ctxt replay_data xfacts (map Thm.prop_of prems) (Thm.term_of concl) output 280 end 281 handle SMT_Failure.SMT fail => {outcome = SOME fail, fact_ids = NONE, atp_proof = K []} 282 283 284(* SMT tactic *) 285 286local 287 fun str_of ctxt fail = 288 "Solver " ^ SMT_Config.solver_of ctxt ^ ": " ^ SMT_Failure.string_of_failure fail 289 290 fun safe_solve ctxt facts = SOME (apply_solver_and_replay ctxt facts) 291 handle 292 SMT_Failure.SMT (fail as SMT_Failure.Counterexample _) => 293 (SMT_Config.verbose_msg ctxt (str_of ctxt) fail; NONE) 294 | SMT_Failure.SMT (fail as SMT_Failure.Time_Out) => 295 error ("SMT: Solver " ^ quote (SMT_Config.solver_of ctxt) ^ ": " ^ 296 SMT_Failure.string_of_failure fail ^ " (setting the " ^ 297 "configuration option " ^ quote (Config.name_of SMT_Config.timeout) ^ " might help)") 298 | SMT_Failure.SMT fail => error (str_of ctxt fail) 299 300 fun resolve ctxt (SOME thm) = resolve_tac ctxt [thm] 1 301 | resolve _ NONE = no_tac 302 303 fun tac prove ctxt rules = 304 CONVERSION (SMT_Normalize.atomize_conv ctxt) 305 THEN' resolve_tac ctxt @{thms ccontr} 306 THEN' SUBPROOF (fn {context = ctxt', prems, ...} => 307 resolve ctxt' (prove ctxt' (rules @ prems))) ctxt 308in 309 310val smt_tac = tac safe_solve 311val smt_tac' = tac (SOME oo apply_solver_and_replay) 312 313end 314 315end; 316