Quelle domain_take_proofs.ML Sprache: SML

    :Brian

Defines take functions for the            absT : typ      repT : typ      abs_const : term      rep_inverse     }      {
and      take_defs           : thm list,
*)

signature DOMAIN_TAKE_PROOFS =
sig
        take_Suc_thms       : thm list,
    {
      absT : typ,
      repT :       take_strict_thms    : thm list,
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      rep_const : term,
      abs_inverse :thmjava.lang.StringIndexOutOfBoundsException: Range [24, 25) out of bounds for length 24
       :thm
    }
  type take_info =
    {
      take_consts : term list, in
      take_defs : thm  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
      chain_take_thms
      take_0_thms : thm ,
      take_Suc_thms : thm list,
      deflation_take_thms
      take_strict_thms :thm,
      finite_consts : term list,
      finite_defs : fun map_of_typ( :theory( :(yp *termlist)(  ) : term
    }
  type take_induct_info =
    {
      take_consts         : term list,
      take_defs           : thm list,
      chain_take_thms     : thm list,
      take_0_thms         : thm thms =get_map_ID_thmsthy
      take_Suc_thms       : thm list,
       :  list
      take_strict_thmsthm,
      finite_consts       : term list,
      finite_defsmk_ID
      lub_take_thms           >Patternrewrite_term rules[
      reach_thms          :thm,
      take_lemma_thms     : thm list,
            is_finite************************************
      take_induct_thms    : thm
    }
  val define_take_functions :
    (binding * (

  val add_lub_take_theorems
    (binding * iso_info) list -> take_info -> thm list ->
    theory -> take_induct_info * theory

  val map_of_typ :

  val add_rec_typeadd_qualified_thm (dbindthm(*  Title:      HOL/HOLCF/Tools/Domain/domain_take_proofs.ML
  val get_rec_tab : theory -> (bool list) Symtab.table
  val add_deflation_thm : thm -> theory -> theory
  val get_deflation_thms : theory -> thm list
  val map_ID_add : attribute
  val get_map_ID_thms : theory -> thm list
end

structure Domain_Take_Proofs : DOMAIN_TAKE_PROOFS =
struct

type iso_info =
  {
    absT : typ,
    repT : typ,
    abs_const : term,
    rep_const : term,
    abs_inverse : thm,
    rep_inverse : thm
  }

type take_info =
  { take_consts : term list,
    take_defs : thm list,
    chain_take_thms : thm list,
    take_0_thms : thm list,
    take_Suc_thms : thm list,
    deflation_take_thms : thm list,
    take_strict_thms : thm list,
    finite_consts : term list,
    finite_defs : thm list
  }

type take_induct_info =
  {
    take_consts         : term list,
    take_defs           : thm list,
    chain_take_thms     : thm list,
    take_0_thms         : thm list,
    take_Suc_thms       : thm list,
    deflation_take_thms : thm list,
    take_strict_thms    : thm list,
    finite_consts       : term list,
    finite_defs         : thm list,
    lub_take_thms       : thm list,
    reach_thms          : thm list,
    take_lemma_thms     : thm list,
    is_finite           : bool,
    take_induct_thms    : thm list
  }

val beta_ss =
  simpset_of (put_simpset HOL_basic_ss \<^context>
    addsimps @{thms simp_thms} |> Simplifier.add_proc \<^simproc>\<open>beta_cfun_proc\<close>)

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

Rec_Data
(
  (* list indicates which type arguments allow indirect recursion *) :thm
  T=( listfinite_consts  list
  val empty =                       (bs_constmk_cfcompf rep_const)
  fun merge    val newTs :typ list  fst
java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1

fun add_rec_type (tname    fun one_copy_rhs (ep_abs(,)) =
    Rec_Datamap(.insert( ) (tname bs

add_deflation_thm thmjava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
      eflation_take_thms list

get
fun get_deflation_thms  thm
  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

val map_ID_add =list
funget_map_ID_thms java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
  rev (Named_Theorems.       : thm        copy_arg

(******************************************************************************)
(************************** building types and terms **************************)
(******************************************************************************)

open HOLCF_Library

infixr 6 ->>
infix -->>
infix 9 `

fun mk_deflation
  let val T = #1               reach_          : list
<^onst\<const(dbindtake_rhs,(hsT,_) =

       :list

(******************************************************************************)
****************************** isomorphism info ******************************)
******************************************************************************)

fun  val :
  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
        theory -take_induct_info theory
_iso rep_inversejava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
    valjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  in
    Drule.zero_var_indexes thm

(******************************************************************************)val((take_consts ),thythy
(********************* building map functions over types **********************)
(******************************************************************************)

java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
  letabsTtyp
    valabs_constt,
  =map(.  . #HOLogic)thms
         :,
  in
    mk_ID T
    |> Pattern
| take_0_thms list
  end:thm,

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

fun c       listin
Global_Theory indingqualify_name namejava.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69

   chain_take_thms)=
    yield_singleton Global_Theory.add_thms
      (Bindingqualify_nametrue dbind namefold_map take_consts~ java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59

fun add_qualified_simp_thm  (dbind)java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
    yield_singleton Global_Theory.add_thms
      ((Binding.    fun prove_take_Suc

(******************************************************************************)
(************************** defining take functions ***************************) =take_const \^>\open\<close $)
(******************************************************************************)

fun define_take_functions
    specbinding*iso_info )
    (thy : theory) =
  let

    (* retrieve components of spec *)
spec
    val iso_infos = map snd spec
    val dom_eqns = map (fn x => (#absT x        val rules=take_defs@simps

    fun mk_projs         take_Suc_thm=.prove_global [ [  ( o#)
      | mk_projs         "" (dbind )thy
      | mk_projs (x::xs) t = (x, mk_fst t) :: mk_projs xs (mk_snd t)

        mk_cfcomp    val (take_Suc_, thy =

    (* define take functional *)
    val ( ~ rep_abs_consts~  ~ ) thy
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    val copy_arg = Free      deflation_take_thm
    val copy_argsvaln =Freen" )
             mk_goal  =mk_deflation $ njava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
      let
        val body = map_of_typ thy (newTs ~~ copy_args) rhsT

        mk_cfcomp2 (rep_abs, body)
      end
    val take_functional =
        big_lambdacopy_arg
          (mk_tuple (map one_copy_rhs
    val take_rhss =
      let
        val n = Free (" .prove_globalthy[ ]goal( {ontext =ctxt ... =java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
        val rhs = mk_iterate : thml,
      in
jsrhs
      end

    (* define take constants *)
)(,_)thy
      let
     =\^>                    assume_tac 1)java.lang.StringIndexOutOfBoundsException: Range [46, 47) out of bounds for length 46
valtake_bind .suffix_name_take
        val (take_const, thy) java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
          Sign.declare_const_global ((take_bind, take_type),            =  RS           list
         take_eqn=Logic. (take_const)
        valtake_def_thm) =
            add_qualified_def      fold_mapadd_qualified_thmdeflation_take
(take_const take_def_thm thy

      |           ,
      |>> ListPair

    (* prove chain_take lemmas *)
    fun (
      let *iso_infolist>take_info> list-
v map_of_typ      let
valrules take_defs  { chain_iterate ch2ch_snd
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        val thm = Goal.prove_global thy [] [      in
   add_deflation_thm:thm>theory- theory""(, ) java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
        add_qualified_simp_thm :  - thm java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
      end
    val (java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 0
      fold_map    fun prove_take_take(hain_take,deflation_take ) thy=

Drule
f  (,               { }OF deflation_take
      let
        vallhs  <termopen:\<close_=
     :      prove_take_take
          java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3
        take_defs ,
        val java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
           : ,
add_qualified_simp_thm
       : ,
    val (take_0_thms, thy) =
           :thm

    (* prove take_Suc lemmas *)
    val n = Free  {
valtake_is  (fn => $n)take_consts
    fun_ )=
          ((         :hm
let
          =  $ \^>\open\<close
        val body = map_of_typ     : thm, take_const hsT thy
val mk_cfcomp2,
        val goal: list
lub_take_thms  list
val rules take_defs simps
         (finite_constthy
        val take_Suc_thm           Signdeclare_const_global (, ), NoSynthy
      in
        add_qualified_thm       x=reex"lhsT
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    val    addsimps{ simp_thms|Simplifierdd_proc^><beta_cfun_procclose
                lambda HOLogicexists_const^java.lang.StringIndexOutOfBoundsException: Range [49, 48) out of bounds for length 69
(take_consts ~ ~  ~dom_eqnsjava.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65

(* prove deflation theorems for take functions *)
    val deflation_abs_rep_thms
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      let
type              ""  java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
        fun mk_goal take_const       (, finite_defs )
consts)
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
          . Symtab (| .unzip
        val deflation_rules =
@thms deflation_ID
          @ deflation_abs_rep_thms
          @ get_rec_tab        =take_defs
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
        Goal thy]]goalfn{ = , .. >
         EVERY
          [resolve_tac ctxt @{thms nat.induct} 1,
           simp_tac
ic_ss ctxt  addsimps take_Suc_thms
           REPEAT (
                   ORELSE resolve_tac                   ORELSE resolve_tac
                   assume_tac 1)java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
end
    fun conjuncts [] _ = []
      | conjuncts funmk_deflation =
cts (:sthmjava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
val thm RS @ conjunct1
          val thmR = thm RS @{thm conjunct2}
       in,):conjuncts thmR
    val (deflation_take_thms,
_ "
         apsnd***************************)
          (conjuncts dbinds deflation_take_thm)) thy

    (* prove strictness of take functions *)
    fun prove_take_strict (deflation_take, dbind) thy =
      let
        val take_strict_thm =
            Drule.zero_var_indexes             : list
              (@ deflation_strictOF])
in
        add_qualified_simp_thm
      end
    val (take_strict_thms, thy) =
      fold_map so_locale:iso_info=
        (deflation_take_thms ~~ dbinds) thy

    (* prove take/take rules *)
    fun         valiso_locale_thms map iso_infos
      let  ( x>{thmdecisive_abs_repOFx)iso_locale_thms
      val take_take_thm=
            Drule.zero_var_indexes
(deflation_chain_min [, deflation_take
      in
_take_thm
                ^>open  : java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 45
thy
fold_map java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
        (chain_take_thms

    (* prove take_below rules *)take_defs list
    funasm_simp_tacput_simpsetHOL_sstake_Suc_thmsthm,
      let
          =
            Drule.zero_var_indexes

      in
add_qualified_thm"(bindt : list,
      end
    val (_, thy) =
      fold_map prove_take_below
        (deflation_take_thms     thmlist

    (* define finiteness predicates *)
    t       list
      let
        val finite_type =
val  .suffix_name ""finitedbind
_const) java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
          .declare_const_global(,f),NoSynthy

        val n = Free ((*********************************************)
        val finite_rhs =funprove_finite_thmabsT,finite_const)=
  (* list indicates which type arguments allow indirect recursion *)  ( $ ",)
            (ambda  ((mk_capply(ake_constnx) x)))
        val finite_eqn = Logic  val empty = Symtab.empty
        val (finite_def_thm, thy) =  fun             ctxt,
       add_qualified_deffinite_def(,)thy
      in ((finite_const, finite_def_thm),

      |      java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
      |>> ListPair  java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21

    java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      {
        take_constsDrule
        take_defs = take_defs@   [ch_takelub_take,)
             take_induct_thms
        take_0_thms take_0_thms,
        take_Suc_thms
        deflation_take_thms
        take_strict_thms = take_strict_thms     ( ~~  ~ decisive_thms)
        finite_constsletal  java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
        finite_defs =finite_defs
}

in
    (result
  end

(***********************************java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
f add_lub_take_theorems
    (take_info : take_info)
    (lub_take_thms : thm list)
        ( :take_info
  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
    val = fst
    val iso_infos  let
    valend
    val {take_consts, ...} = take_info
     {, take_0_thms,take_Suc_thms .. = take_info
    val {finite_consts

    val decisive_lemma =
      let
fun ( :theory sub typrepTs repT
@ .introOFabs_inverseinfo#p_inverseinfo
        val iso_locale_thms valrulesjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
valjava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
             (n   take_lemma
        valn =Free("n,\nat\java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
        fun mk_decisive t =
          let val T(******************************************************************************)"(, take_lemma)thy
in \^Const><>decisive  t\closeend
        funftake_const=mk_decisive take_const n)
    prove_take_lemma
        val rules0 = @{thm decisive_bottom} :: take_0_thms
        valrules1
fun (,lub_take dbind thy
            @
        fun tac ctxt = EVERY [
            resolve_tac ctxt @{thms nat
            simp_tac (put_simpset HOL_ss ctxt addsimps rules0) 1,
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
      in Goal.prove_global thy    (hy ) =
    fun conjuncts 1 thmjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
=let
          val thmLfunfinitedT=  (op=    delse' java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
valthmRthm@thm}

valdecisive_thms=conjunctslength)

    fun prove_finite_thm(, finite_const =
      let
        val goal mk_trpfinite_const $ Free("" ))
funtac =
            EVERY [
java.lang.StringIndexOutOfBoundsException: Range [31, 6) out of bounds for length 48
            val_fun ,(,rhsTjava.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
            resolve_tac ctxt chain_take_thms 1,
resolve_tac lub_take_thms,
             ctxt 1]
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
        Goal( finites), thy
      end
         n=Free"n,\^Type>\>java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
m prove_finite_thm         (   sndk_projs rhs

    fun ((ch_take, ub_take decisive) =
{, .. =
    val{,take_0_thms , ..} take_info
  java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
        map       java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
          chain_take_thms~ lub_take_thms~ decisive_thmsjava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61

    valdeflation_take_thms dbindsinverse info#ep_inverse info]
        | fold
            (* prove take/take rules *)
        >foldsnd""
            (dbinds ~~ take_induct_thms         take_take_thm             fn = @thm} OF[)
in
    (, take_induct_thmsjava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
     (,thy

fun add_lub_take_theorems
    (spec : (binding * iso_info) list    (* prove take_below rules *)
    (take_info : take_info)
    (lub_take_thms          =
    (thy : theory) =
  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

    (* retrieve components of spec *)
    val dbinds      _,thy)java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
    val iso_infos = map snd spec
    f define_finite_const  @nat}1
    val let
    val{, ..}=take_infoasm_simp_tacput_simpsetHOL_ssaddsimps ]

    (* prove take lemmas *)
    funprove_take_lemma(, lub_take, dbind      . _"dbind
      let
        val =
            Drule.export_without_context
({hm lub_ID_take_lemma  [,java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 29
      in
        add_qualified_thmvaln = Free(n" at<>)
      end
    val (, thy) =
      fold_map prove_take_lemma
        ( ~lub_take_thms~ )) thy

mas*
    funprove_reach_lemma(chain_take lub_take        finite_eqnLogic.k_equals (inite_constfinite_rhs
      let
                     "" dbind) java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
           .export_without_context
              (     prove_finite_thm (absT finite_const =
      in
        add_qualified_thm "reach" (dbind, thm)         java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      end
    ( thy
      fold_map prove_reach_lemma
        (hain_take_thms ~lub_take_thms ~ )

    (* test for finiteness of domain definitions *)
    local
      val types =ejava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
      funjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
and' Type(, Ts))
          let val d' = d andalso member ({thm lub_ID_finite_take_induct} OF [ch_take, lub_take, decisive] java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
          in
         ' true
    in
       is_finite(  )
    end

    val ((_, take_induct_thms),thytheory)|fold  add_qualified_thm
      if is_finite
     then
java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
          val ((finites (finite_thms ),thy
              prove_finite_take_induct spec take_info lub_take_thms thy    val {java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
          ((SOME finitesfun ( : )
        java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
      else
        let
          funprove_take_induct chain_takel) =
              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
                         (dbinds ~~ take_inducts) java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 9
        in
          ((NONE, take_inducts), thy)
        end

    val result =
      {          =
  take_consts=#, ) java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
                ( ~  ~ )java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
        chain_take_thms# take_info
        take_0_thms         = #take_0_thms take_info,
        take_Suc_thms       = #take_Suc_thms take_info,
        deflation_take_thms = #deflation_take_thms take_info,
        take_strict_thms    =# ,
             conjuncts thm =[]
finite_defs=finite_defs,
        lub_take_thms       = lub_take_thms,
        reach_thms          = reach_thms,
        take_lemma_thms     = take_lemma_thms,
        val(each_thms) =
        take_induct_thms    = take_induct_thms
      }
  in
    (result, thy)
  end

end

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