author | blanchet |
Thu, 13 Mar 2014 13:18:14 +0100 | |
changeset 56094 | 2adbc6e4cd8f |
parent 56090 | 34bd10a9a2ad |
child 56096 | 3e717b56e955 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/SMT2/smt2_solver.ML |
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Author: Sascha Boehme, TU Muenchen |
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SMT solvers registry and SMT tactic. |
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*) |
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signature SMT2_SOLVER = |
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sig |
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(*configuration*) |
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datatype outcome = Unsat | Sat | Unknown |
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type solver_config = { |
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name: string, |
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class: Proof.context -> SMT2_Util.class, |
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avail: unit -> bool, |
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command: unit -> string list, |
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options: Proof.context -> string list, |
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default_max_relevant: int, |
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supports_filter: bool, |
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outcome: string -> string list -> outcome * string list, |
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cex_parser: (Proof.context -> SMT2_Translate.replay_data -> string list -> |
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term list * term list) option, |
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replay: (Proof.context -> SMT2_Translate.replay_data -> string list -> |
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(int list * Z3_New_Proof.z3_step list) * thm) option } |
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(*registry*) |
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val add_solver: solver_config -> theory -> theory |
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val solver_name_of: Proof.context -> string |
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val available_solvers_of: Proof.context -> string list |
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val apply_solver: Proof.context -> (int * (int option * thm)) list -> |
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(int list * Z3_New_Proof.z3_step list) * thm |
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val default_max_relevant: Proof.context -> string -> int |
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(*filter*) |
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val smt2_filter: Proof.context -> thm list -> thm -> ('a * (int option * thm)) list -> int -> |
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Time.time -> {outcome: SMT2_Failure.failure option, used_facts: ('a * thm) list, |
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z3_steps: Z3_New_Proof.z3_step list} |
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(*tactic*) |
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val smt2_tac: Proof.context -> thm list -> int -> tactic |
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val smt2_tac': Proof.context -> thm list -> int -> tactic |
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end |
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structure SMT2_Solver: SMT2_SOLVER = |
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struct |
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(* interface to external solvers *) |
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local |
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fun make_cmd command options problem_path proof_path = space_implode " " ( |
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"(exec 2>&1;" :: map File.shell_quote (command @ options) @ |
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[File.shell_path problem_path, ")", ">", File.shell_path proof_path]) |
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fun trace_and ctxt msg f x = |
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let val _ = SMT2_Config.trace_msg ctxt (fn () => msg) () |
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in f x end |
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fun run ctxt name mk_cmd input = |
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(case SMT2_Config.certificates_of ctxt of |
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NONE => |
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if not (SMT2_Config.is_available ctxt name) then |
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error ("The SMT solver " ^ quote name ^ " is not installed.") |
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else if Config.get ctxt SMT2_Config.debug_files = "" then |
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trace_and ctxt ("Invoking SMT solver " ^ quote name ^ " ...") |
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(Cache_IO.run mk_cmd) input |
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else |
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let |
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val base_path = Path.explode (Config.get ctxt SMT2_Config.debug_files) |
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val in_path = Path.ext "smt2_in" base_path |
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val out_path = Path.ext "smt2_out" base_path |
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in Cache_IO.raw_run mk_cmd input in_path out_path end |
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| SOME certs => |
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(case Cache_IO.lookup certs input of |
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(NONE, key) => |
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if Config.get ctxt SMT2_Config.read_only_certificates then |
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error ("Bad certificate cache: missing certificate") |
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else |
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Cache_IO.run_and_cache certs key mk_cmd input |
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| (SOME output, _) => |
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trace_and ctxt ("Using cached certificate from " ^ |
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File.shell_path (Cache_IO.cache_path_of certs) ^ " ...") |
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I output)) |
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(* Z3 returns 1 if "get-model" or "get-model" fails *) |
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val normal_return_codes = [0, 1] |
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fun run_solver ctxt name mk_cmd input = |
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let |
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fun pretty tag ls = Pretty.string_of (Pretty.big_list tag (map Pretty.str ls)) |
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val _ = SMT2_Config.trace_msg ctxt (pretty "Problem:" o split_lines) input |
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val {redirected_output=res, output=err, return_code} = |
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SMT2_Config.with_timeout ctxt (run ctxt name mk_cmd) input |
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val _ = SMT2_Config.trace_msg ctxt (pretty "Solver:") err |
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val output = fst (take_suffix (equal "") res) |
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val _ = SMT2_Config.trace_msg ctxt (pretty "Result:") output |
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val _ = member (op =) normal_return_codes return_code orelse |
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raise SMT2_Failure.SMT (SMT2_Failure.Abnormal_Termination return_code) |
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in output end |
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fun trace_assms ctxt = |
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SMT2_Config.trace_msg ctxt (Pretty.string_of o |
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Pretty.big_list "Assertions:" o map (Display.pretty_thm ctxt o snd)) |
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fun trace_replay_data ({context=ctxt, typs, terms, ...} : SMT2_Translate.replay_data) = |
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let |
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fun pretty_eq n p = Pretty.block [Pretty.str n, Pretty.str " = ", p] |
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fun p_typ (n, T) = pretty_eq n (Syntax.pretty_typ ctxt T) |
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fun p_term (n, t) = pretty_eq n (Syntax.pretty_term ctxt t) |
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in |
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SMT2_Config.trace_msg ctxt (fn () => |
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Pretty.string_of (Pretty.big_list "Names:" [ |
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Pretty.big_list "sorts:" (map p_typ (Symtab.dest typs)), |
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Pretty.big_list "functions:" (map p_term (Symtab.dest terms))])) () |
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end |
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in |
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fun invoke name command ithms ctxt = |
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let |
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val options = SMT2_Config.solver_options_of ctxt |
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val cmd = command () |
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val comments = [space_implode " " (cmd @ options)] |
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val (str, replay_data as {context=ctxt', ...}) = |
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ithms |
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|> tap (trace_assms ctxt) |
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|> SMT2_Translate.translate ctxt comments |
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||> tap trace_replay_data |
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in (run_solver ctxt' name (make_cmd cmd options) str, replay_data) end |
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end |
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138 |
|
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(* configuration *) |
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datatype outcome = Unsat | Sat | Unknown |
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type solver_config = { |
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name: string, |
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class: Proof.context -> SMT2_Util.class, |
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avail: unit -> bool, |
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command: unit -> string list, |
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options: Proof.context -> string list, |
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default_max_relevant: int, |
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supports_filter: bool, |
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outcome: string -> string list -> outcome * string list, |
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cex_parser: (Proof.context -> SMT2_Translate.replay_data -> string list -> |
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term list * term list) option, |
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replay: (Proof.context -> SMT2_Translate.replay_data -> string list -> |
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(int list * Z3_New_Proof.z3_step list) * thm) option } |
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|
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|
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(* registry *) |
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|
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type solver_info = { |
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command: unit -> string list, |
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default_max_relevant: int, |
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supports_filter: bool, |
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replay: Proof.context -> string list * SMT2_Translate.replay_data -> |
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(int list * Z3_New_Proof.z3_step list) * thm } |
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|
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structure Solvers = Generic_Data |
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( |
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type T = solver_info Symtab.table |
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val empty = Symtab.empty |
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val extend = I |
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fun merge data = Symtab.merge (K true) data |
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) |
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|
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local |
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fun finish outcome cex_parser replay ocl outer_ctxt |
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(output, (replay_data as {context=ctxt, ...} : SMT2_Translate.replay_data)) = |
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(case outcome output of |
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(Unsat, ls) => |
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if not (Config.get ctxt SMT2_Config.oracle) andalso is_some replay |
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then the replay outer_ctxt replay_data ls |
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else (([], []), ocl ()) |
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| (result, ls) => |
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let |
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val (ts, us) = |
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(case cex_parser of SOME f => f ctxt replay_data ls | _ => ([], [])) |
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in |
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raise SMT2_Failure.SMT (SMT2_Failure.Counterexample { |
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is_real_cex = (result = Sat), |
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free_constraints = ts, |
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const_defs = us}) |
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end) |
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|
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val cfalse = Thm.cterm_of @{theory} (@{const Trueprop} $ @{const False}) |
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in |
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|
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fun add_solver cfg = |
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let |
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val {name, class, avail, command, options, default_max_relevant, |
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supports_filter, outcome, cex_parser, replay} = cfg |
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201 |
|
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fun core_oracle () = cfalse |
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|
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fun solver ocl = { |
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command = command, |
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default_max_relevant = default_max_relevant, |
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supports_filter = supports_filter, |
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replay = finish (outcome name) cex_parser replay ocl } |
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|
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val info = {name=name, class=class, avail=avail, options=options} |
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in |
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Thm.add_oracle (Binding.name name, core_oracle) #-> (fn (_, ocl) => |
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Context.theory_map (Solvers.map (Symtab.update_new (name, solver ocl)))) #> |
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Context.theory_map (SMT2_Config.add_solver info) |
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end |
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|
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end |
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|
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fun get_info ctxt name = |
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the (Symtab.lookup (Solvers.get (Context.Proof ctxt)) name) |
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|
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val solver_name_of = SMT2_Config.solver_of |
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|
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val available_solvers_of = SMT2_Config.available_solvers_of |
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|
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fun name_and_info_of ctxt = |
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let val name = solver_name_of ctxt |
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in (name, get_info ctxt name) end |
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229 |
|
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fun apply_solver ctxt0 iwthms = |
231 |
let |
|
232 |
val (ithms, ctxt) = SMT2_Normalize.normalize iwthms ctxt0 |
|
233 |
val (name, {command, replay, ...}) = name_and_info_of ctxt |
|
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234 |
in |
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invoke name command ithms ctxt |
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|> replay ctxt |
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237 |
end |
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|
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val default_max_relevant = #default_max_relevant oo get_info |
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240 |
|
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val supports_filter = #supports_filter o snd o name_and_info_of |
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|
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243 |
|
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(* check well-sortedness *) |
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|
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val has_topsort = Term.exists_type (Term.exists_subtype (fn |
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TFree (_, []) => true |
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| TVar (_, []) => true |
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| _ => false)) |
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|
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(* without this test, we would run into problems when atomizing the rules: *) |
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fun check_topsort ctxt thm = |
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if has_topsort (Thm.prop_of thm) then |
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(SMT2_Normalize.drop_fact_warning ctxt thm; TrueI) |
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else |
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thm |
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|
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fun check_topsorts ctxt iwthms = map (apsnd (apsnd (check_topsort ctxt))) iwthms |
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|
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|
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(* filter *) |
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val cnot = Thm.cterm_of @{theory} @{const Not} |
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fun smt2_filter ctxt facts goal xwthms i time_limit = |
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let |
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val ctxt = |
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ctxt |
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|> Config.put SMT2_Config.oracle false |
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|> Config.put SMT2_Config.filter_only_facts true |
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|> Config.put SMT2_Config.timeout (Time.toReal time_limit) |
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val ({context=ctxt, prems, concl, ...}, _) = Subgoal.focus ctxt i goal |
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fun negate ct = Thm.dest_comb ct ||> Thm.apply cnot |-> Thm.apply |
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val cprop = |
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(case try negate (Thm.rhs_of (SMT2_Normalize.atomize_conv ctxt concl)) of |
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SOME ct => ct |
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| NONE => raise SMT2_Failure.SMT (SMT2_Failure.Other_Failure "goal is not a HOL term")) |
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val xthms = map (apsnd snd) xwthms |
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||
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val filter_thms = if supports_filter ctxt then map_filter (try (nth xthms)) else K xthms |
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in |
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map snd xwthms |
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|> map_index I |
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|> append (map (pair ~1 o pair NONE) (Thm.assume cprop :: prems @ facts)) |
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|> check_topsorts ctxt |
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|> apply_solver ctxt |
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|> fst |
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|> (fn (is, z3_steps) => {outcome = NONE, used_facts = filter_thms is, z3_steps = z3_steps}) |
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end |
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handle SMT2_Failure.SMT fail => {outcome = SOME fail, used_facts = [], z3_steps = []} |
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|
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|
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(* SMT tactic *) |
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|
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local |
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fun trace_assumptions ctxt iwthms idxs = |
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let |
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val wthms = |
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idxs |
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|> filter (fn i => i >= 0) |
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|> map_filter (AList.lookup (op =) iwthms) |
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in |
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if Config.get ctxt SMT2_Config.trace_used_facts andalso length wthms > 0 |
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then |
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tracing (Pretty.string_of (Pretty.big_list "SMT used facts:" |
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(map (Display.pretty_thm ctxt o snd) wthms))) |
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else () |
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end |
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|
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fun solve ctxt iwthms = |
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iwthms |
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|> check_topsorts ctxt |
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|> apply_solver ctxt |
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|>> apfst (trace_assumptions ctxt iwthms) |
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|> snd |
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|
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fun str_of ctxt fail = |
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SMT2_Failure.string_of_failure ctxt fail |
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|> prefix ("Solver " ^ SMT2_Config.solver_of ctxt ^ ": ") |
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|
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fun safe_solve ctxt iwthms = SOME (solve ctxt iwthms) |
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handle |
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SMT2_Failure.SMT (fail as SMT2_Failure.Counterexample _) => |
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(SMT2_Config.verbose_msg ctxt (str_of ctxt) fail; NONE) |
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| SMT2_Failure.SMT (fail as SMT2_Failure.Time_Out) => |
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error ("SMT: Solver " ^ quote (SMT2_Config.solver_of ctxt) ^ ": " ^ |
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SMT2_Failure.string_of_failure ctxt fail ^ " (setting the " ^ |
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"configuration option " ^ quote (Config.name_of SMT2_Config.timeout) ^ " might help)") |
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| SMT2_Failure.SMT fail => error (str_of ctxt fail) |
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|
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fun tag_rules thms = map_index (apsnd (pair NONE)) thms |
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fun tag_prems thms = map (pair ~1 o pair NONE) thms |
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|
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fun resolve (SOME thm) = rtac thm 1 |
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| resolve NONE = no_tac |
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|
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fun tac prove ctxt rules = |
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CONVERSION (SMT2_Normalize.atomize_conv ctxt) |
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THEN' rtac @{thm ccontr} |
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THEN' SUBPROOF (fn {context, prems, ...} => |
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resolve (prove context (tag_rules rules @ tag_prems prems))) ctxt |
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in |
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|
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val smt2_tac = tac safe_solve |
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val smt2_tac' = tac (SOME oo solve) |
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|
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end |
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|
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end |