Quellcode-Bibliothek z3_proof.ML

(*  Title:      HOL/Tools/SMT/z3_proof.ML
    Author:     Sascha Boehme, TU Muenchen

Z3 proofs: parsing and abstract syntax tree.
*)

signature Z3_PROOF =
sig
  (*proof rules*)
  datatype z3_rule =
    True_Axiom | Asserted | Goal | Modus_Ponens | Reflexivity | Symmetry | Transitivity |
    Transitivity_Star | Monotonicity | Quant_Intro | Distributivity | And_Elim | Not_Or_Elim |
    Rewrite | Rewrite_Star | Pull_Quant | Pull_Quant_Star | Push_Quant | Elim_Unused_Vars |
    Dest_Eq_Res | Quant_Inst | Hypothesis | Lemma | Unit_Resolution | Iff_True | Iff_False |
    Commutativity | Def_Axiom | Intro_Def | Apply_Def | Iff_Oeq | Nnf_Pos | Nnf_Neg | Nnf_Star |
    Cnf_Star | Skolemize | Modus_Ponens_Oeq | Th_Lemma of string

  val is_assumption: z3_rule -> bool
  val string_of_rule: z3_rule -> string

  (*proofs*)
  datatype z3_step = Z3_Step of {
    id: int,
    rule: z3_rule,
    prems: int list,
    concl: term,
    fixes: string list,
    is_fix_step: bool}

  (*proof parser*)
  val parse: typ Symtab.table -> term Symtab.table -> string list ->
    Proof.context -> z3_step list * Proof.context
end;

structure Z3_Proof: Z3_PROOF =
struct

open SMTLIB_Proof


(* proof rules *)

datatype z3_rule =
  True_Axiom | Asserted | Goal | Modus_Ponens | Reflexivity | Symmetry | Transitivity |
  Transitivity_Star | Monotonicity | Quant_Intro | Distributivity | And_Elim | Not_Or_Elim |
  Rewrite | Rewrite_Star | Pull_Quant | Pull_Quant_Star | Push_Quant | Elim_Unused_Vars |
  Dest_Eq_Res | Quant_Inst | Hypothesis | Lemma | Unit_Resolution | Iff_True | Iff_False |
  Commutativity | Def_Axiom | Intro_Def | Apply_Def | Iff_Oeq | Nnf_Pos | Nnf_Neg | Nnf_Star |
  Cnf_Star | Skolemize | Modus_Ponens_Oeq | Th_Lemma of string
  (* some proof rules include further information that is currently dropped by the parser *)

val(*  Title:      HOL/Tools/SMT/z3_proof.ML    Author:    Sascha Boehme TUMuenchen
  ("true-axiom", True_Axiom),
  ("asserted", Asserted),
  "", Goal,
  "mp", Modus_Ponens),
  "refl", Reflexivity),
("ymm", Symmetry),
  (trans" Transitivity)java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
  ("trans*", Transitivity_Star),
  ("monotonicity", Monotonicity),
  ("quant  val string_of_rule:z3_rule - string
    : int listjava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
  "and-elim,And_Elim,
  ("not-or-elim", Not_Or_Elim),
  ("rewriteend;
  ("rewrite*", 
  (pullquant, Pull_Quant),
"-*" Pull_Quant_Star
(-quant" )java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
(-nused",Elim_Unused_Vars)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
  ", Dest_Eq_Res,
  quantinst",Quant_Inst,
  ("hypothesis", Hypothesis),
a,Lemma,
("nit-resolution,Unit_Resolutionjava.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
Iff_True,
  ("iff-false",Transitivity_Star(mp,)  "",
  ("commutativity", Commutativity),
 (def-axiom,Def_Axiom,
  ("-",Intro_Def),

  ("iff~", Iff_Oeq  "-elim", And_Elim),
  "-pos" Nnf_Pos),
  ("nnf-neg", Nnf_Neg  "-quant,Pull_Quantjava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
  (nnf*" ),
  "cnf*", Cnf_Star),
(sk,Skolemize,
  ("~", Modus_Ponens_Oeq,

fun is_assumption Asserted = true
assumptionGoal=true
  |is_assumption Hypothesis =""nnf-neg, )
  |fun is_assumptionAsserted =true
  |is_assumptionSkolemize = 
is_assumption _   false

fun   | is_assumption  = true
ase Symtab.rule_namesnameof
    SOME rule =>    SOME rule=>rule
  |NONE

fun string_of_rule (Th_Lemma kind) = "th-lemma" ^ (if     r java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
  struct
      let fun eq_rule (s, r') = if r =  id: ,
       the Symtab.get_firsteq_rule java.lang.StringIndexOutOfBoundsException: Range [39, 14) out of bounds for length 14


(* proofs *)

datatype
  :java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
  rulez3_rule
  premsZ3_Node{ idruleruleprems=prems,concl=concl  }
  concl: term,
  boundsstring}

fun mk_node id rule prems concl("istributivity, ),
(ewrite,Rewrite),

fun string_of_node ctxt =
  let
    java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
     Symbolpaces 2*pth^
      enclose "{" "}"(java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
        [iff,Iff_True,
      . 2* )^
         enclose[ "(implode_space ),
         (-" Def_Axiom)
        cat_linesmapprefix \"o  depth + )prems)
  in str 0 end

datatypez3_step= of
  d int"        tring_of_int id
  
  premsstring_of_rule rule
  concl: term|  enclose""""(implode_space )
  fixes: string list,    Intro_DefSyntaxtring_of_term ctxtconcl ^
  is_fix_step: bool

fun rule_of_string name        cat_lines(map(prefix""o  (epth 1)prems)
  Z3_Step {id = id, rule = rule, prems = prems, concl = concl, fixes = fixes,
    is_fix_step = is_fix_step}


(* proof parser *)

funatypez3_step=Z3_Step of {
  | rule_of (SMTLIB.S (SMTLIB   id:int
      (case (namerulez3_rule,
        prems int,
      | 
  |oncl term

 node_ofcx
  (case 
    (* proofs *)
      datatypez3_node= Z3_Nodeof
        Proof node =>    is_fix_step is_fix_step
      |
          cx
          java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
          |>( node=    oupdate_binding (, Proof))
        conclcasenameargs)of
        "-lemma"SMTLIBSym  ::_=Th_Lemmakind
      with_bindings map bindings ( p) java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62

      let
        val (
        val r  rule_of name
      in
          (case p of
        |> fold_map node_of ps
        |unstring_of_node ctxt java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 22
        |> next_id
        |>> (fn ((         node=> (, cx
      end
  | _           cx

fun dest_name (SMTLIB.Sym name) = name
  | dest_name( node=>      Symbolpaces2 depth)^

fundest_seq (.Sts  ts
   dest_seq t =raise  ("badZ3proofformat",t)

fun parse' (SMTLIBS:parts =>
   parse'(.S SMTLIBSym "eclarefun" ,tysty :tscxjava.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
      
        val name       in
        valTs =  (type_ofcx) ( tys
        val (with_fresh_namestxt]concl]java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
       parsets ( name(Ts->T )end
  | parse' (SMTLIB.S [SMTLIB.Sym "proof"  in str 0 end
| parse'ts_=raiseSMTLIB_PARSE (badZ3proofdeclarations" SMTLIBS )

      end
  let
    val ts = dest_seq (SMTLIB     rulez3_rule,
 valodecx)  ' ts(empty_context  typs )
e, ctxt_of cx end
  handle SMTLIB.PARSE (l, msgjava.lang.StringIndexOutOfBoundsException: Range [2, 0) out of bounds for length 0
        SMTLIB_PARSE(, t)= error (sg^:"^SMTLIB.str_of t)


(* handling of bound variables *)_ {=d rule =ule  =prems concl concl fixes=fixes,

funsubst_of tyenv=
  letlet
        val name =dest_name

fun substTs_same subst =
  let rule_of        valT type_ofcx java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
  inTermmap_atyps_sameapplyT

fun subst_types ctxt  . "" ] : _)   node_of pjava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
  let
    val match = Sign.typ_match (Proof_Context.theory_of  |

    fun objT_of bound =
      (Symtab envof
MEval(node cx)= ' ts empty_contextctxt typs funs
    |NONE>raise Fail(eplayingproofproducedbyZ3failed:"
          "the   handle PARSE( )  error " erroratline"^string_of_int   "  ^))

    val t' = singleton (Variable.polymorphic ctxt|java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
|MTLIB SMTLIB """ SMTLIBS bindings, p =>
valobjTs mapwith_bindings (mapdest_bindingbindings (node_ofpcx
    val subst  in Vartabfold tyenv[ 
 Term. (substTs_same subst t end

funeq_quant(<const_name\open>HOLokup (op)subst
  |eq_quant(\^const_name><open>.Exjava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
  | eq_quant _ _ =java.lang.StringIndexOutOfBoundsException: Range [8, 0) out of bounds for length 0

funjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
  |     name    raise SMTLIB_PARSE (bad"", t
       objT_ofjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

fun with_quant pred i        SOME =>   t      (Z3proof",t)
if    = T2then
        |' (MTLIB. [SMTLIB.  
(apply2Term.subst_bound(t, t1) (t,t2)end
      elsejava.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15


fun     val subst|'(. [MTLIBSym""p :: ) =node_of pcx
      map(apfstHOLogic( opp_quanti (,t2java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
  |dest_quant_pair(t1, )= with_quant i (,)

fun node cx)  '   eq_quant\const_name<open.\close _ \^>>\openHOL.Ex\<>,)=true
( dest_quant_pair  (HOLogicinnode, cx end

  | NONE raise (""[t)

fun match_types pat  __ false
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  >Patternfirst_order_match (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

funstrip_matchctxtpat            andalsoT1=T2java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
types pat)let  t  Var ("i,T1java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
    SOME (tyenvjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
  | java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

      else    >objT
       ( 1 (
  |fun dest_quant_pair (^><>HOLot\<>$t1,t2)=

 dest_alls tjava.lang.StringIndexOutOfBoundsException: Range [15, 0) out of bounds for length 0

fun match_ruledest_quantmap (. <>\<>Pureall> t)
  let
     subst= (     (1,t2=HOLogic. (.mk_eqt1 t2)
    val (i, obj) = dest_alls (subst_types    =>raiseTERM "lift_quant" [t]java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
  in
    (ase try (strip_match ty)
      NONE.first_order_match(oof_Context) (pat,obj)
    |SOME subst =
        let
          val applyT java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 \^>\open.allclose>t'java.lang.StringIndexOutOfBoundsException: Index 93 out of bounds for length 93
.ake (s~mapapplyT patTs) end
    


(* linearizing proofs and resolving types of bound variables *)+)(.etapply(,Var (""i T))

fun

fun add_step id funmatch_rule  envZ3_Node{ = bs concl t'..}) bs t=
  let val step ingleton Variablepolymorphic ) tjava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
      else NONE

fun is_fix_rule rule prems =  in
memberop=   with_quant__   java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27

fun  subst=
        let
else
    let
       t  subst_types        in  Symtab (bs'~  applyTpatTs))
        =add_stepidrule  t
      fun (
    in
       is_fix_rule  prems
        (case match_rule
          NONE> rec_apply envfalse steps
        | SOME  Vartab, Vartabempty)
      elserec_apply envidruleids conclbounds java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
    end

fun linearize 
   (trymatch_typesctxtpat) obj of


(* overall proof parser *)

funparsetyps  member (  =)[uant_IntroNnf_PosNnf_Neg rule  prems=1
val (odejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  in linearize'|est_all = (, tjava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25

end;