author  wenzelm 
Fri, 27 Aug 2010 17:09:18 +0200  
changeset 38805  b09d8603f865 
parent 36960  01594f816e3a 
permissions  rwrr 
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(* Title: HOL/Library/Sum_Of_Squares/sos_wrapper.ML 
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Author: Philipp Meyer, TU Muenchen 
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Added functionality for sums of squares, e.g. calling a remote prover. 
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*) 
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signature SOS_WRAPPER = 
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sig 
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datatype prover_result = Success  Failure  Error 
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val setup: theory > theory 
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val dest_dir: string Config.T 
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val prover_name: string Config.T 

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end 
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structure SOS_Wrapper: SOS_WRAPPER = 
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struct 
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datatype prover_result = Success  Failure  Error 
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fun str_of_result Success = "Success" 
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 str_of_result Failure = "Failure" 

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 str_of_result Error = "Error" 

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(*** calling provers ***) 
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val (dest_dir, setup_dest_dir) = Attrib.config_string "sos_dest_dir" (K "") 
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fun filename dir name = 
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let 
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val probfile = Path.basic (name ^ serial_string ()) 
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val dir_path = Path.explode dir 
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in 
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if dir = "" then 
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File.tmp_path probfile 
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else if File.exists dir_path then 
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Path.append dir_path probfile 
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else error ("No such directory: " ^ dir) 
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end 
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fun run_solver ctxt name cmd find_failure input = 
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let 
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val _ = warning ("Calling solver: " ^ name) 
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(* create input file *) 
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val dir = Config.get ctxt dest_dir 
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val input_file = filename dir "sos_in" 
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val _ = File.write input_file input 
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(* call solver *) 
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val output_file = filename dir "sos_out" 
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val (output, rv) = 
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bash_output 
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(if File.exists cmd then 
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space_implode " " 
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[File.shell_path cmd, File.shell_path input_file, File.shell_path output_file] 
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else error ("Bad executable: " ^ File.platform_path cmd)) 
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(* read and analyze output *) 
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val (res, res_msg) = find_failure rv 
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val result = if File.exists output_file then File.read output_file else "" 

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(* remove temporary files *) 
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val _ = 
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if dir = "" then 
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(File.rm input_file; if File.exists output_file then File.rm output_file else ()) 
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else () 
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val _ = 
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if Config.get ctxt Sum_Of_Squares.trace 

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then writeln ("Solver output:\n" ^ output) 

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else () 

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val _ = warning (str_of_result res ^ ": " ^ res_msg) 
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in 
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(case res of 
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Success => result 
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 Failure => raise Sum_Of_Squares.Failure res_msg 
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 Error => error ("Prover failed: " ^ res_msg)) 
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end 
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(*** various provers ***) 
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(* local csdp client *) 
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fun find_csdp_failure rv = 
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case rv of 
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0 => (Success, "SDP solved") 
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 1 => (Failure, "SDP is primal infeasible") 
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 2 => (Failure, "SDP is dual infeasible") 
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 3 => (Success, "SDP solved with reduced accuracy") 
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 4 => (Failure, "Maximum iterations reached") 

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 5 => (Failure, "Stuck at edge of primal feasibility") 

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 6 => (Failure, "Stuck at edge of dual infeasibility") 

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 7 => (Failure, "Lack of progress") 

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 8 => (Failure, "X, Z, or O was singular") 

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 9 => (Failure, "Detected NaN or Inf values") 

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 _ => (Error, "return code is " ^ string_of_int rv) 

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val csdp = ("$CSDP_EXE", find_csdp_failure) 
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(* remote neos server *) 
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fun find_neos_failure rv = 
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case rv of 

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20 => (Error, "error submitting job") 

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 21 => (Error, "interrupt") 
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 _ => find_csdp_failure rv 
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val neos_csdp = ("$ISABELLE_SUM_OF_SQUARES/neos_csdp_client", find_neos_failure) 
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(* named provers *) 
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fun prover "remote_csdp" = neos_csdp 
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 prover "csdp" = csdp 
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 prover name = error ("Unknown prover: " ^ name) 
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val (prover_name, setup_prover_name) = Attrib.config_string "sos_prover_name" (K "remote_csdp") 
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fun call_solver ctxt opt_name = 
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let 
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val name = the_default (Config.get ctxt prover_name) opt_name 
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val (cmd, find_failure) = prover name 
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in run_solver ctxt name (Path.explode cmd) find_failure end 
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(* certificate output *) 
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fun output_line cert = 
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"To repeat this proof with a certifiate use this command:\n" ^ 
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Markup.markup Markup.sendback ("by (sos_cert \"" ^ cert ^ "\")") 
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val print_cert = warning o output_line o PositivstellensatzTools.pss_tree_to_cert 
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(* method setup *) 
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fun sos_solver print method = SIMPLE_METHOD' o Sum_Of_Squares.sos_tac print method 
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val setup = 
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setup_dest_dir #> 
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setup_prover_name #> 

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Method.setup @{binding sos} 
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(Scan.lift (Scan.option Parse.xname) 
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>> (fn opt_name => fn ctxt => 
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sos_solver print_cert 

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(Sum_Of_Squares.Prover (call_solver ctxt opt_name)) ctxt)) 

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"prove universal problems over the reals using sums of squares" #> 
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Method.setup @{binding sos_cert} 
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(Scan.lift Parse.string 
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>> (fn cert => fn ctxt => 
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sos_solver ignore 
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(Sum_Of_Squares.Certificate (PositivstellensatzTools.cert_to_pss_tree ctxt cert)) ctxt)) 
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"prove universal problems over the reals using sums of squares with certificates" 
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end 