(* Title: HOL/Tools/record_package.ML
Author: Wolfgang Naraschewski, Norbert Schirmer and Markus Wenzel, TU Muenchen
Extensible records with structural subtyping in HOL.
*)
signature BASIC_RECORD_PACKAGE =
sig
val record_simproc: simproc
val record_eq_simproc: simproc
val record_upd_simproc: simproc
val record_split_simproc: (term -> int) -> simproc
val record_ex_sel_eq_simproc: simproc
val record_split_tac: int -> tactic
val record_split_simp_tac: thm list -> (term -> int) -> int -> tactic
val record_split_name: string
val record_split_wrapper: string * wrapper
val print_record_type_abbr: bool ref
val print_record_type_as_fields: bool ref
end;
signature RECORD_PACKAGE =
sig
include BASIC_RECORD_PACKAGE
val timing: bool ref
val record_quick_and_dirty_sensitive: bool ref
val updateN: string
val updN: string
val ext_typeN: string
val extN: string
val makeN: string
val moreN: string
val ext_dest: string
val last_extT: typ -> (string * typ list) option
val dest_recTs : typ -> (string * typ list) list
val get_extT_fields: theory -> typ -> (string * typ) list * (string * typ)
val get_recT_fields: theory -> typ -> (string * typ) list * (string * typ)
val get_parent: theory -> string -> (typ list * string) option
val get_extension: theory -> string -> (string * typ list) option
val get_extinjects: theory -> thm list
val get_simpset: theory -> simpset
val print_records: theory -> unit
val read_typ: Proof.context -> string -> (string * sort) list -> typ * (string * sort) list
val cert_typ: Proof.context -> typ -> (string * sort) list -> typ * (string * sort) list
val add_record: bool -> string list * string -> string option -> (string * string * mixfix) list
-> theory -> theory
val add_record_i: bool -> string list * string -> (typ list * string) option
-> (string * typ * mixfix) list -> theory -> theory
val setup: theory -> theory
end;
structure RecordPackage: RECORD_PACKAGE =
struct
val eq_reflection = thm "eq_reflection";
val rec_UNIV_I = thm "rec_UNIV_I";
val rec_True_simp = thm "rec_True_simp";
val Pair_eq = thm "Product_Type.prod.inject";
val atomize_all = thm "HOL.atomize_all";
val atomize_imp = thm "HOL.atomize_imp";
val meta_allE = thm "Pure.meta_allE";
val prop_subst = thm "prop_subst";
val Pair_sel_convs = [fst_conv,snd_conv];
val K_record_comp = @{thm "K_record_comp"};
val K_comp_convs = [@{thm o_apply}, K_record_comp]
(** name components **)
val rN = "r";
val wN = "w";
val moreN = "more";
val schemeN = "_scheme";
val ext_typeN = "_ext_type";
val extN ="_ext";
val casesN = "_cases";
val ext_dest = "_sel";
val updateN = "_update";
val updN = "_upd";
val makeN = "make";
val fields_selN = "fields";
val extendN = "extend";
val truncateN = "truncate";
(*see typedef_package.ML*)
val RepN = "Rep_";
val AbsN = "Abs_";
(*** utilities ***)
fun but_last xs = fst (split_last xs);
fun varifyT midx =
let fun varify (a, S) = TVar ((a, midx + 1), S);
in map_type_tfree varify end;
fun domain_type' T =
domain_type T handle Match => T;
fun range_type' T =
range_type T handle Match => T;
(* messages *)
fun trace_thm str thm =
tracing (str ^ (Pretty.string_of (Display.pretty_thm thm)));
fun trace_thms str thms =
(tracing str; map (trace_thm "") thms);
fun trace_term str t =
tracing (str ^ Syntax.string_of_term_global Pure.thy t);
(* timing *)
val timing = ref false;
fun timeit_msg s x = if !timing then (warning s; timeit x) else x ();
fun timing_msg s = if !timing then warning s else ();
(* syntax *)
fun prune n xs = Library.drop (n, xs);
fun prefix_base s = Long_Name.map_base_name (fn bname => s ^ bname);
val Trueprop = HOLogic.mk_Trueprop;
fun All xs t = Term.list_all_free (xs, t);
infix 9 $$;
infix 0 :== ===;
infixr 0 ==>;
val (op $$) = Term.list_comb;
val (op :==) = PrimitiveDefs.mk_defpair;
val (op ===) = Trueprop o HOLogic.mk_eq;
val (op ==>) = Logic.mk_implies;
(* morphisms *)
fun mk_RepN name = suffix ext_typeN (prefix_base RepN name);
fun mk_AbsN name = suffix ext_typeN (prefix_base AbsN name);
fun mk_Rep name repT absT =
Const (suffix ext_typeN (prefix_base RepN name),absT --> repT);
fun mk_Abs name repT absT =
Const (mk_AbsN name,repT --> absT);
(* constructor *)
fun mk_extC (name,T) Ts = (suffix extN name, Ts ---> T);
fun mk_ext (name,T) ts =
let val Ts = map fastype_of ts
in list_comb (Const (mk_extC (name,T) Ts),ts) end;
(* cases *)
fun mk_casesC (name,T,vT) Ts = (suffix casesN name, (Ts ---> vT) --> T --> vT)
fun mk_cases (name,T,vT) f =
let val Ts = binder_types (fastype_of f)
in Const (mk_casesC (name,T,vT) Ts) $ f end;
(* selector *)
fun mk_selC sT (c,T) = (c,sT --> T);
fun mk_sel s (c,T) =
let val sT = fastype_of s
in Const (mk_selC sT (c,T)) $ s end;
(* updates *)
fun mk_updC sfx sT (c,T) = (suffix sfx c, (T --> T) --> sT --> sT);
fun mk_upd' sfx c v sT =
let val vT = domain_type (fastype_of v);
in Const (mk_updC sfx sT (c, vT)) $ v end;
fun mk_upd sfx c v s = mk_upd' sfx c v (fastype_of s) $ s
(* types *)
fun dest_recT (typ as Type (c_ext_type, Ts as (T::_))) =
(case try (unsuffix ext_typeN) c_ext_type of
NONE => raise TYPE ("RecordPackage.dest_recT", [typ], [])
| SOME c => ((c, Ts), List.last Ts))
| dest_recT typ = raise TYPE ("RecordPackage.dest_recT", [typ], []);
fun is_recT T =
(case try dest_recT T of NONE => false | SOME _ => true);
fun dest_recTs T =
let val ((c, Ts), U) = dest_recT T
in (c, Ts) :: dest_recTs U
end handle TYPE _ => [];
fun last_extT T =
let val ((c, Ts), U) = dest_recT T
in (case last_extT U of
NONE => SOME (c,Ts)
| SOME l => SOME l)
end handle TYPE _ => NONE
fun rec_id i T =
let val rTs = dest_recTs T
val rTs' = if i < 0 then rTs else Library.take (i,rTs)
in Library.foldl (fn (s,(c,T)) => s ^ c) ("",rTs') end;
(*** extend theory by record definition ***)
(** record info **)
(* type record_info and parent_info *)
type record_info =
{args: (string * sort) list,
parent: (typ list * string) option,
fields: (string * typ) list,
extension: (string * typ list),
induct: thm
};
fun make_record_info args parent fields extension induct =
{args = args, parent = parent, fields = fields, extension = extension,
induct = induct}: record_info;
type parent_info =
{name: string,
fields: (string * typ) list,
extension: (string * typ list),
induct: thm
};
fun make_parent_info name fields extension induct =
{name = name, fields = fields, extension = extension, induct = induct}: parent_info;
(* theory data *)
type record_data =
{records: record_info Symtab.table,
sel_upd:
{selectors: unit Symtab.table,
updates: string Symtab.table,
simpset: Simplifier.simpset},
equalities: thm Symtab.table,
extinjects: thm list,
extsplit: thm Symtab.table, (* maps extension name to split rule *)
splits: (thm*thm*thm*thm) Symtab.table, (* !!,!,EX - split-equalities,induct rule *)
extfields: (string*typ) list Symtab.table, (* maps extension to its fields *)
fieldext: (string*typ list) Symtab.table (* maps field to its extension *)
};
fun make_record_data
records sel_upd equalities extinjects extsplit splits extfields fieldext =
{records = records, sel_upd = sel_upd,
equalities = equalities, extinjects=extinjects, extsplit = extsplit, splits = splits,
extfields = extfields, fieldext = fieldext }: record_data;
structure RecordsData = TheoryDataFun
(
type T = record_data;
val empty =
make_record_data Symtab.empty
{selectors = Symtab.empty, updates = Symtab.empty, simpset = HOL_basic_ss}
Symtab.empty [] Symtab.empty Symtab.empty Symtab.empty Symtab.empty;
val copy = I;
val extend = I;
fun merge _
({records = recs1,
sel_upd = {selectors = sels1, updates = upds1, simpset = ss1},
equalities = equalities1,
extinjects = extinjects1,
extsplit = extsplit1,
splits = splits1,
extfields = extfields1,
fieldext = fieldext1},
{records = recs2,
sel_upd = {selectors = sels2, updates = upds2, simpset = ss2},
equalities = equalities2,
extinjects = extinjects2,
extsplit = extsplit2,
splits = splits2,
extfields = extfields2,
fieldext = fieldext2}) =
make_record_data
(Symtab.merge (K true) (recs1, recs2))
{selectors = Symtab.merge (K true) (sels1, sels2),
updates = Symtab.merge (K true) (upds1, upds2),
simpset = Simplifier.merge_ss (ss1, ss2)}
(Symtab.merge Thm.eq_thm_prop (equalities1, equalities2))
(Library.merge Thm.eq_thm_prop (extinjects1, extinjects2))
(Symtab.merge Thm.eq_thm_prop (extsplit1,extsplit2))
(Symtab.merge (fn ((a,b,c,d),(w,x,y,z))
=> Thm.eq_thm (a,w) andalso Thm.eq_thm (b,x) andalso
Thm.eq_thm (c,y) andalso Thm.eq_thm (d,z))
(splits1, splits2))
(Symtab.merge (K true) (extfields1,extfields2))
(Symtab.merge (K true) (fieldext1,fieldext2));
);
fun print_records thy =
let
val {records = recs, ...} = RecordsData.get thy;
val prt_typ = Syntax.pretty_typ_global thy;
fun pretty_parent NONE = []
| pretty_parent (SOME (Ts, name)) =
[Pretty.block [prt_typ (Type (name, Ts)), Pretty.str " +"]];
fun pretty_field (c, T) = Pretty.block
[Pretty.str (Sign.extern_const thy c), Pretty.str " ::",
Pretty.brk 1, Pretty.quote (prt_typ T)];
fun pretty_record (name, {args, parent, fields, ...}: record_info) =
Pretty.block (Pretty.fbreaks (Pretty.block
[prt_typ (Type (name, map TFree args)), Pretty.str " = "] ::
pretty_parent parent @ map pretty_field fields));
in map pretty_record (Symtab.dest recs) |> Pretty.chunks |> Pretty.writeln end;
(* access 'records' *)
val get_record = Symtab.lookup o #records o RecordsData.get;
fun put_record name info thy =
let
val {records, sel_upd, equalities, extinjects,extsplit,splits,extfields,fieldext} =
RecordsData.get thy;
val data = make_record_data (Symtab.update (name, info) records)
sel_upd equalities extinjects extsplit splits extfields fieldext;
in RecordsData.put data thy end;
(* access 'sel_upd' *)
val get_sel_upd = #sel_upd o RecordsData.get;
val is_selector = Symtab.defined o #selectors o get_sel_upd;
val get_updates = Symtab.lookup o #updates o get_sel_upd;
fun get_simpset thy = Simplifier.theory_context thy (#simpset (get_sel_upd thy));
fun put_sel_upd names simps = RecordsData.map (fn {records,
sel_upd = {selectors, updates, simpset},
equalities, extinjects, extsplit, splits, extfields, fieldext} =>
make_record_data records
{selectors = fold (fn name => Symtab.update (name, ())) names selectors,
updates = fold (fn name => Symtab.update ((suffix updateN) name, name)) names updates,
simpset = Simplifier.addsimps (simpset, simps)}
equalities extinjects extsplit splits extfields fieldext);
(* access 'equalities' *)
fun add_record_equalities name thm thy =
let
val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
RecordsData.get thy;
val data = make_record_data records sel_upd
(Symtab.update_new (name, thm) equalities) extinjects extsplit
splits extfields fieldext;
in RecordsData.put data thy end;
val get_equalities =Symtab.lookup o #equalities o RecordsData.get;
(* access 'extinjects' *)
fun add_extinjects thm thy =
let
val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
RecordsData.get thy;
val data =
make_record_data records sel_upd equalities (insert Thm.eq_thm_prop thm extinjects) extsplit
splits extfields fieldext;
in RecordsData.put data thy end;
val get_extinjects = rev o #extinjects o RecordsData.get;
(* access 'extsplit' *)
fun add_extsplit name thm thy =
let
val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
RecordsData.get thy;
val data = make_record_data records sel_upd
equalities extinjects (Symtab.update_new (name, thm) extsplit) splits
extfields fieldext;
in RecordsData.put data thy end;
val get_extsplit = Symtab.lookup o #extsplit o RecordsData.get;
(* access 'splits' *)
fun add_record_splits name thmP thy =
let
val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
RecordsData.get thy;
val data = make_record_data records sel_upd
equalities extinjects extsplit (Symtab.update_new (name, thmP) splits)
extfields fieldext;
in RecordsData.put data thy end;
val get_splits = Symtab.lookup o #splits o RecordsData.get;
(* parent/extension of named record *)
val get_parent = (Option.join o Option.map #parent) oo (Symtab.lookup o #records o RecordsData.get);
val get_extension = Option.map #extension oo (Symtab.lookup o #records o RecordsData.get);
(* access 'extfields' *)
fun add_extfields name fields thy =
let
val {records, sel_upd, equalities, extinjects, extsplit,splits, extfields, fieldext} =
RecordsData.get thy;
val data = make_record_data records sel_upd
equalities extinjects extsplit splits
(Symtab.update_new (name, fields) extfields) fieldext;
in RecordsData.put data thy end;
val get_extfields = Symtab.lookup o #extfields o RecordsData.get;
fun get_extT_fields thy T =
let
val ((name,Ts),moreT) = dest_recT T;
val recname = let val (nm::recn::rst) = rev (Long_Name.explode name)
in Long_Name.implode (rev (nm::rst)) end;
val midx = maxidx_of_typs (moreT::Ts);
val varifyT = varifyT midx;
val {records,extfields,...} = RecordsData.get thy;
val (flds,(more,_)) = split_last (Symtab.lookup_list extfields name);
val args = map varifyT (snd (#extension (the (Symtab.lookup records recname))));
val subst = fold (Sign.typ_match thy) (but_last args ~~ but_last Ts) (Vartab.empty);
val flds' = map (apsnd ((Envir.norm_type subst) o varifyT)) flds;
in (flds',(more,moreT)) end;
fun get_recT_fields thy T =
let
val (root_flds,(root_more,root_moreT)) = get_extT_fields thy T;
val (rest_flds,rest_more) =
if is_recT root_moreT then get_recT_fields thy root_moreT
else ([],(root_more,root_moreT));
in (root_flds@rest_flds,rest_more) end;
(* access 'fieldext' *)
fun add_fieldext extname_types fields thy =
let
val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =
RecordsData.get thy;
val fieldext' =
fold (fn field => Symtab.update_new (field, extname_types)) fields fieldext;
val data=make_record_data records sel_upd equalities extinjects extsplit
splits extfields fieldext';
in RecordsData.put data thy end;
val get_fieldext = Symtab.lookup o #fieldext o RecordsData.get;
(* parent records *)
fun add_parents thy NONE parents = parents
| add_parents thy (SOME (types, name)) parents =
let
fun err msg = error (msg ^ " parent record " ^ quote name);
val {args, parent, fields, extension, induct} =
(case get_record thy name of SOME info => info | NONE => err "Unknown");
val _ = if length types <> length args then err "Bad number of arguments for" else ();
fun bad_inst ((x, S), T) =
if Sign.of_sort thy (T, S) then NONE else SOME x
val bads = List.mapPartial bad_inst (args ~~ types);
val _ = null bads orelse err ("Ill-sorted instantiation of " ^ commas bads ^ " in");
val inst = map fst args ~~ types;
val subst = Term.map_type_tfree (the o AList.lookup (op =) inst o fst);
val parent' = Option.map (apfst (map subst)) parent;
val fields' = map (apsnd subst) fields;
val extension' = apsnd (map subst) extension;
in
add_parents thy parent'
(make_parent_info name fields' extension' induct :: parents)
end;
(** concrete syntax for records **)
(* decode type *)
fun decode_type thy t =
let
fun get_sort xs n = AList.lookup (op =) xs (n: indexname) |> the_default (Sign.defaultS thy);
val map_sort = Sign.intern_sort thy;
in
Syntax.typ_of_term (get_sort (Syntax.term_sorts map_sort t)) map_sort t
|> Sign.intern_tycons thy
end;
(* parse translations *)
fun gen_field_tr mark sfx (t as Const (c, _) $ Const (name, _) $ arg) =
if c = mark then Syntax.const (suffix sfx name) $ (Abs ("_",dummyT, arg))
else raise TERM ("gen_field_tr: " ^ mark, [t])
| gen_field_tr mark _ t = raise TERM ("gen_field_tr: " ^ mark, [t]);
fun gen_fields_tr sep mark sfx (tm as Const (c, _) $ t $ u) =
if c = sep then gen_field_tr mark sfx t :: gen_fields_tr sep mark sfx u
else [gen_field_tr mark sfx tm]
| gen_fields_tr _ mark sfx tm = [gen_field_tr mark sfx tm];
fun record_update_tr [t, u] =
Library.foldr (op $) (rev (gen_fields_tr "_updates" "_update" updateN u), t)
| record_update_tr ts = raise TERM ("record_update_tr", ts);
fun update_name_tr (Free (x, T) :: ts) = Free (suffix updateN x, T) $$ ts
| update_name_tr (Const (x, T) :: ts) = Const (suffix updateN x, T) $$ ts
| update_name_tr (((c as Const ("_constrain", _)) $ t $ ty) :: ts) =
(c $ update_name_tr [t] $ (Syntax.const "fun" $ ty $ Syntax.const "dummy")) $$ ts
| update_name_tr ts = raise TERM ("update_name_tr", ts);
fun dest_ext_field mark (t as (Const (c,_) $ Const (name,_) $ arg)) =
if c = mark then (name,arg) else raise TERM ("dest_ext_field: " ^ mark, [t])
| dest_ext_field _ t = raise TERM ("dest_ext_field", [t])
fun dest_ext_fields sep mark (trm as (Const (c,_) $ t $ u)) =
if c = sep then dest_ext_field mark t::dest_ext_fields sep mark u
else [dest_ext_field mark trm]
| dest_ext_fields _ mark t = [dest_ext_field mark t]
fun gen_ext_fields_tr sep mark sfx more ctxt t =
let
val thy = ProofContext.theory_of ctxt;
val msg = "error in record input: ";
val fieldargs = dest_ext_fields sep mark t;
fun splitargs (field::fields) ((name,arg)::fargs) =
if can (unsuffix name) field
then let val (args,rest) = splitargs fields fargs
in (arg::args,rest) end
else raise TERM (msg ^ "expecting field " ^ field ^ " but got " ^ name, [t])
| splitargs [] (fargs as (_::_)) = ([],fargs)
| splitargs (_::_) [] = raise TERM (msg ^ "expecting more fields", [t])
| splitargs _ _ = ([],[]);
fun mk_ext (fargs as (name,arg)::_) =
(case get_fieldext thy (Sign.intern_const thy name) of
SOME (ext,_) => (case get_extfields thy ext of
SOME flds
=> let val (args,rest) =
splitargs (map fst (but_last flds)) fargs;
val more' = mk_ext rest;
in list_comb (Syntax.const (suffix sfx ext),args@[more'])
end
| NONE => raise TERM(msg ^ "no fields defined for "
^ ext,[t]))
| NONE => raise TERM (msg ^ name ^" is no proper field",[t]))
| mk_ext [] = more
in mk_ext fieldargs end;
fun gen_ext_type_tr sep mark sfx more ctxt t =
let
val thy = ProofContext.theory_of ctxt;
val msg = "error in record-type input: ";
val fieldargs = dest_ext_fields sep mark t;
fun splitargs (field::fields) ((name,arg)::fargs) =
if can (unsuffix name) field
then let val (args,rest) = splitargs fields fargs
in (arg::args,rest) end
else raise TERM (msg ^ "expecting field " ^ field ^ " but got " ^ name, [t])
| splitargs [] (fargs as (_::_)) = ([],fargs)
| splitargs (_::_) [] = raise TERM (msg ^ "expecting more fields", [t])
| splitargs _ _ = ([],[]);
fun mk_ext (fargs as (name,arg)::_) =
(case get_fieldext thy (Sign.intern_const thy name) of
SOME (ext,alphas) =>
(case get_extfields thy ext of
SOME flds
=> (let
val flds' = but_last flds;
val types = map snd flds';
val (args,rest) = splitargs (map fst flds') fargs;
val argtypes = map (Sign.certify_typ thy o decode_type thy) args;
val midx = fold (fn T => fn i => Int.max (maxidx_of_typ T, i))
argtypes 0;
val varifyT = varifyT midx;
val vartypes = map varifyT types;
val subst = fold (Sign.typ_match thy) (vartypes ~~ argtypes)
Vartab.empty;
val alphas' = map ((Syntax.term_of_typ (! Syntax.show_sorts)) o
Envir.norm_type subst o varifyT)
(but_last alphas);
val more' = mk_ext rest;
in list_comb (Syntax.const (suffix sfx ext),alphas'@[more'])
end handle TYPE_MATCH => raise
TERM (msg ^ "type is no proper record (extension)", [t]))
| NONE => raise TERM (msg ^ "no fields defined for " ^ ext,[t]))
| NONE => raise TERM (msg ^ name ^" is no proper field",[t]))
| mk_ext [] = more
in mk_ext fieldargs end;
fun gen_adv_record_tr sep mark sfx unit ctxt [t] =
gen_ext_fields_tr sep mark sfx unit ctxt t
| gen_adv_record_tr _ _ _ _ _ ts = raise TERM ("gen_record_tr", ts);
fun gen_adv_record_scheme_tr sep mark sfx ctxt [t, more] =
gen_ext_fields_tr sep mark sfx more ctxt t
| gen_adv_record_scheme_tr _ _ _ _ ts = raise TERM ("gen_record_scheme_tr", ts);
fun gen_adv_record_type_tr sep mark sfx unit ctxt [t] =
gen_ext_type_tr sep mark sfx unit ctxt t
| gen_adv_record_type_tr _ _ _ _ _ ts = raise TERM ("gen_record_tr", ts);
fun gen_adv_record_type_scheme_tr sep mark sfx ctxt [t, more] =
gen_ext_type_tr sep mark sfx more ctxt t
| gen_adv_record_type_scheme_tr _ _ _ _ ts = raise TERM ("gen_record_scheme_tr", ts);
val adv_record_tr = gen_adv_record_tr "_fields" "_field" extN HOLogic.unit;
val adv_record_scheme_tr = gen_adv_record_scheme_tr "_fields" "_field" extN;
val adv_record_type_tr =
gen_adv_record_type_tr "_field_types" "_field_type" ext_typeN
(Syntax.term_of_typ false (HOLogic.unitT));
val adv_record_type_scheme_tr =
gen_adv_record_type_scheme_tr "_field_types" "_field_type" ext_typeN;
val parse_translation =
[("_record_update", record_update_tr),
("_update_name", update_name_tr)];
val adv_parse_translation =
[("_record",adv_record_tr),
("_record_scheme",adv_record_scheme_tr),
("_record_type",adv_record_type_tr),
("_record_type_scheme",adv_record_type_scheme_tr)];
(* print translations *)
val print_record_type_abbr = ref true;
val print_record_type_as_fields = ref true;
fun gen_field_upds_tr' mark sfx (tm as Const (name_field, _) $ k $ u) =
let val t = (case k of (Abs (_,_,(Abs (_,_,t)$Bound 0)))
=> if null (loose_bnos t) then t else raise Match
| Abs (x,_,t) => if null (loose_bnos t) then t else raise Match
| _ => raise Match)
(* (case k of (Const ("K_record",_)$t) => t
| Abs (x,_,Const ("K_record",_)$t$Bound 0) => t
| _ => raise Match)*)
in
(case try (unsuffix sfx) name_field of
SOME name =>
apfst (cons (Syntax.const mark $ Syntax.free name $ t)) (gen_field_upds_tr' mark sfx u)
| NONE => ([], tm))
end
| gen_field_upds_tr' _ _ tm = ([], tm);
fun record_update_tr' tm =
let val (ts, u) = gen_field_upds_tr' "_update" updateN tm in
if null ts then raise Match
else Syntax.const "_record_update" $ u $
foldr1 (fn (v, w) => Syntax.const "_updates" $ v $ w) (rev ts)
end;
fun gen_field_tr' sfx tr' name =
let val name_sfx = suffix sfx name
in (name_sfx, fn [t, u] => tr' (Syntax.const name_sfx $ t $ u) | _ => raise Match) end;
fun record_tr' sep mark record record_scheme unit ctxt t =
let
val thy = ProofContext.theory_of ctxt;
fun field_lst t =
(case strip_comb t of
(Const (ext,_),args as (_::_))
=> (case try (unsuffix extN) (Sign.intern_const thy ext) of
SOME ext'
=> (case get_extfields thy ext' of
SOME flds
=> (let
val (f::fs) = but_last (map fst flds);
val flds' = Sign.extern_const thy f :: map Long_Name.base_name fs;
val (args',more) = split_last args;
in (flds'~~args')@field_lst more end
handle Library.UnequalLengths => [("",t)])
| NONE => [("",t)])
| NONE => [("",t)])
| _ => [("",t)])
val (flds,(_,more)) = split_last (field_lst t);
val _ = if null flds then raise Match else ();
val flds' = map (fn (n,t)=>Syntax.const mark$Syntax.const n$t) flds;
val flds'' = foldr1 (fn (x,y) => Syntax.const sep$x$y) flds';
in if unit more
then Syntax.const record$flds''
else Syntax.const record_scheme$flds''$more
end
fun gen_record_tr' name =
let val name_sfx = suffix extN name;
val unit = (fn Const (@{const_syntax "Product_Type.Unity"},_) => true | _ => false);
fun tr' ctxt ts = record_tr' "_fields" "_field" "_record" "_record_scheme" unit ctxt
(list_comb (Syntax.const name_sfx,ts))
in (name_sfx,tr')
end
fun print_translation names =
map (gen_field_tr' updateN record_update_tr') names;
(* record_type_abbr_tr' tries to reconstruct the record name type abbreviation from *)
(* the (nested) extension types. *)
fun record_type_abbr_tr' default_tr' abbr alphas zeta lastExt schemeT ctxt tm =
let
val thy = ProofContext.theory_of ctxt;
(* tm is term representation of a (nested) field type. We first reconstruct the *)
(* type from tm so that we can continue on the type level rather then the term level.*)
(* WORKAROUND:
* If a record type occurs in an error message of type inference there
* may be some internal frees donoted by ??:
* (Const "_tfree",_)$Free ("??'a",_).
* This will unfortunately be translated to Type ("??'a",[]) instead of
* TFree ("??'a",_) by typ_of_term, which will confuse unify below.
* fixT works around.
*)
fun fixT (T as Type (x,[])) =
if String.isPrefix "??'" x then TFree (x,Sign.defaultS thy) else T
| fixT (Type (x,xs)) = Type (x,map fixT xs)
| fixT T = T;
val T = fixT (decode_type thy tm);
val midx = maxidx_of_typ T;
val varifyT = varifyT midx;
fun mk_type_abbr subst name alphas =
let val abbrT = Type (name, map (fn a => varifyT (TFree (a, Sign.defaultS thy))) alphas);
in Syntax.term_of_typ (! Syntax.show_sorts)
(Sign.extern_typ thy (Envir.norm_type subst abbrT)) end;
fun match rT T = (Sign.typ_match thy (varifyT rT,T)
Vartab.empty);
in if !print_record_type_abbr
then (case last_extT T of
SOME (name,_)
=> if name = lastExt
then
(let
val subst = match schemeT T
in
if HOLogic.is_unitT (Envir.norm_type subst (varifyT (TFree(zeta,Sign.defaultS thy))))
then mk_type_abbr subst abbr alphas
else mk_type_abbr subst (suffix schemeN abbr) (alphas@[zeta])
end handle TYPE_MATCH => default_tr' ctxt tm)
else raise Match (* give print translation of specialised record a chance *)
| _ => raise Match)
else default_tr' ctxt tm
end
fun record_type_tr' sep mark record record_scheme ctxt t =
let
val thy = ProofContext.theory_of ctxt;
val T = decode_type thy t;
val varifyT = varifyT (Term.maxidx_of_typ T);
fun term_of_type T = Syntax.term_of_typ (!Syntax.show_sorts) (Sign.extern_typ thy T);
fun field_lst T =
(case T of
Type (ext, args)
=> (case try (unsuffix ext_typeN) ext of
SOME ext'
=> (case get_extfields thy ext' of
SOME flds
=> (case get_fieldext thy (fst (hd flds)) of
SOME (_, alphas)
=> (let
val (f :: fs) = but_last flds;
val flds' = apfst (Sign.extern_const thy) f
:: map (apfst Long_Name.base_name) fs;
val (args', more) = split_last args;
val alphavars = map varifyT (but_last alphas);
val subst = fold2 (curry (Sign.typ_match thy))
alphavars args' Vartab.empty;
val flds'' = (map o apsnd)
(Envir.norm_type subst o varifyT) flds';
in flds'' @ field_lst more end
handle TYPE_MATCH => [("", T)]
| Library.UnequalLengths => [("", T)])
| NONE => [("", T)])
| NONE => [("", T)])
| NONE => [("", T)])
| _ => [("", T)])
val (flds, (_, moreT)) = split_last (field_lst T);
val flds' = map (fn (n, T) => Syntax.const mark $ Syntax.const n $ term_of_type T) flds;
val flds'' = foldr1 (fn (x, y) => Syntax.const sep $ x $ y) flds' handle Empty => raise Match;
in if not (!print_record_type_as_fields) orelse null flds then raise Match
else if moreT = HOLogic.unitT
then Syntax.const record$flds''
else Syntax.const record_scheme$flds''$term_of_type moreT
end
fun gen_record_type_tr' name =
let val name_sfx = suffix ext_typeN name;
fun tr' ctxt ts = record_type_tr' "_field_types" "_field_type"
"_record_type" "_record_type_scheme" ctxt
(list_comb (Syntax.const name_sfx,ts))
in (name_sfx,tr')
end
fun gen_record_type_abbr_tr' abbr alphas zeta lastExt schemeT name =
let val name_sfx = suffix ext_typeN name;
val default_tr' = record_type_tr' "_field_types" "_field_type"
"_record_type" "_record_type_scheme"
fun tr' ctxt ts =
record_type_abbr_tr' default_tr' abbr alphas zeta lastExt schemeT ctxt
(list_comb (Syntax.const name_sfx,ts))
in (name_sfx, tr') end;
(** record simprocs **)
val record_quick_and_dirty_sensitive = ref false;
fun quick_and_dirty_prove stndrd thy asms prop tac =
if !record_quick_and_dirty_sensitive andalso !quick_and_dirty
then Goal.prove (ProofContext.init thy) [] []
(Logic.list_implies (map Logic.varify asms,Logic.varify prop))
(K (SkipProof.cheat_tac @{theory HOL}))
(* standard can take quite a while for large records, thats why
* we varify the proposition manually here.*)
else let val prf = Goal.prove (ProofContext.init thy) [] asms prop tac;
in if stndrd then standard prf else prf end;
fun quick_and_dirty_prf noopt opt () =
if !record_quick_and_dirty_sensitive andalso !quick_and_dirty
then noopt ()
else opt ();
local
fun abstract_over_fun_app (Abs (f,fT,t)) =
let
val (f',t') = Term.dest_abs (f,fT,t);
val T = domain_type fT;
val (x,T') = hd (Term.variant_frees t' [("x",T)]);
val f_x = Free (f',fT)$(Free (x,T'));
fun is_constr (Const (c,_)$_) = can (unsuffix extN) c
| is_constr _ = false;
fun subst (t as u$w) = if Free (f',fT)=u
then if is_constr w then f_x
else raise TERM ("abstract_over_fun_app",[t])
else subst u$subst w
| subst (Abs (x,T,t)) = (Abs (x,T,subst t))
| subst t = t
val t'' = abstract_over (f_x,subst t');
val vars = strip_qnt_vars "all" t'';
val bdy = strip_qnt_body "all" t'';
in list_abs ((x,T')::vars,bdy) end
| abstract_over_fun_app t = raise TERM ("abstract_over_fun_app",[t]);
(* Generates a theorem of the kind:
* !!f x*. PROP P (f ( r x* ) x* == !!r x*. PROP P r x*
*)
fun mk_fun_apply_eq (Abs (f, fT, t)) thy =
let
val rT = domain_type fT;
val vars = Term.strip_qnt_vars "all" t;
val Ts = map snd vars;
val n = length vars;
fun app_bounds 0 t = t$Bound 0
| app_bounds n t = if n > 0 then app_bounds (n-1) (t$Bound n) else t
val [P,r] = Term.variant_frees t [("P",rT::Ts--->Term.propT),("r",Ts--->rT)];
val prop = Logic.mk_equals
(list_all ((f,fT)::vars,
app_bounds (n - 1) ((Free P)$(Bound n$app_bounds (n-1) (Free r)))),
list_all ((fst r,rT)::vars,
app_bounds (n - 1) ((Free P)$Bound n)));
val prove_standard = quick_and_dirty_prove true thy;
val thm = prove_standard [] prop (fn _ =>
EVERY [rtac equal_intr_rule 1,
Goal.norm_hhf_tac 1,REPEAT (etac meta_allE 1), atac 1,
Goal.norm_hhf_tac 1,REPEAT (etac meta_allE 1), atac 1]);
in thm end
| mk_fun_apply_eq t thy = raise TERM ("mk_fun_apply_eq",[t]);
in
(* During proof of theorems produced by record_simproc you can end up in
* situations like "!!f ... . ... f r ..." where f is an extension update function.
* In order to split "f r" we transform this to "!!r ... . ... r ..." so that the
* usual split rules for extensions can apply.
*)
val record_split_f_more_simproc =
Simplifier.simproc @{theory HOL} "record_split_f_more_simp" ["x"]
(fn thy => fn _ => fn t =>
(case t of (Const ("all", Type (_, [Type (_, [Type("fun",[T,T']), _]), _])))$
(trm as Abs _) =>
(case rec_id (~1) T of
"" => NONE
| n => if T=T'
then (let
val P=cterm_of thy (abstract_over_fun_app trm);
val thm = mk_fun_apply_eq trm thy;
val PV = cterm_of thy (hd (OldTerm.term_vars (prop_of thm)));
val thm' = cterm_instantiate [(PV,P)] thm;
in SOME thm' end handle TERM _ => NONE)
else NONE)
| _ => NONE))
end
fun prove_split_simp thy ss T prop =
let
val {sel_upd={simpset,...},extsplit,...} = RecordsData.get thy;
val extsplits =
Library.foldl (fn (thms,(n,_)) => the_list (Symtab.lookup extsplit n) @ thms)
([],dest_recTs T);
val thms = (case get_splits thy (rec_id (~1) T) of
SOME (all_thm,_,_,_) =>
all_thm::(case extsplits of [thm] => [] | _ => extsplits)
(* [thm] is the same as all_thm *)
| NONE => extsplits)
val thms'=K_comp_convs@thms;
val ss' = (Simplifier.inherit_context ss simpset
addsimps thms'
addsimprocs [record_split_f_more_simproc]);
in
quick_and_dirty_prove true thy [] prop (fn _ => simp_tac ss' 1)
end;
local
fun eq (s1:string) (s2:string) = (s1 = s2);
fun has_field extfields f T =
exists (fn (eN,_) => exists (eq f o fst) (Symtab.lookup_list extfields eN))
(dest_recTs T);
fun K_skeleton n (T as Type (_,[_,kT])) (b as Bound i) (Abs (x,xT,t)) =
if null (loose_bnos t) then ((n,kT),(Abs (x,xT,Bound (i+1)))) else ((n,T),b)
| K_skeleton n T b _ = ((n,T),b);
(*
fun K_skeleton n _ b ((K_rec as Const ("Record.K_record",Type (_,[kT,_])))$_) =
((n,kT),K_rec$b)
| K_skeleton n _ (Bound i)
(Abs (x,T,(K_rec as Const ("Record.K_record",Type (_,[kT,_])))$_$Bound 0)) =
((n,kT),Abs (x,T,(K_rec$Bound (i+1)$Bound 0)))
| K_skeleton n T b _ = ((n,T),b);
*)
fun normalize_rhs thm =
let
val ss = HOL_basic_ss addsimps K_comp_convs;
val rhs = thm |> Thm.cprop_of |> Thm.dest_comb |> snd;
val rhs' = (Simplifier.rewrite ss rhs);
in Thm.transitive thm rhs' end;
in
(* record_simproc *)
(* Simplifies selections of an record update:
* (1) S (S_update k r) = k (S r)
* (2) S (X_update k r) = S r
* The simproc skips multiple updates at once, eg:
* S (X_update x (Y_update y (S_update k r))) = k (S r)
* But be careful in (2) because of the extendibility of records.
* - If S is a more-selector we have to make sure that the update on component
* X does not affect the selected subrecord.
* - If X is a more-selector we have to make sure that S is not in the updated
* subrecord.
*)
val record_simproc =
Simplifier.simproc @{theory HOL} "record_simp" ["x"]
(fn thy => fn ss => fn t =>
(case t of (sel as Const (s, Type (_,[domS,rangeS])))$
((upd as Const (u,Type(_,[_,Type (_,[rT,_])]))) $ k $ r)=>
if is_selector thy s then
(case get_updates thy u of SOME u_name =>
let
val {sel_upd={updates,...},extfields,...} = RecordsData.get thy;
fun mk_eq_terms ((upd as Const (u,Type(_,[kT,_]))) $ k $ r) =
(case Symtab.lookup updates u of
NONE => NONE
| SOME u_name
=> if u_name = s
then (case mk_eq_terms r of
NONE =>
let
val rv = ("r",rT)
val rb = Bound 0
val (kv,kb) = K_skeleton "k" kT (Bound 1) k;
in SOME (upd$kb$rb,kb$(sel$rb),[kv,rv]) end
| SOME (trm,trm',vars) =>
let
val (kv,kb) = K_skeleton "k" kT (Bound (length vars)) k;
in SOME (upd$kb$trm,kb$trm',kv::vars) end)
else if has_field extfields u_name rangeS
orelse has_field extfields s (domain_type kT)
then NONE
else (case mk_eq_terms r of
SOME (trm,trm',vars)
=> let
val (kv,kb) =
K_skeleton "k" kT (Bound (length vars)) k;
in SOME (upd$kb$trm,trm',kv::vars) end
| NONE
=> let
val rv = ("r",rT)
val rb = Bound 0
val (kv,kb) = K_skeleton "k" kT (Bound 1) k;
in SOME (upd$kb$rb,sel$rb,[kv,rv]) end))
| mk_eq_terms r = NONE
in
(case mk_eq_terms (upd$k$r) of
SOME (trm,trm',vars)
=> SOME (prove_split_simp thy ss domS
(list_all(vars, Logic.mk_equals (sel $ trm, trm'))))
| NONE => NONE)
end
| NONE => NONE)
else NONE
| _ => NONE));
(* record_upd_simproc *)
(* simplify multiple updates:
* (1) "N_update y (M_update g (N_update x (M_update f r))) =
(N_update (y o x) (M_update (g o f) r))"
* (2) "r(|M:= M r|) = r"
* For (2) special care of "more" updates has to be taken:
* r(|more := m; A := A r|)
* If A is contained in the fields of m we cannot remove the update A := A r!
* (But r(|more := r; A := A (r(|more := r|))|) = r(|more := r|)
*)
val record_upd_simproc =
Simplifier.simproc @{theory HOL} "record_upd_simp" ["x"]
(fn thy => fn ss => fn t =>
(case t of ((upd as Const (u, Type(_,[_,Type(_,[rT,_])]))) $ k $ r) =>
let datatype ('a,'b) calc = Init of 'b | Inter of 'a
val {sel_upd={selectors,updates,...},extfields,...} = RecordsData.get thy;
(*fun mk_abs_var x t = (x, fastype_of t);*)
fun sel_name u = Long_Name.base_name (unsuffix updateN u);
fun seed s (upd as Const (more,Type(_,[mT,_]))$ k $ r) =
if has_field extfields s (domain_type' mT) then upd else seed s r
| seed _ r = r;
fun grow u uT k kT vars (sprout,skeleton) =
if sel_name u = moreN
then let val (kv,kb) = K_skeleton "k" kT (Bound (length vars)) k;
in ((Const (u,uT)$k$sprout,Const (u,uT)$kb$skeleton),kv::vars) end
else ((sprout,skeleton),vars);
fun dest_k (Abs (x,T,((sel as Const (s,_))$r))) =
if null (loose_bnos r) then SOME (x,T,sel,s,r) else NONE
| dest_k (Abs (_,_,(Abs (x,T,((sel as Const (s,_))$r)))$Bound 0)) =
(* eta expanded variant *)
if null (loose_bnos r) then SOME (x,T,sel,s,r) else NONE
| dest_k _ = NONE;
fun is_upd_same (sprout,skeleton) u k =
(case dest_k k of SOME (x,T,sel,s,r) =>
if (unsuffix updateN u) = s andalso (seed s sprout) = r
then SOME (fn t => Abs (x,T,incr_boundvars 1 t),sel,seed s skeleton)
else NONE
| NONE => NONE);
fun init_seed r = ((r,Bound 0), [("r", rT)]);
fun add (n:string) f fmaps =
(case AList.lookup (op =) fmaps n of
NONE => AList.update (op =) (n,[f]) fmaps
| SOME fs => AList.update (op =) (n,f::fs) fmaps)
fun comps (n:string) T fmaps =
(case AList.lookup (op =) fmaps n of
SOME fs =>
foldr1 (fn (f,g) => Const ("Fun.comp",(T-->T)-->(T-->T)-->(T-->T))$f$g) fs
| NONE => error ("record_upd_simproc.comps"))
(* mk_updterm returns either
* - Init (orig-term, orig-term-skeleton, vars) if no optimisation can be made,
* where vars are the bound variables in the skeleton
* - Inter (orig-term-skeleton,simplified-term-skeleton,
* vars, (term-sprout, skeleton-sprout))
* where "All vars. orig-term-skeleton = simplified-term-skeleton" is
* the desired simplification rule,
* the sprouts accumulate the "more-updates" on the way from the seed
* to the outermost update. It is only relevant to calculate the
* possible simplification for (2)
* The algorithm first walks down the updates to the seed-record while
* memorising the updates in the already-table. While walking up the
* updates again, the optimised term is constructed.
*)
fun mk_updterm upds already
(t as ((upd as Const (u,uT as (Type (_,[kT,_])))) $ k $ r)) =
if Symtab.defined upds u
then let
fun rest already = mk_updterm upds already
in if u mem_string already
then (case (rest already r) of
Init ((sprout,skel),vars) =>
let
val n = sel_name u;
val (kv,kb) = K_skeleton n kT (Bound (length vars)) k;
val (sprout',vars')= grow u uT k kT (kv::vars) (sprout,skel);
in Inter (upd$kb$skel,skel,vars',add n kb [],sprout') end
| Inter (trm,trm',vars,fmaps,sprout) =>
let
val n = sel_name u;
val (kv,kb) = K_skeleton n kT (Bound (length vars)) k;
val (sprout',vars') = grow u uT k kT (kv::vars) sprout;
in Inter(upd$kb$trm,trm',kv::vars',add n kb fmaps,sprout')
end)
else
(case rest (u::already) r of
Init ((sprout,skel),vars) =>
(case is_upd_same (sprout,skel) u k of
SOME (K_rec,sel,skel') =>
let
val (sprout',vars') = grow u uT k kT vars (sprout,skel);
in Inter(upd$(K_rec (sel$skel'))$skel,skel,vars',[],sprout')
end
| NONE =>
let
val n = sel_name u;
val (kv,kb) = K_skeleton n kT (Bound (length vars)) k;
in Init ((upd$k$sprout,upd$kb$skel),kv::vars) end)
| Inter (trm,trm',vars,fmaps,sprout) =>
(case is_upd_same sprout u k of
SOME (K_rec,sel,skel) =>
let
val (sprout',vars') = grow u uT k kT vars sprout
in Inter(upd$(K_rec (sel$skel))$trm,trm',vars',fmaps,sprout')
end
| NONE =>
let
val n = sel_name u
val T = domain_type kT
val (kv,kb) = K_skeleton n kT (Bound (length vars)) k;
val (sprout',vars') = grow u uT k kT (kv::vars) sprout
val fmaps' = add n kb fmaps
in Inter (upd$kb$trm,upd$comps n T fmaps'$trm'
,vars',fmaps',sprout') end))
end
else Init (init_seed t)
| mk_updterm _ _ t = Init (init_seed t);
in (case mk_updterm updates [] t of
Inter (trm,trm',vars,_,_)
=> SOME (normalize_rhs
(prove_split_simp thy ss rT
(list_all(vars, Logic.mk_equals (trm, trm')))))
| _ => NONE)
end
| _ => NONE))
end
(* record_eq_simproc *)
(* looks up the most specific record-equality.
* Note on efficiency:
* Testing equality of records boils down to the test of equality of all components.
* Therefore the complexity is: #components * complexity for single component.
* Especially if a record has a lot of components it may be better to split up
* the record first and do simplification on that (record_split_simp_tac).
* e.g. r(|lots of updates|) = x
*
* record_eq_simproc record_split_simp_tac
* Complexity: #components * #updates #updates
*
*)
val record_eq_simproc =
Simplifier.simproc @{theory HOL} "record_eq_simp" ["r = s"]
(fn thy => fn _ => fn t =>
(case t of Const ("op =", Type (_, [T, _])) $ _ $ _ =>
(case rec_id (~1) T of
"" => NONE
| name => (case get_equalities thy name of
NONE => NONE
| SOME thm => SOME (thm RS Eq_TrueI)))
| _ => NONE));
(* record_split_simproc *)
(* splits quantified occurrences of records, for which P holds. P can peek on the
* subterm starting at the quantified occurrence of the record (including the quantifier)
* P t = 0: do not split
* P t = ~1: completely split
* P t > 0: split up to given bound of record extensions
*)
fun record_split_simproc P =
Simplifier.simproc @{theory HOL} "record_split_simp" ["x"]
(fn thy => fn _ => fn t =>
(case t of (Const (quantifier, Type (_, [Type (_, [T, _]), _])))$trm =>
if quantifier = "All" orelse quantifier = "all" orelse quantifier = "Ex"
then (case rec_id (~1) T of
"" => NONE
| name
=> let val split = P t
in if split <> 0 then
(case get_splits thy (rec_id split T) of
NONE => NONE
| SOME (all_thm, All_thm, Ex_thm,_)
=> SOME (case quantifier of
"all" => all_thm
| "All" => All_thm RS eq_reflection
| "Ex" => Ex_thm RS eq_reflection
| _ => error "record_split_simproc"))
else NONE
end)
else NONE
| _ => NONE))
val record_ex_sel_eq_simproc =
Simplifier.simproc @{theory HOL} "record_ex_sel_eq_simproc" ["Ex t"]
(fn thy => fn ss => fn t =>
let
fun prove prop =
quick_and_dirty_prove true thy [] prop
(fn _ => simp_tac (Simplifier.inherit_context ss (get_simpset thy)
addsimps simp_thms addsimprocs [record_split_simproc (K ~1)]) 1);
fun mkeq (lr,Teq,(sel,Tsel),x) i =
if is_selector thy sel then
let val x' = if not (loose_bvar1 (x,0))
then Free ("x" ^ string_of_int i, range_type Tsel)
else raise TERM ("",[x]);
val sel' = Const (sel,Tsel)$Bound 0;
val (l,r) = if lr then (sel',x') else (x',sel');
in Const ("op =",Teq)$l$r end
else raise TERM ("",[Const (sel,Tsel)]);
fun dest_sel_eq (Const ("op =",Teq)$(Const (sel,Tsel)$Bound 0)$X) =
(true,Teq,(sel,Tsel),X)
| dest_sel_eq (Const ("op =",Teq)$X$(Const (sel,Tsel)$Bound 0)) =
(false,Teq,(sel,Tsel),X)
| dest_sel_eq _ = raise TERM ("",[]);
in
(case t of
(Const ("Ex",Tex)$Abs(s,T,t)) =>
(let val eq = mkeq (dest_sel_eq t) 0;
val prop = list_all ([("r",T)],
Logic.mk_equals (Const ("Ex",Tex)$Abs(s,T,eq),
HOLogic.true_const));
in SOME (prove prop) end
handle TERM _ => NONE)
| _ => NONE)
end)
local
val inductive_atomize = thms "induct_atomize";
val inductive_rulify = thms "induct_rulify";
in
(* record_split_simp_tac *)
(* splits (and simplifies) all records in the goal for which P holds.
* For quantified occurrences of a record
* P can peek on the whole subterm (including the quantifier); for free variables P
* can only peek on the variable itself.
* P t = 0: do not split
* P t = ~1: completely split
* P t > 0: split up to given bound of record extensions
*)
fun record_split_simp_tac thms P i st =
let
val thy = Thm.theory_of_thm st;
val has_rec = exists_Const
(fn (s, Type (_, [Type (_, [T, _]), _])) =>
(s = "all" orelse s = "All" orelse s = "Ex") andalso is_recT T
| _ => false);
val goal = nth (Thm.prems_of st) (i - 1);
val frees = List.filter (is_recT o type_of) (OldTerm.term_frees goal);
fun mk_split_free_tac free induct_thm i =
let val cfree = cterm_of thy free;
val (_$(_$r)) = concl_of induct_thm;
val crec = cterm_of thy r;
val thm = cterm_instantiate [(crec,cfree)] induct_thm;
in EVERY [simp_tac (HOL_basic_ss addsimps inductive_atomize) i,
rtac thm i,
simp_tac (HOL_basic_ss addsimps inductive_rulify) i]
end;
fun split_free_tac P i (free as Free (n,T)) =
(case rec_id (~1) T of
"" => NONE
| name => let val split = P free
in if split <> 0 then
(case get_splits thy (rec_id split T) of
NONE => NONE
| SOME (_,_,_,induct_thm)
=> SOME (mk_split_free_tac free induct_thm i))
else NONE
end)
| split_free_tac _ _ _ = NONE;
val split_frees_tacs = List.mapPartial (split_free_tac P i) frees;
val simprocs = if has_rec goal then [record_split_simproc P] else [];
val thms' = K_comp_convs@thms
in st |> ((EVERY split_frees_tacs)
THEN (Simplifier.full_simp_tac (get_simpset thy addsimps thms' addsimprocs simprocs) i))
end handle Empty => Seq.empty;
end;
(* record_split_tac *)
(* splits all records in the goal, which are quantified by ! or !!. *)
fun record_split_tac i st =
let
val thy = Thm.theory_of_thm st;
val has_rec = exists_Const
(fn (s, Type (_, [Type (_, [T, _]), _])) =>
(s = "all" orelse s = "All") andalso is_recT T
| _ => false);
val goal = nth (Thm.prems_of st) (i - 1);
fun is_all t =
(case t of (Const (quantifier, _)$_) =>
if quantifier = "All" orelse quantifier = "all" then ~1 else 0
| _ => 0);
in if has_rec goal
then Simplifier.full_simp_tac
(HOL_basic_ss addsimprocs [record_split_simproc is_all]) i st
else Seq.empty
end handle Subscript => Seq.empty;
(* wrapper *)
val record_split_name = "record_split_tac";
val record_split_wrapper = (record_split_name, fn tac => record_split_tac ORELSE' tac);
(** theory extender interface **)
(* prepare arguments *)
fun read_raw_parent ctxt raw_T =
(case ProofContext.read_typ_abbrev ctxt raw_T of
Type (name, Ts) => (Ts, name)
| T => error ("Bad parent record specification: " ^ Syntax.string_of_typ ctxt T));
fun read_typ ctxt raw_T env =
let
val ctxt' = fold (Variable.declare_typ o TFree) env ctxt;
val T = Syntax.read_typ ctxt' raw_T;
val env' = OldTerm.add_typ_tfrees (T, env);
in (T, env') end;
fun cert_typ ctxt raw_T env =
let
val thy = ProofContext.theory_of ctxt;
val T = Type.no_tvars (Sign.certify_typ thy raw_T) handle TYPE (msg, _, _) => error msg;
val env' = OldTerm.add_typ_tfrees (T, env);
in (T, env') end;
(* attributes *)
fun case_names_fields x = RuleCases.case_names ["fields"] x;
fun induct_type_global name = [case_names_fields, Induct.induct_type name];
fun cases_type_global name = [case_names_fields, Induct.cases_type name];
(* tactics *)
fun simp_all_tac ss simps = ALLGOALS (Simplifier.asm_full_simp_tac (ss addsimps simps));
(* do case analysis / induction according to rule on last parameter of ith subgoal
* (or on s if there are no parameters);
* Instatiation of record variable (and predicate) in rule is calculated to
* avoid problems with higher order unification.
*)
fun try_param_tac s rule i st =
let
val cert = cterm_of (Thm.theory_of_thm st);
val g = nth (prems_of st) (i - 1);
val params = Logic.strip_params g;
val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl g);
val rule' = Thm.lift_rule (Thm.cprem_of st i) rule;
val (P, ys) = strip_comb (HOLogic.dest_Trueprop
(Logic.strip_assums_concl (prop_of rule')));
(* ca indicates if rule is a case analysis or induction rule *)
val (x, ca) = (case rev (Library.drop (length params, ys)) of
[] => (head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop
(hd (rev (Logic.strip_assums_hyp (hd (prems_of rule')))))))), true)
| [x] => (head_of x, false));
val rule'' = cterm_instantiate (map (pairself cert) (case (rev params) of
[] => (case AList.lookup (op =) (map dest_Free (OldTerm.term_frees (prop_of st))) s of
NONE => sys_error "try_param_tac: no such variable"
| SOME T => [(P, if ca then concl else lambda (Free (s, T)) concl),
(x, Free (s, T))])
| (_, T) :: _ => [(P, list_abs (params, if ca then concl
else incr_boundvars 1 (Abs (s, T, concl)))),
(x, list_abs (params, Bound 0))])) rule'
in compose_tac (false, rule'', nprems_of rule) i st end;
(* !!x1 ... xn. ... ==> EX x1 ... xn. P x1 ... xn;
instantiates x1 ... xn with parameters x1 ... xn *)
fun ex_inst_tac i st =
let
val thy = Thm.theory_of_thm st;
val g = nth (prems_of st) (i - 1);
val params = Logic.strip_params g;
val exI' = Thm.lift_rule (Thm.cprem_of st i) exI;
val (_$(_$x)) = Logic.strip_assums_concl (hd (prems_of exI'));
val cx = cterm_of thy (fst (strip_comb x));
in Seq.single (Library.foldl (fn (st,v) =>
Seq.hd
(compose_tac (false, cterm_instantiate
[(cx,cterm_of thy (list_abs (params,Bound v)))] exI',1)
i st)) (st,((length params) - 1) downto 0))
end;
fun extension_typedef name repT alphas thy =
let
fun get_thms thy name =
let
val SOME { Abs_induct = abs_induct,
Abs_inject=abs_inject, Abs_inverse = abs_inverse, ...} = TypedefPackage.get_info thy name;
val rewrite_rule = MetaSimplifier.rewrite_rule [rec_UNIV_I, rec_True_simp];
in map rewrite_rule [abs_inject, abs_inverse, abs_induct] end;
val tname = Binding.name (Long_Name.base_name name);
in
thy
|> TypecopyPackage.add_typecopy (Binding.suffix_name ext_typeN tname, alphas) repT NONE
|-> (fn (name, _) => `(fn thy => get_thms thy name))
end;
fun mixit convs refls =
let fun f ((res,lhs,rhs),refl) = ((refl,List.revAppend (lhs,refl::tl rhs))::res,hd rhs::lhs,tl rhs);
in #1 (Library.foldl f (([],[],convs),refls)) end;
fun extension_definition full name fields names alphas zeta moreT more vars thy =
let
val base = Long_Name.base_name;
val fieldTs = (map snd fields);
val alphas_zeta = alphas@[zeta];
val alphas_zetaTs = map (fn n => TFree (n, HOLogic.typeS)) alphas_zeta;
val vT = TFree (Name.variant alphas_zeta "'v", HOLogic.typeS);
val extT_name = suffix ext_typeN name
val extT = Type (extT_name, alphas_zetaTs);
val repT = foldr1 HOLogic.mk_prodT (fieldTs@[moreT]);
val fields_more = fields@[(full moreN,moreT)];
val fields_moreTs = fieldTs@[moreT];
val bfields_more = map (apfst base) fields_more;
val r = Free (rN,extT)
val len = length fields;
val idxms = 0 upto len;
(* prepare declarations and definitions *)
(*fields constructor*)
val ext_decl = (mk_extC (name,extT) fields_moreTs);
(*
val ext_spec = Const ext_decl :==
(foldr (uncurry lambda)
(mk_Abs name repT extT $ (foldr1 HOLogic.mk_prod (vars@[more]))) (vars@[more]))
*)
val ext_spec = list_comb (Const ext_decl,vars@[more]) :==
(mk_Abs name repT extT $ (foldr1 HOLogic.mk_prod (vars@[more])));
fun mk_ext args = list_comb (Const ext_decl, args);
(*destructors*)
val _ = timing_msg "record extension preparing definitions";
val dest_decls = map (mk_selC extT o (apfst (suffix ext_dest))) bfields_more;
fun mk_dest_spec (i, (c,T)) =
let val snds = (funpow i HOLogic.mk_snd (mk_Rep name repT extT $ r))
in Const (mk_selC extT (suffix ext_dest c,T))
:== (lambda r (if i=len then snds else HOLogic.mk_fst snds))
end;
val dest_specs =
ListPair.map mk_dest_spec (idxms, fields_more);
(*updates*)
val upd_decls = map (mk_updC updN extT) bfields_more;
fun mk_upd_spec (c,T) =
let
val args = map (fn (n,nT) => if n=c then Free (base c,T --> T)$
(mk_sel r (suffix ext_dest n,nT))
else (mk_sel r (suffix ext_dest n,nT)))
fields_more;
in Const (mk_updC updN extT (c,T))$(Free (base c,T --> T))$r
:== mk_ext args
end;
val upd_specs = map mk_upd_spec fields_more;
(* 1st stage: defs_thy *)
fun mk_defs () =
thy
|> extension_typedef name repT (alphas @ [zeta])
||> Sign.add_consts_i
(map (Syntax.no_syn o apfst Binding.name) (apfst base ext_decl :: dest_decls @ upd_decls))
||>> PureThy.add_defs false
(map (Thm.no_attributes o apfst Binding.name) (ext_spec :: dest_specs))
||>> PureThy.add_defs false
(map (Thm.no_attributes o apfst Binding.name) upd_specs)
|-> (fn args as ((_, dest_defs), upd_defs) =>
fold Code.add_default_eqn dest_defs
#> fold Code.add_default_eqn upd_defs
#> pair args);
val ((([abs_inject, abs_inverse, abs_induct], ext_def :: dest_defs), upd_defs), defs_thy) =
timeit_msg "record extension type/selector/update defs:" mk_defs;
(* prepare propositions *)
val _ = timing_msg "record extension preparing propositions";
val vars_more = vars@[more];
val named_vars_more = (names@[full moreN])~~vars_more;
val variants = map (fn (Free (x,_))=>x) vars_more;
val ext = mk_ext vars_more;
val s = Free (rN, extT);
val w = Free (wN, extT);
val P = Free (Name.variant variants "P", extT-->HOLogic.boolT);
val C = Free (Name.variant variants "C", HOLogic.boolT);
val inject_prop =
let val vars_more' = map (fn (Free (x,T)) => Free (x ^ "'",T)) vars_more;
in All (map dest_Free (vars_more@vars_more'))
((HOLogic.eq_const extT $
mk_ext vars_more$mk_ext vars_more')
===
foldr1 HOLogic.mk_conj (map HOLogic.mk_eq (vars_more ~~ vars_more')))
end;
val induct_prop =
(All (map dest_Free vars_more) (Trueprop (P $ ext)), Trueprop (P $ s));
val cases_prop =
(All (map dest_Free vars_more)
(Trueprop (HOLogic.mk_eq (s,ext)) ==> Trueprop C))
==> Trueprop C;
(*destructors*)
val dest_conv_props =
map (fn (c, x as Free (_,T)) => mk_sel ext (suffix ext_dest c,T) === x) named_vars_more;
(*updates*)
fun mk_upd_prop (i,(c,T)) =
let val x' = Free (Name.variant variants (base c ^ "'"),T --> T)
val args' = nth_map i (K (x'$nth vars_more i)) vars_more
in mk_upd updN c x' ext === mk_ext args' end;
val upd_conv_props = ListPair.map mk_upd_prop (idxms, fields_more);
val surjective_prop =
let val args =
map (fn (c, Free (_,T)) => mk_sel s (suffix ext_dest c,T)) named_vars_more;
in s === mk_ext args end;
val split_meta_prop =
let val P = Free (Name.variant variants "P", extT-->Term.propT) in
Logic.mk_equals
(All [dest_Free s] (P $ s), All (map dest_Free vars_more) (P $ ext))
end;
fun prove stndrd = quick_and_dirty_prove stndrd defs_thy;
val prove_standard = quick_and_dirty_prove true defs_thy;
fun prove_simp stndrd simps =
let val tac = simp_all_tac HOL_ss simps
in fn prop => prove stndrd [] prop (K tac) end;
fun inject_prf () = (prove_simp true [ext_def,abs_inject,Pair_eq] inject_prop);
val inject = timeit_msg "record extension inject proof:" inject_prf;
fun induct_prf () =
let val (assm, concl) = induct_prop
in prove_standard [assm] concl (fn {prems, ...} =>
EVERY [try_param_tac rN abs_induct 1,
simp_tac (HOL_ss addsimps [split_paired_all]) 1,
resolve_tac (map (rewrite_rule [ext_def]) prems) 1])
end;
val induct = timeit_msg "record extension induct proof:" induct_prf;
fun cases_prf_opt () =
let
val (_$(Pvar$_)) = concl_of induct;
val ind = cterm_instantiate
[(cterm_of defs_thy Pvar, cterm_of defs_thy
(lambda w (HOLogic.imp$HOLogic.mk_eq(r,w)$C)))]
induct;
in standard (ObjectLogic.rulify (mp OF [ind, refl])) end;
fun cases_prf_noopt () =
prove_standard [] cases_prop (fn _ =>
EVERY [asm_full_simp_tac (HOL_basic_ss addsimps [atomize_all, atomize_imp]) 1,
try_param_tac rN induct 1,
rtac impI 1,
REPEAT (etac allE 1),
etac mp 1,
rtac refl 1])
val cases_prf = quick_and_dirty_prf cases_prf_noopt cases_prf_opt;
val cases = timeit_msg "record extension cases proof:" cases_prf;
fun dest_convs_prf () = map (prove_simp false
([ext_def,abs_inverse]@Pair_sel_convs@dest_defs)) dest_conv_props;
val dest_convs = timeit_msg "record extension dest_convs proof:" dest_convs_prf;
fun dest_convs_standard_prf () = map standard dest_convs;
val dest_convs_standard =
timeit_msg "record extension dest_convs_standard proof:" dest_convs_standard_prf;
fun upd_convs_prf_noopt () = map (prove_simp true (dest_convs_standard@upd_defs))
upd_conv_props;
fun upd_convs_prf_opt () =
let
fun mkrefl (c,T) = Thm.reflexive
(cterm_of defs_thy (Free (Name.variant variants (base c ^ "'"),T-->T)));
val refls = map mkrefl fields_more;
val dest_convs' = map mk_meta_eq dest_convs;
val map_eqs = map (uncurry Thm.combination) (refls ~~ dest_convs');
val constr_refl = Thm.reflexive (cterm_of defs_thy (head_of ext));
fun mkthm (udef,(fld_refl,thms)) =
let val bdyeq = Library.foldl (uncurry Thm.combination) (constr_refl,thms);
(* (|N=N (|N=N,M=M,K=K,more=more|)
M=M (|N=N,M=M,K=K,more=more|)
K=K'
more = more (|N=N,M=M,K=K,more=more|) =
(|N=N,M=M,K=K',more=more|)
*)
val (_$(_$v$r)$_) = prop_of udef;
val (_$(v'$_)$_) = prop_of fld_refl;
val udef' = cterm_instantiate
[(cterm_of defs_thy v,cterm_of defs_thy v'),
(cterm_of defs_thy r,cterm_of defs_thy ext)] udef;
in standard (Thm.transitive udef' bdyeq) end;
in map mkthm (rev upd_defs ~~ (mixit dest_convs' map_eqs)) end;
val upd_convs_prf = quick_and_dirty_prf upd_convs_prf_noopt upd_convs_prf_opt;
val upd_convs =
timeit_msg "record extension upd_convs proof:" upd_convs_prf;
fun surjective_prf () =
prove_standard [] surjective_prop (fn _ =>
(EVERY [try_param_tac rN induct 1,
simp_tac (HOL_basic_ss addsimps dest_convs_standard) 1]));
val surjective = timeit_msg "record extension surjective proof:" surjective_prf;
fun split_meta_prf () =
prove_standard [] split_meta_prop (fn _ =>
EVERY [rtac equal_intr_rule 1, Goal.norm_hhf_tac 1,
etac meta_allE 1, atac 1,
rtac (prop_subst OF [surjective]) 1,
REPEAT (etac meta_allE 1), atac 1]);
val split_meta = timeit_msg "record extension split_meta proof:" split_meta_prf;
val (([inject',induct',cases',surjective',split_meta'],
[dest_convs',upd_convs']),
thm_thy) =
defs_thy
|> (PureThy.add_thms o map (Thm.no_attributes o apfst Binding.name))
[("ext_inject", inject),
("ext_induct", induct),
("ext_cases", cases),
("ext_surjective", surjective),
("ext_split", split_meta)]
||>> (PureThy.add_thmss o map (Thm.no_attributes o apfst Binding.name))
[("dest_convs", dest_convs_standard), ("upd_convs", upd_convs)]
in (thm_thy,extT,induct',inject',dest_convs',split_meta',upd_convs')
end;
fun chunks [] [] = []
| chunks [] xs = [xs]
| chunks (l::ls) xs = Library.take (l,xs)::chunks ls (Library.drop (l,xs));
fun chop_last [] = error "last: list should not be empty"
| chop_last [x] = ([],x)
| chop_last (x::xs) = let val (tl,l) = chop_last xs in (x::tl,l) end;
fun subst_last s [] = error "subst_last: list should not be empty"
| subst_last s ([x]) = [s]
| subst_last s (x::xs) = (x::subst_last s xs);
(* mk_recordT builds up the record type from the current extension tpye extT and a list
* of parent extensions, starting with the root of the record hierarchy
*)
fun mk_recordT extT =
fold_rev (fn (parent, Ts) => fn T => Type (parent, subst_last T Ts)) extT;
fun obj_to_meta_all thm =
let
fun E thm = case (SOME (spec OF [thm]) handle THM _ => NONE) of
SOME thm' => E thm'
| NONE => thm;
val th1 = E thm;
val th2 = Drule.forall_intr_vars th1;
in th2 end;
fun meta_to_obj_all thm =
let
val thy = Thm.theory_of_thm thm;
val prop = Thm.prop_of thm;
val params = Logic.strip_params prop;
val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl prop);
val ct = cterm_of thy
(HOLogic.mk_Trueprop (HOLogic.list_all (params, concl)));
val thm' = Seq.hd (REPEAT (rtac allI 1) (Thm.trivial ct));
in
Thm.implies_elim thm' thm
end;
(* record_definition *)
fun record_definition (args, bname) parent (parents: parent_info list) raw_fields thy =
let
val external_names = NameSpace.external_names (Sign.naming_of thy);
val alphas = map fst args;
val name = Sign.full_bname thy bname;
val full = Sign.full_bname_path thy bname;
val base = Long_Name.base_name;
val (bfields, field_syntax) = split_list (map (fn (x, T, mx) => ((x, T), mx)) raw_fields);
val parent_fields = List.concat (map #fields parents);
val parent_chunks = map (length o #fields) parents;
val parent_names = map fst parent_fields;
val parent_types = map snd parent_fields;
val parent_fields_len = length parent_fields;
val parent_variants = Name.variant_list [moreN, rN, rN ^ "'", wN] (map base parent_names);
val parent_vars = ListPair.map Free (parent_variants, parent_types);
val parent_len = length parents;
val parents_idx = (map #name parents) ~~ (0 upto (parent_len - 1));
val fields = map (apfst full) bfields;
val names = map fst fields;
val extN = full bname;
val types = map snd fields;
val alphas_fields = List.foldr OldTerm.add_typ_tfree_names [] types;
val alphas_ext = alphas inter alphas_fields;
val len = length fields;
val variants =
Name.variant_list (moreN :: rN :: (rN ^ "'") :: wN :: parent_variants) (map fst bfields);
val vars = ListPair.map Free (variants, types);
val named_vars = names ~~ vars;
val idxs = 0 upto (len - 1);
val idxms = 0 upto len;
val all_fields = parent_fields @ fields;
val all_names = parent_names @ names;
val all_types = parent_types @ types;
val all_len = parent_fields_len + len;
val all_variants = parent_variants @ variants;
val all_vars = parent_vars @ vars;
val all_named_vars = (parent_names ~~ parent_vars) @ named_vars;
val zeta = Name.variant alphas "'z";
val moreT = TFree (zeta, HOLogic.typeS);
val more = Free (moreN, moreT);
val full_moreN = full moreN;
val bfields_more = bfields @ [(moreN,moreT)];
val fields_more = fields @ [(full_moreN,moreT)];
val vars_more = vars @ [more];
val named_vars_more = named_vars @[(full_moreN,more)];
val all_vars_more = all_vars @ [more];
val all_named_vars_more = all_named_vars @ [(full_moreN,more)];
(* 1st stage: extension_thy *)
val (extension_thy,extT,ext_induct,ext_inject,ext_dest_convs,ext_split,u_convs) =
thy
|> Sign.add_path bname
|> extension_definition full extN fields names alphas_ext zeta moreT more vars;
val _ = timing_msg "record preparing definitions";
val Type extension_scheme = extT;
val extension_name = unsuffix ext_typeN (fst extension_scheme);
val extension = let val (n,Ts) = extension_scheme in (n,subst_last HOLogic.unitT Ts) end;
val extension_names =
(map ((unsuffix ext_typeN) o fst o #extension) parents) @ [extN];
val extension_id = Library.foldl (op ^) ("",extension_names);
fun rec_schemeT n = mk_recordT (map #extension (prune n parents)) extT;
val rec_schemeT0 = rec_schemeT 0;
fun recT n =
let val (c,Ts) = extension
in mk_recordT (map #extension (prune n parents)) (Type (c,subst_last HOLogic.unitT Ts))
end;
val recT0 = recT 0;
fun mk_rec args n =
let val (args',more) = chop_last args;
fun mk_ext' (((name,T),args),more) = mk_ext (name,T) (args@[more]);
fun build Ts =
List.foldr mk_ext' more (prune n (extension_names ~~ Ts ~~ (chunks parent_chunks args')))
in
if more = HOLogic.unit
then build (map recT (0 upto parent_len))
else build (map rec_schemeT (0 upto parent_len))
end;
val r_rec0 = mk_rec all_vars_more 0;
val r_rec_unit0 = mk_rec (all_vars@[HOLogic.unit]) 0;
fun r n = Free (rN, rec_schemeT n)
val r0 = r 0;
fun r_unit n = Free (rN, recT n)
val r_unit0 = r_unit 0;
val w = Free (wN, rec_schemeT 0)
(* prepare print translation functions *)
val field_tr's =
print_translation (distinct (op =) (maps external_names (full_moreN :: names)));
val adv_ext_tr's =
let
val trnames = external_names extN;
in map (gen_record_tr') trnames end;
val adv_record_type_abbr_tr's =
let val trnames = external_names (hd extension_names);
val lastExt = unsuffix ext_typeN (fst extension);
in map (gen_record_type_abbr_tr' name alphas zeta lastExt rec_schemeT0) trnames
end;
val adv_record_type_tr's =
let val trnames = if parent_len > 0 then external_names extN else [];
(* avoid conflict with adv_record_type_abbr_tr's *)
in map (gen_record_type_tr') trnames
end;
(* prepare declarations *)
val sel_decls = map (mk_selC rec_schemeT0) bfields_more;
val upd_decls = map (mk_updC updateN rec_schemeT0) bfields_more;
val make_decl = (makeN, all_types ---> recT0);
val fields_decl = (fields_selN, types ---> Type extension);
val extend_decl = (extendN, recT0 --> moreT --> rec_schemeT0);
val truncate_decl = (truncateN, rec_schemeT0 --> recT0);
(* prepare definitions *)
fun parent_more s =
if null parents then s
else mk_sel s (Long_Name.qualify (#name (List.last parents)) moreN, extT);
fun parent_more_upd v s =
if null parents then v$s
else let val mp = Long_Name.qualify (#name (List.last parents)) moreN;
in mk_upd updateN mp v s end;
(*record (scheme) type abbreviation*)
val recordT_specs =
[(Binding.name (suffix schemeN bname), alphas @ [zeta], rec_schemeT0, Syntax.NoSyn),
(Binding.name bname, alphas, recT0, Syntax.NoSyn)];
(*selectors*)
fun mk_sel_spec (c,T) =
Const (mk_selC rec_schemeT0 (c,T))
:== (lambda r0 (Const (mk_selC extT (suffix ext_dest c,T))$parent_more r0));
val sel_specs = map mk_sel_spec fields_more;
(*updates*)
fun mk_upd_spec (c,T) =
let
val new = mk_upd' updN c (Free (base c,T-->T)) extT(*(parent_more r0)*);
in Const (mk_updC updateN rec_schemeT0 (c,T))$(Free (base c,T-->T))$r0
:== (parent_more_upd new r0)
end;
val upd_specs = map mk_upd_spec fields_more;
(*derived operations*)
val make_spec = Const (full makeN, all_types ---> recT0) $$ all_vars :==
mk_rec (all_vars @ [HOLogic.unit]) 0;
val fields_spec = Const (full fields_selN, types ---> Type extension) $$ vars :==
mk_rec (all_vars @ [HOLogic.unit]) parent_len;
val extend_spec =
Const (full extendN, recT0-->moreT-->rec_schemeT0) $ r_unit0 $ more :==
mk_rec ((map (mk_sel r_unit0) all_fields) @ [more]) 0;
val truncate_spec = Const (full truncateN, rec_schemeT0 --> recT0) $ r0 :==
mk_rec ((map (mk_sel r0) all_fields) @ [HOLogic.unit]) 0;
(* 2st stage: defs_thy *)
fun mk_defs () =
extension_thy
|> Sign.add_trfuns
([],[],field_tr's, [])
|> Sign.add_advanced_trfuns
([],[],adv_ext_tr's @ adv_record_type_tr's @ adv_record_type_abbr_tr's,[])
|> Sign.parent_path
|> Sign.add_tyabbrs_i recordT_specs
|> Sign.add_path bname
|> Sign.add_consts_i
(map2 (fn (x, T) => fn mx => (Binding.name x, T, mx))
sel_decls (field_syntax @ [Syntax.NoSyn]))
|> (Sign.add_consts_i o map (fn (x, T) => (Binding.name x, T, Syntax.NoSyn)))
(upd_decls @ [make_decl, fields_decl, extend_decl, truncate_decl])
|> ((PureThy.add_defs false o map (Thm.no_attributes o apfst Binding.name)) sel_specs)
||>> ((PureThy.add_defs false o map (Thm.no_attributes o apfst Binding.name)) upd_specs)
||>> ((PureThy.add_defs false o map (Thm.no_attributes o apfst Binding.name))
[make_spec, fields_spec, extend_spec, truncate_spec])
|-> (fn defs as ((sel_defs, upd_defs), derived_defs) =>
fold Code.add_default_eqn sel_defs
#> fold Code.add_default_eqn upd_defs
#> fold Code.add_default_eqn derived_defs
#> pair defs)
val (((sel_defs, upd_defs), derived_defs), defs_thy) =
timeit_msg "record trfuns/tyabbrs/selectors/updates/make/fields/extend/truncate defs:"
mk_defs;
(* prepare propositions *)
val _ = timing_msg "record preparing propositions";
val P = Free (Name.variant all_variants "P", rec_schemeT0-->HOLogic.boolT);
val C = Free (Name.variant all_variants "C", HOLogic.boolT);
val P_unit = Free (Name.variant all_variants "P", recT0-->HOLogic.boolT);
(*selectors*)
val sel_conv_props =
map (fn (c, x as Free (_,T)) => mk_sel r_rec0 (c,T) === x) named_vars_more;
(*updates*)
fun mk_upd_prop (i,(c,T)) =
let val x' = Free (Name.variant all_variants (base c ^ "'"),T-->T);
val n = parent_fields_len + i;
val args' = nth_map n (K (x'$nth all_vars_more n)) all_vars_more
in mk_upd updateN c x' r_rec0 === mk_rec args' 0 end;
val upd_conv_props = ListPair.map mk_upd_prop (idxms, fields_more);
(*induct*)
val induct_scheme_prop =
All (map dest_Free all_vars_more) (Trueprop (P $ r_rec0)) ==> Trueprop (P $ r0);
val induct_prop =
(All (map dest_Free all_vars) (Trueprop (P_unit $ r_rec_unit0)),
Trueprop (P_unit $ r_unit0));
(*surjective*)
val surjective_prop =
let val args = map (fn (c,Free (_,T)) => mk_sel r0 (c,T)) all_named_vars_more
in r0 === mk_rec args 0 end;
(*cases*)
val cases_scheme_prop =
(All (map dest_Free all_vars_more)
(Trueprop (HOLogic.mk_eq (r0,r_rec0)) ==> Trueprop C))
==> Trueprop C;
val cases_prop =
(All (map dest_Free all_vars)
(Trueprop (HOLogic.mk_eq (r_unit0,r_rec_unit0)) ==> Trueprop C))
==> Trueprop C;
(*split*)
val split_meta_prop =
let val P = Free (Name.variant all_variants "P", rec_schemeT0-->Term.propT) in
Logic.mk_equals
(All [dest_Free r0] (P $ r0), All (map dest_Free all_vars_more) (P $ r_rec0))
end;
val split_object_prop =
let fun ALL vs t = List.foldr (fn ((v,T),t) => HOLogic.mk_all (v,T,t)) t vs
in (ALL [dest_Free r0] (P $ r0)) === (ALL (map dest_Free all_vars_more) (P $ r_rec0))
end;
val split_ex_prop =
let fun EX vs t = List.foldr (fn ((v,T),t) => HOLogic.mk_exists (v,T,t)) t vs
in (EX [dest_Free r0] (P $ r0)) === (EX (map dest_Free all_vars_more) (P $ r_rec0))
end;
(*equality*)
val equality_prop =
let
val s' = Free (rN ^ "'", rec_schemeT0)
fun mk_sel_eq (c,Free (_,T)) = mk_sel r0 (c,T) === mk_sel s' (c,T)
val seleqs = map mk_sel_eq all_named_vars_more
in All (map dest_Free [r0,s']) (Logic.list_implies (seleqs,r0 === s')) end;
(* 3rd stage: thms_thy *)
fun prove stndrd = quick_and_dirty_prove stndrd defs_thy;
val prove_standard = quick_and_dirty_prove true defs_thy;
fun prove_simp stndrd ss simps =
let val tac = simp_all_tac ss simps
in fn prop => prove stndrd [] prop (K tac) end;
val ss = get_simpset defs_thy;
fun sel_convs_prf () = map (prove_simp false ss
(sel_defs@ext_dest_convs)) sel_conv_props;
val sel_convs = timeit_msg "record sel_convs proof:" sel_convs_prf;
fun sel_convs_standard_prf () = map standard sel_convs
val sel_convs_standard =
timeit_msg "record sel_convs_standard proof:" sel_convs_standard_prf;
fun upd_convs_prf () =
map (prove_simp true ss (upd_defs@u_convs)) upd_conv_props;
val upd_convs = timeit_msg "record upd_convs proof:" upd_convs_prf;
val parent_induct = if null parents then [] else [#induct (hd (rev parents))];
fun induct_scheme_prf () = prove_standard [] induct_scheme_prop (fn _ =>
(EVERY [if null parent_induct
then all_tac else try_param_tac rN (hd parent_induct) 1,
try_param_tac rN ext_induct 1,
asm_simp_tac HOL_basic_ss 1]));
val induct_scheme = timeit_msg "record induct_scheme proof:" induct_scheme_prf;
fun induct_prf () =
let val (assm, concl) = induct_prop;
in
prove_standard [assm] concl (fn {prems, ...} =>
try_param_tac rN induct_scheme 1
THEN try_param_tac "more" @{thm unit.induct} 1
THEN resolve_tac prems 1)
end;
val induct = timeit_msg "record induct proof:" induct_prf;
fun surjective_prf () =
prove_standard [] surjective_prop (fn prems =>
(EVERY [try_param_tac rN induct_scheme 1,
simp_tac (ss addsimps sel_convs_standard) 1]))
val surjective = timeit_msg "record surjective proof:" surjective_prf;
fun cases_scheme_prf_opt () =
let
val (_$(Pvar$_)) = concl_of induct_scheme;
val ind = cterm_instantiate
[(cterm_of defs_thy Pvar, cterm_of defs_thy
(lambda w (HOLogic.imp$HOLogic.mk_eq(r0,w)$C)))]
induct_scheme;
in standard (ObjectLogic.rulify (mp OF [ind, refl])) end;
fun cases_scheme_prf_noopt () =
prove_standard [] cases_scheme_prop (fn _ =>
EVERY [asm_full_simp_tac (HOL_basic_ss addsimps [atomize_all, atomize_imp]) 1,
try_param_tac rN induct_scheme 1,
rtac impI 1,
REPEAT (etac allE 1),
etac mp 1,
rtac refl 1])
val cases_scheme_prf = quick_and_dirty_prf cases_scheme_prf_noopt cases_scheme_prf_opt;
val cases_scheme = timeit_msg "record cases_scheme proof:" cases_scheme_prf;
fun cases_prf () =
prove_standard [] cases_prop (fn _ =>
try_param_tac rN cases_scheme 1
THEN simp_all_tac HOL_basic_ss [unit_all_eq1]);
val cases = timeit_msg "record cases proof:" cases_prf;
fun split_meta_prf () =
prove false [] split_meta_prop (fn _ =>
EVERY [rtac equal_intr_rule 1, Goal.norm_hhf_tac 1,
etac meta_allE 1, atac 1,
rtac (prop_subst OF [surjective]) 1,
REPEAT (etac meta_allE 1), atac 1]);
val split_meta = timeit_msg "record split_meta proof:" split_meta_prf;
val split_meta_standard = standard split_meta;
fun split_object_prf_opt () =
let
val cPI= cterm_of defs_thy (lambda r0 (Trueprop (P$r0)));
val (_$Abs(_,_,P$_)) = fst (Logic.dest_equals (concl_of split_meta_standard));
val cP = cterm_of defs_thy P;
val split_meta' = cterm_instantiate [(cP,cPI)] split_meta_standard;
val (l,r) = HOLogic.dest_eq (HOLogic.dest_Trueprop split_object_prop);
val cl = cterm_of defs_thy (HOLogic.mk_Trueprop l);
val cr = cterm_of defs_thy (HOLogic.mk_Trueprop r);
val thl = assume cl (*All r. P r*) (* 1 *)
|> obj_to_meta_all (*!!r. P r*)
|> equal_elim split_meta' (*!!n m more. P (ext n m more)*)
|> meta_to_obj_all (*All n m more. P (ext n m more)*) (* 2*)
|> implies_intr cl (* 1 ==> 2 *)
val thr = assume cr (*All n m more. P (ext n m more)*)
|> obj_to_meta_all (*!!n m more. P (ext n m more)*)
|> equal_elim (symmetric split_meta') (*!!r. P r*)
|> meta_to_obj_all (*All r. P r*)
|> implies_intr cr (* 2 ==> 1 *)
in standard (thr COMP (thl COMP iffI)) end;
fun split_object_prf_noopt () =
prove_standard [] split_object_prop (fn _ =>
EVERY [rtac iffI 1,
REPEAT (rtac allI 1), etac allE 1, atac 1,
rtac allI 1, rtac induct_scheme 1,REPEAT (etac allE 1),atac 1]);
val split_object_prf = quick_and_dirty_prf split_object_prf_noopt split_object_prf_opt;
val split_object = timeit_msg "record split_object proof:" split_object_prf;
fun split_ex_prf () =
prove_standard [] split_ex_prop (fn _ =>
EVERY [rtac iffI 1,
etac exE 1,
simp_tac (HOL_basic_ss addsimps [split_meta_standard]) 1,
ex_inst_tac 1,
(*REPEAT (rtac exI 1),*)
atac 1,
REPEAT (etac exE 1),
rtac exI 1,
atac 1]);
val split_ex = timeit_msg "record split_ex proof:" split_ex_prf;
fun equality_tac thms =
let val (s'::s::eqs) = rev thms;
val ss' = ss addsimps (s'::s::sel_convs_standard);
val eqs' = map (simplify ss') eqs;
in simp_tac (HOL_basic_ss addsimps (s'::s::eqs')) 1 end;
fun equality_prf () = prove_standard [] equality_prop (fn {context, ...} =>
fn st => let val [s, s'] = map #1 (rev (Tactic.innermost_params 1 st)) in
st |> (res_inst_tac context [((rN, 0), s)] cases_scheme 1
THEN res_inst_tac context [((rN, 0), s')] cases_scheme 1
THEN (METAHYPS equality_tac 1))
(* simp_all_tac ss (sel_convs) would also work but is less efficient *)
end);
val equality = timeit_msg "record equality proof:" equality_prf;
val ((([sel_convs',upd_convs',sel_defs',upd_defs',[split_meta',split_object',split_ex'],derived_defs'],
[surjective',equality']),[induct_scheme',induct',cases_scheme',cases']), thms_thy) =
defs_thy
|> (PureThy.add_thmss o map (Thm.no_attributes o apfst Binding.name))
[("select_convs", sel_convs_standard),
("update_convs", upd_convs),
("select_defs", sel_defs),
("update_defs", upd_defs),
("splits", [split_meta_standard,split_object,split_ex]),
("defs", derived_defs)]
||>> (PureThy.add_thms o map (Thm.no_attributes o apfst Binding.name))
[("surjective", surjective),
("equality", equality)]
||>> (PureThy.add_thms o (map o apfst o apfst) Binding.name)
[(("induct_scheme", induct_scheme), induct_type_global (suffix schemeN name)),
(("induct", induct), induct_type_global name),
(("cases_scheme", cases_scheme), cases_type_global (suffix schemeN name)),
(("cases", cases), cases_type_global name)];
val sel_upd_simps = sel_convs' @ upd_convs';
val iffs = [ext_inject]
val final_thy =
thms_thy
|> (snd oo PureThy.add_thmss)
[((Binding.name "simps", sel_upd_simps),
[Simplifier.simp_add, Nitpick_Const_Simp_Thms.add]),
((Binding.name "iffs", iffs), [iff_add])]
|> put_record name (make_record_info args parent fields extension induct_scheme')
|> put_sel_upd (names @ [full_moreN]) sel_upd_simps
|> add_record_equalities extension_id equality'
|> add_extinjects ext_inject
|> add_extsplit extension_name ext_split
|> add_record_splits extension_id (split_meta',split_object',split_ex',induct_scheme')
|> add_extfields extension_name (fields @ [(full_moreN,moreT)])
|> add_fieldext (extension_name,snd extension) (names @ [full_moreN])
|> Sign.parent_path;
in final_thy
end;
(* add_record *)
(*we do all preparations and error checks here, deferring the real
work to record_definition*)
fun gen_add_record prep_typ prep_raw_parent quiet_mode (params, bname) raw_parent raw_fields thy =
let
val _ = Theory.requires thy "Record" "record definitions";
val _ = if quiet_mode then () else writeln ("Defining record " ^ quote bname ^ " ...");
val ctxt = ProofContext.init thy;
(* parents *)
fun prep_inst T = fst (cert_typ ctxt T []);
val parent = Option.map (apfst (map prep_inst) o prep_raw_parent ctxt) raw_parent
handle ERROR msg => cat_error msg ("The error(s) above in parent record specification");
val parents = add_parents thy parent [];
val init_env =
(case parent of
NONE => []
| SOME (types, _) => List.foldr OldTerm.add_typ_tfrees [] types);
(* fields *)
fun prep_field (c, raw_T, mx) env =
let val (T, env') = prep_typ ctxt raw_T env handle ERROR msg =>
cat_error msg ("The error(s) above occured in record field " ^ quote c)
in ((c, T, mx), env') end;
val (bfields, envir) = fold_map prep_field raw_fields init_env;
val envir_names = map fst envir;
(* args *)
val defaultS = Sign.defaultS thy;
val args = map (fn x => (x, AList.lookup (op =) envir x |> the_default defaultS)) params;
(* errors *)
val name = Sign.full_bname thy bname;
val err_dup_record =
if is_none (get_record thy name) then []
else ["Duplicate definition of record " ^ quote name];
val err_dup_parms =
(case duplicates (op =) params of
[] => []
| dups => ["Duplicate parameter(s) " ^ commas dups]);
val err_extra_frees =
(case subtract (op =) params envir_names of
[] => []
| extras => ["Extra free type variable(s) " ^ commas extras]);
val err_no_fields = if null bfields then ["No fields present"] else [];
val err_dup_fields =
(case duplicates (op =) (map #1 bfields) of
[] => []
| dups => ["Duplicate field(s) " ^ commas_quote dups]);
val err_bad_fields =
if forall (not_equal moreN o #1) bfields then []
else ["Illegal field name " ^ quote moreN];
val err_dup_sorts =
(case duplicates (op =) envir_names of
[] => []
| dups => ["Inconsistent sort constraints for " ^ commas dups]);
val errs =
err_dup_record @ err_dup_parms @ err_extra_frees @ err_no_fields @
err_dup_fields @ err_bad_fields @ err_dup_sorts;
in
if null errs then () else error (cat_lines errs) ;
thy |> record_definition (args, bname) parent parents bfields
end
handle ERROR msg => cat_error msg ("Failed to define record " ^ quote bname);
val add_record = gen_add_record read_typ read_raw_parent;
val add_record_i = gen_add_record cert_typ (K I);
(* setup theory *)
val setup =
Sign.add_trfuns ([], parse_translation, [], []) #>
Sign.add_advanced_trfuns ([], adv_parse_translation, [], []) #>
Simplifier.map_simpset (fn ss =>
ss addsimprocs [record_simproc, record_upd_simproc, record_eq_simproc]);
(* outer syntax *)
local structure P = OuterParse and K = OuterKeyword in
val record_decl =
P.type_args -- P.name --
(P.$$$ "=" |-- Scan.option (P.typ --| P.$$$ "+") -- Scan.repeat1 P.const);
val _ =
OuterSyntax.command "record" "define extensible record" K.thy_decl
(record_decl >> (fn (x, (y, z)) => Toplevel.theory (add_record false x y z)));
end;
end;
structure BasicRecordPackage: BASIC_RECORD_PACKAGE = RecordPackage;
open BasicRecordPackage;