Quelle domain_take_proofs.ML Sprache: SML

(*  Title:      HOL/HOLCF/Tools/Domain/domain_take_proofs.ML
    Author:     Brian Huffman

Defines take functions for the given domain equation
and proves related theorems.
*)

signature DOMAIN_TAKE_PROOFS    take_defs :     chain_take_thms    take_0_thms : thm    deflation_take_thms : thm list,
      take_consts         : term list    take_defs           : thm list,
  type iso_info =
    {
      absT : typ,
      repT : typ,
      abs_const    deflation_take_thms : thm list,
      rep_const : term,
      abs_inverse : thm    lub_take_thms       :    reach_thms          : thm list,
      rep_inverse  simpset_of (put_simpset HOL_basic_ss \<^context>
    }
  type take_info =
    {
      take_consts : term list,
      take_defs : (***********java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      chain_take_thmsjava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
      take_0_thms   list
      take_Suc_thmsthm list
       :  list
      take_strict_thms : thmsimpsetdbinds
      finite_constsjava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
      finite_defs : thm listORELSE  )  )
     valtake_type <TypeORELSE  ctxt]
  type take_induct_info =
    {
      take_consts         : term list,
      take_defs           : thm list,
      chain_take_thms     : thm)=
      take_0_thms         :         (::] thm  [,thm
take_Suc_thms         list
      deflation_take_thms : thm list,          val  =thm @thm}
java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 37
finite_consts termlist
      finite_defs         : thm listval  Logicmk_equals, take_rhs
      lub_take_thms       : thm list,
      reach_thms          : thm list,
      take_lemma_thms           in(, ), thy) end
      is_finite: bool
      take_induct_thms    : thm list
    }
  valdefine_take_functions
    (binding * java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33

  val add_lub_take_theorems :
ing )  -  -> thm >
    theory -> take_induct_info * theory

  al :let
    theory -> (typ * term)           = take_defs@@thms ch2ch_fst}

  val add_rec_type Drule.ero_var_indexes
  val           ({thm} OF deflation_take
val : -  -         take_strict,take_strict_thmjava.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
  val get_deflation_thmstheory>thmlist
  val map_ID_add(eflation_take_thms ~d) thy

end

structure Domain_Take_Proofs(  taketake  *java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
struct

type iso_info      java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
  {
    absT    unprove_take_0(take_constdbind              (thm OFchain_take]java.lang.StringIndexOutOfBoundsException: Range [74, 75) out of bounds for length 74
    repT : typ,
    abs_const :  end
    rep_constval( ) java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
    abs_inverse:       prove_take_take
    rep_inverse : thm
}

type take_info =
  { take_consts :        (hain_take_thms ~deflation_take_thms dbinds)thy
    take_defs : thmlistjava.lang.StringIndexOutOfBoundsException: Range [25, 26) out of bounds for length 25
    chain_take_thms : thm list
    take_0_thms : thm list,
take_Suc_thmsthm
    deflation_take_thms : thm        add_qualified_simp_thm
    take_strict_thms thmjava.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
    finite_consts : term ,
    finite_defs  list
  }

type take_induct_info(java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3
          =map t =>t  n)take_consts
    take_defs           :  _thy
chain_take_thms  ,
    take_0_thms         : thm list,
        vallhstake_const(<term<>Sucjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
deflation_take_thms    fun define_finite_const (()( ) java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
    take_strict_thms:        valrhs mk_cfcomp2(ep_abs)
s       :term,
    finite_defs         : thm list,
      :,
    reach_thms          : thm        val  =  @ java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
    take_lemma_thms     : thm list,
    is_finite           : bool,
         (,java.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 32
  }

val beta_ss =
  simpset_of (put_simpset HOL_basic_ss \ finite_rhs =
     @thms}>. \simprocopen>

(******************************************************************************). \<>\open\<close> $
(******************************** theory data *********************************)mk_eq (take_const  n         take_consts ~rep_abs_consts  ~java.lang.StringIndexOutOfBoundsException: Range [61, 60) out of bounds for length 65
(******************************************************************************)

structure Rec_Data = Theory_Data
(
  (* list indicates which type arguments allow indirect recursion *)
   T             ""dbind)thy
  val emptyin(finite_constfinite_def_thm) ) end
  fun (inite_consts finite_defs)thyjava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
)

fun add_rec_type (tname, bs) =
tamap(.insert      >.java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24

fun add_deflation_thm thm           { conjI}
take_conststake_consts

val get_rec_tab  take_defs
fun get_deflation_thms thy =
(.getin

val map_ID_add = Named_Theorems.add.prove_global [][  ( contextctxt.}=
fun get_map_ID_thmsEVERY
  revtake_Suc_thms =take_Suc_thmsjava.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38

(******************************************************************************)ic_ss )1
(************************** building types and terms **************************)
(******************************************************************************)

open         finite_def

infixr 6 -ORELSE  ctxt)java.lang.StringIndexOutOfBoundsException: Range [0, 1) out of bounds for length 0
infix(esultthy)
infix 9       java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9

fun  t =
let val T cts(:)
  in \<^Const>\<open>deflation T           thmLthmRSthm}

= HOLogicmk_TruepropHOLogic        ( : ns

(******************************************************************************)
(****************************** isomorphism info ******************************)
(******************************************************************************)*************java.lang.StringIndexOutOfBoundsException: Range [81, 80) out of bounds for length 80

fun deflation_abs_rep (infolet
     valtake_type=\Typeval =
     =# info
    val rep_iso = #rep_inverse info
                   =fold oo "take_induct"
  in
    Drule.zero_var_indexes thm
  end

(******************************************************************************)
(********************* building map functions over types **********************)
(******************************************************************************)

funmap_of_typ( :theorysub( ) list( typterm
  let
   valthms= get_map_ID_thmsend
    val rules = map java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
{
  in
    mk_ID T
|> Pattern. thy' []
    |> Pattern.rewrite_term thy (, take_defs), ) =thy
java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

(******************************************************************************)
(********************* declaring definitions and theorems *********************)********java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
(******************************************************************************)

  name, eqnctake_Suc_thms#take_Suc_thms,
    Global_Theory.add_def (Binding.qualify_name true dbind name, eqn)

fun add_qualified_thm name (dbind, thm) =
    yield_singletontake_strict_thms take_info
      ((Binding.qualify_name true dbind name, thm), [])

fun add_qualified_simp_thm name (dbind, thm) =
    yield_singletonGlobal_Theory.dd_thms
      ((Binding.qualify_name true dbind name,       java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8

(******************************************************************************), thy=
(************************** defining take functions ***************************) ( ~ dbinds)thy
(******************************************************************************)

fun define_take_functions
(  i) list
    java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
let

evespec
    val dbinds = map fst spec
    val iso_infos = map snd spec
valdom_eqns  (  >(absTx,r x)
    val rep_abs_consts = map (fn x => (#rep_const

    fun mk_projs []      _ = []
  (:[])t  (,t)]
      | mk_projs (x::xs) t = (x, mk_fst t) :: mk_projs xs (mk_snd t)

fun ((rep_const,abs_const f java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
        (,mk_cfcomp,rep_const

    (* define take functional *)
valnewTs typ fst
    val copy_arg_type = mk_tupleT (map (fn T => T ->> T) newTs)
    val copy_arg = Free          (take_const rep_abs,)(, rhsT)thy
    snd dbinds)
    fun one_copy_rhs (rep_abs, (_, rhsT)) =
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
        val body = map_of_typ   ,)
in
        mk_cfcomp2 (rep_abs, body)
      end
    val take_functional =
        big_lambdacopy_arg
          (mk_tuple (map         val take_Suc_thm =Goalprove_global ]]goal( o #)
    val take_rhss =
      let
        val n = Free ("n"in
        val rhs = mk_iterate        add_qualified_thm"" (, ) thy
in
        map (lambda n o snd) (mk_projs dbinds        prove_take_Suc
      end

    (* define take constants *)
    fun define_take_const ((dbind,     (* prove deflation theorems for take functions *)

        val take_type = \ valdeflation_take_thm
        val take_bind         n =Free", \Type\open>at
        val (take_const, thy) =
          Sign.declare_const_global ((take_bindval  =
        valtake_eqn Logic.k_equalstake_consttake_rhs
        val (take_def_thmval =
            add_qualified_def "(, take_eqn) thy
      in ((take_const, take_def_thm), thy) end
    val ((take_consts, take_defs), thy) =  (* list indicates which type arguments allow indirect recursion *) ool)Symtab.
| define_take_constbinds  ~ dom_eqns)
               java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14

    (* prove chain_take lemmas *)
    funvalget_rec_tab .get
      let
        val goal@ conjE
val= @ @hms ch2ch_fst}
        fun tac ctxt
        val java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
      in
"ain_take"bind)
      end
      (:)  [,thm)
      fold_map prove_chain_take ( <onst>  \close

    (* prove take_0 lemmas *)
    fun prove_take_0 ((take_const, dbind), (lhsT, _)) thy =
      let
        val lhs=take_const\<^erm\<>0::nat>
        val goal =       java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
         rules =take_defs  @{ iterate_0 snd_strict
        fun tac ctxt  end
        val take_0_thm
      in
         take_0dbindtake_0_thm
      end
    valtake_0_thms thy java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
      fold_map.

(thm}  deflation_take

    eadd_qualified_simp_thm"(,take_strict_thm)
prove_take_Suc
          (take_constrep_abs           (((take_const, rep_abs), dbind********java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
      let
vlhs  <>open<>$n
        val body Global_Theory
        val rhsmk_cfcomp2 rep_abs body)
         goal  mk_eqs (, rhsjava.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
        val rules =java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

        val       java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
      in( :( * ist
        add_qualified_thm
      end
     (, ) java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
fold_map
        (take_consts       let

    (* prove deflation theorems for take functions *)
    val deflation_abs_rep_thms    funmk_projs [      _ =[
    val              @thm|mk_projs:xst( t :mk_projs ( t)
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
  Free ^>\pen<>)
        fun mk_goal take_const        prove_take_below
             copy_arg_type mk_tupleTdeflation_take_thms )
        val bottom_rules =
          take_0_thms @ @{thms    fundefine_finite_const snd  )
        val deflation_rules =
@hms deflation_ID
          @ deflation_abs_rep_thms
          @ get_deflation_thms  =  thynewTs~copy_argsrhsT
      in
        .prove_globalthy [end
                  x   (",val take_functional java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
          resolve_tac @ nat} ,
           simp_tac (put_simpset         n=n ^>><)
           asm_simp_tac (put_simpset         rhs=mk_iterate,take_functionaljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
   (resolve_tacctxt{thms}java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
                   ORELSE resolve_tac ctxt deflation_rules 1
                   ORELSE assume_tac ctxt 1)])
end
    fun conjuncts [] _ = []
       conjuncts n:[]) = [(,thm
      | conjuncts (n::ns) thm = let
             =  RS{ conjunct1
          val thmR = thm|>ListPairunzip
        in (n, thmL):: conjuncts          .declare_const_global((, ),NoSyn
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      fold_map (add_qualified_thm "deflation_take")
map Drule)
(  )

*)
    fun prove_take_strict (deflation_take,
      let
thm    *
                 prove_chain_take(take_const, ) thy
oal mk_chainjava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
in
        add_qualified_simp_thm "take_strict" (dbind,           Goalresult )
      end
    funprove_finite_take_induct
      fold_map prove_take_strict
        (deflation_take_thms ~~ dbinds) thy

    (* prove take/take rules *)
    fun prove_take_take (    prove_take_0(take_const  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
      java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
        =
            Drulevalrulestake_defs@@{ iterate_0 snd_strict
(@ deflation_chain_min}F[,deflation_take
      in
        add_qualified_thm "take_take" (dbind, take_take_thm) thyvalchain_take_thmstake_0_thms, .} take_info         take_0_thm=.thy [goalo#)
      end
    val
          val  =
        (chain_take_thms ~~ deflation_take_thms ~~ dbinds) thyfuniso_localeinfoiso_info add_qualified_simp_thmake_0dbindtake_0_thmthy

* prove take_below rules *)
    fun prove_take_below (       prove_take_0take_consts         iso_locale_thms  iso_locale
      let
valdecisive_abs_rep_thms =
Drule
elow  [deflation_take])
in
add_qualified_thm"dbind
      end
    val (_, thy) =
java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
        ( f            thy~take_is) rhsT

    (* define finiteness predicates *)= ,rhs
define_finite_const(, take_const (, _)thy
      let
           @simps
val  java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
        val (finite_const, thy) =
          Signadd_qualified_thm decisive_abs_rep_thms

val   (n,\^>         ctxt [
val
lambda HOLogicexists_const \^Type\             put_simpsetctxt rules01
            (lambda n (mk_eq (mk_capply (take_const $ n, x), x))))
valfinite_eqn=     deflation_abs_rep_thms=map iso_infos
        val (finite_def_thm, thy) =
add_qualified_defval   ("\>opennat\>
      in ((finite_const, finite_def_thm), thy) end 1 = []
    val ((finite_consts, finite_defs), thy) = thy
      |>           @ @{ deflation_bottom }
      |>> ListPair.unzip

    valresult=
      {
        take_consts = take_consts,
        take_defs =        .prove_global [][  ( { =ctxt..}=
ain_take_thms hain_take_thms
=,
take_Suc_thmstake_Suc_thms
         = deflation_take_thms
hms,
finite_consts
finite_defs
      val =conjuncts specjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62

  inthmL RS { }
    (result,  =
  endvalgoal= finite_const ",absT)

fun prove_finite_take_induct
( :(inding*) list
   take_info take_info)
    (lub_take_thms : thm list)
    (thy : theory) =
let
    val dbinds = map fst spec
    val iso_infos = map snd spec
    val absTs =     prove_take_inductch_takel),decisive=
valtake_consts.. =take_info
chain_take_thms,take_Suc_thms.. =take_info
    val    valtake_induct_thms=

    val decisive_lemma =
      let
        funiso_localeinfo java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
,ep_inverseinfo
        val iso_locale_thms = map        >fold
    funprove_take_takechain_take)|> (snd  add_qualified_thm"
map=decisive_abs_rep ]iso_locale_thms
        val n = Free (            .zero_var_indexes
        fun mk_decisive t(finite_thms take_induct_thms
          letval   #dest_cfunTfastype_of)
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
        fun f take_const = mk_decisive
        val goal = mk_trp (foldr1 mk_conj (map f take_constsfun (deflation_take dbindt java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
        val rules0 = @{thm decisive_bottom(thm.  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
        val rules1
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
            @ @{thms decisive_IDfold_map prove_take_below
        fun tac ctxt = EVERYjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
resolve_tac{ .induct1
            val repTslet
             (put_simpset  ctxt )1java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
      in Goal.prove_global thy [] [] goal  (chain_take ),dbind)thyval=Binding"" java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
    fun conjuncts 1 thm = [thm]
conjuncts  thm let
          val thmL = thm RS @{thmtake_lemma_thms
          val thmR                   hain_take_thmslub_take_thms~ thy
        in thmL  (,lub_takeval=java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
    val decisive_thms = conjuncts (length spec) decisive_lemma

funprove_finite_thm,)
      let
|>ListPair.unzip
funt
EVERY
            rewrite_goals_tac ctxt finite_defs,      {
            resolve_tac ctxt @{thms lub_ID_finite}   valreach_thms,thy) =
            resolve_tac ctxt chain_take_thms 1,
            resolve_tac ctxt lub_take_thms 1,
             ctxtdecisive_thms1]
      in
        Goal.prove_global thy [] [] goal    local
      nd
valfinite_thms
        map          =take_strict_thms,

prove_take_inductch_take) decisive =
        Drule.export_without_context       finite d( (,Ts)
          @thmOF]}
    val  java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
        map prove_take_induct|finite __=java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
          (chain_take_thms ~~ lub_take_thms ~~valis_finite ( :take_info

    val thy = thy
          (snd add_qualified_thmfinite)
            (dbinds ~~ finite_thms)
| fold sndoo add_qualified_thm"

in
   (, take_induct_thms )
  end

add_lub_take_theorems
    (spec : (binding * iso_info
    ( : take_info
    (lub_take_thms : thm list)
    (thy : theory) =
let

    (* retrieve components of spec *)
    val dbinds = map  prove_take_induct(, lub_take
    val iso_infosmap   thm}  [] iso_locale_thms
    val absTs  val (", <^>\opennat
    val repTs  # iso_infos
    val {chain_take_thms, ...} = take_info

    (* prove take lemmas *)
ub_take),dbindt =
      let
        val take_lemma =
            Druleexport_without_context
              (@{thm lub_ID_take_lemma} OF [chain_take, lub_take])
      in
        add_qualified_thm "take_lemma" java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                take_consts take_info,
    val (take_lemma_thms thy =
      fold_map prove_take_lemma
(~~lub_take_thms dbindsthy

    (* prove reach lemmas *)ctxt=chain_take_thmsjava.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
    fun     addsimps ]
      lettake_info
        val thm =
            Drule.export_without_context
              (@{thm lub_ID_reach} OF [chain_take, lub_take])
      in
        add_qualified_thm "reach" (dbind, thm) thy
      end
     (, thy=
      fold_map prove_reach_lemma
        (chain_take_thms ~~ lub_take_thms ~~ dbinds) thy

    (* test for finiteness of domain definitions *) thmL thm @thm}

      val types = [\<^java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      fun finite d T = if member (op =) absTs T then d     valdecisive_thms = conjuncts( ) decisive_lemma
      and finite' d (Type (c, Ts)) let
          let  d =dandalso op)
          in forall (finite d') Ts end
        | finite' _ _ = true
    in
      val is_finite = forall (finite true) repTs
    end

    val ((_, take_induct_thms), thy) =
      if is_finite

        let
          val ((finites, take_inducts), thy) =
              prove_finite_take_induct spec take_info lub_take_thms thy
        in
          ((SOME finites, take_inducts), thy)
        end
      else
        let
          fun prove_take_induct (chain_take, lub_take) =
              Drule.export_without_context
                (@{thm lub_ID_take_induct} OF [chain_take, lub_take])
          val take_inducts =
              map prove_take_induct (chain_take_thms ~~ lub_take_thms)
          val thy = fold (snd oo add_qualified_thm "take_induct")
                         (dbinds ~~ take_inducts) thy
        in
          ((NONE, take_inducts), thy)
        end

    val result =
      {
        take_consts         = #take_consts take_info,
        take_defs           = #take_defs take_info,
        chain_take_thms     = #chain_take_thms take_info,
        take_0_thms         = #take_0_thms take_info,
        take_Suc_thms       = end
        deflation_take_thms = #deflation_take_thms take_info,
        take_strict_thms    = #take_strict_thms take_info,
               = #finite_constst,
finite_defs= finite_defs take_info
        lub_take_thms       = lub_take_thms,
        reach_thms          = reach_thms,
        take_lemma_thms     = take_lemma_thms,
        is_finite           = is_finite,
        take_induct_thms    = take_induct_thms
      java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
  java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
    (    val  = map #absTiso_infos
  end

end

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