(* Title: HOL/Tools/Lifting/lifting_def.ML
Author: Ondrej Kuncar
Definitions for constants on quotient types.
*)
signature LIFTING_DEF =
sig
type lift_def
val rty_of_lift_def: lift_def -> typ
val qty_of_lift_def: lift_def -> typ
val rhs_of_lift_def: lift_def -> term
val lift_const_of_lift_def: lift_def -> term
val def_thm_of_lift_def: lift_def -> thm
val rsp_thm_of_lift_def: lift_def -> thm
val abs_eq_of_lift_def: lift_def -> thm
val rep_eq_of_lift_def: lift_def -> thm option
val transfer_rules_of_lift_def: lift_def -> thm list
val morph_lift_def: morphism -> lift_def -> lift_def
val inst_of_lift_def: Proof.context -> typ -> lift_def -> lift_def
val mk_lift_const_of_lift_def: typ -> lift_def -> term
val generate_parametric_transfer_rule:
Proof.context -> thm -> thm -> thm
val add_lift_def:
binding * mixfix -> typ -> term -> thm -> thm list -> local_theory -> lift_def * local_theory
val lift_def:
binding * mixfix -> typ -> term -> (Proof.context -> tactic) -> thm list ->
local_theory -> lift_def * local_theory
val lift_def_cmd:
(binding * string option * mixfix) * string * (Facts.ref * Token.src list) list ->
local_theory -> Proof.state
val can_generate_code_cert: thm -> bool
end
structure Lifting_Def: LIFTING_DEF =
struct
open Lifting_Util
infix 0 MRSL
datatype lift_def = LIFT_DEF of {
rty: typ,
qty: typ,
rhs: term,
lift_const: term,
def_thm: thm,
rsp_thm: thm,
abs_eq: thm,
rep_eq: thm option,
transfer_rules: thm list
};
fun rep_lift_def (LIFT_DEF lift_def) = lift_def;
val rty_of_lift_def = #rty o rep_lift_def;
val qty_of_lift_def = #qty o rep_lift_def;
val rhs_of_lift_def = #rhs o rep_lift_def;
val lift_const_of_lift_def = #lift_const o rep_lift_def;
val def_thm_of_lift_def = #def_thm o rep_lift_def;
val rsp_thm_of_lift_def = #rsp_thm o rep_lift_def;
val abs_eq_of_lift_def = #abs_eq o rep_lift_def;
val rep_eq_of_lift_def = #rep_eq o rep_lift_def;
val transfer_rules_of_lift_def = #transfer_rules o rep_lift_def;
fun mk_lift_def rty qty rhs lift_const def_thm rsp_thm abs_eq rep_eq transfer_rules =
LIFT_DEF {rty = rty, qty = qty,
rhs = rhs, lift_const = lift_const,
def_thm = def_thm, rsp_thm = rsp_thm, abs_eq = abs_eq, rep_eq = rep_eq,
transfer_rules = transfer_rules };
fun map_lift_def f1 f2 f3 f4 f5 f6 f7 f8 f9
(LIFT_DEF {rty = rty, qty = qty, rhs = rhs, lift_const = lift_const,
def_thm = def_thm, rsp_thm = rsp_thm, abs_eq = abs_eq, rep_eq = rep_eq,
transfer_rules = transfer_rules }) =
LIFT_DEF {rty = f1 rty, qty = f2 qty, rhs = f3 rhs, lift_const = f4 lift_const,
def_thm = f5 def_thm, rsp_thm = f6 rsp_thm, abs_eq = f7 abs_eq, rep_eq = f8 rep_eq,
transfer_rules = f9 transfer_rules }
fun morph_lift_def phi =
let
val mtyp = Morphism.typ phi
val mterm = Morphism.term phi
val mthm = Morphism.thm phi
in
map_lift_def mtyp mtyp mterm mterm mthm mthm mthm (Option.map mthm) (map mthm)
end
fun mk_inst_of_lift_def qty lift_def = Vartab.empty |> Type.raw_match (qty_of_lift_def lift_def, qty)
fun mk_lift_const_of_lift_def qty lift_def = Envir.subst_term_types (mk_inst_of_lift_def qty lift_def)
(lift_const_of_lift_def lift_def)
fun inst_of_lift_def ctxt qty lift_def = mk_inst_of_lift_def qty lift_def
|> instT_morphism ctxt |> (fn phi => morph_lift_def phi lift_def)
(* Reflexivity prover *)
fun mono_eq_prover ctxt prop =
let
val refl_rules = Lifting_Info.get_reflexivity_rules ctxt
val transfer_rules = Transfer.get_transfer_raw ctxt
fun main_tac i = (REPEAT_ALL_NEW (DETERM o resolve_tac ctxt refl_rules) THEN_ALL_NEW
(REPEAT_ALL_NEW (DETERM o resolve_tac ctxt transfer_rules))) i
in
SOME (Goal.prove ctxt [] [] prop (K (main_tac 1)))
handle ERROR _ => NONE
end
fun try_prove_refl_rel ctxt rel =
let
fun mk_ge_eq x =
let
val T = fastype_of x
in
Const (@{const_name "less_eq"}, T --> T --> HOLogic.boolT) $
(Const (@{const_name HOL.eq}, T)) $ x
end;
val goal = HOLogic.mk_Trueprop (mk_ge_eq rel);
in
mono_eq_prover ctxt goal
end;
fun try_prove_reflexivity ctxt prop =
let
val cprop = Thm.cterm_of ctxt prop
val rule = @{thm ge_eq_refl}
val concl_pat = Drule.strip_imp_concl (Thm.cprop_of rule)
val insts = Thm.first_order_match (concl_pat, cprop)
val rule = Drule.instantiate_normalize insts rule
val prop = hd (Thm.prems_of rule)
in
case mono_eq_prover ctxt prop of
SOME thm => SOME (thm RS rule)
| NONE => NONE
end
(*
Generates a parametrized transfer rule.
transfer_rule - of the form T t f
parametric_transfer_rule - of the form par_R t' t
Result: par_T t' f, after substituing op= for relations in par_R that relate
a type constructor to the same type constructor, it is a merge of (par_R' OO T) t' f
using Lifting_Term.merge_transfer_relations
*)
fun generate_parametric_transfer_rule ctxt transfer_rule parametric_transfer_rule =
let
fun preprocess ctxt thm =
let
val tm = (strip_args 2 o HOLogic.dest_Trueprop o Thm.concl_of) thm;
val param_rel = (snd o dest_comb o fst o dest_comb) tm;
val free_vars = Term.add_vars param_rel [];
fun make_subst (var as (_, typ)) subst =
let
val [rty, rty'] = binder_types typ
in
if (Term.is_TVar rty andalso is_Type rty') then
(Var var, HOLogic.eq_const rty')::subst
else
subst
end;
val subst = fold make_subst free_vars [];
val csubst = map (apply2 (Thm.cterm_of ctxt)) subst;
val inst_thm = Drule.cterm_instantiate csubst thm;
in
Conv.fconv_rule
((Conv.concl_conv (Thm.nprems_of inst_thm) o
HOLogic.Trueprop_conv o Conv.fun2_conv o Conv.arg1_conv)
(Raw_Simplifier.rewrite ctxt false (Transfer.get_sym_relator_eq ctxt))) inst_thm
end
fun inst_relcomppI ctxt ant1 ant2 =
let
val t1 = (HOLogic.dest_Trueprop o Thm.concl_of) ant1
val t2 = (HOLogic.dest_Trueprop o Thm.prop_of) ant2
val fun1 = Thm.cterm_of ctxt (strip_args 2 t1)
val args1 = map (Thm.cterm_of ctxt) (get_args 2 t1)
val fun2 = Thm.cterm_of ctxt (strip_args 2 t2)
val args2 = map (Thm.cterm_of ctxt) (get_args 1 t2)
val relcomppI = Drule.incr_indexes2 ant1 ant2 @{thm relcomppI}
val vars = (rev (Term.add_vars (Thm.prop_of relcomppI) []))
val subst = map (apfst (Thm.cterm_of ctxt o Var)) (vars ~~ ([fun1] @ args1 @ [fun2] @ args2))
in
Drule.cterm_instantiate subst relcomppI
end
fun zip_transfer_rules ctxt thm =
let
fun mk_POS ty = Const (@{const_name POS}, ty --> ty --> HOLogic.boolT)
val rel = (Thm.dest_fun2 o Thm.dest_arg o Thm.cprop_of) thm
val typ = Thm.typ_of_cterm rel
val POS_const = Thm.cterm_of ctxt (mk_POS typ)
val var = Thm.cterm_of ctxt (Var (("X", Thm.maxidx_of_cterm rel + 1), typ))
val goal =
Thm.apply (Thm.cterm_of ctxt HOLogic.Trueprop) (Thm.apply (Thm.apply POS_const rel) var)
in
[Lifting_Term.merge_transfer_relations ctxt goal, thm] MRSL @{thm POS_apply}
end
val thm =
inst_relcomppI ctxt parametric_transfer_rule transfer_rule
OF [parametric_transfer_rule, transfer_rule]
val preprocessed_thm = preprocess ctxt thm
val orig_ctxt = ctxt
val (fixed_thm, ctxt) = yield_singleton (apfst snd oo Variable.import true) preprocessed_thm ctxt
val assms = cprems_of fixed_thm
val add_transfer_rule = Thm.attribute_declaration Transfer.transfer_add
val (prems, ctxt) = fold_map Thm.assume_hyps assms ctxt
val ctxt = Context.proof_map (fold add_transfer_rule prems) ctxt
val zipped_thm =
fixed_thm
|> undisch_all
|> zip_transfer_rules ctxt
|> implies_intr_list assms
|> singleton (Variable.export ctxt orig_ctxt)
in
zipped_thm
end
fun print_generate_transfer_info msg =
let
val error_msg = cat_lines
["Generation of a parametric transfer rule failed.",
(Pretty.string_of (Pretty.block
[Pretty.str "Reason:", Pretty.brk 2, msg]))]
in
error error_msg
end
fun map_ter _ x [] = x
| map_ter f _ xs = map f xs
fun generate_transfer_rules lthy quot_thm rsp_thm def_thm par_thms =
let
val transfer_rule =
([quot_thm, rsp_thm, def_thm] MRSL @{thm Quotient_to_transfer})
|> Lifting_Term.parametrize_transfer_rule lthy
in
(map_ter (generate_parametric_transfer_rule lthy transfer_rule) [transfer_rule] par_thms
handle Lifting_Term.MERGE_TRANSFER_REL msg => (print_generate_transfer_info msg; [transfer_rule]))
end
(* Generation of the code certificate from the rsp theorem *)
fun get_body_types (Type ("fun", [_, U]), Type ("fun", [_, V])) = get_body_types (U, V)
| get_body_types (U, V) = (U, V)
fun get_binder_types (Type ("fun", [T, U]), Type ("fun", [V, W])) = (T, V) :: get_binder_types (U, W)
| get_binder_types _ = []
fun get_binder_types_by_rel (Const (@{const_name "rel_fun"}, _) $ _ $ S) (Type ("fun", [T, U]), Type ("fun", [V, W])) =
(T, V) :: get_binder_types_by_rel S (U, W)
| get_binder_types_by_rel _ _ = []
fun get_body_type_by_rel (Const (@{const_name "rel_fun"}, _) $ _ $ S) (Type ("fun", [_, U]), Type ("fun", [_, V])) =
get_body_type_by_rel S (U, V)
| get_body_type_by_rel _ (U, V) = (U, V)
fun get_binder_rels (Const (@{const_name "rel_fun"}, _) $ R $ S) = R :: get_binder_rels S
| get_binder_rels _ = []
fun force_rty_type ctxt rty rhs =
let
val thy = Proof_Context.theory_of ctxt
val rhs_schematic = singleton (Variable.polymorphic ctxt) rhs
val rty_schematic = fastype_of rhs_schematic
val match = Sign.typ_match thy (rty_schematic, rty) Vartab.empty
in
Envir.subst_term_types match rhs_schematic
end
fun unabs_def ctxt def =
let
val (_, rhs) = Thm.dest_equals (Thm.cprop_of def)
fun dest_abs (Abs (var_name, T, _)) = (var_name, T)
| dest_abs tm = raise TERM("get_abs_var",[tm])
val (var_name, T) = dest_abs (Thm.term_of rhs)
val (new_var_names, ctxt') = Variable.variant_fixes [var_name] ctxt
val refl_thm = Thm.reflexive (Thm.cterm_of ctxt' (Free (hd new_var_names, T)))
in
Thm.combination def refl_thm |>
singleton (Proof_Context.export ctxt' ctxt)
end
fun unabs_all_def ctxt def =
let
val (_, rhs) = Thm.dest_equals (Thm.cprop_of def)
val xs = strip_abs_vars (Thm.term_of rhs)
in
fold (K (unabs_def ctxt)) xs def
end
val map_fun_unfolded =
@{thm map_fun_def[abs_def]} |>
unabs_def @{context} |>
unabs_def @{context} |>
Local_Defs.unfold @{context} [@{thm comp_def}]
fun unfold_fun_maps ctm =
let
fun unfold_conv ctm =
case (Thm.term_of ctm) of
Const (@{const_name "map_fun"}, _) $ _ $ _ =>
(Conv.arg_conv unfold_conv then_conv Conv.rewr_conv map_fun_unfolded) ctm
| _ => Conv.all_conv ctm
in
(Conv.fun_conv unfold_conv) ctm
end
fun unfold_fun_maps_beta ctm =
let val try_beta_conv = Conv.try_conv (Thm.beta_conversion false)
in
(unfold_fun_maps then_conv try_beta_conv) ctm
end
fun prove_rel ctxt rsp_thm (rty, qty) =
let
val ty_args = get_binder_types (rty, qty)
fun disch_arg args_ty thm =
let
val quot_thm = Lifting_Term.prove_quot_thm ctxt args_ty
in
[quot_thm, thm] MRSL @{thm apply_rsp''}
end
in
fold disch_arg ty_args rsp_thm
end
exception CODE_CERT_GEN of string
fun simplify_code_eq ctxt def_thm =
Local_Defs.unfold ctxt [@{thm o_apply}, @{thm map_fun_def}, @{thm id_apply}] def_thm
(*
quot_thm - quotient theorem (Quotient R Abs Rep T).
returns: whether the Lifting package is capable to generate code for the abstract type
represented by quot_thm
*)
fun can_generate_code_cert quot_thm =
case quot_thm_rel quot_thm of
Const (@{const_name HOL.eq}, _) => true
| Const (@{const_name eq_onp}, _) $ _ => true
| _ => false
fun generate_rep_eq ctxt def_thm rsp_thm (rty, qty) =
let
val unfolded_def = Conv.fconv_rule (Conv.arg_conv unfold_fun_maps_beta) def_thm
val unabs_def = unabs_all_def ctxt unfolded_def
in
if body_type rty = body_type qty then
SOME (simplify_code_eq ctxt (unabs_def RS @{thm meta_eq_to_obj_eq}))
else
let
val quot_thm = Lifting_Term.prove_quot_thm ctxt (get_body_types (rty, qty))
val rel_fun = prove_rel ctxt rsp_thm (rty, qty)
val rep_abs_thm = [quot_thm, rel_fun] MRSL @{thm Quotient_rep_abs_eq}
in
case mono_eq_prover ctxt (hd (Thm.prems_of rep_abs_thm)) of
SOME mono_eq_thm =>
let
val rep_abs_eq = mono_eq_thm RS rep_abs_thm
val rep = Thm.cterm_of ctxt (quot_thm_rep quot_thm)
val rep_refl = Thm.reflexive rep RS @{thm meta_eq_to_obj_eq}
val repped_eq = [rep_refl, unabs_def RS @{thm meta_eq_to_obj_eq}] MRSL @{thm cong}
val code_cert = [repped_eq, rep_abs_eq] MRSL trans
in
SOME (simplify_code_eq ctxt code_cert)
end
| NONE => NONE
end
end
fun generate_abs_eq ctxt def_thm rsp_thm quot_thm =
let
val abs_eq_with_assms =
let
val (rty, qty) = quot_thm_rty_qty quot_thm
val rel = quot_thm_rel quot_thm
val ty_args = get_binder_types_by_rel rel (rty, qty)
val body_type = get_body_type_by_rel rel (rty, qty)
val quot_ret_thm = Lifting_Term.prove_quot_thm ctxt body_type
val rep_abs_folded_unmapped_thm =
let
val rep_id = [quot_thm, def_thm] MRSL @{thm Quotient_Rep_eq}
val ctm = Thm.dest_equals_lhs (Thm.cprop_of rep_id)
val unfolded_maps_eq = unfold_fun_maps ctm
val t1 = [quot_thm, def_thm, rsp_thm] MRSL @{thm Quotient_rep_abs_fold_unmap}
val prems_pat = (hd o Drule.cprems_of) t1
val insts = Thm.first_order_match (prems_pat, Thm.cprop_of unfolded_maps_eq)
in
unfolded_maps_eq RS (Drule.instantiate_normalize insts t1)
end
in
rep_abs_folded_unmapped_thm
|> fold (fn _ => fn thm => thm RS @{thm rel_funD2}) ty_args
|> (fn x => x RS (@{thm Quotient_rel_abs2} OF [quot_ret_thm]))
end
val prem_rels = get_binder_rels (quot_thm_rel quot_thm);
val proved_assms = prem_rels |> map (try_prove_refl_rel ctxt)
|> map_index (apfst (fn x => x + 1)) |> filter (is_some o snd) |> map (apsnd the)
|> map (apsnd (fn assm => assm RS @{thm ge_eq_refl}))
val abs_eq = fold_rev (fn (i, assm) => fn thm => assm RSN (i, thm)) proved_assms abs_eq_with_assms
in
simplify_code_eq ctxt abs_eq
end
fun register_code_eq_thy abs_eq_thm opt_rep_eq_thm (rty, qty) thy =
let
fun no_abstr (t $ u) = no_abstr t andalso no_abstr u
| no_abstr (Abs (_, _, t)) = no_abstr t
| no_abstr (Const (name, _)) = not (Code.is_abstr thy name)
| no_abstr _ = true
fun is_valid_eq eqn = can (Code.assert_eqn thy) (mk_meta_eq eqn, true)
andalso no_abstr (Thm.prop_of eqn)
fun is_valid_abs_eq abs_eq = can (Code.assert_abs_eqn thy NONE) (mk_meta_eq abs_eq)
in
if is_valid_eq abs_eq_thm then
Code.add_default_eqn abs_eq_thm thy
else
let
val (rty_body, qty_body) = get_body_types (rty, qty)
in
if rty_body = qty_body then
Code.add_default_eqn (the opt_rep_eq_thm) thy
else
if is_some opt_rep_eq_thm andalso is_valid_abs_eq (the opt_rep_eq_thm)
then
Code.add_abs_default_eqn (the opt_rep_eq_thm) thy
else
thy
end
end
local
fun encode_code_eq ctxt abs_eq opt_rep_eq (rty, qty) =
let
fun mk_type typ = typ |> Logic.mk_type |> Thm.cterm_of ctxt |> Drule.mk_term
in
Conjunction.intr_balanced [abs_eq, (the_default TrueI opt_rep_eq), mk_type rty, mk_type qty]
end
exception DECODE
fun decode_code_eq thm =
if Thm.nprems_of thm > 0 then raise DECODE
else
let
val [abs_eq, rep_eq, rty, qty] = Conjunction.elim_balanced 4 thm
val opt_rep_eq = if Thm.eq_thm_prop (rep_eq, TrueI) then NONE else SOME rep_eq
fun dest_type typ = typ |> Drule.dest_term |> Thm.term_of |> Logic.dest_type
in
(abs_eq, opt_rep_eq, (dest_type rty, dest_type qty))
end
fun register_encoded_code_eq thm thy =
let
val (abs_eq_thm, opt_rep_eq_thm, (rty, qty)) = decode_code_eq thm
in
register_code_eq_thy abs_eq_thm opt_rep_eq_thm (rty, qty) thy
end
handle DECODE => thy
val register_code_eq_attribute = Thm.declaration_attribute
(fn thm => Context.mapping (register_encoded_code_eq thm) I)
val register_code_eq_attrib = Attrib.internal (K register_code_eq_attribute)
fun no_no_code ctxt (rty, qty) =
if same_type_constrs (rty, qty) then
forall (no_no_code ctxt) (Targs rty ~~ Targs qty)
else
if is_Type qty then
if Lifting_Info.is_no_code_type ctxt (Tname qty) then false
else
let
val (rty', rtyq) = Lifting_Term.instantiate_rtys ctxt (rty, qty)
val (rty's, rtyqs) = (Targs rty', Targs rtyq)
in
forall (no_no_code ctxt) (rty's ~~ rtyqs)
end
else
true
in
fun register_code_eq abs_eq_thm opt_rep_eq_thm (rty, qty) lthy =
let
val encoded_code_eq = encode_code_eq lthy abs_eq_thm opt_rep_eq_thm (rty, qty)
in
if no_no_code lthy (rty, qty) then
(snd oo Local_Theory.note) ((Binding.empty, [register_code_eq_attrib]), [encoded_code_eq]) lthy
else
lthy
end
end
(*
Defines an operation on an abstract type in terms of a corresponding operation
on a representation type.
var - a binding and a mixfix of the new constant being defined
qty - an abstract type of the new constant
rhs - a term representing the new constant on the raw level
rsp_thm - a respectfulness theorem in the internal tagged form (like '(R ===> R ===> R) f f'),
i.e. "(Lifting_Term.equiv_relation (fastype_of rhs, qty)) $ rhs $ rhs"
par_thms - a parametricity theorem for rhs
*)
fun add_lift_def var qty rhs rsp_thm par_thms lthy =
let
val rty = fastype_of rhs
val quot_thm = Lifting_Term.prove_quot_thm lthy (rty, qty)
val absrep_trm = quot_thm_abs quot_thm
val rty_forced = (domain_type o fastype_of) absrep_trm
val forced_rhs = force_rty_type lthy rty_forced rhs
val lhs = Free (Binding.name_of (#1 var), qty)
val prop = Logic.mk_equals (lhs, absrep_trm $ forced_rhs)
val (_, prop') = Local_Defs.cert_def lthy prop
val (_, newrhs) = Local_Defs.abs_def prop'
val ((lift_const, (_ , def_thm)), lthy') =
Local_Theory.define (var, ((Thm.def_binding (#1 var), []), newrhs)) lthy
val transfer_rules = generate_transfer_rules lthy' quot_thm rsp_thm def_thm par_thms
val abs_eq_thm = generate_abs_eq lthy' def_thm rsp_thm quot_thm
val opt_rep_eq_thm = generate_rep_eq lthy' def_thm rsp_thm (rty_forced, qty)
fun qualify defname suffix = Binding.qualified true suffix defname
val lhs_name = (#1 var)
val rsp_thm_name = qualify lhs_name "rsp"
val abs_eq_thm_name = qualify lhs_name "abs_eq"
val rep_eq_thm_name = qualify lhs_name "rep_eq"
val transfer_rule_name = qualify lhs_name "transfer"
val transfer_attr = Attrib.internal (K Transfer.transfer_add)
val lift_def = mk_lift_def rty_forced qty newrhs lift_const def_thm rsp_thm abs_eq_thm
opt_rep_eq_thm transfer_rules
in
lthy'
|> (snd oo Local_Theory.note) ((rsp_thm_name, []), [rsp_thm])
|> (snd oo Local_Theory.note) ((transfer_rule_name, [transfer_attr]), transfer_rules)
|> (snd oo Local_Theory.note) ((abs_eq_thm_name, []), [abs_eq_thm])
|> (case opt_rep_eq_thm of
SOME rep_eq_thm => (snd oo Local_Theory.note) ((rep_eq_thm_name, []), [rep_eq_thm])
| NONE => I)
|> register_code_eq abs_eq_thm opt_rep_eq_thm (rty_forced, qty)
|> ` (fn lthy => morph_lift_def (Local_Theory.target_morphism lthy) lift_def)
||> Local_Theory.restore
end
local
val eq_onp_assms_tac_fixed_rules = map (Transfer.prep_transfer_domain_thm @{context})
[@{thm pcr_Domainp_total}, @{thm pcr_Domainp_par_left_total}, @{thm pcr_Domainp_par},
@{thm pcr_Domainp}]
in
fun mk_readable_rsp_thm_eq tm lthy =
let
val ctm = Thm.cterm_of lthy tm
fun assms_rewr_conv tactic rule ct =
let
fun prove_extra_assms thm =
let
val assms = cprems_of thm
fun finish thm = if Thm.no_prems thm then SOME (Goal.conclude thm) else NONE
fun prove ctm = Option.mapPartial finish (SINGLE tactic (Goal.init ctm))
in
map_interrupt prove assms
end
fun cconl_of thm = Drule.strip_imp_concl (Thm.cprop_of thm)
fun lhs_of thm = fst (Thm.dest_equals (cconl_of thm))
fun rhs_of thm = snd (Thm.dest_equals (cconl_of thm))
val rule1 = Thm.incr_indexes (Thm.maxidx_of_cterm ct + 1) rule;
val lhs = lhs_of rule1;
val rule2 = Thm.rename_boundvars (Thm.term_of lhs) (Thm.term_of ct) rule1;
val rule3 =
Thm.instantiate (Thm.match (lhs, ct)) rule2
handle Pattern.MATCH => raise CTERM ("assms_rewr_conv", [lhs, ct]);
val proved_assms = prove_extra_assms rule3
in
case proved_assms of
SOME proved_assms =>
let
val rule3 = proved_assms MRSL rule3
val rule4 =
if lhs_of rule3 aconvc ct then rule3
else
let val ceq = Thm.dest_fun2 (Thm.cprop_of rule3)
in rule3 COMP Thm.trivial (Thm.mk_binop ceq ct (rhs_of rule3)) end
in Thm.transitive rule4 (Thm.beta_conversion true (rhs_of rule4)) end
| NONE => Conv.no_conv ct
end
fun assms_rewrs_conv tactic rules = Conv.first_conv (map (assms_rewr_conv tactic) rules)
fun simp_arrows_conv ctm =
let
val unfold_conv = Conv.rewrs_conv
[@{thm rel_fun_eq_eq_onp[THEN eq_reflection]},
@{thm rel_fun_eq_onp_rel[THEN eq_reflection]},
@{thm rel_fun_eq[THEN eq_reflection]},
@{thm rel_fun_eq_rel[THEN eq_reflection]},
@{thm rel_fun_def[THEN eq_reflection]}]
fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
val eq_onp_assms_tac_rules = @{thm left_unique_OO} ::
eq_onp_assms_tac_fixed_rules @ (Transfer.get_transfer_raw lthy)
val intro_top_rule = @{thm eq_onp_top_eq_eq[symmetric, THEN eq_reflection]}
val kill_tops = Transfer.top_sweep_rewr_conv [@{thm eq_onp_top_eq_eq[THEN eq_reflection]}]
val eq_onp_assms_tac = (CONVERSION kill_tops THEN'
TRY o REPEAT_ALL_NEW (resolve_tac lthy eq_onp_assms_tac_rules)
THEN_ALL_NEW (DETERM o Transfer.eq_tac lthy)) 1
val relator_eq_onp_conv = Conv.bottom_conv
(K (Conv.try_conv (assms_rewrs_conv eq_onp_assms_tac
(intro_top_rule :: Lifting_Info.get_relator_eq_onp_rules lthy)))) lthy
then_conv kill_tops
val relator_eq_conv = Conv.bottom_conv
(K (Conv.try_conv (Conv.rewrs_conv (Transfer.get_relator_eq lthy)))) lthy
in
case (Thm.term_of ctm) of
Const (@{const_name "rel_fun"}, _) $ _ $ _ =>
(binop_conv2 simp_arrows_conv simp_arrows_conv then_conv unfold_conv) ctm
| _ => (relator_eq_onp_conv then_conv relator_eq_conv) ctm
end
val unfold_ret_val_invs = Conv.bottom_conv
(K (Conv.try_conv (Conv.rewr_conv @{thm eq_onp_same_args[THEN eq_reflection]}))) lthy
val unfold_inv_conv =
Conv.top_sweep_conv (K (Conv.rewr_conv @{thm eq_onp_def[THEN eq_reflection]})) lthy
val simp_conv = HOLogic.Trueprop_conv (Conv.fun2_conv simp_arrows_conv)
val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) lthy
val beta_conv = Thm.beta_conversion true
val eq_thm =
(simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs
then_conv unfold_inv_conv) ctm
in
Object_Logic.rulify lthy (eq_thm RS Drule.equal_elim_rule2)
end
end
fun rename_to_tnames ctxt term =
let
fun all_typs (Const (@{const_name Pure.all}, _) $ Abs (_, T, t)) = T :: all_typs t
| all_typs _ = []
fun rename (Const (@{const_name Pure.all}, T1) $ Abs (_, T2, t)) (new_name :: names) =
(Const (@{const_name Pure.all}, T1) $ Abs (new_name, T2, rename t names))
| rename t _ = t
val (fixed_def_t, _) = yield_singleton (Variable.importT_terms) term ctxt
val new_names = Old_Datatype_Prop.make_tnames (all_typs fixed_def_t)
in
rename term new_names
end
(* This is not very cheap way of getting the rules but we have only few active
liftings in the current setting *)
fun get_cr_pcr_eqs ctxt =
let
fun collect (data : Lifting_Info.quotient) l =
if is_some (#pcr_info data)
then ((Thm.symmetric o safe_mk_meta_eq o #pcr_cr_eq o the o #pcr_info) data :: l)
else l
val table = Lifting_Info.get_quotients ctxt
in
Symtab.fold (fn (_, data) => fn l => collect data l) table []
end
fun prepare_lift_def var qty rhs par_thms lthy =
let
val rsp_rel = Lifting_Term.equiv_relation lthy (fastype_of rhs, qty)
val rty_forced = (domain_type o fastype_of) rsp_rel;
val forced_rhs = force_rty_type lthy rty_forced rhs;
val cr_to_pcr_conv = HOLogic.Trueprop_conv (Conv.fun2_conv
(Raw_Simplifier.rewrite lthy false (get_cr_pcr_eqs lthy)))
val (prsp_tm, rsp_prsp_eq) = HOLogic.mk_Trueprop (rsp_rel $ forced_rhs $ forced_rhs)
|> Thm.cterm_of lthy
|> cr_to_pcr_conv
|> `Thm.concl_of
|>> Logic.dest_equals
|>> snd
val to_rsp = rsp_prsp_eq RS Drule.equal_elim_rule2
val opt_proven_rsp_thm = try_prove_reflexivity lthy prsp_tm
fun after_qed internal_rsp_thm lthy =
add_lift_def var qty rhs (internal_rsp_thm RS to_rsp) par_thms lthy
in
case opt_proven_rsp_thm of
SOME thm => (NONE, K (after_qed thm))
| NONE =>
let
val readable_rsp_thm_eq = mk_readable_rsp_thm_eq prsp_tm lthy
val (readable_rsp_tm, _) = Logic.dest_implies (Thm.prop_of readable_rsp_thm_eq)
val readable_rsp_tm_tnames = rename_to_tnames lthy readable_rsp_tm
fun after_qed' thm_list lthy =
let
val internal_rsp_thm = Goal.prove lthy [] [] prsp_tm
(fn {context = ctxt, ...} =>
rtac readable_rsp_thm_eq 1 THEN Proof_Context.fact_tac ctxt (hd thm_list) 1)
in
after_qed internal_rsp_thm lthy
end
in
(SOME readable_rsp_tm_tnames, after_qed')
end
end
fun lift_def var qty rhs tac par_thms lthy =
let
val (goal, after_qed) = prepare_lift_def var qty rhs par_thms lthy
in
case goal of
SOME goal =>
let
val rsp_thm = Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} => tac ctxt)
|> Thm.close_derivation
in
after_qed [[rsp_thm]] lthy
end
| NONE => after_qed [[Drule.dummy_thm]] lthy
end
(*
lifting_definition command. It opens a proof of a corresponding respectfulness
theorem in a user-friendly, readable form. Then add_lift_def is called internally.
*)
fun lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy =
let
val ((binding, SOME qty, mx), lthy) = yield_singleton Proof_Context.read_vars raw_var lthy
val var = (binding, mx)
val rhs = (Syntax.check_term lthy o Syntax.parse_term lthy) rhs_raw
val par_thms = Attrib.eval_thms lthy par_xthms
val (goal, after_qed) = prepare_lift_def var qty rhs par_thms lthy
in
Proof.theorem NONE (snd oo after_qed) [map (rpair []) (the_list goal)] lthy
end
fun quot_thm_err ctxt (rty, qty) pretty_msg =
let
val error_msg = cat_lines
["Lifting failed for the following types:",
Pretty.string_of (Pretty.block
[Pretty.str "Raw type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty]),
Pretty.string_of (Pretty.block
[Pretty.str "Abstract type:", Pretty.brk 2, Syntax.pretty_typ ctxt qty]),
"",
(Pretty.string_of (Pretty.block
[Pretty.str "Reason:", Pretty.brk 2, pretty_msg]))]
in
error error_msg
end
fun check_rty_err ctxt (rty_schematic, rty_forced) (raw_var, rhs_raw) =
let
val (_, ctxt') = yield_singleton Proof_Context.read_vars raw_var ctxt
val rhs = (Syntax.check_term ctxt' o Syntax.parse_term ctxt') rhs_raw
val error_msg = cat_lines
["Lifting failed for the following term:",
Pretty.string_of (Pretty.block
[Pretty.str "Term:", Pretty.brk 2, Syntax.pretty_term ctxt rhs]),
Pretty.string_of (Pretty.block
[Pretty.str "Type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty_schematic]),
"",
(Pretty.string_of (Pretty.block
[Pretty.str "Reason:",
Pretty.brk 2,
Pretty.str "The type of the term cannot be instantiated to",
Pretty.brk 1,
Pretty.quote (Syntax.pretty_typ ctxt rty_forced),
Pretty.str "."]))]
in
error error_msg
end
fun lift_def_cmd_with_err_handling (raw_var, rhs_raw, par_xthms) lthy =
(lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy
handle Lifting_Term.QUOT_THM (rty, qty, msg) => quot_thm_err lthy (rty, qty) msg)
handle Lifting_Term.CHECK_RTY (rty_schematic, rty_forced) =>
check_rty_err lthy (rty_schematic, rty_forced) (raw_var, rhs_raw)
(* parser and command *)
val liftdef_parser =
(((Parse.binding -- (@{keyword "::"} |-- (Parse.typ >> SOME) -- Parse.opt_mixfix')) >> Parse.triple2)
--| @{keyword "is"} -- Parse.term --
Scan.optional (@{keyword "parametric"} |-- Parse.!!! Parse.xthms1) []) >> Parse.triple1
val _ =
Outer_Syntax.local_theory_to_proof @{command_keyword lift_definition}
"definition for constants over the quotient type"
(liftdef_parser >> lift_def_cmd_with_err_handling)
end (* structure *)