(* Title: HOL/Tools/Lifting/lifting_info.ML
Author: Ondrej Kuncar
Context data for the lifting package.
*)
signature LIFTING_INFO =
sig
type quot_map = {rel_quot_thm: thm}
val lookup_quot_maps: Proof.context -> string -> quot_map option
val print_quot_maps: Proof.context -> unit
type pcr = {pcrel_def: thm, pcr_cr_eq: thm}
type quotient = {quot_thm: thm, pcr_info: pcr option}
val pcr_eq: pcr * pcr -> bool
val quotient_eq: quotient * quotient -> bool
val transform_quotient: morphism -> quotient -> quotient
val lookup_quotients: Proof.context -> string -> quotient option
val update_quotients: string -> quotient -> Context.generic -> Context.generic
val delete_quotients: thm -> Context.generic -> Context.generic
val print_quotients: Proof.context -> unit
type restore_data = {quotient : quotient, transfer_rules: thm Item_Net.T}
val lookup_restore_data: Proof.context -> string -> restore_data option
val init_restore_data: string -> quotient -> Context.generic -> Context.generic
val add_transfer_rules_in_restore_data: string -> thm Item_Net.T -> Context.generic -> Context.generic
val get_invariant_commute_rules: Proof.context -> thm list
val get_reflexivity_rules: Proof.context -> thm list
val add_reflexivity_rule_raw_attribute: attribute
val add_reflexivity_rule_attribute: attribute
type relator_distr_data = {pos_mono_rule: thm, neg_mono_rule: thm,
pos_distr_rules: thm list, neg_distr_rules: thm list}
val lookup_relator_distr_data: Proof.context -> string -> relator_distr_data option
val get_quot_maps : Proof.context -> quot_map Symtab.table
val get_quotients : Proof.context -> quotient Symtab.table
val get_relator_distr_data : Proof.context -> relator_distr_data Symtab.table
val get_restore_data : Proof.context -> restore_data Symtab.table
val setup: theory -> theory
end
structure Lifting_Info: LIFTING_INFO =
struct
open Lifting_Util
(** data container **)
type quot_map = {rel_quot_thm: thm}
type pcr = {pcrel_def: thm, pcr_cr_eq: thm}
type quotient = {quot_thm: thm, pcr_info: pcr option}
type relator_distr_data = {pos_mono_rule: thm, neg_mono_rule: thm,
pos_distr_rules: thm list, neg_distr_rules: thm list}
type restore_data = {quotient : quotient, transfer_rules: thm Item_Net.T}
structure Data = Generic_Data
(
type T =
{ quot_maps : quot_map Symtab.table,
quotients : quotient Symtab.table,
reflexivity_rules : thm Item_Net.T,
relator_distr_data : relator_distr_data Symtab.table,
restore_data : restore_data Symtab.table
}
val empty =
{ quot_maps = Symtab.empty,
quotients = Symtab.empty,
reflexivity_rules = Thm.full_rules,
relator_distr_data = Symtab.empty,
restore_data = Symtab.empty
}
val extend = I
fun merge
( { quot_maps = qm1, quotients = q1, reflexivity_rules = rr1, relator_distr_data = rdd1,
restore_data = rd1 },
{ quot_maps = qm2, quotients = q2, reflexivity_rules = rr2, relator_distr_data = rdd2,
restore_data = rd2 } ) =
{ quot_maps = Symtab.merge (K true) (qm1, qm2),
quotients = Symtab.merge (K true) (q1, q2),
reflexivity_rules = Item_Net.merge (rr1, rr2),
relator_distr_data = Symtab.merge (K true) (rdd1, rdd2),
restore_data = Symtab.merge (K true) (rd1, rd2) }
)
fun map_data f1 f2 f3 f4 f5
{ quot_maps, quotients, reflexivity_rules, relator_distr_data, restore_data } =
{ quot_maps = f1 quot_maps,
quotients = f2 quotients,
reflexivity_rules = f3 reflexivity_rules,
relator_distr_data = f4 relator_distr_data,
restore_data = f5 restore_data }
fun map_quot_maps f = map_data f I I I I
fun map_quotients f = map_data I f I I I
fun map_reflexivity_rules f = map_data I I f I I
fun map_relator_distr_data f = map_data I I I f I
fun map_restore_data f = map_data I I I I f
val get_quot_maps' = #quot_maps o Data.get
val get_quotients' = #quotients o Data.get
val get_reflexivity_rules' = #reflexivity_rules o Data.get
val get_relator_distr_data' = #relator_distr_data o Data.get
val get_restore_data' = #restore_data o Data.get
fun get_quot_maps ctxt = get_quot_maps' (Context.Proof ctxt)
fun get_quotients ctxt = get_quotients' (Context.Proof ctxt)
fun get_relator_distr_data ctxt = get_relator_distr_data' (Context.Proof ctxt)
fun get_restore_data ctxt = get_restore_data' (Context.Proof ctxt)
(* info about Quotient map theorems *)
val lookup_quot_maps = Symtab.lookup o get_quot_maps
fun quot_map_thm_sanity_check rel_quot_thm ctxt =
let
fun quot_term_absT ctxt quot_term =
let
val (_, abs, _, _) = (dest_Quotient o HOLogic.dest_Trueprop) quot_term
handle TERM (_, [t]) => error (Pretty.string_of (Pretty.block
[Pretty.str "The Quotient map theorem is not in the right form.",
Pretty.brk 1,
Pretty.str "The following term is not the Quotient predicate:",
Pretty.brk 1,
Syntax.pretty_term ctxt t]))
in
fastype_of abs
end
val ((_, [rel_quot_thm_fixed]), ctxt') = Variable.importT [rel_quot_thm] ctxt
val rel_quot_thm_prop = prop_of rel_quot_thm_fixed
val rel_quot_thm_concl = Logic.strip_imp_concl rel_quot_thm_prop
val rel_quot_thm_prems = Logic.strip_imp_prems rel_quot_thm_prop;
val concl_absT = quot_term_absT ctxt' rel_quot_thm_concl
val concl_tfrees = Term.add_tfree_namesT (concl_absT) []
val prems_tfrees = fold (fn typ => fn list => Term.add_tfree_namesT (quot_term_absT ctxt' typ) list)
rel_quot_thm_prems []
val extra_prem_tfrees =
case subtract (op =) concl_tfrees prems_tfrees of
[] => []
| extras => [Pretty.block ([Pretty.str "Extra type variables in the premises:",
Pretty.brk 1] @
((Pretty.commas o map (Pretty.str o quote)) extras) @
[Pretty.str "."])]
val errs = extra_prem_tfrees
in
if null errs then () else error (cat_lines (["Sanity check of the quotient map theorem failed:",""]
@ (map Pretty.string_of errs)))
end
fun add_quot_map rel_quot_thm ctxt =
let
val _ = Context.cases (K ()) (quot_map_thm_sanity_check rel_quot_thm) ctxt
val rel_quot_thm_concl = (Logic.strip_imp_concl o prop_of) rel_quot_thm
val (_, abs, _, _) = (dest_Quotient o HOLogic.dest_Trueprop) rel_quot_thm_concl
val relatorT_name = (fst o dest_Type o fst o dest_funT o fastype_of) abs
val minfo = {rel_quot_thm = rel_quot_thm}
in
Data.map (map_quot_maps (Symtab.update (relatorT_name, minfo))) ctxt
end
val quot_map_attribute_setup =
Attrib.setup @{binding quot_map} (Scan.succeed (Thm.declaration_attribute add_quot_map))
"declaration of the Quotient map theorem"
fun print_quot_maps ctxt =
let
fun prt_map (ty_name, {rel_quot_thm}) =
Pretty.block (separate (Pretty.brk 2)
[Pretty.str "type:",
Pretty.str ty_name,
Pretty.str "quot. theorem:",
Syntax.pretty_term ctxt (prop_of rel_quot_thm)])
in
map prt_map (Symtab.dest (get_quot_maps ctxt))
|> Pretty.big_list "maps for type constructors:"
|> Pretty.writeln
end
(* info about quotient types *)
fun pcr_eq ({pcrel_def = pcrel_def1, pcr_cr_eq = pcr_cr_eq1},
{pcrel_def = pcrel_def2, pcr_cr_eq = pcr_cr_eq2}) =
Thm.eq_thm (pcrel_def1, pcrel_def2) andalso Thm.eq_thm (pcr_cr_eq1, pcr_cr_eq2)
fun option_eq _ (NONE,NONE) = true
| option_eq _ (NONE,_) = false
| option_eq _ (_,NONE) = false
| option_eq cmp (SOME x, SOME y) = cmp (x,y);
fun quotient_eq ({quot_thm = quot_thm1, pcr_info = pcr_info1},
{quot_thm = quot_thm2, pcr_info = pcr_info2}) =
Thm.eq_thm (quot_thm1, quot_thm2) andalso option_eq pcr_eq (pcr_info1, pcr_info2)
fun transform_pcr_info phi {pcrel_def, pcr_cr_eq} =
{pcrel_def = Morphism.thm phi pcrel_def, pcr_cr_eq = Morphism.thm phi pcr_cr_eq}
fun transform_quotient phi {quot_thm, pcr_info} =
{quot_thm = Morphism.thm phi quot_thm, pcr_info = Option.map (transform_pcr_info phi) pcr_info}
fun lookup_quotients ctxt type_name = Symtab.lookup (get_quotients ctxt) type_name
fun update_quotients type_name qinfo ctxt =
Data.map (map_quotients (Symtab.update (type_name, qinfo))) ctxt
fun delete_quotients quot_thm ctxt =
let
val (_, qtyp) = quot_thm_rty_qty quot_thm
val qty_full_name = (fst o dest_Type) qtyp
val symtab = get_quotients' ctxt
fun compare_data (_, data:quotient) = Thm.eq_thm_prop (#quot_thm data, quot_thm)
in
if Symtab.member compare_data symtab (qty_full_name, quot_thm)
then Data.map (map_quotients (Symtab.delete qty_full_name)) ctxt
else ctxt
end
fun print_quotients ctxt =
let
fun prt_quot (qty_name, {quot_thm, pcr_info}: quotient) =
Pretty.block (separate (Pretty.brk 2)
[Pretty.str "type:",
Pretty.str qty_name,
Pretty.str "quot. thm:",
Syntax.pretty_term ctxt (prop_of quot_thm),
Pretty.str "pcrel_def thm:",
option_fold (Pretty.str "-") ((Syntax.pretty_term ctxt) o prop_of o #pcrel_def) pcr_info,
Pretty.str "pcr_cr_eq thm:",
option_fold (Pretty.str "-") ((Syntax.pretty_term ctxt) o prop_of o #pcr_cr_eq) pcr_info])
in
map prt_quot (Symtab.dest (get_quotients ctxt))
|> Pretty.big_list "quotients:"
|> Pretty.writeln
end
val quot_del_attribute_setup =
Attrib.setup @{binding quot_del} (Scan.succeed (Thm.declaration_attribute delete_quotients))
"deletes the Quotient theorem"
(* data for restoring Transfer/Lifting context *)
fun lookup_restore_data ctxt bundle_name = Symtab.lookup (get_restore_data ctxt) bundle_name
fun update_restore_data bundle_name restore_data ctxt =
Data.map (map_restore_data (Symtab.update (bundle_name, restore_data))) ctxt
fun init_restore_data bundle_name qinfo ctxt =
update_restore_data bundle_name { quotient = qinfo, transfer_rules = Thm.full_rules } ctxt
fun add_transfer_rules_in_restore_data bundle_name transfer_rules ctxt =
case Symtab.lookup (get_restore_data' ctxt) bundle_name of
SOME restore_data => update_restore_data bundle_name { quotient = #quotient restore_data,
transfer_rules = Item_Net.merge ((#transfer_rules restore_data), transfer_rules) } ctxt
| NONE => error ("The restore data " ^ quote bundle_name ^ " is not defined.")
(* theorems that a relator of an invariant is an invariant of the corresponding predicate *)
structure Invariant_Commute = Named_Thms
(
val name = @{binding invariant_commute}
val description = "theorems that a relator of an invariant is an invariant of the corresponding predicate"
)
fun get_invariant_commute_rules ctxt = map safe_mk_meta_eq (Invariant_Commute.get ctxt)
(* info about reflexivity rules *)
fun get_reflexivity_rules ctxt = Item_Net.content (get_reflexivity_rules' (Context.Proof ctxt))
(* Conversion to create a reflp' variant of a reflexivity rule *)
fun safe_reflp_conv ct =
Conv.try_conv (HOLogic.Trueprop_conv (Conv.rewr_conv (Thm.symmetric @{thm reflp'_def}))) ct
fun prep_reflp_conv ct = (
Conv.implies_conv safe_reflp_conv prep_reflp_conv
else_conv
safe_reflp_conv
else_conv
Conv.all_conv) ct
fun add_reflexivity_rule_raw thm = Data.map (map_reflexivity_rules (Item_Net.update thm))
val add_reflexivity_rule_raw_attribute = Thm.declaration_attribute add_reflexivity_rule_raw
fun add_reflexivity_rule thm = add_reflexivity_rule_raw thm #>
add_reflexivity_rule_raw (Conv.fconv_rule prep_reflp_conv thm)
val add_reflexivity_rule_attribute = Thm.declaration_attribute add_reflexivity_rule
val relfexivity_rule_setup =
let
val name = @{binding reflexivity_rule}
fun del_thm_raw thm = Data.map (map_reflexivity_rules (Item_Net.remove thm))
fun del_thm thm = del_thm_raw thm #>
del_thm_raw (Conv.fconv_rule prep_reflp_conv thm)
val del = Thm.declaration_attribute del_thm
val text = "rules that are used to prove that a relation is reflexive"
val content = Item_Net.content o get_reflexivity_rules'
in
Attrib.setup name (Attrib.add_del add_reflexivity_rule_attribute del) text
#> Global_Theory.add_thms_dynamic (name, content)
end
(* info about relator distributivity theorems *)
fun map_relator_distr_data' f1 f2 f3 f4
{pos_mono_rule, neg_mono_rule, pos_distr_rules, neg_distr_rules} =
{pos_mono_rule = f1 pos_mono_rule,
neg_mono_rule = f2 neg_mono_rule,
pos_distr_rules = f3 pos_distr_rules,
neg_distr_rules = f4 neg_distr_rules}
fun map_pos_mono_rule f = map_relator_distr_data' f I I I
fun map_neg_mono_rule f = map_relator_distr_data' I f I I
fun map_pos_distr_rules f = map_relator_distr_data' I I f I
fun map_neg_distr_rules f = map_relator_distr_data' I I I f
fun introduce_polarities rule =
let
val dest_less_eq = HOLogic.dest_bin @{const_name "less_eq"} dummyT
val prems_pairs = map (dest_less_eq o HOLogic.dest_Trueprop) (prems_of rule)
val equal_prems = filter op= prems_pairs
val _ = if null equal_prems then ()
else error "The rule contains reflexive assumptions."
val concl_pairs = rule
|> concl_of
|> HOLogic.dest_Trueprop
|> dest_less_eq
|> pairself (snd o strip_comb)
|> op~~
|> filter_out op=
val _ = if has_duplicates op= concl_pairs
then error "The rule contains duplicated variables in the conlusion." else ()
fun rewrite_prem prem_pair =
if member op= concl_pairs prem_pair
then HOLogic.Trueprop_conv (Conv.rewr_conv (Thm.symmetric @{thm POS_def}))
else if member op= concl_pairs (swap prem_pair)
then HOLogic.Trueprop_conv (Conv.rewr_conv (Thm.symmetric @{thm NEG_def}))
else error "The rule contains a non-relevant assumption."
fun rewrite_prems [] = Conv.all_conv
| rewrite_prems (x::xs) = Conv.implies_conv (rewrite_prem x) (rewrite_prems xs)
val rewrite_prems_conv = rewrite_prems prems_pairs
val rewrite_concl_conv =
Conv.concl_conv ~1 (HOLogic.Trueprop_conv (Conv.rewr_conv (Thm.symmetric @{thm POS_def})))
in
(Conv.fconv_rule (rewrite_prems_conv then_conv rewrite_concl_conv)) rule
end
handle
TERM _ => error "The rule has a wrong format."
| CTERM _ => error "The rule has a wrong format."
fun negate_mono_rule mono_rule =
let
val rewr_conv = HOLogic.Trueprop_conv (Conv.rewrs_conv [@{thm POS_NEG}, @{thm NEG_POS}])
in
Conv.fconv_rule (Conv.prems_conv ~1 rewr_conv then_conv Conv.concl_conv ~1 rewr_conv) mono_rule
end;
fun add_mono_rule mono_rule ctxt =
let
val mono_rule = introduce_polarities mono_rule
val mono_ruleT_name = (fst o dest_Type o fst o relation_types o fst o relation_types o snd o
dest_Const o head_of o HOLogic.dest_Trueprop o concl_of) mono_rule
val _ = if Symtab.defined (get_relator_distr_data' ctxt) mono_ruleT_name
then error ("Monotocity rule for type " ^ quote mono_ruleT_name ^ " is already_defined.")
else ()
val neg_mono_rule = negate_mono_rule mono_rule
val relator_distr_data = {pos_mono_rule = mono_rule, neg_mono_rule = neg_mono_rule,
pos_distr_rules = [], neg_distr_rules = []}
in
Data.map (map_relator_distr_data (Symtab.update (mono_ruleT_name, relator_distr_data))) ctxt
end;
local
fun add_distr_rule update_entry distr_rule ctxt =
let
val distr_ruleT_name = (fst o dest_Type o fst o relation_types o fst o relation_types o snd o
dest_Const o head_of o HOLogic.dest_Trueprop o concl_of) distr_rule
in
if Symtab.defined (get_relator_distr_data' ctxt) distr_ruleT_name then
Data.map (map_relator_distr_data (Symtab.map_entry distr_ruleT_name (update_entry distr_rule)))
ctxt
else error "The monoticity rule is not defined."
end
fun rewrite_concl_conv thm ctm =
Conv.concl_conv ~1 (HOLogic.Trueprop_conv (Conv.rewr_conv (Thm.symmetric thm))) ctm
handle CTERM _ => error "The rule has a wrong format."
in
fun add_pos_distr_rule distr_rule ctxt =
let
val distr_rule = Conv.fconv_rule (rewrite_concl_conv @{thm POS_def}) distr_rule
fun update_entry distr_rule data =
map_pos_distr_rules (cons (@{thm POS_trans} OF [distr_rule, #pos_mono_rule data])) data
in
add_distr_rule update_entry distr_rule ctxt
end
handle THM _ => error "Combining of the distr. rule and the monotonicity rule together has failed."
fun add_neg_distr_rule distr_rule ctxt =
let
val distr_rule = Conv.fconv_rule (rewrite_concl_conv @{thm NEG_def}) distr_rule
fun update_entry distr_rule data =
map_neg_distr_rules (cons (@{thm NEG_trans} OF [distr_rule, #neg_mono_rule data])) data
in
add_distr_rule update_entry distr_rule ctxt
end
handle THM _ => error "Combining of the distr. rule and the monotonicity rule together has failed."
end
local
val eq_refl2 = sym RS @{thm eq_refl}
in
fun add_eq_distr_rule distr_rule ctxt =
let
val pos_distr_rule = @{thm eq_refl} OF [distr_rule]
val neg_distr_rule = eq_refl2 OF [distr_rule]
in
ctxt
|> add_pos_distr_rule pos_distr_rule
|> add_neg_distr_rule neg_distr_rule
end
end;
local
fun sanity_check rule =
let
val assms = map (perhaps (try HOLogic.dest_Trueprop)) (prems_of rule)
val concl = (perhaps (try HOLogic.dest_Trueprop)) (concl_of rule);
val (lhs, rhs) = case concl of
Const ("Orderings.ord_class.less_eq", _) $ (lhs as Const ("Relation.relcompp",_) $ _ $ _) $ rhs =>
(lhs, rhs)
| Const ("Orderings.ord_class.less_eq", _) $ rhs $ (lhs as Const ("Relation.relcompp",_) $ _ $ _) =>
(lhs, rhs)
| Const ("HOL.eq", _) $ (lhs as Const ("Relation.relcompp",_) $ _ $ _) $ rhs => (lhs, rhs)
| _ => error "The rule has a wrong format."
val lhs_vars = Term.add_vars lhs []
val rhs_vars = Term.add_vars rhs []
val assms_vars = fold Term.add_vars assms [];
val _ = if has_duplicates op= lhs_vars then error "Left-hand side has variable duplicates" else ()
val _ = if subset op= (rhs_vars, lhs_vars) then ()
else error "Extra variables in the right-hand side of the rule"
val _ = if subset op= (assms_vars, lhs_vars) then ()
else error "Extra variables in the assumptions of the rule"
val rhs_args = (snd o strip_comb) rhs;
fun check_comp t = case t of
Const ("Relation.relcompp", _) $ Var (_, _) $ Var (_,_) => ()
| _ => error "There is an argument on the rhs that is not a composition."
val _ = map check_comp rhs_args
in
()
end
in
fun add_distr_rule distr_rule ctxt =
let
val _ = sanity_check distr_rule
val concl = (perhaps (try HOLogic.dest_Trueprop)) (concl_of distr_rule)
in
case concl of
Const ("Orderings.ord_class.less_eq", _) $ (Const ("Relation.relcompp",_) $ _ $ _) $ _ =>
add_pos_distr_rule distr_rule ctxt
| Const ("Orderings.ord_class.less_eq", _) $ _ $ (Const ("Relation.relcompp",_) $ _ $ _) =>
add_neg_distr_rule distr_rule ctxt
| Const ("HOL.eq", _) $ (Const ("Relation.relcompp",_) $ _ $ _) $ _ =>
add_eq_distr_rule distr_rule ctxt
end
end
fun get_distr_rules_raw ctxt = Symtab.fold
(fn (_, {pos_distr_rules, neg_distr_rules, ...}) => fn rules => pos_distr_rules @ neg_distr_rules @ rules)
(get_relator_distr_data' ctxt) []
fun get_mono_rules_raw ctxt = Symtab.fold
(fn (_, {pos_mono_rule, neg_mono_rule, ...}) => fn rules => [pos_mono_rule, neg_mono_rule] @ rules)
(get_relator_distr_data' ctxt) []
val lookup_relator_distr_data = Symtab.lookup o get_relator_distr_data
val relator_distr_attribute_setup =
Attrib.setup @{binding relator_mono} (Scan.succeed (Thm.declaration_attribute add_mono_rule))
"declaration of relator's monoticity"
#> Attrib.setup @{binding relator_distr} (Scan.succeed (Thm.declaration_attribute add_distr_rule))
"declaration of relator's distributivity over OO"
#> Global_Theory.add_thms_dynamic
(@{binding relator_distr_raw}, get_distr_rules_raw)
#> Global_Theory.add_thms_dynamic
(@{binding relator_mono_raw}, get_mono_rules_raw)
(* theory setup *)
val setup =
quot_map_attribute_setup
#> quot_del_attribute_setup
#> Invariant_Commute.setup
#> relfexivity_rule_setup
#> relator_distr_attribute_setup
(* outer syntax commands *)
val _ =
Outer_Syntax.improper_command @{command_spec "print_quot_maps"} "print quotient map functions"
(Scan.succeed (Toplevel.keep (print_quot_maps o Toplevel.context_of)))
val _ =
Outer_Syntax.improper_command @{command_spec "print_quotients"} "print quotients"
(Scan.succeed (Toplevel.keep (print_quotients o Toplevel.context_of)))
end