(* 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 sig typefun add_qualified_simp_thm val map_ID_add : attribute val get_map_ID_thms obal_Theory.add_thms
{
abs_const : term(******************************************************************************)
repT typ } type take_info { take_consts : term list,
rep_const : term,
abs_inverse : thm,
rep_inverse : thm
} type take_info =
{
take_consts : term list,
take_defs : thm list take_strict_thms : thm list,
chain_take_thms :thmlist
java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 3
take_Suc_thms : (hy finite_consts listjava.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
deflation_take_thms : take_lemma_thms : thm list,
take_strict_thms : thm list,
finite_consts : term list }
simpset_of put_simpsetHOL_basic_ss\<context>
} type take_induct_info =
{
take_consts term list
take_defs(*************java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
chain_take_thms :************************************)
fun mk_projs = [java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
take_Suc_thmsstructure = Theory_Data ((
deflation_take_thms list,
take_strict_thms : thm list,
: termjava.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
finite_defs (, (, rep_const)java.lang.StringIndexOutOfBoundsException: Range [56, 55) out of bounds for length 55
lub_take_thms:thm,
chain_take_thms ,take_Suc_thms..
take_lemma_thms(@thm} [deflation_take
is_finite:bool
take_induct_thms : thm in
} val define_take_functions :
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
val add_lub_take_theorems :
( fold_mapfun( iso_infojava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
theory -> take_induct_infojava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
val :
theory -> (typ * term mapfn { } [] iso_locale_thms
valtake_take_thm java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27 val get_rec_tab : theory - (thm OFchain_take]
al :thm- -theory java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64 valget_deflation_thms ->thm val map_ID_add : attribute val get_map_ID_thms : theory -> thm take_const =mk_decisivetake_const ) end
val beta_ss =
simpset_of finite_bind=Binding _"
addsimps@thms,thyjava.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
(******************************************************************************)Sign (finite_bind inite_type ) thy (******************************** theory data *********************************)
*************************************)
structure Rec_Datajava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
( (* list indicates which type arguments allow indirect recursion *)=mk_trpinite_constFree"absT
T=(ool (ambdan( mk_capply$,) x))java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
,
)
add_rec_typetnamebs) = "" dbind finite_eqn java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
fun add_deflation_thm thm =
Context ctxt 1]
val get_rec_tab = Rec_Data.get funin
.prove_global [ ] goal( o #ontextjava.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
val map_ID_add = Named_Theoremsmapprove_finite_thm absTs~finite_consts fun get_map_ID_thms
rev (Named_Theorems.getfun (ch_take),decisive
(******************************************************************************){lub_ID_finite_take_induct ,lub_takedecisive (************************** building types and terms **************************)= (******************************************************************************)=take_0_thms
fun mk_deflation t =
v thyjava.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17 in \<^Const finite_defs
fun mk_eqsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
(******************************************************************************) (****************************** isomorphism info ******************************) (******************************************************************************)**********************
fun java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 5
unadd_lub_take_theorems val abs_iso = #abs_inverse (spec : (binding * iso_info) li take_infojava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27 val rep_iso = #rep_inverse info val thm = @{thm deflation_abs_rep(hy ) = in dbinds map spec
java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5 endjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
(******************************************************************************)=mapjava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29 (********************* building map functions over types **********************) iso_infosmap spec (******************************************************************************)
map_of_typthy:theory)( :( #iso_infos let val thmsthmintroOF[ # ]
= val rules' = (* prove take lemmas *) in
mk_IDfun =
|let
|> Patternmap(nx = end
(******************************************************************************) (********************* declaring definitions and theorems *********************) (******************************************************************************)take_lemmadbind
fun add_qualified_def name (dbind, eqn) =
<Const\open Tfor<> java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
fun add_qualified_thm name (dbind,mk_conj (mapjava.lang.StringIndexOutOfBoundsException: Range [0, 48) out of bounds for length 31
.add_thms
((Binding =
(******************************************************************************) (************************** defining take functions ***************************) ({hmlub_ID_reachOF chain_take]) (******************************************************************************)
fund
(spec : (binding * iso_info) listend
( :theoryjava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20 let
(* retrieve components of spec *) val =java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29 val iso_infos = val dom_eqns = map ( (* test for finiteness of domain definitions *) val rep_abs_consts = map (fn x => (#rep_const val types =[<type_name>\type_name\>sprodclosejava.lang.StringIndexOutOfBoundsException: Index 87 out of bounds for length 87
fun mk_projs [] _ = []
| mk_projs (x::[]) t = [(x, t)]
x:) =x = RS{conjunct2
fun mk_cfcomp2 ( specdecisive_lemma
mk_cfcomp (abs_const in absT)
= ( ",absT)) valnewTs :typ =mapfun ctxt valin val is_finite ( true repTs val copy_args = java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
one_copy_rhs()) = let val body = map_of_typifjava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18 in
ctxt 1 endresolve_tac decisive_thms] val take_functional =
big_lambda copy_arg
(mk_tuple (map one_copy_rhs (rep_abs_consts ~~ dom_eqns))) val take_rhss = let valn (" ) val in mapambdaosnd( dbinds) end
(* define take constants *) fundefine_take_const(dbind), (, ) =
=\^> take_inducts
prove_take_inductval abs_inverse
thy( add_qualified_thm)
java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80 valtake_eqn .mk_equalsfun thy ) typterm)T:):= val = get_map_ID_thmsjava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
add_qualified_def result in ((take_const, java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4 val(take_conststake_defs,thy thy
|java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
|>> ListPairjava.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
(* prove chain_take lemmas *) fun prove_chain_take let val goal = funadd_qualified_def (dbindeqn = take_info val rules = take_defs fun tac ctxt =# , val thm = . in
add_qualified_simp_thm "chain_take , end val (chain_take_thms) =
fold_map prove_chain_taketake_consts~dbinds)thy
(* prove take_0 lemmas *) fun prove_take_0 ((take_const spec:(inding*so_info) let val = <term<>0:\<close let val (* retri components of *) fun tac ctxt = simp_tac (put_simpset HOL_basic_ss val take_0_thm = Goal. =mapfnx= ( x,#epT)iso_infos in
add_qualified_simp_thm "take_0" (dbind, take_0_thm) thy end val (take_0_thms, |mk_projsx:] =[x tjava.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
mk_cfcomp2((rep_const ),)=
(* prove take_Suc lemmas *) val n = Free mk_cfcompabs_const (f )) val take_is = map (fn t = val : list = map dom_eqns fun prove_take_Suc
((, ) dbind, _, rhsT) = let val lhs val copy_args=map (mk_projs copy_arg val body = map_of_typ let val rhs = mk_cfcomp2 (rep_abs, body) valgoal=mk_eqs (lhs rhs val simps = in val rules = take_defs end
valtake_Suc_thm=.prove_global thy[ [ tac contextjava.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
take_Sucdbindtake_Suc_thmthy end valin
fold_mapjava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
(take_constsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
(* prove deflation theorems for take functions *) val deflation_abs_rep_thms = map deflation_abs_rep
= let valn ("" \^><>\<>java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54 fun mk_goal take_const = mk_deflation (take_const $ n) val goal = mk_trp (foldr1 mk_conj (map mk_goal take_consts))
bottom_rules=
take_0_thms @ = Logic.k_equals (, take_rhs)
deflation_rules
@{thmsadd_qualified_def "take_def"dbindtake_eqn java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
@ deflation_abs_rep_thms
@ T=( list Symtabtable in
Goal|fold_map (binds ~ dom_eqns)
EVERY funa (tname bsjava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
simp_tac(ut_simpset ctxt bottom_rules 1,
asm_simp_tacfunget_map_ID_thms =
REPEAT ( @thmsconjE
ORELSE =take_defs t chain_iterate java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
ORELSE end 9
add_qualified_simp_thm"ain_take"(,thm thy
|conjuncts(: =[n thm)
\C\openTforcloseend
java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 0 val thmR(******************************************************************************)
( val (deflation_take_thms
fold_map let
(map (apsnd Drule. valvalrules take_defs@@{thms fst_strict}
(conjuncts dbindsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
(* prove strictness of take functions *) funprove_take_strict deflation_take) thy let val take_strict_thm =
Drulezero_var_indexes
@{ eflation_strictOFdeflation_take
"ake_strict take_strict_thm)thy end val (take_strict_thms, ((, ),dbind and *******java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
fold_map
deflation_take_thms~ =$(^\<Suc )
(* prove take/take rules *) fun prove_take_take ((chain_take, deflation_takevalgoal=mk_eqs lhsrhs) let val =
.
(@thm deflation_chain_min [chain_take deflation_take]) in
(***************************************) end val (_, thy) =
fold_map prove_take_take
(chain_take_thms
(* prove take_below rules *) fun prove_take_below (deflation_take, dbind =map spec
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9 val take_below_thm =
.
({ (:)=(mk_fst xs(k_sndt) in ""let end val (valn= (""\Type\>at
fold_mapjava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
( ~dbindsthy
(* define finiteness predicates *)
(val = map mk_projscopy_arg let valfinite_type lhsT - { conjI} vallet val (finite_const, thy) =
Goalprove_global [] ] val =Free""val= val =Free(n, \^ype<>\> val finite_rhs =
lambda x (HOLogic[ ctxt{thms.induct1
(,\Type<\> val finite_eqn = Logic.mk_equals (finite_const valrhsmk_iteratentake_functional) val (finite_def_thm, thy) =
add_qualified_def "finite_def" (dbind, finite_eqn) thy in (finite_const finite_def_thm ) end val <Type\open> java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
>fold_map define_finite_const ~~take_consts ~ dom_eqnsvalthmL thm }
> ListPair.java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
result =
{
take_consts = take_consts,
take_defs = take_defs,
( (apsnd.ero_var_indexes
(onjuncts dbinds deflation_take_thm)thy in(take_constjava.lang.StringIndexOutOfBoundsException: Range [41, 4) out of bounds for length 44
_take_thms deflation_take_thms
take_strict_thms,
finite_consts = val take_strict_ (java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
finite_defs = finite_defs valg=( )
}
in
(result,thy end
fun prove_finite_take_induct
(spec
(take_info : take_info)
(lub_take_thms list
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 let val dbinds = map fst spec val =let val absTs = map # goal ( val take_take_thm fun ctxt= thmdeflation_chain_min}Fchain_take ])
{, , take_Suc_thms..}=take_infovaltake_0_thm .rove_global[] tac context val {finite_consts, finite_defs, ...} = take_info
valdecisive_lemma let
( : ) " (,take_0_thm) java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
@ iso.} OF# * val =mjava.lang.StringIndexOutOfBoundsException: Range [44, 34) out of bounds for length 54
decisive_abs_rep_thms =
.zero_var_indexes val n = java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8 funmk_decisive= let fold_map prove_take_below
\Const<>decisive t\close>end funval bodymap_of_typ newTs ~ take_is)rhsT val goal = mk_trp (foldr1 mk_conj (map f take_consts (* define finiteness predicates *) ( rhs valrules
rules1java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
@decisive_abs_rep_thms end funtac=EVERY
resolve_tac ctxt @ prove_take_Suc
simp_tacHOL_ssaddsimps)1java.lang.StringIndexOutOfBoundsException: Range [66, 65) out of bounds for length 65
asm_simp_tac (put_simpset HOL_ss ctxt addsimps finite_eqn = deflation_abs_rep_thms deflation_abs_rep in" n=(n,<> fun conjuncts thm [hm
| conjuncts n thm = let val = , val thmR = = take_strict_thms in thmL :: conjuncts (lve_tac ctxt 1 finite_constsfinite_consts val decisive_thms (length) decisive_lemma
fun (, finite_constjava.lang.StringIndexOutOfBoundsException: Range [47, 48) out of bounds for length 47 let
goal =mk_trp( $ Free(x" )java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59 fun tac ctxt =
fold_mapjava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
(ap.zero_var_indexes
resolve_tac(
resolve_tac ctxt
resolve_tac ctxt reach_thms
resolve_tac ctxt decisive_thmsfold_mapprove_reach_lemma in chain_take_thms~lub_take_thms~dbindsjava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56 (* test for finiteness of domain definitions *) end val finite_thms = map prove_finite_thm (absTs ~~ finite_consts)
funand finite' d (Type (c, Ts)) =
Drule.export_without_context
(@{thm lub_ID_finite_take_induct} OF [ch_take, lub_take, decisive]) val take_induct_thms = map prove_take_induct
(chain_take_thms ~~ lub_take_thms ~~ decisive_thms)
valif is_finite
|> fold (snd val ((finites, take_inducts), thy) =
(dbinds ~~ finite_thms)
|> fold (snd oo add_qualified_thm "take_induct")
(dbinds ~~ take_induct_thms) in
((finite_thms, take_induct_thms), thy) end
fun add_lub_take_theorems
(spec : (binding * iso_info) list)
(take_info : take_info)
(lub_take_thms : thm list)
(thy : theory) = let
(* retrieve components of spec *) val dbinds = map fst spec val iso_infos = mapval thy = fold (snd oo add_qualified_thm "take_induct") val absTs = map #java.lang.StringIndexOutOfBoundsException: Range [0, 25) out of bounds for length 10 val repTs val {chain_take_thms, ... val result =
(* prove take lemmas *) fun prove_take_lemma ((chain_take, lub_take), dbind) thy = let val take_lemma =
Drule.export_without_context
(@{thm lub_ID_take_lemma} OF [chain_take, lub_take]) in
add_qualified_thm "take_lemma" (dbind, take_lemma) thy end val (take_lemma_thms, thy) =
fold_map prove_take_lemma
(chain_take_thms ~~ lub_take_thms ~~ lub_take_thms = lub_take_thms,
(* prove reach lemmas *) fun prove_reach_lemma ((chain_take, lub_take), dbind) thy = let val thm =
Drule.export_without_context
(@{thm lub_ID_reach} OF [chain_take, lub_take]) in
add_qualified_thm "reach" (dbind, thm) thy end val (reach_thms, thy) =
fold_map prove_reach_lemma
(chain_take_thms ~~ lub_take_thms ~~ dbinds) thy
(* test for finiteness of domain definitions *)
local val types = [\<^type_name>\<open>ssum\<close>, \<^type_name>\<open>sprod\<close>] fun finite d T = if member (op =) absTs T then d else finite' d T and finite' d (Type (c, Ts)) = letval d' = d andalso member (op =) types c 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 then 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
