kuncar@48153
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(* Title: HOL/Tools/Lifting/lifting_def.ML
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kuncar@48153
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Author: Ondrej Kuncar
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kuncar@48153
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kuncar@48153
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Definitions for constants on quotient types.
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*)
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kuncar@48153
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kuncar@48153
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signature LIFTING_DEF =
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kuncar@48153
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sig
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kuncar@52511
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val generate_parametric_transfer_rule:
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kuncar@52511
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Proof.context -> thm -> thm -> thm
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kuncar@52511
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kuncar@48153
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val add_lift_def:
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kuncar@55088
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(binding * mixfix) -> typ -> term -> thm -> thm list -> local_theory -> local_theory
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kuncar@48153
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kuncar@48153
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val lift_def_cmd:
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kuncar@55088
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(binding * string option * mixfix) * string * (Facts.ref * Args.src list) list -> local_theory -> Proof.state
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kuncar@48153
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kuncar@48153
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val can_generate_code_cert: thm -> bool
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kuncar@54788
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end
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kuncar@48153
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kuncar@48153
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structure Lifting_Def: LIFTING_DEF =
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struct
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open Lifting_Util
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infix 0 MRSL
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(* Reflexivity prover *)
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fun mono_eq_prover ctxt prop =
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let
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kuncar@57860
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val refl_rules = Lifting_Info.get_reflexivity_rules ctxt
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kuncar@57860
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val transfer_rules = Transfer.get_transfer_raw ctxt
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kuncar@57860
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kuncar@57882
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fun main_tac i = (REPEAT_ALL_NEW (DETERM o resolve_tac refl_rules) THEN_ALL_NEW
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kuncar@57882
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(REPEAT_ALL_NEW (DETERM o resolve_tac transfer_rules))) i
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in
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SOME (Goal.prove ctxt [] [] prop (K (main_tac 1)))
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handle ERROR _ => NONE
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kuncar@53131
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end
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kuncar@57860
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kuncar@58984
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fun try_prove_refl_rel ctxt rel =
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kuncar@58984
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let
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kuncar@58984
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fun mk_ge_eq x =
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kuncar@58984
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let
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val T = fastype_of x
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kuncar@58984
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in
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kuncar@58984
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Const (@{const_name "less_eq"}, T --> T --> HOLogic.boolT) $
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kuncar@58984
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(Const (@{const_name HOL.eq}, T)) $ x
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end;
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val goal = HOLogic.mk_Trueprop (mk_ge_eq rel);
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in
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mono_eq_prover ctxt goal
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end;
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kuncar@53131
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fun try_prove_reflexivity ctxt prop =
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let
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val thy = Proof_Context.theory_of ctxt
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val cprop = cterm_of thy prop
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val rule = @{thm ge_eq_refl}
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val concl_pat = Drule.strip_imp_concl (cprop_of rule)
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val insts = Thm.first_order_match (concl_pat, cprop)
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val rule = Drule.instantiate_normalize insts rule
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val prop = hd (prems_of rule)
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in
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case mono_eq_prover ctxt prop of
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SOME thm => SOME (thm RS rule)
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| NONE => NONE
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kuncar@56951
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end
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kuncar@53131
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kuncar@55223
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(*
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Generates a parametrized transfer rule.
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transfer_rule - of the form T t f
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parametric_transfer_rule - of the form par_R t' t
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Result: par_T t' f, after substituing op= for relations in par_R that relate
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a type constructor to the same type constructor, it is a merge of (par_R' OO T) t' f
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using Lifting_Term.merge_transfer_relations
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*)
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kuncar@52511
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fun generate_parametric_transfer_rule ctxt transfer_rule parametric_transfer_rule =
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let
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fun preprocess ctxt thm =
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let
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val tm = (strip_args 2 o HOLogic.dest_Trueprop o concl_of) thm;
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val param_rel = (snd o dest_comb o fst o dest_comb) tm;
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val thy = Proof_Context.theory_of ctxt;
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val free_vars = Term.add_vars param_rel [];
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fun make_subst (var as (_, typ)) subst =
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let
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val [rty, rty'] = binder_types typ
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in
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if (Term.is_TVar rty andalso is_Type rty') then
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(Var var, HOLogic.eq_const rty')::subst
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else
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subst
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end;
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val subst = fold make_subst free_vars [];
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val csubst = map (pairself (cterm_of thy)) subst;
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val inst_thm = Drule.cterm_instantiate csubst thm;
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in
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Conv.fconv_rule
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((Conv.concl_conv (nprems_of inst_thm) o HOLogic.Trueprop_conv o Conv.fun2_conv o Conv.arg1_conv)
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wenzelm@56084
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(Raw_Simplifier.rewrite ctxt false (Transfer.get_sym_relator_eq ctxt))) inst_thm
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end
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fun inst_relcomppI thy ant1 ant2 =
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let
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val t1 = (HOLogic.dest_Trueprop o concl_of) ant1
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val t2 = (HOLogic.dest_Trueprop o prop_of) ant2
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val fun1 = cterm_of thy (strip_args 2 t1)
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val args1 = map (cterm_of thy) (get_args 2 t1)
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val fun2 = cterm_of thy (strip_args 2 t2)
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val args2 = map (cterm_of thy) (get_args 1 t2)
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val relcomppI = Drule.incr_indexes2 ant1 ant2 @{thm relcomppI}
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val vars = (rev (Term.add_vars (prop_of relcomppI) []))
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val subst = map (apfst ((cterm_of thy) o Var)) (vars ~~ ([fun1] @ args1 @ [fun2] @ args2))
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in
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Drule.cterm_instantiate subst relcomppI
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end
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kuncar@52511
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wenzelm@56337
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fun zip_transfer_rules ctxt thm =
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wenzelm@56337
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let
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val thy = Proof_Context.theory_of ctxt
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kuncar@52511
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fun mk_POS ty = Const (@{const_name POS}, ty --> ty --> HOLogic.boolT)
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val rel = (Thm.dest_fun2 o Thm.dest_arg o cprop_of) thm
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val typ = (typ_of o ctyp_of_term) rel
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val POS_const = cterm_of thy (mk_POS typ)
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kuncar@52511
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val var = cterm_of thy (Var (("X", #maxidx (rep_cterm (rel)) + 1), typ))
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kuncar@52511
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val goal = Thm.apply (cterm_of thy HOLogic.Trueprop) (Thm.apply (Thm.apply POS_const rel) var)
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kuncar@52511
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in
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kuncar@52511
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[Lifting_Term.merge_transfer_relations ctxt goal, thm] MRSL @{thm POS_apply}
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kuncar@52511
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end
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kuncar@52511
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kuncar@52511
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val thm = (inst_relcomppI (Proof_Context.theory_of ctxt) parametric_transfer_rule transfer_rule)
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kuncar@52511
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OF [parametric_transfer_rule, transfer_rule]
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kuncar@52511
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val preprocessed_thm = preprocess ctxt thm
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kuncar@52511
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val orig_ctxt = ctxt
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kuncar@52511
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val (fixed_thm, ctxt) = yield_singleton (apfst snd oo Variable.import true) preprocessed_thm ctxt
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kuncar@52511
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val assms = cprems_of fixed_thm
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kuncar@52511
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val add_transfer_rule = Thm.attribute_declaration Transfer.transfer_add
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wenzelm@56337
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val (prems, ctxt) = fold_map Thm.assume_hyps assms ctxt
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wenzelm@56337
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val ctxt = Context.proof_map (fold add_transfer_rule prems) ctxt
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kuncar@52511
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val zipped_thm =
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kuncar@52511
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fixed_thm
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kuncar@52511
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|> undisch_all
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kuncar@52511
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|> zip_transfer_rules ctxt
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kuncar@52511
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|> implies_intr_list assms
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kuncar@52511
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|> singleton (Variable.export ctxt orig_ctxt)
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kuncar@52511
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in
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kuncar@52511
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zipped_thm
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kuncar@52511
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end
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kuncar@52511
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kuncar@52511
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fun print_generate_transfer_info msg =
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kuncar@52511
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let
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kuncar@52511
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val error_msg = cat_lines
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kuncar@52511
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["Generation of a parametric transfer rule failed.",
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kuncar@52511
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(Pretty.string_of (Pretty.block
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kuncar@52511
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[Pretty.str "Reason:", Pretty.brk 2, msg]))]
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kuncar@52511
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in
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kuncar@52511
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error error_msg
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kuncar@52511
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end
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kuncar@52511
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kuncar@55088
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fun map_ter _ x [] = x
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kuncar@55088
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| map_ter f _ xs = map f xs
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kuncar@55088
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kuncar@55088
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fun generate_transfer_rules lthy quot_thm rsp_thm def_thm par_thms =
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kuncar@52511
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let
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kuncar@52511
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val transfer_rule =
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kuncar@52511
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([quot_thm, rsp_thm, def_thm] MRSL @{thm Quotient_to_transfer})
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kuncar@52511
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|> Lifting_Term.parametrize_transfer_rule lthy
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kuncar@52511
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in
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(map_ter (generate_parametric_transfer_rule lthy transfer_rule) [transfer_rule] par_thms
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kuncar@55088
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handle Lifting_Term.MERGE_TRANSFER_REL msg => (print_generate_transfer_info msg; [transfer_rule]))
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kuncar@52511
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end
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kuncar@52511
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kuncar@48569
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(* Generation of the code certificate from the rsp theorem *)
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kuncar@48153
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kuncar@48153
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fun get_body_types (Type ("fun", [_, U]), Type ("fun", [_, V])) = get_body_types (U, V)
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kuncar@48153
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| get_body_types (U, V) = (U, V)
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kuncar@48153
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kuncar@48153
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fun get_binder_types (Type ("fun", [T, U]), Type ("fun", [V, W])) = (T, V) :: get_binder_types (U, W)
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kuncar@48153
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| get_binder_types _ = []
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kuncar@48153
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blanchet@57287
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fun get_binder_types_by_rel (Const (@{const_name "rel_fun"}, _) $ _ $ S) (Type ("fun", [T, U]), Type ("fun", [V, W])) =
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kuncar@48952
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(T, V) :: get_binder_types_by_rel S (U, W)
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kuncar@48952
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| get_binder_types_by_rel _ _ = []
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kuncar@48952
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blanchet@57287
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fun get_body_type_by_rel (Const (@{const_name "rel_fun"}, _) $ _ $ S) (Type ("fun", [_, U]), Type ("fun", [_, V])) =
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kuncar@48952
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get_body_type_by_rel S (U, V)
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kuncar@48952
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| get_body_type_by_rel _ (U, V) = (U, V)
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kuncar@48952
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kuncar@58984
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fun get_binder_rels (Const (@{const_name "rel_fun"}, _) $ R $ S) = R :: get_binder_rels S
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kuncar@58984
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| get_binder_rels _ = []
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kuncar@58984
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kuncar@48153
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fun force_rty_type ctxt rty rhs =
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kuncar@48153
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let
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kuncar@48153
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val thy = Proof_Context.theory_of ctxt
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kuncar@48153
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val rhs_schematic = singleton (Variable.polymorphic ctxt) rhs
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kuncar@48153
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val rty_schematic = fastype_of rhs_schematic
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kuncar@48153
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val match = Sign.typ_match thy (rty_schematic, rty) Vartab.empty
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kuncar@48153
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in
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kuncar@48153
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Envir.subst_term_types match rhs_schematic
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kuncar@48153
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end
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kuncar@48153
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kuncar@48153
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fun unabs_def ctxt def =
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kuncar@48153
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let
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kuncar@48153
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val (_, rhs) = Thm.dest_equals (cprop_of def)
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kuncar@48153
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fun dest_abs (Abs (var_name, T, _)) = (var_name, T)
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kuncar@48153
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| dest_abs tm = raise TERM("get_abs_var",[tm])
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kuncar@48153
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val (var_name, T) = dest_abs (term_of rhs)
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kuncar@48153
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val (new_var_names, ctxt') = Variable.variant_fixes [var_name] ctxt
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kuncar@48153
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val thy = Proof_Context.theory_of ctxt'
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kuncar@48153
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val refl_thm = Thm.reflexive (cterm_of thy (Free (hd new_var_names, T)))
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kuncar@48153
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in
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kuncar@48153
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Thm.combination def refl_thm |>
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kuncar@48153
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singleton (Proof_Context.export ctxt' ctxt)
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kuncar@48153
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end
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kuncar@48153
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kuncar@48153
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fun unabs_all_def ctxt def =
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kuncar@48153
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let
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kuncar@48153
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val (_, rhs) = Thm.dest_equals (cprop_of def)
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kuncar@48153
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val xs = strip_abs_vars (term_of rhs)
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kuncar@48153
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in
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kuncar@48153
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fold (K (unabs_def ctxt)) xs def
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kuncar@48153
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end
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kuncar@48153
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kuncar@48153
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val map_fun_unfolded =
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kuncar@48153
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@{thm map_fun_def[abs_def]} |>
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kuncar@48153
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unabs_def @{context} |>
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kuncar@48153
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unabs_def @{context} |>
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kuncar@48153
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Local_Defs.unfold @{context} [@{thm comp_def}]
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kuncar@48153
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kuncar@48153
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fun unfold_fun_maps ctm =
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kuncar@48153
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let
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kuncar@48153
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fun unfold_conv ctm =
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kuncar@48153
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case (Thm.term_of ctm) of
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kuncar@48153
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Const (@{const_name "map_fun"}, _) $ _ $ _ =>
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kuncar@48153
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(Conv.arg_conv unfold_conv then_conv Conv.rewr_conv map_fun_unfolded) ctm
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kuncar@48153
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| _ => Conv.all_conv ctm
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kuncar@48153
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in
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kuncar@48952
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(Conv.fun_conv unfold_conv) ctm
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kuncar@48952
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end
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kuncar@48952
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kuncar@48952
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fun unfold_fun_maps_beta ctm =
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kuncar@48952
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let val try_beta_conv = Conv.try_conv (Thm.beta_conversion false)
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kuncar@48952
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in
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kuncar@48952
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(unfold_fun_maps then_conv try_beta_conv) ctm
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kuncar@48153
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end
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kuncar@48153
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kuncar@48153
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fun prove_rel ctxt rsp_thm (rty, qty) =
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kuncar@48153
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let
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kuncar@48153
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val ty_args = get_binder_types (rty, qty)
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kuncar@48153
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fun disch_arg args_ty thm =
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kuncar@48153
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let
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kuncar@48375
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val quot_thm = Lifting_Term.prove_quot_thm ctxt args_ty
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kuncar@48153
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in
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kuncar@48153
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[quot_thm, thm] MRSL @{thm apply_rsp''}
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kuncar@48153
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end
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kuncar@48153
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in
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kuncar@48153
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fold disch_arg ty_args rsp_thm
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kuncar@48153
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end
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kuncar@48153
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kuncar@48153
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exception CODE_CERT_GEN of string
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kuncar@48153
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kuncar@48153
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fun simplify_code_eq ctxt def_thm =
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kuncar@49039
|
269 |
Local_Defs.unfold ctxt [@{thm o_apply}, @{thm map_fun_def}, @{thm id_apply}] def_thm
|
kuncar@48153
|
270 |
|
kuncar@48723
|
271 |
(*
|
kuncar@48723
|
272 |
quot_thm - quotient theorem (Quotient R Abs Rep T).
|
kuncar@48723
|
273 |
returns: whether the Lifting package is capable to generate code for the abstract type
|
kuncar@48723
|
274 |
represented by quot_thm
|
kuncar@48723
|
275 |
*)
|
kuncar@48723
|
276 |
|
kuncar@48153
|
277 |
fun can_generate_code_cert quot_thm =
|
kuncar@48966
|
278 |
case quot_thm_rel quot_thm of
|
kuncar@48153
|
279 |
Const (@{const_name HOL.eq}, _) => true
|
kuncar@57861
|
280 |
| Const (@{const_name eq_onp}, _) $ _ => true
|
kuncar@48153
|
281 |
| _ => false
|
kuncar@48153
|
282 |
|
kuncar@56952
|
283 |
fun generate_rep_eq ctxt def_thm rsp_thm (rty, qty) =
|
kuncar@48153
|
284 |
let
|
kuncar@48952
|
285 |
val unfolded_def = Conv.fconv_rule (Conv.arg_conv unfold_fun_maps_beta) def_thm
|
kuncar@48153
|
286 |
val unabs_def = unabs_all_def ctxt unfolded_def
|
kuncar@56952
|
287 |
in
|
kuncar@56952
|
288 |
if body_type rty = body_type qty then
|
kuncar@57065
|
289 |
SOME (simplify_code_eq ctxt (unabs_def RS @{thm meta_eq_to_obj_eq}))
|
kuncar@56952
|
290 |
else
|
kuncar@56952
|
291 |
let
|
kuncar@56952
|
292 |
val thy = Proof_Context.theory_of ctxt
|
kuncar@56952
|
293 |
val quot_thm = Lifting_Term.prove_quot_thm ctxt (get_body_types (rty, qty))
|
blanchet@57287
|
294 |
val rel_fun = prove_rel ctxt rsp_thm (rty, qty)
|
blanchet@57287
|
295 |
val rep_abs_thm = [quot_thm, rel_fun] MRSL @{thm Quotient_rep_abs_eq}
|
kuncar@56952
|
296 |
in
|
kuncar@56952
|
297 |
case mono_eq_prover ctxt (hd(prems_of rep_abs_thm)) of
|
kuncar@56952
|
298 |
SOME mono_eq_thm =>
|
kuncar@56952
|
299 |
let
|
kuncar@56952
|
300 |
val rep_abs_eq = mono_eq_thm RS rep_abs_thm
|
kuncar@56952
|
301 |
val rep = (cterm_of thy o quot_thm_rep) quot_thm
|
kuncar@56952
|
302 |
val rep_refl = Thm.reflexive rep RS @{thm meta_eq_to_obj_eq}
|
kuncar@56952
|
303 |
val repped_eq = [rep_refl, unabs_def RS @{thm meta_eq_to_obj_eq}] MRSL @{thm cong}
|
kuncar@56952
|
304 |
val code_cert = [repped_eq, rep_abs_eq] MRSL trans
|
kuncar@56952
|
305 |
in
|
kuncar@56952
|
306 |
SOME (simplify_code_eq ctxt code_cert)
|
kuncar@56952
|
307 |
end
|
kuncar@56952
|
308 |
| NONE => NONE
|
kuncar@56952
|
309 |
end
|
kuncar@48153
|
310 |
end
|
kuncar@48153
|
311 |
|
kuncar@48952
|
312 |
fun generate_abs_eq ctxt def_thm rsp_thm quot_thm =
|
kuncar@48952
|
313 |
let
|
kuncar@48952
|
314 |
val abs_eq_with_assms =
|
kuncar@48952
|
315 |
let
|
kuncar@48966
|
316 |
val (rty, qty) = quot_thm_rty_qty quot_thm
|
kuncar@48966
|
317 |
val rel = quot_thm_rel quot_thm
|
kuncar@48952
|
318 |
val ty_args = get_binder_types_by_rel rel (rty, qty)
|
kuncar@48952
|
319 |
val body_type = get_body_type_by_rel rel (rty, qty)
|
kuncar@48952
|
320 |
val quot_ret_thm = Lifting_Term.prove_quot_thm ctxt body_type
|
kuncar@48952
|
321 |
|
kuncar@48952
|
322 |
val rep_abs_folded_unmapped_thm =
|
kuncar@48952
|
323 |
let
|
kuncar@48952
|
324 |
val rep_id = [quot_thm, def_thm] MRSL @{thm Quotient_Rep_eq}
|
kuncar@48952
|
325 |
val ctm = Thm.dest_equals_lhs (cprop_of rep_id)
|
kuncar@48952
|
326 |
val unfolded_maps_eq = unfold_fun_maps ctm
|
kuncar@48952
|
327 |
val t1 = [quot_thm, def_thm, rsp_thm] MRSL @{thm Quotient_rep_abs_fold_unmap}
|
kuncar@48952
|
328 |
val prems_pat = (hd o Drule.cprems_of) t1
|
kuncar@48952
|
329 |
val insts = Thm.first_order_match (prems_pat, cprop_of unfolded_maps_eq)
|
kuncar@48952
|
330 |
in
|
kuncar@48952
|
331 |
unfolded_maps_eq RS (Drule.instantiate_normalize insts t1)
|
kuncar@48952
|
332 |
end
|
kuncar@48952
|
333 |
in
|
kuncar@48952
|
334 |
rep_abs_folded_unmapped_thm
|
blanchet@57287
|
335 |
|> fold (fn _ => fn thm => thm RS @{thm rel_funD2}) ty_args
|
kuncar@48952
|
336 |
|> (fn x => x RS (@{thm Quotient_rel_abs2} OF [quot_ret_thm]))
|
kuncar@48952
|
337 |
end
|
kuncar@48952
|
338 |
|
kuncar@58984
|
339 |
val prem_rels = get_binder_rels (quot_thm_rel quot_thm);
|
kuncar@58984
|
340 |
val proved_assms = prem_rels |> map (try_prove_refl_rel ctxt)
|
kuncar@58984
|
341 |
|> map_index (apfst (fn x => x + 1)) |> filter (is_some o snd) |> map (apsnd the)
|
kuncar@58984
|
342 |
|> map (apsnd (fn assm => assm RS @{thm ge_eq_refl}))
|
kuncar@58984
|
343 |
val abs_eq = fold_rev (fn (i, assm) => fn thm => assm RSN (i, thm)) proved_assms abs_eq_with_assms
|
kuncar@48952
|
344 |
in
|
kuncar@48952
|
345 |
simplify_code_eq ctxt abs_eq
|
kuncar@48952
|
346 |
end
|
kuncar@48952
|
347 |
|
kuncar@57066
|
348 |
|
kuncar@57066
|
349 |
fun register_code_eq_thy abs_eq_thm opt_rep_eq_thm (rty, qty) thy =
|
kuncar@57066
|
350 |
let
|
kuncar@57066
|
351 |
fun no_abstr (t $ u) = no_abstr t andalso no_abstr u
|
kuncar@57066
|
352 |
| no_abstr (Abs (_, _, t)) = no_abstr t
|
kuncar@57066
|
353 |
| no_abstr (Const (name, _)) = not (Code.is_abstr thy name)
|
kuncar@57066
|
354 |
| no_abstr _ = true
|
kuncar@57066
|
355 |
fun is_valid_eq eqn = can (Code.assert_eqn thy) (mk_meta_eq eqn, true)
|
kuncar@57066
|
356 |
andalso no_abstr (prop_of eqn)
|
kuncar@57066
|
357 |
fun is_valid_abs_eq abs_eq = can (Code.assert_abs_eqn thy NONE) (mk_meta_eq abs_eq)
|
kuncar@57066
|
358 |
|
kuncar@57066
|
359 |
in
|
kuncar@57066
|
360 |
if is_valid_eq abs_eq_thm then
|
kuncar@57066
|
361 |
Code.add_default_eqn abs_eq_thm thy
|
kuncar@57066
|
362 |
else
|
kuncar@48153
|
363 |
let
|
kuncar@57066
|
364 |
val (rty_body, qty_body) = get_body_types (rty, qty)
|
kuncar@48153
|
365 |
in
|
kuncar@57066
|
366 |
if rty_body = qty_body then
|
kuncar@57066
|
367 |
Code.add_default_eqn (the opt_rep_eq_thm) thy
|
kuncar@48952
|
368 |
else
|
kuncar@57066
|
369 |
if is_some opt_rep_eq_thm andalso is_valid_abs_eq (the opt_rep_eq_thm)
|
kuncar@57066
|
370 |
then
|
kuncar@57066
|
371 |
Code.add_abs_eqn (the opt_rep_eq_thm) thy
|
kuncar@57066
|
372 |
else
|
kuncar@57066
|
373 |
thy
|
kuncar@48952
|
374 |
end
|
kuncar@48952
|
375 |
end
|
kuncar@48153
|
376 |
|
kuncar@57066
|
377 |
local
|
kuncar@57066
|
378 |
fun encode_code_eq thy abs_eq opt_rep_eq (rty, qty) =
|
kuncar@57066
|
379 |
let
|
kuncar@57066
|
380 |
fun mk_type typ = typ |> Logic.mk_type |> cterm_of thy |> Drule.mk_term
|
kuncar@57066
|
381 |
in
|
kuncar@57066
|
382 |
Conjunction.intr_balanced [abs_eq, (the_default TrueI opt_rep_eq), mk_type rty, mk_type qty]
|
kuncar@57066
|
383 |
end
|
kuncar@57066
|
384 |
|
kuncar@57066
|
385 |
fun decode_code_eq thm =
|
kuncar@57066
|
386 |
let
|
kuncar@57066
|
387 |
val [abs_eq, rep_eq, rty, qty] = Conjunction.elim_balanced 4 thm
|
kuncar@57066
|
388 |
val opt_rep_eq = if Thm.eq_thm_prop (rep_eq, TrueI) then NONE else SOME rep_eq
|
kuncar@57066
|
389 |
fun dest_type typ = typ |> Drule.dest_term |> term_of |> Logic.dest_type
|
kuncar@57066
|
390 |
in
|
kuncar@57066
|
391 |
(abs_eq, opt_rep_eq, (dest_type rty, dest_type qty))
|
kuncar@57066
|
392 |
end
|
kuncar@57066
|
393 |
|
kuncar@57066
|
394 |
fun register_encoded_code_eq thm thy =
|
kuncar@57066
|
395 |
let
|
kuncar@57066
|
396 |
val (abs_eq_thm, opt_rep_eq_thm, (rty, qty)) = decode_code_eq thm
|
kuncar@57066
|
397 |
in
|
kuncar@57066
|
398 |
register_code_eq_thy abs_eq_thm opt_rep_eq_thm (rty, qty) thy
|
kuncar@57066
|
399 |
end
|
kuncar@57066
|
400 |
|
kuncar@57066
|
401 |
val register_code_eq_attribute = Thm.declaration_attribute
|
kuncar@57066
|
402 |
(fn thm => Context.mapping (register_encoded_code_eq thm) I)
|
kuncar@57066
|
403 |
val register_code_eq_attrib = Attrib.internal (K register_code_eq_attribute)
|
kuncar@57066
|
404 |
in
|
kuncar@57066
|
405 |
|
kuncar@57066
|
406 |
fun register_code_eq abs_eq_thm opt_rep_eq_thm (rty, qty) lthy =
|
kuncar@57066
|
407 |
let
|
kuncar@57066
|
408 |
val thy = Proof_Context.theory_of lthy
|
kuncar@57066
|
409 |
val encoded_code_eq = encode_code_eq thy abs_eq_thm opt_rep_eq_thm (rty, qty)
|
kuncar@57066
|
410 |
in
|
kuncar@57066
|
411 |
(snd oo Local_Theory.note) ((Binding.empty, [register_code_eq_attrib]),
|
kuncar@57066
|
412 |
[encoded_code_eq]) lthy
|
kuncar@57066
|
413 |
end
|
kuncar@57066
|
414 |
end
|
kuncar@57066
|
415 |
|
kuncar@48723
|
416 |
(*
|
kuncar@48723
|
417 |
Defines an operation on an abstract type in terms of a corresponding operation
|
kuncar@48723
|
418 |
on a representation type.
|
kuncar@48723
|
419 |
|
kuncar@48723
|
420 |
var - a binding and a mixfix of the new constant being defined
|
kuncar@48723
|
421 |
qty - an abstract type of the new constant
|
kuncar@48723
|
422 |
rhs - a term representing the new constant on the raw level
|
kuncar@48952
|
423 |
rsp_thm - a respectfulness theorem in the internal tagged form (like '(R ===> R ===> R) f f'),
|
kuncar@48723
|
424 |
i.e. "(Lifting_Term.equiv_relation (fastype_of rhs, qty)) $ rhs $ rhs"
|
kuncar@55223
|
425 |
par_thms - a parametricity theorem for rhs
|
kuncar@48723
|
426 |
*)
|
kuncar@48153
|
427 |
|
kuncar@55088
|
428 |
fun add_lift_def var qty rhs rsp_thm par_thms lthy =
|
kuncar@48153
|
429 |
let
|
kuncar@48153
|
430 |
val rty = fastype_of rhs
|
kuncar@48952
|
431 |
val quot_thm = Lifting_Term.prove_quot_thm lthy (rty, qty)
|
kuncar@48966
|
432 |
val absrep_trm = quot_thm_abs quot_thm
|
kuncar@48153
|
433 |
val rty_forced = (domain_type o fastype_of) absrep_trm
|
kuncar@48153
|
434 |
val forced_rhs = force_rty_type lthy rty_forced rhs
|
wenzelm@54344
|
435 |
val lhs = Free (Binding.name_of (#1 var), qty)
|
kuncar@48153
|
436 |
val prop = Logic.mk_equals (lhs, absrep_trm $ forced_rhs)
|
kuncar@48153
|
437 |
val (_, prop') = Local_Defs.cert_def lthy prop
|
kuncar@48153
|
438 |
val (_, newrhs) = Local_Defs.abs_def prop'
|
kuncar@48153
|
439 |
|
kuncar@48153
|
440 |
val ((_, (_ , def_thm)), lthy') =
|
kuncar@48153
|
441 |
Local_Theory.define (var, ((Thm.def_binding (#1 var), []), newrhs)) lthy
|
kuncar@48153
|
442 |
|
kuncar@55088
|
443 |
val transfer_rules = generate_transfer_rules lthy' quot_thm rsp_thm def_thm par_thms
|
huffman@50990
|
444 |
|
kuncar@48952
|
445 |
val abs_eq_thm = generate_abs_eq lthy' def_thm rsp_thm quot_thm
|
kuncar@52511
|
446 |
val opt_rep_eq_thm = generate_rep_eq lthy' def_thm rsp_thm (rty_forced, qty)
|
huffman@48209
|
447 |
|
kuncar@48411
|
448 |
fun qualify defname suffix = Binding.qualified true suffix defname
|
kuncar@48153
|
449 |
|
kuncar@48411
|
450 |
val lhs_name = (#1 var)
|
kuncar@48153
|
451 |
val rsp_thm_name = qualify lhs_name "rsp"
|
kuncar@48952
|
452 |
val abs_eq_thm_name = qualify lhs_name "abs_eq"
|
kuncar@48952
|
453 |
val rep_eq_thm_name = qualify lhs_name "rep_eq"
|
kuncar@52511
|
454 |
val transfer_rule_name = qualify lhs_name "transfer"
|
huffman@48231
|
455 |
val transfer_attr = Attrib.internal (K Transfer.transfer_add)
|
kuncar@48153
|
456 |
in
|
kuncar@48153
|
457 |
lthy'
|
kuncar@48153
|
458 |
|> (snd oo Local_Theory.note) ((rsp_thm_name, []), [rsp_thm])
|
kuncar@55088
|
459 |
|> (snd oo Local_Theory.note) ((transfer_rule_name, [transfer_attr]), transfer_rules)
|
kuncar@48952
|
460 |
|> (snd oo Local_Theory.note) ((abs_eq_thm_name, []), [abs_eq_thm])
|
kuncar@52511
|
461 |
|> (case opt_rep_eq_thm of
|
kuncar@48952
|
462 |
SOME rep_eq_thm => (snd oo Local_Theory.note) ((rep_eq_thm_name, []), [rep_eq_thm])
|
kuncar@48952
|
463 |
| NONE => I)
|
kuncar@57066
|
464 |
|> register_code_eq abs_eq_thm opt_rep_eq_thm (rty_forced, qty)
|
kuncar@48153
|
465 |
end
|
kuncar@48153
|
466 |
|
kuncar@57073
|
467 |
local
|
kuncar@57861
|
468 |
val eq_onp_assms_tac_fixed_rules = map (Transfer.prep_transfer_domain_thm @{context})
|
kuncar@57073
|
469 |
[@{thm pcr_Domainp_total}, @{thm pcr_Domainp_par_left_total}, @{thm pcr_Domainp_par},
|
kuncar@57073
|
470 |
@{thm pcr_Domainp}]
|
kuncar@57073
|
471 |
in
|
kuncar@48153
|
472 |
fun mk_readable_rsp_thm_eq tm lthy =
|
kuncar@48153
|
473 |
let
|
kuncar@48153
|
474 |
val ctm = cterm_of (Proof_Context.theory_of lthy) tm
|
kuncar@48153
|
475 |
|
kuncar@57073
|
476 |
fun assms_rewr_conv tactic rule ct =
|
kuncar@57073
|
477 |
let
|
kuncar@57073
|
478 |
fun prove_extra_assms thm =
|
kuncar@57073
|
479 |
let
|
kuncar@57073
|
480 |
val assms = cprems_of thm
|
kuncar@57073
|
481 |
fun finish thm = if Thm.no_prems thm then SOME (Goal.conclude thm) else NONE
|
kuncar@57073
|
482 |
fun prove ctm = Option.mapPartial finish (SINGLE tactic (Goal.init ctm))
|
kuncar@57073
|
483 |
in
|
kuncar@57073
|
484 |
map_interrupt prove assms
|
kuncar@57073
|
485 |
end
|
kuncar@57073
|
486 |
|
kuncar@57073
|
487 |
fun cconl_of thm = Drule.strip_imp_concl (cprop_of thm)
|
kuncar@57073
|
488 |
fun lhs_of thm = fst (Thm.dest_equals (cconl_of thm))
|
kuncar@57073
|
489 |
fun rhs_of thm = snd (Thm.dest_equals (cconl_of thm))
|
kuncar@57073
|
490 |
val rule1 = Thm.incr_indexes (#maxidx (Thm.rep_cterm ct) + 1) rule;
|
kuncar@57073
|
491 |
val lhs = lhs_of rule1;
|
kuncar@57073
|
492 |
val rule2 = Thm.rename_boundvars (Thm.term_of lhs) (Thm.term_of ct) rule1;
|
kuncar@57073
|
493 |
val rule3 =
|
kuncar@57073
|
494 |
Thm.instantiate (Thm.match (lhs, ct)) rule2
|
kuncar@57073
|
495 |
handle Pattern.MATCH => raise CTERM ("assms_rewr_conv", [lhs, ct]);
|
kuncar@57073
|
496 |
val proved_assms = prove_extra_assms rule3
|
kuncar@57073
|
497 |
in
|
kuncar@57073
|
498 |
case proved_assms of
|
kuncar@57073
|
499 |
SOME proved_assms =>
|
kuncar@57073
|
500 |
let
|
kuncar@57073
|
501 |
val rule3 = proved_assms MRSL rule3
|
kuncar@57073
|
502 |
val rule4 =
|
kuncar@57073
|
503 |
if lhs_of rule3 aconvc ct then rule3
|
kuncar@57073
|
504 |
else
|
kuncar@57073
|
505 |
let val ceq = Thm.dest_fun2 (Thm.cprop_of rule3)
|
kuncar@57073
|
506 |
in rule3 COMP Thm.trivial (Thm.mk_binop ceq ct (rhs_of rule3)) end
|
kuncar@57073
|
507 |
in Thm.transitive rule4 (Thm.beta_conversion true (rhs_of rule4)) end
|
kuncar@57073
|
508 |
| NONE => Conv.no_conv ct
|
kuncar@57073
|
509 |
end
|
kuncar@57073
|
510 |
|
kuncar@57073
|
511 |
fun assms_rewrs_conv tactic rules = Conv.first_conv (map (assms_rewr_conv tactic) rules)
|
kuncar@57073
|
512 |
|
kuncar@48153
|
513 |
fun simp_arrows_conv ctm =
|
kuncar@48153
|
514 |
let
|
kuncar@48153
|
515 |
val unfold_conv = Conv.rewrs_conv
|
kuncar@57861
|
516 |
[@{thm rel_fun_eq_eq_onp[THEN eq_reflection]},
|
kuncar@57861
|
517 |
@{thm rel_fun_eq_onp_rel[THEN eq_reflection]},
|
blanchet@57287
|
518 |
@{thm rel_fun_eq[THEN eq_reflection]},
|
blanchet@57287
|
519 |
@{thm rel_fun_eq_rel[THEN eq_reflection]},
|
blanchet@57287
|
520 |
@{thm rel_fun_def[THEN eq_reflection]}]
|
kuncar@48153
|
521 |
fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
|
kuncar@57861
|
522 |
val eq_onp_assms_tac_rules = @{thm left_unique_OO} ::
|
kuncar@57861
|
523 |
eq_onp_assms_tac_fixed_rules @ (Transfer.get_transfer_raw lthy)
|
kuncar@57861
|
524 |
val eq_onp_assms_tac = (TRY o REPEAT_ALL_NEW (resolve_tac eq_onp_assms_tac_rules)
|
kuncar@57073
|
525 |
THEN_ALL_NEW (DETERM o Transfer.eq_tac lthy)) 1
|
kuncar@57861
|
526 |
val relator_eq_onp_conv = Conv.bottom_conv
|
kuncar@57861
|
527 |
(K (Conv.try_conv (assms_rewrs_conv eq_onp_assms_tac
|
kuncar@57861
|
528 |
(Lifting_Info.get_relator_eq_onp_rules lthy)))) lthy
|
kuncar@50641
|
529 |
val relator_eq_conv = Conv.bottom_conv
|
kuncar@50641
|
530 |
(K (Conv.try_conv (Conv.rewrs_conv (Transfer.get_relator_eq lthy)))) lthy
|
kuncar@48153
|
531 |
in
|
kuncar@48153
|
532 |
case (Thm.term_of ctm) of
|
blanchet@57287
|
533 |
Const (@{const_name "rel_fun"}, _) $ _ $ _ =>
|
kuncar@50641
|
534 |
(binop_conv2 simp_arrows_conv simp_arrows_conv then_conv unfold_conv) ctm
|
kuncar@57861
|
535 |
| _ => (relator_eq_onp_conv then_conv relator_eq_conv) ctm
|
kuncar@48153
|
536 |
end
|
kuncar@48952
|
537 |
|
kuncar@48153
|
538 |
val unfold_ret_val_invs = Conv.bottom_conv
|
kuncar@57866
|
539 |
(K (Conv.try_conv (Conv.rewr_conv @{thm eq_onp_same_args[THEN eq_reflection]}))) lthy
|
kuncar@57115
|
540 |
val unfold_inv_conv =
|
kuncar@57861
|
541 |
Conv.top_sweep_conv (K (Conv.rewr_conv @{thm eq_onp_def[THEN eq_reflection]})) lthy
|
kuncar@57882
|
542 |
val simp_conv = HOLogic.Trueprop_conv (Conv.fun2_conv simp_arrows_conv)
|
kuncar@48153
|
543 |
val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
|
kuncar@48153
|
544 |
val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) lthy
|
kuncar@48153
|
545 |
val beta_conv = Thm.beta_conversion true
|
kuncar@48153
|
546 |
val eq_thm =
|
kuncar@57115
|
547 |
(simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs
|
kuncar@57115
|
548 |
then_conv unfold_inv_conv) ctm
|
kuncar@48153
|
549 |
in
|
wenzelm@56084
|
550 |
Object_Logic.rulify lthy (eq_thm RS Drule.equal_elim_rule2)
|
kuncar@48153
|
551 |
end
|
kuncar@57073
|
552 |
end
|
kuncar@48153
|
553 |
|
kuncar@48470
|
554 |
fun rename_to_tnames ctxt term =
|
kuncar@48470
|
555 |
let
|
wenzelm@57587
|
556 |
fun all_typs (Const (@{const_name Pure.all}, _) $ Abs (_, T, t)) = T :: all_typs t
|
kuncar@48470
|
557 |
| all_typs _ = []
|
kuncar@48153
|
558 |
|
wenzelm@57587
|
559 |
fun rename (Const (@{const_name Pure.all}, T1) $ Abs (_, T2, t)) (new_name :: names) =
|
wenzelm@57587
|
560 |
(Const (@{const_name Pure.all}, T1) $ Abs (new_name, T2, rename t names))
|
kuncar@48470
|
561 |
| rename t _ = t
|
kuncar@48470
|
562 |
|
kuncar@48470
|
563 |
val (fixed_def_t, _) = yield_singleton (Variable.importT_terms) term ctxt
|
kuncar@48470
|
564 |
val new_names = Datatype_Prop.make_tnames (all_typs fixed_def_t)
|
kuncar@48470
|
565 |
in
|
kuncar@48470
|
566 |
rename term new_names
|
kuncar@48470
|
567 |
end
|
kuncar@48153
|
568 |
|
kuncar@57882
|
569 |
(* This is not very cheap way of getting the rules but we have only few active
|
kuncar@57882
|
570 |
liftings in the current setting *)
|
kuncar@57882
|
571 |
fun get_cr_pcr_eqs ctxt =
|
kuncar@57882
|
572 |
let
|
kuncar@57882
|
573 |
fun collect (data : Lifting_Info.quotient) l =
|
kuncar@57882
|
574 |
if is_some (#pcr_info data)
|
kuncar@57882
|
575 |
then ((Thm.symmetric o safe_mk_meta_eq o #pcr_cr_eq o the o #pcr_info) data :: l)
|
kuncar@57882
|
576 |
else l
|
kuncar@57882
|
577 |
val table = Lifting_Info.get_quotients ctxt
|
kuncar@57882
|
578 |
in
|
kuncar@57882
|
579 |
Symtab.fold (fn (_, data) => fn l => collect data l) table []
|
kuncar@57882
|
580 |
end
|
kuncar@57882
|
581 |
|
kuncar@48723
|
582 |
(*
|
kuncar@48723
|
583 |
|
kuncar@48723
|
584 |
lifting_definition command. It opens a proof of a corresponding respectfulness
|
kuncar@48723
|
585 |
theorem in a user-friendly, readable form. Then add_lift_def is called internally.
|
kuncar@48723
|
586 |
|
kuncar@48723
|
587 |
*)
|
kuncar@48723
|
588 |
|
kuncar@55088
|
589 |
fun lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy =
|
kuncar@48153
|
590 |
let
|
kuncar@53131
|
591 |
val ((binding, SOME qty, mx), lthy) = yield_singleton Proof_Context.read_vars raw_var lthy
|
kuncar@53131
|
592 |
val rhs = (Syntax.check_term lthy o Syntax.parse_term lthy) rhs_raw
|
kuncar@53131
|
593 |
val rsp_rel = Lifting_Term.equiv_relation lthy (fastype_of rhs, qty)
|
kuncar@48153
|
594 |
val rty_forced = (domain_type o fastype_of) rsp_rel;
|
kuncar@53131
|
595 |
val forced_rhs = force_rty_type lthy rty_forced rhs;
|
kuncar@57882
|
596 |
val cr_to_pcr_conv = HOLogic.Trueprop_conv (Conv.fun2_conv
|
kuncar@57882
|
597 |
(Raw_Simplifier.rewrite lthy false (get_cr_pcr_eqs lthy)))
|
kuncar@57882
|
598 |
val (prsp_tm, rsp_prsp_eq) = HOLogic.mk_Trueprop (rsp_rel $ forced_rhs $ forced_rhs)
|
kuncar@57882
|
599 |
|> cterm_of (Proof_Context.theory_of lthy)
|
kuncar@57882
|
600 |
|> cr_to_pcr_conv
|
kuncar@57882
|
601 |
|> ` concl_of
|
kuncar@57882
|
602 |
|>> Logic.dest_equals
|
kuncar@57882
|
603 |
|>> snd
|
kuncar@57882
|
604 |
val to_rsp = rsp_prsp_eq RS Drule.equal_elim_rule2
|
kuncar@57882
|
605 |
val opt_proven_rsp_thm = try_prove_reflexivity lthy prsp_tm
|
kuncar@55088
|
606 |
val par_thms = Attrib.eval_thms lthy par_xthms
|
kuncar@53131
|
607 |
|
kuncar@53131
|
608 |
fun after_qed internal_rsp_thm lthy =
|
kuncar@57882
|
609 |
add_lift_def (binding, mx) qty rhs (internal_rsp_thm RS to_rsp) par_thms lthy
|
kuncar@48153
|
610 |
in
|
kuncar@52511
|
611 |
case opt_proven_rsp_thm of
|
kuncar@53131
|
612 |
SOME thm => Proof.theorem NONE (K (after_qed thm)) [] lthy
|
kuncar@53131
|
613 |
| NONE =>
|
kuncar@53131
|
614 |
let
|
kuncar@57882
|
615 |
val readable_rsp_thm_eq = mk_readable_rsp_thm_eq prsp_tm lthy
|
kuncar@53131
|
616 |
val (readable_rsp_tm, _) = Logic.dest_implies (prop_of readable_rsp_thm_eq)
|
kuncar@53131
|
617 |
val readable_rsp_tm_tnames = rename_to_tnames lthy readable_rsp_tm
|
kuncar@53131
|
618 |
|
kuncar@53131
|
619 |
fun after_qed' thm_list lthy =
|
kuncar@53131
|
620 |
let
|
kuncar@57882
|
621 |
val internal_rsp_thm = Goal.prove lthy [] [] prsp_tm
|
wenzelm@56084
|
622 |
(fn {context = ctxt, ...} =>
|
wenzelm@56084
|
623 |
rtac readable_rsp_thm_eq 1 THEN Proof_Context.fact_tac ctxt (hd thm_list) 1)
|
kuncar@53131
|
624 |
in
|
kuncar@53131
|
625 |
after_qed internal_rsp_thm lthy
|
kuncar@53131
|
626 |
end
|
kuncar@53131
|
627 |
in
|
kuncar@53131
|
628 |
Proof.theorem NONE after_qed' [[(readable_rsp_tm_tnames,[])]] lthy
|
kuncar@53131
|
629 |
end
|
kuncar@48153
|
630 |
end
|
kuncar@48153
|
631 |
|
kuncar@48237
|
632 |
fun quot_thm_err ctxt (rty, qty) pretty_msg =
|
kuncar@48237
|
633 |
let
|
kuncar@48237
|
634 |
val error_msg = cat_lines
|
kuncar@48237
|
635 |
["Lifting failed for the following types:",
|
kuncar@48237
|
636 |
Pretty.string_of (Pretty.block
|
kuncar@48237
|
637 |
[Pretty.str "Raw type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty]),
|
kuncar@48237
|
638 |
Pretty.string_of (Pretty.block
|
kuncar@48237
|
639 |
[Pretty.str "Abstract type:", Pretty.brk 2, Syntax.pretty_typ ctxt qty]),
|
kuncar@48237
|
640 |
"",
|
kuncar@48237
|
641 |
(Pretty.string_of (Pretty.block
|
kuncar@48237
|
642 |
[Pretty.str "Reason:", Pretty.brk 2, pretty_msg]))]
|
kuncar@48237
|
643 |
in
|
kuncar@48237
|
644 |
error error_msg
|
kuncar@48237
|
645 |
end
|
kuncar@48237
|
646 |
|
kuncar@48375
|
647 |
fun check_rty_err ctxt (rty_schematic, rty_forced) (raw_var, rhs_raw) =
|
kuncar@48237
|
648 |
let
|
kuncar@48375
|
649 |
val (_, ctxt') = yield_singleton Proof_Context.read_vars raw_var ctxt
|
kuncar@48375
|
650 |
val rhs = (Syntax.check_term ctxt' o Syntax.parse_term ctxt') rhs_raw
|
kuncar@48237
|
651 |
val error_msg = cat_lines
|
kuncar@48237
|
652 |
["Lifting failed for the following term:",
|
kuncar@48237
|
653 |
Pretty.string_of (Pretty.block
|
kuncar@48237
|
654 |
[Pretty.str "Term:", Pretty.brk 2, Syntax.pretty_term ctxt rhs]),
|
kuncar@48237
|
655 |
Pretty.string_of (Pretty.block
|
kuncar@48375
|
656 |
[Pretty.str "Type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty_schematic]),
|
kuncar@48237
|
657 |
"",
|
kuncar@48237
|
658 |
(Pretty.string_of (Pretty.block
|
kuncar@48237
|
659 |
[Pretty.str "Reason:",
|
kuncar@48237
|
660 |
Pretty.brk 2,
|
kuncar@53094
|
661 |
Pretty.str "The type of the term cannot be instantiated to",
|
kuncar@48237
|
662 |
Pretty.brk 1,
|
kuncar@48375
|
663 |
Pretty.quote (Syntax.pretty_typ ctxt rty_forced),
|
kuncar@48237
|
664 |
Pretty.str "."]))]
|
kuncar@48237
|
665 |
in
|
kuncar@48237
|
666 |
error error_msg
|
kuncar@48237
|
667 |
end
|
kuncar@48237
|
668 |
|
kuncar@55088
|
669 |
fun lift_def_cmd_with_err_handling (raw_var, rhs_raw, par_xthms) lthy =
|
kuncar@55088
|
670 |
(lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy
|
kuncar@48237
|
671 |
handle Lifting_Term.QUOT_THM (rty, qty, msg) => quot_thm_err lthy (rty, qty) msg)
|
kuncar@48375
|
672 |
handle Lifting_Term.CHECK_RTY (rty_schematic, rty_forced) =>
|
kuncar@48375
|
673 |
check_rty_err lthy (rty_schematic, rty_forced) (raw_var, rhs_raw)
|
kuncar@48237
|
674 |
|
kuncar@48153
|
675 |
(* parser and command *)
|
kuncar@48153
|
676 |
val liftdef_parser =
|
kuncar@52511
|
677 |
(((Parse.binding -- (@{keyword "::"} |-- (Parse.typ >> SOME) -- Parse.opt_mixfix')) >> Parse.triple2)
|
kuncar@55088
|
678 |
--| @{keyword "is"} -- Parse.term --
|
kuncar@55088
|
679 |
Scan.optional (@{keyword "parametric"} |-- Parse.!!! Parse_Spec.xthms1) []) >> Parse.triple1
|
kuncar@48153
|
680 |
val _ =
|
kuncar@48153
|
681 |
Outer_Syntax.local_theory_to_proof @{command_spec "lift_definition"}
|
kuncar@48153
|
682 |
"definition for constants over the quotient type"
|
kuncar@48237
|
683 |
(liftdef_parser >> lift_def_cmd_with_err_handling)
|
kuncar@48153
|
684 |
|
kuncar@48153
|
685 |
|
kuncar@54788
|
686 |
end (* structure *)
|