(* Title: HOL/Tools/Lifting/lifting_setup.ML
Author: Ondrej Kuncar
Setting up the lifting infrastructure.
*)
signature LIFTING_SETUP =
sig
exception SETUP_LIFTING_INFR of string
val setup_by_quotient: bool -> thm -> thm option -> thm option -> local_theory -> local_theory
val setup_by_typedef_thm: bool -> thm -> local_theory -> local_theory
val lifting_restore: Lifting_Info.quotient -> Context.generic -> Context.generic
end
structure Lifting_Setup: LIFTING_SETUP =
struct
open Lifting_Util
infix 0 MRSL
exception SETUP_LIFTING_INFR of string
fun define_crel rep_fun lthy =
let
val (qty, rty) = (dest_funT o fastype_of) rep_fun
val rep_fun_graph = (HOLogic.eq_const rty) $ Bound 1 $ (rep_fun $ Bound 0)
val def_term = Abs ("x", rty, Abs ("y", qty, rep_fun_graph))
val qty_name = (Binding.name o Long_Name.base_name o fst o dest_Type) qty
val crel_name = Binding.prefix_name "cr_" qty_name
val (fixed_def_term, lthy') = yield_singleton (Variable.importT_terms) def_term lthy
val ((_, (_ , def_thm)), lthy'') =
Local_Theory.define ((crel_name, NoSyn), ((Thm.def_binding crel_name, []), fixed_def_term)) lthy'
in
(def_thm, lthy'')
end
fun print_define_pcrel_warning msg =
let
val warning_msg = cat_lines
["Generation of a parametrized correspondence relation failed.",
(Pretty.string_of (Pretty.block
[Pretty.str "Reason:", Pretty.brk 2, msg]))]
in
warning warning_msg
end
fun define_pcrel crel lthy =
let
val (fixed_crel, lthy) = yield_singleton Variable.importT_terms crel lthy
val [rty', qty] = (binder_types o fastype_of) fixed_crel
val (param_rel, args) = Lifting_Term.generate_parametrized_relator lthy rty'
val rty_raw = (domain_type o range_type o fastype_of) param_rel
val thy = Proof_Context.theory_of lthy
val tyenv_match = Sign.typ_match thy (rty_raw, rty') Vartab.empty
val param_rel_subst = Envir.subst_term (tyenv_match,Vartab.empty) param_rel
val args_subst = map (Envir.subst_term (tyenv_match,Vartab.empty)) args
val lthy = Variable.declare_names fixed_crel lthy
val (instT, lthy) = Variable.importT_inst (param_rel_subst :: args_subst) lthy
val args_fixed = (map (Term_Subst.instantiate (instT, []))) args_subst
val param_rel_fixed = Term_Subst.instantiate (instT, []) param_rel_subst
val rty = (domain_type o fastype_of) param_rel_fixed
val relcomp_op = Const (@{const_name "relcompp"},
(rty --> rty' --> HOLogic.boolT) -->
(rty' --> qty --> HOLogic.boolT) -->
rty --> qty --> HOLogic.boolT)
val relator_type = foldr1 (op -->) ((map type_of args_fixed) @ [rty, qty, HOLogic.boolT])
val qty_name = (fst o dest_Type) qty
val pcrel_name = Binding.prefix_name "pcr_" ((Binding.name o Long_Name.base_name) qty_name)
val lhs = Library.foldl (op $) ((Free (Binding.name_of pcrel_name, relator_type)), args_fixed)
val rhs = relcomp_op $ param_rel_fixed $ fixed_crel
val definition_term = Logic.mk_equals (lhs, rhs)
val ((_, (_, def_thm)), lthy) = Specification.definition ((SOME (pcrel_name, SOME relator_type, NoSyn)),
((Binding.empty, []), definition_term)) lthy
in
(SOME def_thm, lthy)
end
handle Lifting_Term.PARAM_QUOT_THM (_, msg) => (print_define_pcrel_warning msg; (NONE, lthy))
local
val eq_OO_meta = mk_meta_eq @{thm eq_OO}
fun print_generate_pcr_cr_eq_error ctxt term =
let
val goal = Const (@{const_name HOL.eq}, dummyT) $ term $ Const (@{const_name HOL.eq}, dummyT)
val error_msg = cat_lines
["Generation of a pcr_cr_eq failed.",
(Pretty.string_of (Pretty.block
[Pretty.str "Reason: Cannot prove this: ", Pretty.brk 2, Syntax.pretty_term ctxt goal])),
"Most probably a relator_eq rule for one of the involved types is missing."]
in
error error_msg
end
in
fun define_pcr_cr_eq lthy pcr_rel_def =
let
val lhs = (term_of o Thm.lhs_of) pcr_rel_def
val qty_name = (Binding.name o Long_Name.base_name o fst o dest_Type o List.last o binder_types o fastype_of) lhs
val args = (snd o strip_comb) lhs
fun make_inst var ctxt =
let
val typ = (snd o relation_types o snd o dest_Var) var
val sort = Type.sort_of_atyp typ
val (fresh_var, ctxt) = yield_singleton Variable.invent_types sort ctxt
val thy = Proof_Context.theory_of ctxt
in
((cterm_of thy var, cterm_of thy (HOLogic.eq_const (TFree fresh_var))), ctxt)
end
val orig_lthy = lthy
val (args_inst, lthy) = fold_map make_inst args lthy
val pcr_cr_eq =
pcr_rel_def
|> Drule.cterm_instantiate args_inst
|> Conv.fconv_rule (Conv.arg_conv (Conv.arg1_conv
(Transfer.bottom_rewr_conv (Transfer.get_relator_eq lthy))))
in
case (term_of o Thm.rhs_of) pcr_cr_eq of
Const (@{const_name "relcompp"}, _) $ Const (@{const_name HOL.eq}, _) $ _ =>
let
val thm =
pcr_cr_eq
|> Conv.fconv_rule (Conv.arg_conv (Conv.rewr_conv eq_OO_meta))
|> mk_HOL_eq
|> singleton (Variable.export lthy orig_lthy)
val ((_, [thm]), lthy) =
Local_Theory.note ((Binding.qualified true "pcr_cr_eq" qty_name, []), [thm]) lthy
in
(thm, lthy)
end
| Const (@{const_name "relcompp"}, _) $ t $ _ => print_generate_pcr_cr_eq_error lthy t
| _ => error "generate_pcr_cr_eq: implementation error"
end
end
fun define_code_constr gen_code quot_thm lthy =
let
val abs = quot_thm_abs quot_thm
in
if gen_code andalso is_Const abs then
let
val (fixed_abs, lthy') = yield_singleton(Variable.importT_terms) abs lthy
in
Local_Theory.background_theory(Code.add_datatype [dest_Const fixed_abs]) lthy'
end
else
lthy
end
fun define_abs_type gen_code quot_thm lthy =
if gen_code andalso Lifting_Def.can_generate_code_cert quot_thm then
let
val abs_type_thm = quot_thm RS @{thm Quotient_abs_rep}
val add_abstype_attribute =
Thm.declaration_attribute (fn thm => Context.mapping (Code.add_abstype thm) I)
val add_abstype_attrib = Attrib.internal (K add_abstype_attribute)
in
lthy
|> (snd oo Local_Theory.note) ((Binding.empty, [add_abstype_attrib]), [abs_type_thm])
end
else
lthy
local
exception QUOT_ERROR of Pretty.T list
in
fun quot_thm_sanity_check ctxt quot_thm =
let
val _ =
if (nprems_of quot_thm > 0) then
raise QUOT_ERROR [Pretty.block
[Pretty.str "The Quotient theorem has extra assumptions:",
Pretty.brk 1,
Display.pretty_thm ctxt quot_thm]]
else ()
val _ = quot_thm |> concl_of |> HOLogic.dest_Trueprop |> dest_Quotient
handle TERM _ => raise QUOT_ERROR
[Pretty.block
[Pretty.str "The Quotient theorem is not of the right form:",
Pretty.brk 1,
Display.pretty_thm ctxt quot_thm]]
val ((_, [quot_thm_fixed]), ctxt') = Variable.importT [quot_thm] ctxt
val (rty, qty) = quot_thm_rty_qty quot_thm_fixed
val rty_tfreesT = Term.add_tfree_namesT rty []
val qty_tfreesT = Term.add_tfree_namesT qty []
val extra_rty_tfrees =
case subtract (op =) qty_tfreesT rty_tfreesT of
[] => []
| extras => [Pretty.block ([Pretty.str "Extra variables in the raw type:",
Pretty.brk 1] @
((Pretty.commas o map (Pretty.str o quote)) extras) @
[Pretty.str "."])]
val not_type_constr =
case qty of
Type _ => []
| _ => [Pretty.block [Pretty.str "The quotient type ",
Pretty.quote (Syntax.pretty_typ ctxt' qty),
Pretty.brk 1,
Pretty.str "is not a type constructor."]]
val errs = extra_rty_tfrees @ not_type_constr
in
if null errs then () else raise QUOT_ERROR errs
end
handle QUOT_ERROR errs => error (cat_lines (["Sanity check of the quotient theorem failed:"]
@ (map (Pretty.string_of o Pretty.item o single) errs)))
end
fun lifting_bundle qty_full_name qinfo lthy =
let
fun qualify suffix defname = Binding.qualified true suffix defname
val binding = qty_full_name |> Long_Name.base_name |> Binding.name |> qualify "lifting"
val morphed_binding = Morphism.binding (Local_Theory.target_morphism lthy) binding
val bundle_name = Name_Space.full_name (Name_Space.naming_of
(Context.Theory (Proof_Context.theory_of lthy))) morphed_binding
fun phi_qinfo phi = Lifting_Info.transform_quotient phi qinfo
val thy = Proof_Context.theory_of lthy
val dummy_thm = Thm.transfer thy Drule.dummy_thm
val pointer = Outer_Syntax.scan Position.none bundle_name
val restore_lifting_att =
([dummy_thm], [Args.src ("Lifting.lifting_restore_internal", Position.none) pointer])
in
lthy
|> Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Lifting_Info.init_restore_data bundle_name (phi_qinfo phi))
|> Bundle.bundle ((binding, [restore_lifting_att])) []
end
fun setup_lifting_infr gen_code quot_thm opt_reflp_thm lthy =
let
val _ = quot_thm_sanity_check lthy quot_thm
val (_, qtyp) = quot_thm_rty_qty quot_thm
val (pcrel_def, lthy) = define_pcrel (quot_thm_crel quot_thm) lthy
(**)
val pcrel_def = Option.map (Morphism.thm (Local_Theory.target_morphism lthy)) pcrel_def
(**)
val (pcr_cr_eq, lthy) = case pcrel_def of
SOME pcrel_def => apfst SOME (define_pcr_cr_eq lthy pcrel_def)
| NONE => (NONE, lthy)
val pcr_info = case pcrel_def of
SOME pcrel_def => SOME { pcrel_def = pcrel_def, pcr_cr_eq = the pcr_cr_eq }
| NONE => NONE
val quotients = { quot_thm = quot_thm, pcr_info = pcr_info }
val qty_full_name = (fst o dest_Type) qtyp
fun quot_info phi = Lifting_Info.transform_quotient phi quotients
val reflexivity_rule_attr = Attrib.internal (K Lifting_Info.add_reflexivity_rule_attribute)
val lthy = case opt_reflp_thm of
SOME reflp_thm => lthy
|> (snd oo Local_Theory.note) ((Binding.empty, [reflexivity_rule_attr]),
[reflp_thm RS @{thm reflp_ge_eq}])
|> (snd oo Local_Theory.note) ((Binding.empty, [reflexivity_rule_attr]),
[[quot_thm, reflp_thm] MRSL @{thm Quotient_to_left_total}])
|> define_code_constr gen_code quot_thm
| NONE => lthy
|> define_abs_type gen_code quot_thm
in
lthy
|> Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Lifting_Info.update_quotients qty_full_name (quot_info phi))
|> lifting_bundle qty_full_name quotients
end
local
fun importT_inst_exclude exclude ts ctxt =
let
val tvars = rev (subtract op= exclude (fold Term.add_tvars ts []))
val (tfrees, ctxt') = Variable.invent_types (map #2 tvars) ctxt
in (tvars ~~ map TFree tfrees, ctxt') end
fun import_inst_exclude exclude ts ctxt =
let
val excludeT = fold (Term.add_tvarsT o snd) exclude []
val (instT, ctxt') = importT_inst_exclude excludeT ts ctxt
val vars = map (apsnd (Term_Subst.instantiateT instT))
(rev (subtract op= exclude (fold Term.add_vars ts [])))
val (xs, ctxt'') = Variable.variant_fixes (map (#1 o #1) vars) ctxt'
val inst = vars ~~ map Free (xs ~~ map #2 vars)
in ((instT, inst), ctxt'') end
fun import_terms_exclude exclude ts ctxt =
let val (inst, ctxt') = import_inst_exclude exclude ts ctxt
in (map (Term_Subst.instantiate inst) ts, ctxt') end
in
fun reduce_goal not_fix goal tac ctxt =
let
val thy = Proof_Context.theory_of ctxt
val orig_ctxt = ctxt
val (fixed_goal, ctxt) = yield_singleton (import_terms_exclude not_fix) goal ctxt
val init_goal = Goal.init (cterm_of thy fixed_goal)
in
(singleton (Variable.export ctxt orig_ctxt) o Goal.conclude) (the (SINGLE tac init_goal))
end
end
local
val OO_rules = [@{thm bi_total_OO}, @{thm bi_unique_OO}, @{thm right_total_OO}, @{thm right_unique_OO}]
in
fun parametrize_class_constraint ctxt pcr_def constraint =
let
fun generate_transfer_rule pcr_def constraint goal ctxt =
let
val thy = Proof_Context.theory_of ctxt
val orig_ctxt = ctxt
val (fixed_goal, ctxt) = yield_singleton (Variable.import_terms true) goal ctxt
val init_goal = Goal.init (cterm_of thy fixed_goal)
val rules = Transfer.get_transfer_raw ctxt
val rules = constraint :: OO_rules @ rules
val tac = K (Local_Defs.unfold_tac ctxt [pcr_def]) THEN' REPEAT_ALL_NEW (resolve_tac rules)
in
(singleton (Variable.export ctxt orig_ctxt) o Goal.conclude) (the (SINGLE (tac 1) init_goal))
end
fun make_goal pcr_def constr =
let
val pred_name = (fst o dest_Const o strip_args 1 o HOLogic.dest_Trueprop o prop_of) constr
val arg = (fst o Logic.dest_equals o prop_of) pcr_def
in
HOLogic.mk_Trueprop ((Const (pred_name, (fastype_of arg) --> HOLogic.boolT)) $ arg)
end
val check_assms =
let
val right_names = ["bi_total", "bi_unique", "right_total", "right_unique"]
fun is_right_name name = member op= right_names (Long_Name.base_name name)
fun is_trivial_assm (Const (name, _) $ Var (_, _)) = is_right_name name
| is_trivial_assm (Const (name, _) $ Free (_, _)) = is_right_name name
| is_trivial_assm _ = false
in
fn thm =>
let
val prems = map HOLogic.dest_Trueprop (prems_of thm)
val thm_name = (Long_Name.base_name o fst o dest_Const o strip_args 1 o HOLogic.dest_Trueprop o concl_of) thm
val non_trivial_assms = filter_out is_trivial_assm prems
in
if null non_trivial_assms then ()
else
let
val pretty_msg = Pretty.block ([Pretty.str "Non-trivial assumptions in ",
Pretty.str thm_name,
Pretty.str " transfer rule found:",
Pretty.brk 1] @
((Pretty.commas o map (Syntax.pretty_term ctxt)) non_trivial_assms) @
[Pretty.str "."])
in
warning (Pretty.str_of pretty_msg)
end
end
end
val goal = make_goal pcr_def constraint
val thm = generate_transfer_rule pcr_def constraint goal ctxt
val _ = check_assms thm
in
thm
end
end
local
val id_unfold = (Conv.rewr_conv (mk_meta_eq @{thm id_def}))
in
fun generate_parametric_id lthy rty id_transfer_rule =
let
val orig_lthy = lthy
(* it doesn't raise an exception because it would have already raised it in define_pcrel *)
val (quot_thm, _, lthy) = Lifting_Term.prove_param_quot_thm lthy rty
val parametrized_relator = singleton (Variable.export_terms lthy orig_lthy) (quot_thm_crel quot_thm)
val lthy = orig_lthy
val id_transfer =
@{thm id_transfer}
|> Thm.incr_indexes (Term.maxidx_of_term parametrized_relator + 1)
|> Conv.fconv_rule(HOLogic.Trueprop_conv (Conv.arg_conv id_unfold then_conv Conv.arg1_conv id_unfold))
val var = Var (hd (Term.add_vars (prop_of id_transfer) []))
val thy = Proof_Context.theory_of lthy
val inst = [(cterm_of thy var, cterm_of thy parametrized_relator)]
val id_par_thm = Drule.cterm_instantiate inst id_transfer
in
Lifting_Def.generate_parametric_transfer_rule lthy id_transfer_rule id_par_thm
end
handle Lifting_Term.MERGE_TRANSFER_REL msg =>
let
val error_msg = cat_lines
["Generation of a parametric transfer rule for the abs. or the rep. function failed.",
"A non-parametric version will be used.",
(Pretty.string_of (Pretty.block
[Pretty.str "Reason:", Pretty.brk 2, msg]))]
in
(warning error_msg; id_transfer_rule)
end
end
local
fun rewrite_first_Domainp_arg rewr_thm thm = Conv.fconv_rule (Conv.concl_conv ~1 (HOLogic.Trueprop_conv
(Conv.arg1_conv (Conv.arg_conv (Conv.rewr_conv rewr_thm))))) thm
fun fold_Domainp_pcrel pcrel_def thm =
let
val ct = thm |> cprop_of |> Drule.strip_imp_concl |> Thm.dest_arg |> Thm.dest_arg1 |> Thm.dest_arg
val pcrel_def = Thm.incr_indexes (#maxidx (Thm.rep_cterm ct) + 1) pcrel_def
val thm = Thm.instantiate (Thm.match (ct, Thm.rhs_of pcrel_def)) thm
handle Pattern.MATCH => raise CTERM ("fold_Domainp_pcrel", [ct, Thm.rhs_of pcrel_def])
in
rewrite_first_Domainp_arg (Thm.symmetric pcrel_def) thm
end
fun reduce_Domainp ctxt rules thm =
let
val goal = thm |> prems_of |> hd
val var = goal |> HOLogic.dest_Trueprop |> dest_comb |> snd |> dest_Var
val reduced_assm = reduce_goal [var] goal (TRY (REPEAT_ALL_NEW (resolve_tac rules) 1)) ctxt
in
reduced_assm RS thm
end
in
fun parametrize_domain dom_thm (pcr_info : Lifting_Info.pcr) ctxt =
let
fun reduce_first_assm ctxt rules thm =
let
val goal = thm |> prems_of |> hd
val reduced_assm = reduce_goal [] goal (TRY (REPEAT_ALL_NEW (resolve_tac rules) 1)) ctxt
in
reduced_assm RS thm
end
val pcr_cr_met_eq = #pcr_cr_eq pcr_info RS @{thm eq_reflection}
val pcr_Domainp_eq = rewrite_first_Domainp_arg (Thm.symmetric pcr_cr_met_eq) dom_thm
val pcrel_def = #pcrel_def pcr_info
val pcr_Domainp_par_left_total =
(dom_thm RS @{thm pcr_Domainp_par_left_total})
|> fold_Domainp_pcrel pcrel_def
|> reduce_first_assm ctxt (Lifting_Info.get_reflexivity_rules ctxt)
val pcr_Domainp_par =
(dom_thm RS @{thm pcr_Domainp_par})
|> fold_Domainp_pcrel pcrel_def
|> reduce_Domainp ctxt (Transfer.get_relator_domain ctxt)
val pcr_Domainp =
(dom_thm RS @{thm pcr_Domainp})
|> fold_Domainp_pcrel pcrel_def
val thms =
[("domain", pcr_Domainp),
("domain_par", pcr_Domainp_par),
("domain_par_left_total", pcr_Domainp_par_left_total),
("domain_eq", pcr_Domainp_eq)]
in
thms
end
fun parametrize_total_domain bi_total pcrel_def ctxt =
let
val thm =
(bi_total RS @{thm pcr_Domainp_total})
|> fold_Domainp_pcrel pcrel_def
|> reduce_Domainp ctxt (Transfer.get_relator_domain ctxt)
in
[("domain", thm)]
end
end
fun get_pcrel_info ctxt qty_full_name =
#pcr_info (the (Lifting_Info.lookup_quotients ctxt qty_full_name))
fun get_Domainp_thm quot_thm =
the (get_first (try(curry op RS quot_thm)) [@{thm invariant_to_Domainp}, @{thm Quotient_to_Domainp}])
(*
Sets up the Lifting package by a quotient theorem.
gen_code - flag if an abstract type given by quot_thm should be registred
as an abstract type in the code generator
quot_thm - a quotient theorem (Quotient R Abs Rep T)
opt_reflp_thm - a theorem saying that a relation from quot_thm is reflexive
(in the form "reflp R")
opt_par_thm - a parametricity theorem for R
*)
fun setup_by_quotient gen_code quot_thm opt_reflp_thm opt_par_thm lthy =
let
(**)
val quot_thm = Morphism.thm (Local_Theory.target_morphism lthy) quot_thm
(**)
val transfer_attr = Attrib.internal (K Transfer.transfer_add)
val transfer_domain_attr = Attrib.internal (K Transfer.transfer_domain_add)
val (rty, qty) = quot_thm_rty_qty quot_thm
val induct_attr = Attrib.internal (K (Induct.induct_type (fst (dest_Type qty))))
val qty_full_name = (fst o dest_Type) qty
val qty_name = (Binding.name o Long_Name.base_name) qty_full_name
fun qualify suffix = Binding.qualified true suffix qty_name
val lthy = case opt_reflp_thm of
SOME reflp_thm =>
let
val thms =
[("abs_induct", @{thm Quotient_total_abs_induct}, [induct_attr]),
("abs_eq_iff", @{thm Quotient_total_abs_eq_iff}, [] )]
in
lthy
|> fold (fn (name, thm, attr) => (snd oo Local_Theory.note) ((qualify name, attr),
[[quot_thm, reflp_thm] MRSL thm])) thms
end
| NONE =>
let
val thms =
[("abs_induct", @{thm Quotient_abs_induct}, [induct_attr])]
in
fold (fn (name, thm, attr) => (snd oo Local_Theory.note) ((qualify name, attr),
[quot_thm RS thm])) thms lthy
end
val dom_thm = get_Domainp_thm quot_thm
fun setup_transfer_rules_nonpar lthy =
let
val lthy =
case opt_reflp_thm of
SOME reflp_thm =>
let
val thms =
[("id_abs_transfer",@{thm Quotient_id_abs_transfer}),
("bi_total", @{thm Quotient_bi_total} )]
in
fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_attr]),
[[quot_thm, reflp_thm] MRSL thm])) thms lthy
end
| NONE =>
lthy
|> (snd oo Local_Theory.note) ((qualify "domain", [transfer_domain_attr]), [dom_thm])
val thms =
[("rel_eq_transfer", @{thm Quotient_rel_eq_transfer}),
("right_unique", @{thm Quotient_right_unique} ),
("right_total", @{thm Quotient_right_total} )]
in
fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_attr]),
[quot_thm RS thm])) thms lthy
end
fun generate_parametric_rel_eq lthy transfer_rule opt_param_thm =
option_fold transfer_rule (Lifting_Def.generate_parametric_transfer_rule lthy transfer_rule) opt_param_thm
handle Lifting_Term.MERGE_TRANSFER_REL msg =>
let
val error_msg = cat_lines
["Generation of a parametric transfer rule for the quotient relation failed.",
(Pretty.string_of (Pretty.block
[Pretty.str "Reason:", Pretty.brk 2, msg]))]
in
error error_msg
end
fun setup_transfer_rules_par lthy =
let
val pcrel_info = (the (get_pcrel_info lthy qty_full_name))
val pcrel_def = #pcrel_def pcrel_info
val lthy =
case opt_reflp_thm of
SOME reflp_thm =>
let
val bi_total = ([quot_thm, reflp_thm] MRSL @{thm Quotient_bi_total})
val domain_thms = parametrize_total_domain bi_total pcrel_def lthy
val id_abs_transfer = generate_parametric_id lthy rty
(Lifting_Term.parametrize_transfer_rule lthy
([quot_thm, reflp_thm] MRSL @{thm Quotient_id_abs_transfer}))
val bi_total = parametrize_class_constraint lthy pcrel_def bi_total
val thms =
[("id_abs_transfer",id_abs_transfer),
("bi_total", bi_total )]
in
lthy
|> fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_attr]),
[thm])) thms
|> fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_domain_attr]),
[thm])) domain_thms
end
| NONE =>
let
val thms = parametrize_domain dom_thm pcrel_info lthy
in
fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_domain_attr]),
[thm])) thms lthy
end
val rel_eq_transfer = generate_parametric_rel_eq lthy
(Lifting_Term.parametrize_transfer_rule lthy (quot_thm RS @{thm Quotient_rel_eq_transfer}))
opt_par_thm
val right_unique = parametrize_class_constraint lthy pcrel_def
(quot_thm RS @{thm Quotient_right_unique})
val right_total = parametrize_class_constraint lthy pcrel_def
(quot_thm RS @{thm Quotient_right_total})
val thms =
[("rel_eq_transfer", rel_eq_transfer),
("right_unique", right_unique ),
("right_total", right_total )]
in
fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_attr]),
[thm])) thms lthy
end
fun setup_transfer_rules lthy =
if is_some (get_pcrel_info lthy qty_full_name) then setup_transfer_rules_par lthy
else setup_transfer_rules_nonpar lthy
in
lthy
|> setup_lifting_infr gen_code quot_thm opt_reflp_thm
|> setup_transfer_rules
end
(*
Sets up the Lifting package by a typedef theorem.
gen_code - flag if an abstract type given by typedef_thm should be registred
as an abstract type in the code generator
typedef_thm - a typedef theorem (type_definition Rep Abs S)
*)
fun setup_by_typedef_thm gen_code typedef_thm lthy =
let
val transfer_attr = Attrib.internal (K Transfer.transfer_add)
val transfer_domain_attr = Attrib.internal (K Transfer.transfer_domain_add)
val (_ $ rep_fun $ _ $ typedef_set) = (HOLogic.dest_Trueprop o prop_of) typedef_thm
val (T_def, lthy) = define_crel rep_fun lthy
(**)
val T_def = Morphism.thm (Local_Theory.target_morphism lthy) T_def
(**)
val quot_thm = case typedef_set of
Const (@{const_name top}, _) =>
[typedef_thm, T_def] MRSL @{thm UNIV_typedef_to_Quotient}
| Const (@{const_name "Collect"}, _) $ Abs (_, _, _) =>
[typedef_thm, T_def] MRSL @{thm open_typedef_to_Quotient}
| _ =>
[typedef_thm, T_def] MRSL @{thm typedef_to_Quotient}
val (rty, qty) = quot_thm_rty_qty quot_thm
val qty_full_name = (fst o dest_Type) qty
val qty_name = (Binding.name o Long_Name.base_name) qty_full_name
fun qualify suffix = Binding.qualified true suffix qty_name
val opt_reflp_thm =
case typedef_set of
Const (@{const_name top}, _) =>
SOME ((typedef_thm RS @{thm UNIV_typedef_to_equivp}) RS @{thm equivp_reflp2})
| _ => NONE
val dom_thm = get_Domainp_thm quot_thm
val reflexivity_rule_attr = Attrib.internal (K Lifting_Info.add_reflexivity_rule_attribute)
fun setup_transfer_rules_nonpar lthy =
let
val lthy =
case opt_reflp_thm of
SOME reflp_thm =>
let
val thms =
[("id_abs_transfer",@{thm Quotient_id_abs_transfer}),
("bi_total", @{thm Quotient_bi_total} )]
in
fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_attr]),
[[quot_thm, reflp_thm] MRSL thm])) thms lthy
end
| NONE =>
lthy
|> (snd oo Local_Theory.note) ((qualify "domain", [transfer_domain_attr]), [dom_thm])
val thms =
[("rep_transfer", @{thm typedef_rep_transfer}),
("bi_unique", @{thm typedef_bi_unique} ),
("right_unique", @{thm typedef_right_unique}),
("right_total", @{thm typedef_right_total} )]
in
fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_attr]),
[[typedef_thm, T_def] MRSL thm])) thms lthy
end
fun setup_transfer_rules_par lthy =
let
val pcrel_info = (the (get_pcrel_info lthy qty_full_name))
val pcrel_def = #pcrel_def pcrel_info
val lthy =
case opt_reflp_thm of
SOME reflp_thm =>
let
val bi_total = ([quot_thm, reflp_thm] MRSL @{thm Quotient_bi_total})
val domain_thms = parametrize_total_domain bi_total pcrel_def lthy
val bi_total = parametrize_class_constraint lthy pcrel_def bi_total
val id_abs_transfer = generate_parametric_id lthy rty
(Lifting_Term.parametrize_transfer_rule lthy
([quot_thm, reflp_thm] MRSL @{thm Quotient_id_abs_transfer}))
val thms =
[("bi_total", bi_total ),
("id_abs_transfer",id_abs_transfer)]
in
lthy
|> fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_attr]),
[thm])) thms
|> fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_domain_attr]),
[thm])) domain_thms
end
| NONE =>
let
val thms = parametrize_domain dom_thm pcrel_info lthy
in
fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_domain_attr]),
[thm])) thms lthy
end
val thms =
("rep_transfer", generate_parametric_id lthy rty
(Lifting_Term.parametrize_transfer_rule lthy ([typedef_thm, T_def] MRSL @{thm typedef_rep_transfer})))
::
(map_snd (fn thm => parametrize_class_constraint lthy pcrel_def ([typedef_thm, T_def] MRSL thm))
[("bi_unique", @{thm typedef_bi_unique} ),
("right_unique", @{thm typedef_right_unique}),
("right_total", @{thm typedef_right_total} )])
in
fold (fn (name, thm) => (snd oo Local_Theory.note) ((qualify name, [transfer_attr]),
[thm])) thms lthy
end
fun setup_transfer_rules lthy =
if is_some (get_pcrel_info lthy qty_full_name) then setup_transfer_rules_par lthy
else setup_transfer_rules_nonpar lthy
in
lthy
|> (snd oo Local_Theory.note) ((Binding.prefix_name "Quotient_" qty_name, []),
[quot_thm])
|> (snd oo Local_Theory.note) ((Binding.empty, [reflexivity_rule_attr]),
[[typedef_thm, T_def] MRSL @{thm typedef_left_unique}])
|> setup_lifting_infr gen_code quot_thm opt_reflp_thm
|> setup_transfer_rules
end
fun setup_lifting_cmd gen_code xthm opt_reflp_xthm opt_par_xthm lthy =
let
val input_thm = singleton (Attrib.eval_thms lthy) xthm
val input_term = (HOLogic.dest_Trueprop o prop_of) input_thm
handle TERM _ => error "Unsupported type of a theorem. Only Quotient or type_definition are supported."
fun sanity_check_reflp_thm reflp_thm =
let
val reflp_tm = (HOLogic.dest_Trueprop o prop_of) reflp_thm
handle TERM _ => error "Invalid form of the reflexivity theorem. Use \"reflp R\"."
in
case reflp_tm of
Const (@{const_name reflp}, _) $ _ => ()
| _ => error "Invalid form of the reflexivity theorem. Use \"reflp R\"."
end
fun check_qty qty = if not (is_Type qty)
then error "The abstract type must be a type constructor."
else ()
fun setup_quotient () =
let
val opt_reflp_thm = Option.map (singleton (Attrib.eval_thms lthy)) opt_reflp_xthm
val _ = if is_some opt_reflp_thm then sanity_check_reflp_thm (the opt_reflp_thm) else ()
val opt_par_thm = Option.map (singleton (Attrib.eval_thms lthy)) opt_par_xthm
val _ = check_qty (snd (quot_thm_rty_qty input_thm))
in
setup_by_quotient gen_code input_thm opt_reflp_thm opt_par_thm lthy
end
fun setup_typedef () =
let
val qty = (range_type o fastype_of o hd o get_args 2) input_term
val _ = check_qty qty
in
case opt_reflp_xthm of
SOME _ => error "The reflexivity theorem cannot be specified if the type_definition theorem is used."
| NONE => (
case opt_par_xthm of
SOME _ => error "The parametricity theorem cannot be specified if the type_definition theorem is used."
| NONE => setup_by_typedef_thm gen_code input_thm lthy
)
end
in
case input_term of
(Const (@{const_name Quotient}, _) $ _ $ _ $ _ $ _) => setup_quotient ()
| (Const (@{const_name type_definition}, _) $ _ $ _ $ _) => setup_typedef ()
| _ => error "Unsupported type of a theorem. Only Quotient or type_definition are supported."
end
val opt_gen_code =
Scan.optional (@{keyword "("} |-- Parse.!!! ((Parse.reserved "no_code" >> K false) --| @{keyword ")"})) true
val _ =
Outer_Syntax.local_theory @{command_spec "setup_lifting"}
"setup lifting infrastructure"
(opt_gen_code -- Parse_Spec.xthm -- Scan.option Parse_Spec.xthm
-- Scan.option (@{keyword "parametric"} |-- Parse.!!! Parse_Spec.xthm) >>
(fn (((gen_code, xthm), opt_reflp_xthm), opt_par_xthm) =>
setup_lifting_cmd gen_code xthm opt_reflp_xthm opt_par_xthm))
(* restoring lifting infrastructure *)
local
exception PCR_ERROR of Pretty.T list
in
fun lifting_restore_sanity_check ctxt (qinfo:Lifting_Info.quotient) =
let
val quot_thm = (#quot_thm qinfo)
val _ = quot_thm_sanity_check ctxt quot_thm
val pcr_info_err =
(case #pcr_info qinfo of
SOME pcr =>
let
val pcrel_def = #pcrel_def pcr
val pcr_cr_eq = #pcr_cr_eq pcr
val (def_lhs, _) = Logic.dest_equals (prop_of pcrel_def)
handle TERM _ => raise PCR_ERROR [Pretty.block
[Pretty.str "The pcr definiton theorem is not a plain meta equation:",
Pretty.brk 1,
Display.pretty_thm ctxt pcrel_def]]
val pcr_const_def = head_of def_lhs
val (eq_lhs, eq_rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of pcr_cr_eq))
handle TERM _ => raise PCR_ERROR [Pretty.block
[Pretty.str "The pcr_cr equation theorem is not a plain equation:",
Pretty.brk 1,
Display.pretty_thm ctxt pcr_cr_eq]]
val (pcr_const_eq, eqs) = strip_comb eq_lhs
fun is_eq (Const (@{const_name HOL.eq}, _)) = true
| is_eq _ = false
fun eq_Const (Const (name1, _)) (Const (name2, _)) = (name1 = name2)
| eq_Const _ _ = false
val all_eqs = if not (forall is_eq eqs) then
[Pretty.block
[Pretty.str "Arguments of the lhs of the pcr_cr equation theorem are not only equalities:",
Pretty.brk 1,
Display.pretty_thm ctxt pcr_cr_eq]]
else []
val pcr_consts_not_equal = if not (eq_Const pcr_const_def pcr_const_eq) then
[Pretty.block
[Pretty.str "Parametrized correspondence relation constants in pcr_def and pcr_cr_eq are not equal:",
Pretty.brk 1,
Syntax.pretty_term ctxt pcr_const_def,
Pretty.brk 1,
Pretty.str "vs.",
Pretty.brk 1,
Syntax.pretty_term ctxt pcr_const_eq]]
else []
val crel = quot_thm_crel quot_thm
val cr_consts_not_equal = if not (eq_Const crel eq_rhs) then
[Pretty.block
[Pretty.str "Correspondence relation constants in the Quotient theorem and pcr_cr_eq are not equal:",
Pretty.brk 1,
Syntax.pretty_term ctxt crel,
Pretty.brk 1,
Pretty.str "vs.",
Pretty.brk 1,
Syntax.pretty_term ctxt eq_rhs]]
else []
in
all_eqs @ pcr_consts_not_equal @ cr_consts_not_equal
end
| NONE => [])
val errs = pcr_info_err
in
if null errs then () else raise PCR_ERROR errs
end
handle PCR_ERROR errs => error (cat_lines (["Sanity check failed:"]
@ (map (Pretty.string_of o Pretty.item o single) errs)))
end
(*
Registers the data in qinfo in the Lifting infrastructure.
*)
fun lifting_restore qinfo ctxt =
let
val _ = lifting_restore_sanity_check (Context.proof_of ctxt) qinfo
val (_, qty) = quot_thm_rty_qty (#quot_thm qinfo)
val qty_full_name = (fst o dest_Type) qty
val stored_qinfo = Lifting_Info.lookup_quotients (Context.proof_of ctxt) qty_full_name
in
if is_some (stored_qinfo) andalso not (Lifting_Info.quotient_eq (qinfo, (the stored_qinfo)))
then error (Pretty.string_of
(Pretty.block
[Pretty.str "Lifting is already setup for the type",
Pretty.brk 1,
Pretty.quote (Syntax.pretty_typ (Context.proof_of ctxt) qty)]))
else Lifting_Info.update_quotients qty_full_name qinfo ctxt
end
val parse_opt_pcr =
Scan.optional (Attrib.thm -- Attrib.thm >>
(fn (pcrel_def, pcr_cr_eq) => SOME {pcrel_def = pcrel_def, pcr_cr_eq = pcr_cr_eq})) NONE
val lifting_restore_attribute_setup =
Attrib.setup @{binding lifting_restore}
((Attrib.thm -- parse_opt_pcr) >>
(fn (quot_thm, opt_pcr) =>
let val qinfo = { quot_thm = quot_thm, pcr_info = opt_pcr}
in Thm.declaration_attribute (K (lifting_restore qinfo)) end))
"restoring lifting infrastructure"
val _ = Theory.setup lifting_restore_attribute_setup
fun lifting_restore_internal bundle_name ctxt =
let
val restore_info = Lifting_Info.lookup_restore_data (Context.proof_of ctxt) bundle_name
in
case restore_info of
SOME restore_info =>
ctxt
|> lifting_restore (#quotient restore_info)
|> fold_rev Transfer.transfer_raw_add (Item_Net.content (#transfer_rules restore_info))
| NONE => ctxt
end
val lifting_restore_internal_attribute_setup =
Attrib.setup @{binding lifting_restore_internal}
(Scan.lift Args.name >> (fn name => Thm.declaration_attribute (K (lifting_restore_internal name))))
"restoring lifting infrastructure; internal attribute; not meant to be used directly by regular users"
val _ = Theory.setup lifting_restore_internal_attribute_setup
(* lifting_forget *)
val monotonicity_names = [@{const_name right_unique}, @{const_name left_unique}, @{const_name right_total},
@{const_name left_total}, @{const_name bi_unique}, @{const_name bi_total}]
fun fold_transfer_rel f (Const (@{const_name "Transfer.Rel"}, _) $ rel $ _ $ _) = f rel
| fold_transfer_rel f (Const (@{const_name "HOL.eq"}, _) $
(Const (@{const_name Domainp}, _) $ rel) $ _) = f rel
| fold_transfer_rel f (Const (name, _) $ rel) =
if member op= monotonicity_names name then f rel else f @{term undefined}
| fold_transfer_rel f _ = f @{term undefined}
fun filter_transfer_rules_by_rel transfer_rel transfer_rules =
let
val transfer_rel_name = transfer_rel |> dest_Const |> fst;
fun has_transfer_rel thm =
let
val concl = thm |> concl_of |> HOLogic.dest_Trueprop
in
member op= (fold_transfer_rel (fn tm => Term.add_const_names tm []) concl) transfer_rel_name
end
handle TERM _ => false
in
filter has_transfer_rel transfer_rules
end
type restore_data = {quotient : Lifting_Info.quotient, transfer_rules: thm Item_Net.T}
fun get_transfer_rel (qinfo : Lifting_Info.quotient) =
let
fun get_pcrel pcr_def = pcr_def |> concl_of |> Logic.dest_equals |> fst |> head_of
in
if is_some (#pcr_info qinfo)
then get_pcrel (#pcrel_def (the (#pcr_info qinfo)))
else quot_thm_crel (#quot_thm qinfo)
end
fun pointer_of_bundle_name bundle_name ctxt =
let
val bundle = Bundle.get_bundle_cmd ctxt bundle_name
in
case bundle of
[(_, [arg_src])] =>
let
val (name, _) = Args.syntax (Scan.lift Args.name) arg_src ctxt
handle ERROR _ => error "The provided bundle is not a lifting bundle."
in name end
| _ => error "The provided bundle is not a lifting bundle."
end
fun lifting_forget pointer lthy =
let
fun get_transfer_rules_to_delete qinfo ctxt =
let
val transfer_rel = get_transfer_rel qinfo
in
filter_transfer_rules_by_rel transfer_rel (Transfer.get_transfer_raw ctxt)
end
in
case Lifting_Info.lookup_restore_data lthy pointer of
SOME restore_info =>
let
val qinfo = #quotient restore_info
val quot_thm = #quot_thm qinfo
val transfer_rules = get_transfer_rules_to_delete qinfo lthy
in
Local_Theory.declaration {syntax = false, pervasive = true}
(K (fold (Transfer.transfer_raw_del) transfer_rules #> Lifting_Info.delete_quotients quot_thm))
lthy
end
| NONE => error "The lifting bundle refers to non-existent restore data."
end
fun lifting_forget_cmd bundle_name lthy =
lifting_forget (pointer_of_bundle_name bundle_name lthy) lthy
val _ =
Outer_Syntax.local_theory @{command_spec "lifting_forget"}
"unsetup Lifting and Transfer for the given lifting bundle"
(Parse.position Parse.xname >> (lifting_forget_cmd))
(* lifting_update *)
fun update_transfer_rules pointer lthy =
let
fun new_transfer_rules ({ quotient = qinfo, ... }:Lifting_Info.restore_data) lthy =
let
val transfer_rel = get_transfer_rel qinfo
val transfer_rules = filter_transfer_rules_by_rel transfer_rel (Transfer.get_transfer_raw lthy)
in
fn phi => fold_rev
(Item_Net.update o Morphism.thm phi) transfer_rules Thm.full_rules
end
in
case Lifting_Info.lookup_restore_data lthy pointer of
SOME refresh_data =>
Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Lifting_Info.add_transfer_rules_in_restore_data pointer
(new_transfer_rules refresh_data lthy phi)) lthy
| NONE => error "The lifting bundle refers to non-existent restore data."
end
fun lifting_update_cmd bundle_name lthy =
update_transfer_rules (pointer_of_bundle_name bundle_name lthy) lthy
val _ =
Outer_Syntax.local_theory @{command_spec "lifting_update"}
"add newly introduced transfer rules to a bundle storing the state of Lifting and Transfer"
(Parse.position Parse.xname >> lifting_update_cmd)
end