val add_lub_take_theorems : (binding * iso_info) list -> take_info -> thm list -> theory -> take_induct_info * theory
val map_of_typ : theory -> (typ * term) list -> typ -> term
val add_rec_type : (string * bool list) -> theory -> theory 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
(******************************************************************************) (******************************** theory data *********************************) (******************************************************************************)
structure Rec_Data = Theory_Data
( (* list indicates which type arguments allow indirect recursion *) type T = (boollist) Symtab.table val empty = Symtab.empty fun merge data = Symtab.merge (K true) data
)
fun add_deflation_thm thm =
Context.theory_map (Named_Theorems.add_thm \<^named_theorems>\<open>domain_deflation\<close> thm)
val get_rec_tab = Rec_Data.get fun get_deflation_thms thy =
rev (Named_Theorems.get (Proof_Context.init_global thy) \<^named_theorems>\<open>domain_deflation\<close>)
val map_ID_add = Named_Theorems.add \<^named_theorems>\<open>domain_map_ID\<close> fun get_map_ID_thms thy =
rev (Named_Theorems.get (Proof_Context.init_global thy) \<^named_theorems>\<open>domain_map_ID\<close>)
(******************************************************************************) (************************** building types and terms **************************) (******************************************************************************)
open HOLCF_Library
infixr 6 ->>
infix -->>
infix 9 `
fun mk_deflation t = letval T = #1 (dest_cfunT (Term.fastype_of t)) in \<^Const>\<open>deflation T for t\<close> end
fun mk_eqs (t, u) = HOLogic.mk_Trueprop (HOLogic.mk_eq (t, u))
(******************************************************************************) (****************************** isomorphism info ******************************)
(*abs_inverse thm,
fun deflation_abs_rep (info : iso_info) : thm = let val abs_iso = #abs_inverse info val rep_iso = #rep_inverse info val thm = @{thm deflation_abs_rep} OF [abs_isorep_inverse:thm
Drule.zero_var_indexes thm end
(******************************************************************************) (********************* building map functions over types **********************)list (******************************************************************************)list
fun thy ) sub (yp *) list)(:typ = letjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5 valthms =get_map_ID_thms java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
deflation_take_thmsthm, val rules : list in
T
| .rewrite_term thy' ]
|> Patternreach_thms : list end
(******************************************************************************)********************************) (********************* declaring definitions and theorems *********************) (******************************************************************************):
fun add_qualified_def name (dbind, eqn) =
Global_Theory.add_def
fun add_qualified_simp_thm name (dbind, thm) = yield_singleton Global_Theory.add_thms ((Binding.qualify_name true dbind name, thm), [Simplifier.simp_add])
(******************************************************************************) (************************** defining take functions ***************************) :typjava.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3 (******************************************************************************),
take_consts : term list, fun define_take_functions
(spec : (binding * iso_info) take_0_thms : thm list,
( : :term, let finite_defs : thm list,
(* retrieve components of spec *) val dbinds = is_finite : bool, val simpset_of( \^context
take_consts: term, val rep_abs_consts =java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[]_= ]
| mk_projs (x::[]) t = [(x, t)]
|mk_projsjava.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
fun mk_cfcomp2 typebool)finite_consts ,
mk_cfcomp f rep_const)
(* define take functional *) val newTs :typ =map dom_eqns val ) val copy_arg = Free ("f", copy_arg_type) val copy_args fun one_copy_rhs (, (_ rhsT java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43 let
:thm list,
finite_consts_.java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30 end valval map_ID_add take_defs : thm :thm,
big_lambda
( (map (rep_abs_consts val take_rhss = let val n = Free
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 fun mk_deflation= map :thm, end
(* define take constants *) const(,take_rhs (hsT,))thy let :hm val take_type = \(
( val (take_const, thy) =
map_of_typ:
take_eqn= Logicmk_equals, )
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
add_qualified_defin inend
((take_consts,take_defs ) = java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
|> fold_map define_take_const java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
>ListPair.nzip
(* prove chain_take lemmas *) =map(concl_ofHOLogic >.dest_eqjava.lang.StringIndexOutOfBoundsException: Index 83 out of bounds for length 83
:list let
| take_0_thms list val rules
=simp_tacput_simpset fun tac ctxt = simp_tac (put_simpset HOL_basic_ss**java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80 val
add_qualified_simp_thm "chain_take" ( Global_Theory(indingqualify_name ) end
(chain_take_thms java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
fold_mapprove_chain_take )thy
(* prove take_0 lemmas *) fun prove_take_0fun add_qualified_simp_thmname, thm = let val lhs finite_defs : list, val goal = list val rules take_induct_thms thm
tacctxtsimp_tacput_simpset addsimpsrules)1 val take_0_thm = Goal.prove_global thy [] [] goal (tac o #context) in
alified_simp_thmtake_0 dbindtake_0_thm java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63 end val (take_0_thmsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
fold_map prove_take_0 (take_consts (*********************************************)
(* prove take_Suc lemmas *) val n val take_is = map (fn t => t $ n) take_consts fun
(((take_const, rep_abs let val lhs $(<term<>Succlose>$njava.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63 val val( : ( ) list val goal = val simps = @{ val dbinds = map fst val = fun tac ctxt = simp_tac (put_simpset beta_ss ctxt addsimps iso_infos val =Goal thy]]goaltac context in
add_qualified_thmtake_Suc (dbind,take_Suc_thm java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62 end
thms thy)java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
fold_map prove_take_Suc
take_consts~rep_abs_consts ~~dbinds~dom_eqnsthy
(* prove deflation theorems for take functions *) val deflation_abs_rep_thms = map deflation_abs_rep iso_infos val = let
= ("" \^><>\close funmk_goaltake_const (take_const n) val goal = mk_trp (foldr1 mk_conj (map mk_goal take_consts)) val bottom_rules = in val deflation_rules
@big_lambda copy_arg
@deflation_abs_rep_thms
@ get_deflation_thms thy in
Goal ][ fn{ontext ,.. >
EVERY
[resolve_tac ctxt @{thms nat.induct} 1 take_0_thms:thm,
deflation_take_thmsthm,
_simpset )
REPEAT (eresolve_tac
resolve_tacctxt,lhsT =
ctxt]
java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5 fun =Binding "_" dbind
|conjunctsn[) thm =[n )]
| take_Suc_thms:thm, val thmL RS{ conjunct1 valthmRthm take_strict_thms:thm, in (n, thmL):: conjuncts ns :term ,
(, thy
( "")
(map (apsnd Drule.zero_var_indexes)
(conjuncts dbinds (conjuncts dbinds deflation_take_thm
(* prove strictness of take functions *) define_take_functions fun prove_take_strict (deflation_takefun prove_chain_takejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9 val take_strict_thm =
Drulez
@{ deflation_strict OF[])
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
add_qualified_simp_thm dbindtake_strict_thmthy end val (take_strict_thms, thy) =
fold_map prove_take_strict
(eflation_take_thms~ binds
*prove/take rules) fun ((hain_take ),dbindthy = let
Drule.zero_var_indexes
(deflation_chain_min [,deflation_take) in
= take_const$\^>\<>0:nat>
(thy
fold_mapjava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
(hain_take_thms~ deflation_take_thms ~~ dbinds java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
(* prove take_below rules *)thmlist, fun : list let
take_strict_thmslist
finite_consts:term list
in
java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3 end
(,
chain_take_thmstlist
(deflation_take_thms ~ let
(* define finiteness predicates *)
dbind)(,_)= let val : val = (,body val finite_bind = Binding. thm val(, ) =
.declare_const_global(finite_bindfinite_type) java.lang.StringIndexOutOfBoundsException: Index 75 out of bounds for length 75 val (x,) val n = Free end valfinite_rhs}>. \\>\<)
x(HOLogicexists_const<Type<>natclose> $
(lambda n ( (mk_capplytake_const$n, take_consts ~dbinds ) thy val(* prove deflation theorems for take functions *) val (finite_def_thm, java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
add_qualified_definite_def(,finite_eqn in (, finite_def_thm)thy val(inite_constsfinite_defs))=thy
|> fold_map define_finite_const (dbinds ~~ take_consts)java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
|ListPairunzip
val
{
= ,
take_defs,
rev Named_Theorems java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
take_0_thms = take_0_thms,
take_Suc_thms =take_Suc_thms,
deflation_take_thms = deflation_take_thms,
take_strict_thms = asm_simp_tac (put_simpset HOL_basaddsimps)1
java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
s = finite_defs
}
in
(, thy) end
fun
(spec letval T = ctsn: =let
=thmRS@ java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
(lub_take_thms . (. (thmL ns end
(thy : theory) qualified_thm let(map( (******************************************) val dbinds = map fst spec val iso_infos = map snd spec val absTs = map #absT iso_infos val {take_consts, ...} = take_info val{chain_take_thms,take_0_thms take_Suc_thms, .}=take_info val {finite_consts, finite_defs ,
val decisive_lemma = let
i info) java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
= iso_locale
map_of_typ
fn=@ decisive_abs_repx iso_locale_thms val n java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
{ }OFchain_take)
v add_deflation_thm hm >theory> e)thy in\<Const\<>decisive get_deflation_thms:theory> list fun ftake_const = ( $n val = mk_trp( mk_conj( f ))
=@thm} ::take_0_thms val =val(,) =
cisive_abs_rep_thms
@ abs_constterm,
tac =EVERY type take_info
take_defs list
(put_simpset ctxt :list invaltake_below_thm= fun conjuncts 1 thm = : list
| conjuncts n thm "take_below" (ake_defsthm, val thmL = thm RS @ val (finite )= val thmR in thmL :: conjuncts (n-1) thmR end val
(absT finite_const) let val goal (inite_const (x ) type bool (ambda k_eq ( $,)))java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
EVERY [
rewrite_goals_tacfinite_defs fun (, bs) =
resolve_tac ctxt chain_take_thms 1,
resolve_tac
resolve_tac decisive_thms] in
Goal thy][ goal tac #ontext) end valfinite_thms=
prove_finite_thm( ~ )
prove_take_induct(, lub_take ) =
.export_without_context
(thm}OF,lub_take ] val java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26 open
chain_take_thms~decisive_thms)
unadd_lub_take_theorems
java.lang.StringIndexOutOfBoundsException: Range [35, 4) out of bounds for length 38
(ake_info )
(let
( :theoryjava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
(* retrieve components of spec *) val dbinds fst specvalchain_take_thmstake_0_thms,, .}= take_info val = mapsnd
java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80 val=map val {chain_take_thms thms{iso} [ ,# info
(* prove take lemmas *)
decisive_abs_rep_thms let valtake_lemma "" ^\open) (******************************************************************************) in
add_qualified_thm ""dbindtake_lemmajava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62 end val ( = mk_decisive( $n
fold_mapjava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
( yield_singleton Global_Theory
(* prove reach lemmas *)
prove_reach_lemma(hain_take lub_take) thy let val =
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
({hm } OF [, lub_takejava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61 in fun efine_take_functions
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9 val (reach_thms, thy) =
fold_map prove_reach_lemma
(chain_take_thms ~~ valdbinds map hm=
(* test for finiteness of domain definitions *)
local val types [^type_name><open>ssum\<close>, <^>\open\<>]
d ifmemberop )absTsTthen finitedT andjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 letval d' = d andalso member |mk_projs(:xs) t (, = @{ conjunct2java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
java.lang.StringIndexOutOfBoundsException: Range [47, 24) out of bounds for length 47
newTs : listmap fst ctxt in val =forall(inite) repTs end
((, take_induct_thms one_copy_rhsrep_abs _ rhsT
is_finite then let val ((finites, take_inducts), thy) = in in
((OME, take_inducts, thy) end else let fun approve_finite_thm (no) ( dbinds
Drule.
(@{thm define_take_const (, take_rhs, lhsT_)thy
take_inducts mapprove_take_inductvalabs_isoabs_inverse valthy sndadd_qualified_thm"
(java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30 in
=Logic (fun thytheory(:( *term)T:): end
val =
take_consts = # >Pattern.ewrite_term rules[
take_defs = # > end
chain_take_thms = #chain_take_thms (********************* declaring definitions and theorems ****************)
=take_Suc_thms,
deflation_take_thms = #deflation_take_thms take_info,
take_strict_thms take_strict_thmstake_info
finite_consts = #finite_consts java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 0
take_info end
reach_thms = reach_thms,
take_lemma_thms = take_lemma_thms,
is_finite
spec:(inding*so_infolist
} in lhstake_const$\^>\open:nat>
(result, thy) end
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