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(* 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 lookup_quot_thm_quotients: Proof.context -> thm -> 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_relator_eq_onp_rules: Proof.context -> thm list
val get_reflexivity_rules: Proof.context -> thm list
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 add_no_code_type: string -> Context.generic -> Context.generic
val is_no_code_type: Proof.context -> string -> bool
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 get_no_code_types : Proof.context -> unit Symtab.table
end
structure Lifting_Info: LIFTING_INFO =
struct
open Lifting_Util
(* context data *)
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}
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 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 eq_option pcr_eq (pcr_info1, pcr_info2)
fun join_restore_data key (rd1:restore_data, rd2) =
if pointer_eq (rd1, rd2) then raise Symtab.SAME else
if not (quotient_eq (#quotient rd1, #quotient rd2)) then raise Symtab.DUP key else
{ quotient = #quotient rd1,
transfer_rules = Item_Net.merge (#transfer_rules rd1, #transfer_rules rd2)}
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,
no_code_types : unit 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,
no_code_types = Symtab.empty
}
val extend = I
fun merge
( { quot_maps = qm1, quotients = q1, reflexivity_rules = rr1, relator_distr_data = rdd1,
restore_data = rd1, no_code_types = nct1 },
{ quot_maps = qm2, quotients = q2, reflexivity_rules = rr2, relator_distr_data = rdd2,
restore_data = rd2, no_code_types = nct2 } ) =
{ 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.join join_restore_data (rd1, rd2),
no_code_types = Symtab.merge (K true) (nct1, nct2)
}
)
fun map_data f1 f2 f3 f4 f5 f6
{ quot_maps, quotients, reflexivity_rules, relator_distr_data, restore_data, no_code_types } =
{ 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,
no_code_types = f6 no_code_types
}
fun map_quot_maps f = map_data f I I I I I
fun map_quotients f = map_data I f I I I I
fun map_reflexivity_rules f = map_data I I f I I I
fun map_relator_distr_data f = map_data I I I f I I
fun map_restore_data f = map_data I I I I f I
fun map_no_code_types f = map_data I 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
val get_no_code_types' = #no_code_types o Data.get
val get_quot_maps = get_quot_maps' o Context.Proof
val get_quotients = get_quotients' o Context.Proof
val get_relator_distr_data = get_relator_distr_data' o Context.Proof
val get_restore_data = get_restore_data' o Context.Proof
val get_no_code_types = get_no_code_types' o Context.Proof
(* 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 = Thm.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 context =
let
val _ = Context.cases (K ()) (quot_map_thm_sanity_check rel_quot_thm) context
val rel_quot_thm_concl = (Logic.strip_imp_concl o Thm.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 = Thm.trim_context rel_quot_thm}
in
Data.map (map_quot_maps (Symtab.update (relatorT_name, minfo))) context
end
val _ =
Theory.setup
(Attrib.setup \<^binding>\<open>quot_map\<close> (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 (Thm.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 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
|> Option.map (transform_quotient (Morphism.transfer_morphism' ctxt))
fun lookup_quot_thm_quotients ctxt quot_thm =
let
val (_, qtyp) = quot_thm_rty_qty quot_thm
val qty_full_name = (fst o dest_Type) qtyp
fun compare_data (data:quotient) = Thm.eq_thm_prop (#quot_thm data, quot_thm)
in
case lookup_quotients ctxt qty_full_name of
SOME quotient => if compare_data quotient then SOME quotient else NONE
| NONE => NONE
end
fun update_quotients type_name qinfo context =
let val qinfo' = transform_quotient Morphism.trim_context_morphism qinfo
in Data.map (map_quotients (Symtab.update (type_name, qinfo'))) context end
fun delete_quotients quot_thm context =
let
val (_, qtyp) = quot_thm_rty_qty quot_thm
val qty_full_name = (fst o dest_Type) qtyp
in
if is_some (lookup_quot_thm_quotients (Context.proof_of context) quot_thm)
then Data.map (map_quotients (Symtab.delete qty_full_name)) context
else context
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:", Thm.pretty_thm ctxt quot_thm] @
(case pcr_info of
NONE => []
| SOME {pcrel_def, pcr_cr_eq, ...} =>
[Pretty.str "pcrel_def thm:", Thm.pretty_thm ctxt pcrel_def,
Pretty.str "pcr_cr_eq thm:", Thm.pretty_thm ctxt pcr_cr_eq])))
in
map prt_quot (Symtab.dest (get_quotients ctxt))
|> Pretty.big_list "quotients:"
|> Pretty.writeln
end
val _ =
Theory.setup
(Attrib.setup \<^binding>\<open>quot_del\<close> (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 context =
Data.map (map_restore_data (Symtab.update (bundle_name, restore_data))) context
fun init_restore_data bundle_name qinfo context =
update_restore_data bundle_name { quotient = qinfo, transfer_rules = Thm.full_rules } context
fun add_transfer_rules_in_restore_data bundle_name transfer_rules context =
(case Symtab.lookup (get_restore_data' context) 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) } context
| NONE => error ("The restore data " ^ quote bundle_name ^ " is not defined."))
(* theorems that a relator of an eq_onp is an eq_onp of the corresponding predicate *)
fun get_relator_eq_onp_rules ctxt =
map safe_mk_meta_eq (rev (Named_Theorems.get ctxt \<^named_theorems>\<open>relator_eq_onp\<close>))
(* info about reflexivity rules *)
fun get_reflexivity_rules ctxt =
Item_Net.content (get_reflexivity_rules' (Context.Proof ctxt))
|> map (Thm.transfer' ctxt)
fun add_reflexivity_rule thm =
Data.map (map_reflexivity_rules (Item_Net.update (Thm.trim_context thm)))
val add_reflexivity_rule_attribute = Thm.declaration_attribute add_reflexivity_rule
(* 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>\<open>less_eq\<close> dummyT
val prems_pairs = map (dest_less_eq o HOLogic.dest_Trueprop) (Thm.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
|> Thm.concl_of
|> HOLogic.dest_Trueprop
|> dest_less_eq
|> apply2 (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_reflexivity_rules mono_rule context =
let
val ctxt = Context.proof_of context
val thy = Context.theory_of context
fun find_eq_rule thm =
let
val concl_rhs = (hd o get_args 1 o HOLogic.dest_Trueprop o Thm.concl_of) thm
val rules = Transfer.retrieve_relator_eq ctxt concl_rhs
in
find_first (fn th => Pattern.matches thy (concl_rhs,
(fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.concl_of) th)) rules
end
val eq_rule = find_eq_rule mono_rule;
val eq_rule = if is_some eq_rule then the eq_rule else error
"No corresponding rule that the relator preserves equality was found."
in
context
|> add_reflexivity_rule (Drule.zero_var_indexes (@{thm ord_le_eq_trans} OF [mono_rule, eq_rule]))
|> add_reflexivity_rule
(Drule.zero_var_indexes (@{thm ord_eq_le_trans} OF [sym OF [eq_rule], mono_rule]))
end
fun add_mono_rule mono_rule context =
let
val pol_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 Thm.concl_of) pol_mono_rule
in
if Symtab.defined (get_relator_distr_data' context) mono_ruleT_name
then
(if Context_Position.is_visible_generic context then
warning ("Monotonicity rule for type " ^ quote mono_ruleT_name ^ " is already_defined.")
else (); context)
else
let
val neg_mono_rule = negate_mono_rule pol_mono_rule
val relator_distr_data = {pos_mono_rule = pol_mono_rule, neg_mono_rule = neg_mono_rule,
pos_distr_rules = [], neg_distr_rules = []}
in
context
|> Data.map (map_relator_distr_data (Symtab.update (mono_ruleT_name, relator_distr_data)))
|> add_reflexivity_rules mono_rule
end
end;
local
fun add_distr_rule update_entry distr_rule context =
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 Thm.concl_of) distr_rule
in
if Symtab.defined (get_relator_distr_data' context) distr_ruleT_name then
Data.map (map_relator_distr_data (Symtab.map_entry distr_ruleT_name (update_entry distr_rule)))
context
else error "The monotonicity 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 context =
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 context
end
handle THM _ => error "Combining of the distr. rule and the monotonicity rule together has failed."
fun add_neg_distr_rule distr_rule context =
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 context
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 context =
let
val pos_distr_rule = @{thm eq_refl} OF [distr_rule]
val neg_distr_rule = eq_refl2 OF [distr_rule]
in
context
|> 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)) (Thm.prems_of rule)
val concl = (perhaps (try HOLogic.dest_Trueprop)) (Thm.concl_of rule);
val (lhs, rhs) =
(case concl of
Const (\<^const_name>\<open>less_eq\<close>, _) $ (lhs as Const (\<^const_name>\<open>relcompp\<close>,_) $ _ $ _) $ rhs =>
(lhs, rhs)
| Const (\<^const_name>\<open>less_eq\<close>, _) $ rhs $ (lhs as Const (\<^const_name>\<open>relcompp\<close>,_) $ _ $ _) =>
(lhs, rhs)
| Const (\<^const_name>\<open>HOL.eq\<close>, _) $ (lhs as Const (\<^const_name>\<open>relcompp\<close>,_) $ _ $ _) $ 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 (\<^const_name>\<open>relcompp\<close>, _) $ 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 context =
let
val _ = sanity_check distr_rule
val concl = (perhaps (try HOLogic.dest_Trueprop)) (Thm.concl_of distr_rule)
in
(case concl of
Const (\<^const_name>\<open>less_eq\<close>, _) $ (Const (\<^const_name>\<open>relcompp\<close>,_) $ _ $ _) $ _ =>
add_pos_distr_rule distr_rule context
| Const (\<^const_name>\<open>less_eq\<close>, _) $ _ $ (Const (\<^const_name>\<open>relcompp\<close>,_) $ _ $ _) =>
add_neg_distr_rule distr_rule context
| Const (\<^const_name>\<open>HOL.eq\<close>, _) $ (Const (\<^const_name>\<open>relcompp\<close>,_) $ _ $ _) $ _ =>
add_eq_distr_rule distr_rule context)
end
end
fun get_distr_rules_raw context =
Symtab.fold (fn (_, {pos_distr_rules, neg_distr_rules, ...}) => fn rules =>
pos_distr_rules @ neg_distr_rules @ rules)
(get_relator_distr_data' context) []
|> map (Thm.transfer'' context)
fun get_mono_rules_raw context =
Symtab.fold (fn (_, {pos_mono_rule, neg_mono_rule, ...}) => fn rules =>
[pos_mono_rule, neg_mono_rule] @ rules)
(get_relator_distr_data' context) []
|> map (Thm.transfer'' context)
val lookup_relator_distr_data = Symtab.lookup o get_relator_distr_data
val _ =
Theory.setup
(Attrib.setup \<^binding>\<open>relator_mono\<close> (Scan.succeed (Thm.declaration_attribute add_mono_rule))
"declaration of relator's monotonicity"
#> Attrib.setup \<^binding>\<open>relator_distr\<close> (Scan.succeed (Thm.declaration_attribute add_distr_rule))
"declaration of relator's distributivity over OO"
#> Global_Theory.add_thms_dynamic
(\<^binding>\<open>relator_distr_raw\<close>, get_distr_rules_raw)
#> Global_Theory.add_thms_dynamic
(\<^binding>\<open>relator_mono_raw\<close>, get_mono_rules_raw))
(* no_code types *)
fun add_no_code_type type_name context =
Data.map (map_no_code_types (Symtab.update (type_name, ()))) context;
fun is_no_code_type context type_name = (Symtab.defined o get_no_code_types) context type_name
(* setup fixed eq_onp rules *)
val _ = Context.>>
(fold (Named_Theorems.add_thm \<^named_theorems>\<open>relator_eq_onp\<close> o
Transfer.prep_transfer_domain_thm \<^context>)
@{thms composed_equiv_rel_eq_onp composed_equiv_rel_eq_eq_onp})
(* setup fixed reflexivity rules *)
val _ = Context.>> (fold add_reflexivity_rule
@{thms order_refl[of "(=)"] eq_onp_le_eq Quotient_composition_le_eq Quotient_composition_ge_eq
bi_unique_OO bi_total_OO right_unique_OO right_total_OO left_unique_OO left_total_OO})
(* outer syntax commands *)
val _ =
Outer_Syntax.command \<^command_keyword>\<open>print_quot_maps\<close> "print quotient map functions"
(Scan.succeed (Toplevel.keep (print_quot_maps o Toplevel.context_of)))
val _ =
Outer_Syntax.command \<^command_keyword>\<open>print_quotients\<close> "print quotients"
(Scan.succeed (Toplevel.keep (print_quotients o Toplevel.context_of)))
end
¤ Dauer der Verarbeitung: 0.4 Sekunden
(vorverarbeitet)
¤
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