src/Pure/drule.ML
author wenzelm
Tue Apr 05 20:03:24 2016 +0200 (2016-04-05)
changeset 62876 507c90523113
parent 61852 d273c24b5776
child 63068 8b9401bfd9fd
permissions -rw-r--r--
clarified modules -- simplified bootstrap;
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(*  Title:      Pure/drule.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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Derived rules and other operations on theorems.
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*)
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infix 0 RS RSN RL RLN MRS OF COMP INCR_COMP COMP_INCR;
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signature BASIC_DRULE =
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sig
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  val mk_implies: cterm * cterm -> cterm
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  val list_implies: cterm list * cterm -> cterm
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  val strip_imp_prems: cterm -> cterm list
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  val strip_imp_concl: cterm -> cterm
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  val cprems_of: thm -> cterm list
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  val forall_intr_list: cterm list -> thm -> thm
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  val forall_intr_vars: thm -> thm
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  val forall_elim_list: cterm list -> thm -> thm
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  val lift_all: Proof.context -> cterm -> thm -> thm
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  val implies_elim_list: thm -> thm list -> thm
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  val implies_intr_list: cterm list -> thm -> thm
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  val instantiate_normalize: ((indexname * sort) * ctyp) list * ((indexname * typ) * cterm) list ->
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    thm -> thm
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  val infer_instantiate_types: Proof.context -> ((indexname * typ) * cterm) list -> thm -> thm
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  val infer_instantiate: Proof.context -> (indexname * cterm) list -> thm -> thm
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  val infer_instantiate': Proof.context -> cterm option list -> thm -> thm
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  val zero_var_indexes_list: thm list -> thm list
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  val zero_var_indexes: thm -> thm
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  val implies_intr_hyps: thm -> thm
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  val rotate_prems: int -> thm -> thm
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  val rearrange_prems: int list -> thm -> thm
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  val RSN: thm * (int * thm) -> thm
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  val RS: thm * thm -> thm
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  val RLN: thm list * (int * thm list) -> thm list
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  val RL: thm list * thm list -> thm list
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  val MRS: thm list * thm -> thm
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  val OF: thm * thm list -> thm
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  val COMP: thm * thm -> thm
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  val INCR_COMP: thm * thm -> thm
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  val COMP_INCR: thm * thm -> thm
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  val size_of_thm: thm -> int
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  val reflexive_thm: thm
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  val symmetric_thm: thm
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  val transitive_thm: thm
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  val extensional: thm -> thm
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  val asm_rl: thm
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  val cut_rl: thm
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  val revcut_rl: thm
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  val thin_rl: thm
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end;
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signature DRULE =
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sig
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  include BASIC_DRULE
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  val outer_params: term -> (string * typ) list
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  val generalize: string list * string list -> thm -> thm
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  val list_comb: cterm * cterm list -> cterm
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  val strip_comb: cterm -> cterm * cterm list
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  val strip_type: ctyp -> ctyp list * ctyp
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  val beta_conv: cterm -> cterm -> cterm
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  val flexflex_unique: Proof.context option -> thm -> thm
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  val export_without_context: thm -> thm
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  val export_without_context_open: thm -> thm
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  val store_thm: binding -> thm -> thm
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  val store_standard_thm: binding -> thm -> thm
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  val store_thm_open: binding -> thm -> thm
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  val store_standard_thm_open: binding -> thm -> thm
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  val multi_resolve: Proof.context option -> thm list -> thm -> thm Seq.seq
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  val multi_resolves: Proof.context option -> thm list -> thm list -> thm Seq.seq
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  val compose: thm * int * thm -> thm
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  val equals_cong: thm
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  val imp_cong: thm
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  val swap_prems_eq: thm
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  val imp_cong_rule: thm -> thm -> thm
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  val arg_cong_rule: cterm -> thm -> thm
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  val binop_cong_rule: cterm -> thm -> thm -> thm
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  val fun_cong_rule: thm -> cterm -> thm
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  val beta_eta_conversion: cterm -> thm
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  val eta_contraction_rule: thm -> thm
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  val norm_hhf_eq: thm
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  val norm_hhf_eqs: thm list
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  val is_norm_hhf: term -> bool
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  val norm_hhf: theory -> term -> term
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  val norm_hhf_cterm: Proof.context -> cterm -> cterm
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  val protect: cterm -> cterm
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  val protectI: thm
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  val protectD: thm
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  val protect_cong: thm
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  val implies_intr_protected: cterm list -> thm -> thm
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  val termI: thm
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  val mk_term: cterm -> thm
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  val dest_term: thm -> cterm
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  val cterm_rule: (thm -> thm) -> cterm -> cterm
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  val cterm_add_frees: cterm -> cterm list -> cterm list
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  val cterm_add_vars: cterm -> cterm list -> cterm list
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  val dummy_thm: thm
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  val free_dummy_thm: thm
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  val is_sort_constraint: term -> bool
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  val sort_constraintI: thm
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  val sort_constraint_eq: thm
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  val with_subgoal: int -> (thm -> thm) -> thm -> thm
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  val comp_no_flatten: thm * int -> int -> thm -> thm
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  val rename_bvars: (string * string) list -> thm -> thm
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  val rename_bvars': string option list -> thm -> thm
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  val incr_indexes: thm -> thm -> thm
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  val incr_indexes2: thm -> thm -> thm -> thm
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  val triv_forall_equality: thm
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  val distinct_prems_rl: thm
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  val equal_intr_rule: thm
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  val equal_elim_rule1: thm
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  val equal_elim_rule2: thm
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  val remdups_rl: thm
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  val abs_def: thm -> thm
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end;
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structure Drule: DRULE =
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struct
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(** some cterm->cterm operations: faster than calling cterm_of! **)
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(* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
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fun strip_imp_prems ct =
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  let val (cA, cB) = Thm.dest_implies ct
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  in cA :: strip_imp_prems cB end
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  handle TERM _ => [];
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(* A1==>...An==>B  goes to B, where B is not an implication *)
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fun strip_imp_concl ct =
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  (case Thm.term_of ct of
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    Const ("Pure.imp", _) $ _ $ _ => strip_imp_concl (Thm.dest_arg ct)
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  | _ => ct);
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(*The premises of a theorem, as a cterm list*)
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val cprems_of = strip_imp_prems o Thm.cprop_of;
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fun certify t = Thm.global_cterm_of (Context.the_global_context ()) t;
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val implies = certify Logic.implies;
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fun mk_implies (A, B) = Thm.apply (Thm.apply implies A) B;
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(*cterm version of list_implies: [A1,...,An], B  goes to [|A1;==>;An|]==>B *)
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fun list_implies([], B) = B
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  | list_implies(A::AS, B) = mk_implies (A, list_implies(AS,B));
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(*cterm version of list_comb: maps  (f, [t1,...,tn])  to  f(t1,...,tn) *)
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fun list_comb (f, []) = f
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  | list_comb (f, t::ts) = list_comb (Thm.apply f t, ts);
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(*cterm version of strip_comb: maps  f(t1,...,tn)  to  (f, [t1,...,tn]) *)
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fun strip_comb ct =
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  let
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    fun stripc (p as (ct, cts)) =
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      let val (ct1, ct2) = Thm.dest_comb ct
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      in stripc (ct1, ct2 :: cts) end handle CTERM _ => p
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  in stripc (ct, []) end;
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(* cterm version of strip_type: maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T) *)
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fun strip_type cT = (case Thm.typ_of cT of
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    Type ("fun", _) =>
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      let
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        val [cT1, cT2] = Thm.dest_ctyp cT;
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        val (cTs, cT') = strip_type cT2
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      in (cT1 :: cTs, cT') end
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  | _ => ([], cT));
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(*Beta-conversion for cterms, where x is an abstraction. Simply returns the rhs
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  of the meta-equality returned by the beta_conversion rule.*)
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fun beta_conv x y =
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  Thm.dest_arg (Thm.cprop_of (Thm.beta_conversion false (Thm.apply x y)));
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(** Standardization of rules **)
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(*Generalization over a list of variables*)
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val forall_intr_list = fold_rev Thm.forall_intr;
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(*Generalization over Vars -- canonical order*)
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fun forall_intr_vars th = fold Thm.forall_intr (Thm.add_vars th []) th;
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fun outer_params t =
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  let val vs = Term.strip_all_vars t
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  in Name.variant_list [] (map (Name.clean o #1) vs) ~~ map #2 vs end;
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(*lift vars wrt. outermost goal parameters
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  -- reverses the effect of gen_all modulo higher-order unification*)
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fun lift_all ctxt raw_goal raw_th =
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  let
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    val thy = Proof_Context.theory_of ctxt;
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    val goal = Thm.transfer_cterm thy raw_goal;
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    val th = Thm.transfer thy raw_th;
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    val maxidx = Thm.maxidx_of th;
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    val ps = outer_params (Thm.term_of goal)
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      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
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    val Ts = map Term.fastype_of ps;
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    val inst =
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      Thm.fold_terms Term.add_vars th []
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      |> map (fn (xi, T) => ((xi, T), Thm.cterm_of ctxt (Term.list_comb (Var (xi, Ts ---> T), ps))));
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  in
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    th
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    |> Thm.instantiate ([], inst)
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    |> fold_rev (Thm.forall_intr o Thm.cterm_of ctxt) ps
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  end;
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(*direct generalization*)
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fun generalize names th = Thm.generalize names (Thm.maxidx_of th + 1) th;
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(*specialization over a list of cterms*)
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val forall_elim_list = fold Thm.forall_elim;
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(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
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val implies_intr_list = fold_rev Thm.implies_intr;
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(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
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fun implies_elim_list impth ths = fold Thm.elim_implies ths impth;
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(*Reset Var indexes to zero, renaming to preserve distinctness*)
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fun zero_var_indexes_list [] = []
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  | zero_var_indexes_list ths =
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      let
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        val (instT, inst) = Term_Subst.zero_var_indexes_inst (map Thm.full_prop_of ths);
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        val tvars = fold Thm.add_tvars ths [];
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        fun the_tvar v = the (find_first (fn cT => v = dest_TVar (Thm.typ_of cT)) tvars);
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        val instT' = map (fn (v, TVar (b, _)) => (v, Thm.rename_tvar b (the_tvar v))) instT;
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        val vars = fold (Thm.add_vars o Thm.instantiate (instT', [])) ths [];
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        fun the_var v = the (find_first (fn ct => v = dest_Var (Thm.term_of ct)) vars);
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        val inst' = map (fn (v, Var (b, _)) => (v, Thm.var (b, Thm.ctyp_of_cterm (the_var v)))) inst;
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      in map (Thm.adjust_maxidx_thm ~1 o Thm.instantiate (instT', inst')) ths end;
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val zero_var_indexes = singleton zero_var_indexes_list;
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(** Standard form of object-rule: no hypotheses, flexflex constraints,
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    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
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(*Discharge all hypotheses.*)
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fun implies_intr_hyps th = fold Thm.implies_intr (Thm.chyps_of th) th;
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(*Squash a theorem's flexflex constraints provided it can be done uniquely.
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  This step can lose information.*)
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fun flexflex_unique opt_ctxt th =
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  if null (Thm.tpairs_of th) then th
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  else
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    (case distinct Thm.eq_thm (Seq.list_of (Thm.flexflex_rule opt_ctxt th)) of
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      [th] => th
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    | [] => raise THM ("flexflex_unique: impossible constraints", 0, [th])
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    | _ => raise THM ("flexflex_unique: multiple unifiers", 0, [th]));
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(* old-style export without context *)
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val export_without_context_open =
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  implies_intr_hyps
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  #> Thm.forall_intr_frees
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  #> `Thm.maxidx_of
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  #-> (fn maxidx =>
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    Thm.forall_elim_vars (maxidx + 1)
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    #> Thm.strip_shyps
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    #> zero_var_indexes
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    #> Thm.varifyT_global);
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val export_without_context =
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  flexflex_unique NONE
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  #> export_without_context_open
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  #> Thm.close_derivation;
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(*Rotates a rule's premises to the left by k*)
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fun rotate_prems 0 = I
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  | rotate_prems k = Thm.permute_prems 0 k;
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fun with_subgoal i f = rotate_prems (i - 1) #> f #> rotate_prems (1 - i);
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(*Permute prems, where the i-th position in the argument list (counting from 0)
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  gives the position within the original thm to be transferred to position i.
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  Any remaining trailing positions are left unchanged.*)
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val rearrange_prems =
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  let
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    fun rearr new [] thm = thm
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      | rearr new (p :: ps) thm =
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          rearr (new + 1)
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            (map (fn q => if new <= q andalso q < p then q + 1 else q) ps)
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            (Thm.permute_prems (new + 1) (new - p) (Thm.permute_prems new (p - new) thm))
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  in rearr 0 end;
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(*Resolution: multiple arguments, multiple results*)
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local
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  fun res opt_ctxt th i rule =
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    Thm.biresolution opt_ctxt false [(false, th)] i rule handle THM _ => Seq.empty;
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  fun multi_res _ _ [] rule = Seq.single rule
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    | multi_res opt_ctxt i (th :: ths) rule =
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        Seq.maps (res opt_ctxt th i) (multi_res opt_ctxt (i + 1) ths rule);
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in
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  fun multi_resolve opt_ctxt = multi_res opt_ctxt 1;
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  fun multi_resolves opt_ctxt facts rules =
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    Seq.maps (multi_resolve opt_ctxt facts) (Seq.of_list rules);
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end;
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(*Resolution: exactly one resolvent must be produced*)
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fun tha RSN (i, thb) =
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  (case Seq.chop 2 (Thm.biresolution NONE false [(false, tha)] i thb) of
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    ([th], _) => th
wenzelm@47427
   309
  | ([], _) => raise THM ("RSN: no unifiers", i, [tha, thb])
wenzelm@47427
   310
  | _ => raise THM ("RSN: multiple unifiers", i, [tha, thb]));
wenzelm@47427
   311
wenzelm@47427
   312
(*Resolution: P==>Q, Q==>R gives P==>R*)
clasohm@0
   313
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   314
clasohm@0
   315
(*For joining lists of rules*)
wenzelm@47427
   316
fun thas RLN (i, thbs) =
wenzelm@59773
   317
  let
wenzelm@59773
   318
    val resolve = Thm.biresolution NONE false (map (pair false) thas) i
wenzelm@59773
   319
    fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   320
  in maps resb thbs end;
clasohm@0
   321
wenzelm@47427
   322
fun thas RL thbs = thas RLN (1, thbs);
wenzelm@47427
   323
wenzelm@47427
   324
(*Isar-style multi-resolution*)
wenzelm@47427
   325
fun bottom_rl OF rls =
wenzelm@58950
   326
  (case Seq.chop 2 (multi_resolve NONE rls bottom_rl) of
wenzelm@47427
   327
    ([th], _) => th
wenzelm@47427
   328
  | ([], _) => raise THM ("OF: no unifiers", 0, bottom_rl :: rls)
wenzelm@47427
   329
  | _ => raise THM ("OF: multiple unifiers", 0, bottom_rl :: rls));
clasohm@0
   330
lcp@11
   331
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   332
  makes proof trees*)
wenzelm@47427
   333
fun rls MRS bottom_rl = bottom_rl OF rls;
wenzelm@9288
   334
wenzelm@252
   335
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   336
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   337
  ALWAYS deletes premise i *)
wenzelm@52467
   338
fun compose (tha, i, thb) =
wenzelm@58950
   339
  Thm.bicompose NONE {flatten = true, match = false, incremented = false} (false, tha, 0) i thb
wenzelm@52467
   340
  |> Seq.list_of |> distinct Thm.eq_thm
wenzelm@52467
   341
  |> (fn [th] => th | _ => raise THM ("compose: unique result expected", i, [tha, thb]));
wenzelm@6946
   342
wenzelm@13105
   343
wenzelm@4016
   344
(** theorem equality **)
clasohm@0
   345
clasohm@0
   346
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   347
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   348
lcp@1194
   349
lcp@1194
   350
clasohm@0
   351
(*** Meta-Rewriting Rules ***)
clasohm@0
   352
wenzelm@33384
   353
val read_prop = certify o Simple_Syntax.read_prop;
wenzelm@26487
   354
wenzelm@26487
   355
fun store_thm name th =
wenzelm@39557
   356
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm (name, th)));
paulson@4610
   357
wenzelm@26487
   358
fun store_thm_open name th =
wenzelm@39557
   359
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm_open (name, th)));
wenzelm@26487
   360
wenzelm@35021
   361
fun store_standard_thm name th = store_thm name (export_without_context th);
wenzelm@60367
   362
fun store_standard_thm_open name th = store_thm_open name (export_without_context_open th);
wenzelm@4016
   363
clasohm@0
   364
val reflexive_thm =
wenzelm@26487
   365
  let val cx = certify (Var(("x",0),TVar(("'a",0),[])))
wenzelm@56436
   366
  in store_standard_thm_open (Binding.make ("reflexive", @{here})) (Thm.reflexive cx) end;
clasohm@0
   367
clasohm@0
   368
val symmetric_thm =
wenzelm@33277
   369
  let
wenzelm@33277
   370
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   371
    val thm = Thm.implies_intr xy (Thm.symmetric (Thm.assume xy));
wenzelm@56436
   372
  in store_standard_thm_open (Binding.make ("symmetric", @{here})) thm end;
clasohm@0
   373
clasohm@0
   374
val transitive_thm =
wenzelm@33277
   375
  let
wenzelm@33277
   376
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   377
    val yz = read_prop "y::'a == z::'a";
wenzelm@33277
   378
    val xythm = Thm.assume xy;
wenzelm@33277
   379
    val yzthm = Thm.assume yz;
wenzelm@33277
   380
    val thm = Thm.implies_intr yz (Thm.transitive xythm yzthm);
wenzelm@56436
   381
  in store_standard_thm_open (Binding.make ("transitive", @{here})) thm end;
clasohm@0
   382
berghofe@11512
   383
fun extensional eq =
berghofe@11512
   384
  let val eq' =
wenzelm@59582
   385
    Thm.abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (Thm.cprop_of eq)))) eq
wenzelm@59582
   386
  in Thm.equal_elim (Thm.eta_conversion (Thm.cprop_of eq')) eq' end;
berghofe@11512
   387
wenzelm@18820
   388
val equals_cong =
wenzelm@56436
   389
  store_standard_thm_open (Binding.make ("equals_cong", @{here}))
wenzelm@33277
   390
    (Thm.reflexive (read_prop "x::'a == y::'a"));
wenzelm@18820
   391
berghofe@10414
   392
val imp_cong =
berghofe@10414
   393
  let
wenzelm@24241
   394
    val ABC = read_prop "A ==> B::prop == C::prop"
wenzelm@24241
   395
    val AB = read_prop "A ==> B"
wenzelm@24241
   396
    val AC = read_prop "A ==> C"
wenzelm@24241
   397
    val A = read_prop "A"
berghofe@10414
   398
  in
wenzelm@56436
   399
    store_standard_thm_open (Binding.make ("imp_cong", @{here}))
wenzelm@56436
   400
      (Thm.implies_intr ABC (Thm.equal_intr
wenzelm@56436
   401
        (Thm.implies_intr AB (Thm.implies_intr A
wenzelm@56436
   402
          (Thm.equal_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A))
wenzelm@56436
   403
            (Thm.implies_elim (Thm.assume AB) (Thm.assume A)))))
wenzelm@56436
   404
        (Thm.implies_intr AC (Thm.implies_intr A
wenzelm@56436
   405
          (Thm.equal_elim (Thm.symmetric (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)))
wenzelm@56436
   406
            (Thm.implies_elim (Thm.assume AC) (Thm.assume A)))))))
berghofe@10414
   407
  end;
berghofe@10414
   408
berghofe@10414
   409
val swap_prems_eq =
berghofe@10414
   410
  let
wenzelm@24241
   411
    val ABC = read_prop "A ==> B ==> C"
wenzelm@24241
   412
    val BAC = read_prop "B ==> A ==> C"
wenzelm@24241
   413
    val A = read_prop "A"
wenzelm@24241
   414
    val B = read_prop "B"
berghofe@10414
   415
  in
wenzelm@56436
   416
    store_standard_thm_open (Binding.make ("swap_prems_eq", @{here}))
wenzelm@36944
   417
      (Thm.equal_intr
wenzelm@36944
   418
        (Thm.implies_intr ABC (Thm.implies_intr B (Thm.implies_intr A
wenzelm@36944
   419
          (Thm.implies_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)) (Thm.assume B)))))
wenzelm@36944
   420
        (Thm.implies_intr BAC (Thm.implies_intr A (Thm.implies_intr B
wenzelm@36944
   421
          (Thm.implies_elim (Thm.implies_elim (Thm.assume BAC) (Thm.assume B)) (Thm.assume A))))))
berghofe@10414
   422
  end;
lcp@229
   423
wenzelm@22938
   424
val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
wenzelm@22938
   425
wenzelm@23537
   426
fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM in LCF/HOL*)
wenzelm@23537
   427
fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM in LCF/HOL*)
wenzelm@23568
   428
fun binop_cong_rule ct th1 th2 = Thm.combination (arg_cong_rule ct th1) th2;
clasohm@0
   429
wenzelm@60316
   430
fun beta_eta_conversion ct =
wenzelm@60316
   431
  let val thm = Thm.beta_conversion true ct
wenzelm@60316
   432
  in Thm.transitive thm (Thm.eta_conversion (Thm.rhs_of thm)) end;
skalberg@15001
   433
paulson@20861
   434
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   435
fun eta_contraction_rule th =
wenzelm@59582
   436
  Thm.equal_elim (Thm.eta_conversion (Thm.cprop_of th)) th;
paulson@20861
   437
wenzelm@24947
   438
wenzelm@24947
   439
(* abs_def *)
wenzelm@24947
   440
wenzelm@24947
   441
(*
wenzelm@24947
   442
   f ?x1 ... ?xn == u
wenzelm@24947
   443
  --------------------
wenzelm@24947
   444
   f == %x1 ... xn. u
wenzelm@24947
   445
*)
wenzelm@24947
   446
wenzelm@24947
   447
local
wenzelm@24947
   448
wenzelm@24947
   449
fun contract_lhs th =
wenzelm@24947
   450
  Thm.transitive (Thm.symmetric (beta_eta_conversion
wenzelm@59582
   451
    (fst (Thm.dest_equals (Thm.cprop_of th))))) th;
wenzelm@24947
   452
wenzelm@24947
   453
fun var_args ct =
wenzelm@24947
   454
  (case try Thm.dest_comb ct of
wenzelm@24947
   455
    SOME (f, arg) =>
wenzelm@24947
   456
      (case Thm.term_of arg of
wenzelm@24947
   457
        Var ((x, _), _) => update (eq_snd (op aconvc)) (x, arg) (var_args f)
wenzelm@24947
   458
      | _ => [])
wenzelm@24947
   459
  | NONE => []);
wenzelm@24947
   460
wenzelm@24947
   461
in
wenzelm@24947
   462
wenzelm@24947
   463
fun abs_def th =
wenzelm@18337
   464
  let
wenzelm@24947
   465
    val th' = contract_lhs th;
wenzelm@24947
   466
    val args = var_args (Thm.lhs_of th');
wenzelm@24947
   467
  in contract_lhs (fold (uncurry Thm.abstract_rule) args th') end;
wenzelm@24947
   468
wenzelm@24947
   469
end;
wenzelm@24947
   470
wenzelm@18337
   471
wenzelm@18468
   472
wenzelm@15669
   473
(*** Some useful meta-theorems ***)
clasohm@0
   474
clasohm@0
   475
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@56436
   476
val asm_rl =
wenzelm@56436
   477
  store_standard_thm_open (Binding.make ("asm_rl", @{here}))
wenzelm@56436
   478
    (Thm.trivial (read_prop "?psi"));
clasohm@0
   479
clasohm@0
   480
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   481
val cut_rl =
wenzelm@56436
   482
  store_standard_thm_open (Binding.make ("cut_rl", @{here}))
wenzelm@24241
   483
    (Thm.trivial (read_prop "?psi ==> ?theta"));
clasohm@0
   484
wenzelm@252
   485
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   486
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   487
val revcut_rl =
wenzelm@33277
   488
  let
wenzelm@33277
   489
    val V = read_prop "V";
wenzelm@33277
   490
    val VW = read_prop "V ==> W";
wenzelm@4016
   491
  in
wenzelm@56436
   492
    store_standard_thm_open (Binding.make ("revcut_rl", @{here}))
wenzelm@56436
   493
      (Thm.implies_intr V
wenzelm@56436
   494
        (Thm.implies_intr VW (Thm.implies_elim (Thm.assume VW) (Thm.assume V))))
clasohm@0
   495
  end;
clasohm@0
   496
lcp@668
   497
(*for deleting an unwanted assumption*)
lcp@668
   498
val thin_rl =
wenzelm@33277
   499
  let
wenzelm@33277
   500
    val V = read_prop "V";
wenzelm@33277
   501
    val W = read_prop "W";
wenzelm@36944
   502
    val thm = Thm.implies_intr V (Thm.implies_intr W (Thm.assume W));
wenzelm@56436
   503
  in store_standard_thm_open (Binding.make ("thin_rl", @{here})) thm end;
lcp@668
   504
clasohm@0
   505
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   506
val triv_forall_equality =
wenzelm@33277
   507
  let
wenzelm@33277
   508
    val V = read_prop "V";
wenzelm@33277
   509
    val QV = read_prop "!!x::'a. V";
wenzelm@33277
   510
    val x = certify (Free ("x", Term.aT []));
wenzelm@4016
   511
  in
wenzelm@56436
   512
    store_standard_thm_open (Binding.make ("triv_forall_equality", @{here}))
wenzelm@36944
   513
      (Thm.equal_intr (Thm.implies_intr QV (Thm.forall_elim x (Thm.assume QV)))
wenzelm@36944
   514
        (Thm.implies_intr V (Thm.forall_intr x (Thm.assume V))))
clasohm@0
   515
  end;
clasohm@0
   516
wenzelm@19051
   517
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   518
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   519
*)
wenzelm@19051
   520
val distinct_prems_rl =
wenzelm@19051
   521
  let
wenzelm@33277
   522
    val AAB = read_prop "Phi ==> Phi ==> Psi";
wenzelm@24241
   523
    val A = read_prop "Phi";
wenzelm@19051
   524
  in
wenzelm@56436
   525
    store_standard_thm_open (Binding.make ("distinct_prems_rl", @{here}))
wenzelm@56436
   526
      (implies_intr_list [AAB, A]
wenzelm@56436
   527
        (implies_elim_list (Thm.assume AAB) [Thm.assume A, Thm.assume A]))
wenzelm@19051
   528
  end;
wenzelm@19051
   529
nipkow@3653
   530
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   531
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   532
   Introduction rule for == as a meta-theorem.
nipkow@3653
   533
*)
nipkow@3653
   534
val equal_intr_rule =
wenzelm@33277
   535
  let
wenzelm@33277
   536
    val PQ = read_prop "phi ==> psi";
wenzelm@33277
   537
    val QP = read_prop "psi ==> phi";
wenzelm@4016
   538
  in
wenzelm@56436
   539
    store_standard_thm_open (Binding.make ("equal_intr_rule", @{here}))
wenzelm@56436
   540
      (Thm.implies_intr PQ
wenzelm@56436
   541
        (Thm.implies_intr QP (Thm.equal_intr (Thm.assume PQ) (Thm.assume QP))))
nipkow@3653
   542
  end;
nipkow@3653
   543
wenzelm@19421
   544
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   545
val equal_elim_rule1 =
wenzelm@33277
   546
  let
wenzelm@33277
   547
    val eq = read_prop "phi::prop == psi::prop";
wenzelm@33277
   548
    val P = read_prop "phi";
wenzelm@33277
   549
  in
wenzelm@56436
   550
    store_standard_thm_open (Binding.make ("equal_elim_rule1", @{here}))
wenzelm@36944
   551
      (Thm.equal_elim (Thm.assume eq) (Thm.assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   552
  end;
wenzelm@4285
   553
wenzelm@19421
   554
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   555
val equal_elim_rule2 =
wenzelm@56436
   556
  store_standard_thm_open (Binding.make ("equal_elim_rule2", @{here}))
wenzelm@33277
   557
    (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   558
wenzelm@28618
   559
(* PROP ?phi ==> PROP ?phi ==> PROP ?psi ==> PROP ?psi *)
wenzelm@12297
   560
val remdups_rl =
wenzelm@33277
   561
  let
wenzelm@33277
   562
    val P = read_prop "phi";
wenzelm@33277
   563
    val Q = read_prop "psi";
wenzelm@33277
   564
    val thm = implies_intr_list [P, P, Q] (Thm.assume Q);
wenzelm@56436
   565
  in store_standard_thm_open (Binding.make ("remdups_rl", @{here})) thm end;
wenzelm@12297
   566
wenzelm@12297
   567
wenzelm@28618
   568
wenzelm@28618
   569
(** embedded terms and types **)
wenzelm@28618
   570
wenzelm@28618
   571
local
wenzelm@28618
   572
  val A = certify (Free ("A", propT));
wenzelm@62876
   573
  val axiom = Thm.unvarify_axiom (Context.the_global_context ());
wenzelm@28674
   574
  val prop_def = axiom "Pure.prop_def";
wenzelm@28674
   575
  val term_def = axiom "Pure.term_def";
wenzelm@28674
   576
  val sort_constraint_def = axiom "Pure.sort_constraint_def";
wenzelm@28618
   577
  val C = Thm.lhs_of sort_constraint_def;
wenzelm@28618
   578
  val T = Thm.dest_arg C;
wenzelm@28618
   579
  val CA = mk_implies (C, A);
wenzelm@28618
   580
in
wenzelm@28618
   581
wenzelm@28618
   582
(* protect *)
wenzelm@28618
   583
wenzelm@46497
   584
val protect = Thm.apply (certify Logic.protectC);
wenzelm@28618
   585
wenzelm@33277
   586
val protectI =
wenzelm@59859
   587
  store_standard_thm (Binding.concealed (Binding.make ("protectI", @{here})))
wenzelm@35021
   588
    (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A));
wenzelm@28618
   589
wenzelm@33277
   590
val protectD =
wenzelm@59859
   591
  store_standard_thm (Binding.concealed (Binding.make ("protectD", @{here})))
wenzelm@35021
   592
    (Thm.equal_elim prop_def (Thm.assume (protect A)));
wenzelm@28618
   593
wenzelm@33277
   594
val protect_cong =
wenzelm@56436
   595
  store_standard_thm_open (Binding.make ("protect_cong", @{here}))
wenzelm@56436
   596
    (Thm.reflexive (protect A));
wenzelm@28618
   597
wenzelm@28618
   598
fun implies_intr_protected asms th =
wenzelm@28618
   599
  let val asms' = map protect asms in
wenzelm@28618
   600
    implies_elim_list
wenzelm@28618
   601
      (implies_intr_list asms th)
wenzelm@28618
   602
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@28618
   603
    |> implies_intr_list asms'
wenzelm@28618
   604
  end;
wenzelm@28618
   605
wenzelm@28618
   606
wenzelm@28618
   607
(* term *)
wenzelm@28618
   608
wenzelm@33277
   609
val termI =
wenzelm@59859
   610
  store_standard_thm (Binding.concealed (Binding.make ("termI", @{here})))
wenzelm@35021
   611
    (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)));
wenzelm@9554
   612
wenzelm@28618
   613
fun mk_term ct =
wenzelm@28618
   614
  let
wenzelm@60642
   615
    val cT = Thm.ctyp_of_cterm ct;
wenzelm@60642
   616
    val T = Thm.typ_of cT;
wenzelm@60642
   617
  in Thm.instantiate ([((("'a", 0), []), cT)], [((("x", 0), T), ct)]) termI end;
wenzelm@28618
   618
wenzelm@28618
   619
fun dest_term th =
wenzelm@28618
   620
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@28618
   621
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@28618
   622
      Thm.dest_arg cprop
wenzelm@28618
   623
    else raise THM ("dest_term", 0, [th])
wenzelm@28618
   624
  end;
wenzelm@28618
   625
wenzelm@28618
   626
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@28618
   627
wenzelm@60818
   628
val cterm_add_frees = Thm.add_frees o mk_term;
wenzelm@60818
   629
val cterm_add_vars = Thm.add_vars o mk_term;
wenzelm@60818
   630
wenzelm@45156
   631
val dummy_thm = mk_term (certify Term.dummy_prop);
wenzelm@61852
   632
val free_dummy_thm = Thm.tag_free_dummy dummy_thm;
wenzelm@28618
   633
wenzelm@28618
   634
wenzelm@28618
   635
(* sort_constraint *)
wenzelm@28618
   636
wenzelm@60240
   637
fun is_sort_constraint (Const ("Pure.sort_constraint", _) $ Const ("Pure.type", _)) = true
wenzelm@60240
   638
  | is_sort_constraint _ = false;
wenzelm@60240
   639
wenzelm@33277
   640
val sort_constraintI =
wenzelm@59859
   641
  store_standard_thm (Binding.concealed (Binding.make ("sort_constraintI", @{here})))
wenzelm@35021
   642
    (Thm.equal_elim (Thm.symmetric sort_constraint_def) (mk_term T));
wenzelm@28618
   643
wenzelm@33277
   644
val sort_constraint_eq =
wenzelm@59859
   645
  store_standard_thm (Binding.concealed (Binding.make ("sort_constraint_eq", @{here})))
wenzelm@35021
   646
    (Thm.equal_intr
wenzelm@35845
   647
      (Thm.implies_intr CA (Thm.implies_elim (Thm.assume CA)
wenzelm@62876
   648
        (Thm.unvarify_global (Context.the_global_context ()) sort_constraintI)))
wenzelm@35021
   649
      (implies_intr_list [A, C] (Thm.assume A)));
wenzelm@28618
   650
wenzelm@28618
   651
end;
wenzelm@28618
   652
wenzelm@28618
   653
wenzelm@28618
   654
(* HHF normalization *)
wenzelm@28618
   655
wenzelm@46214
   656
(* (PROP ?phi ==> (!!x. PROP ?psi x)) == (!!x. PROP ?phi ==> PROP ?psi x) *)
wenzelm@9554
   657
val norm_hhf_eq =
wenzelm@9554
   658
  let
wenzelm@14854
   659
    val aT = TFree ("'a", []);
wenzelm@9554
   660
    val x = Free ("x", aT);
wenzelm@9554
   661
    val phi = Free ("phi", propT);
wenzelm@9554
   662
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   663
wenzelm@26487
   664
    val cx = certify x;
wenzelm@26487
   665
    val cphi = certify phi;
wenzelm@46214
   666
    val lhs = certify (Logic.mk_implies (phi, Logic.all x (psi $ x)));
wenzelm@46214
   667
    val rhs = certify (Logic.all x (Logic.mk_implies (phi, psi $ x)));
wenzelm@9554
   668
  in
wenzelm@9554
   669
    Thm.equal_intr
wenzelm@9554
   670
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   671
        |> Thm.forall_elim cx
wenzelm@9554
   672
        |> Thm.implies_intr cphi
wenzelm@9554
   673
        |> Thm.forall_intr cx
wenzelm@9554
   674
        |> Thm.implies_intr lhs)
wenzelm@9554
   675
      (Thm.implies_elim
wenzelm@9554
   676
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   677
        |> Thm.forall_intr cx
wenzelm@9554
   678
        |> Thm.implies_intr cphi
wenzelm@9554
   679
        |> Thm.implies_intr rhs)
wenzelm@56436
   680
    |> store_standard_thm_open (Binding.make ("norm_hhf_eq", @{here}))
wenzelm@9554
   681
  end;
wenzelm@9554
   682
wenzelm@18179
   683
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@28618
   684
val norm_hhf_eqs = [norm_hhf_eq, sort_constraint_eq];
wenzelm@18179
   685
wenzelm@30553
   686
fun is_norm_hhf (Const ("Pure.sort_constraint", _)) = false
wenzelm@56245
   687
  | is_norm_hhf (Const ("Pure.imp", _) $ _ $ (Const ("Pure.all", _) $ _)) = false
wenzelm@30553
   688
  | is_norm_hhf (Abs _ $ _) = false
wenzelm@30553
   689
  | is_norm_hhf (t $ u) = is_norm_hhf t andalso is_norm_hhf u
wenzelm@30553
   690
  | is_norm_hhf (Abs (_, _, t)) = is_norm_hhf t
wenzelm@30553
   691
  | is_norm_hhf _ = true;
wenzelm@12800
   692
wenzelm@16425
   693
fun norm_hhf thy t =
wenzelm@12800
   694
  if is_norm_hhf t then t
wenzelm@18179
   695
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   696
wenzelm@60315
   697
fun norm_hhf_cterm ctxt raw_ct =
wenzelm@60315
   698
  let
wenzelm@60315
   699
    val thy = Proof_Context.theory_of ctxt;
wenzelm@60315
   700
    val ct = Thm.transfer_cterm thy raw_ct;
wenzelm@60315
   701
    val t = Thm.term_of ct;
wenzelm@60315
   702
  in if is_norm_hhf t then ct else Thm.cterm_of ctxt (norm_hhf thy t) end;
wenzelm@20298
   703
wenzelm@12800
   704
wenzelm@21603
   705
(* var indexes *)
wenzelm@21603
   706
wenzelm@21603
   707
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   708
wenzelm@21603
   709
fun incr_indexes2 th1 th2 =
wenzelm@21603
   710
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   711
wenzelm@52224
   712
local
wenzelm@52224
   713
wenzelm@52224
   714
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
wenzelm@52224
   715
fun comp incremented th1 th2 =
wenzelm@59773
   716
  Thm.bicompose NONE {flatten = true, match = false, incremented = incremented}
wenzelm@59773
   717
    (false, th1, 0) 1 th2
wenzelm@52224
   718
  |> Seq.list_of |> distinct Thm.eq_thm
wenzelm@52224
   719
  |> (fn [th] => th | _ => raise THM ("COMP", 1, [th1, th2]));
wenzelm@52224
   720
wenzelm@52224
   721
in
wenzelm@52224
   722
wenzelm@52224
   723
fun th1 COMP th2 = comp false th1 th2;
wenzelm@52224
   724
fun th1 INCR_COMP th2 = comp true (incr_indexes th2 th1) th2;
wenzelm@52224
   725
fun th1 COMP_INCR th2 = comp true th1 (incr_indexes th1 th2);
wenzelm@52224
   726
wenzelm@52224
   727
end;
wenzelm@21603
   728
wenzelm@29344
   729
fun comp_no_flatten (th, n) i rule =
wenzelm@29344
   730
  (case distinct Thm.eq_thm (Seq.list_of
wenzelm@58950
   731
      (Thm.bicompose NONE {flatten = false, match = false, incremented = true}
wenzelm@52223
   732
        (false, th, n) i (incr_indexes th rule))) of
wenzelm@29344
   733
    [th'] => th'
wenzelm@29344
   734
  | [] => raise THM ("comp_no_flatten", i, [th, rule])
wenzelm@29344
   735
  | _ => raise THM ("comp_no_flatten: unique result expected", i, [th, rule]));
wenzelm@29344
   736
wenzelm@29344
   737
wenzelm@9554
   738
wenzelm@45348
   739
(** variations on Thm.instantiate **)
paulson@8129
   740
wenzelm@43333
   741
fun instantiate_normalize instpair th =
wenzelm@21603
   742
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   743
wenzelm@60778
   744
(*instantiation with type-inference for variables*)
wenzelm@60795
   745
fun infer_instantiate_types _ [] th = th
wenzelm@60798
   746
  | infer_instantiate_types ctxt args raw_th =
wenzelm@60794
   747
      let
wenzelm@60794
   748
        val thy = Proof_Context.theory_of ctxt;
wenzelm@60798
   749
        val th = Thm.transfer thy raw_th;
wenzelm@60794
   750
wenzelm@60794
   751
        fun infer ((xi, T), cu) (tyenv, maxidx) =
wenzelm@60794
   752
          let
wenzelm@60798
   753
            val _ = Thm.ctyp_of ctxt T;
wenzelm@60798
   754
            val _ = Thm.transfer_cterm thy cu;
wenzelm@60794
   755
            val U = Thm.typ_of_cterm cu;
wenzelm@60794
   756
            val maxidx' = maxidx
wenzelm@60794
   757
              |> Integer.max (#2 xi)
wenzelm@60794
   758
              |> Term.maxidx_typ T
wenzelm@60794
   759
              |> Integer.max (Thm.maxidx_of_cterm cu);
wenzelm@60794
   760
            val (tyenv', maxidx'') = Sign.typ_unify thy (T, U) (tyenv, maxidx')
wenzelm@60794
   761
              handle Type.TUNIFY =>
wenzelm@60794
   762
                let
wenzelm@60794
   763
                  val t = Var (xi, T);
wenzelm@60794
   764
                  val u = Thm.term_of cu;
wenzelm@60794
   765
                in
wenzelm@60795
   766
                  raise THM ("infer_instantiate_types: type " ^
wenzelm@60794
   767
                    Syntax.string_of_typ ctxt (Envir.norm_type tyenv T) ^ " of variable " ^
wenzelm@60794
   768
                    Syntax.string_of_term ctxt (Term.map_types (Envir.norm_type tyenv) t) ^
wenzelm@60794
   769
                    "\ncannot be unified with type " ^
wenzelm@60794
   770
                    Syntax.string_of_typ ctxt (Envir.norm_type tyenv U) ^ " of term " ^
wenzelm@60794
   771
                    Syntax.string_of_term ctxt (Term.map_types (Envir.norm_type tyenv) u),
wenzelm@60794
   772
                    0, [th])
wenzelm@60794
   773
                end;
wenzelm@60794
   774
          in (tyenv', maxidx'') end;
wenzelm@60794
   775
wenzelm@60794
   776
        val (tyenv, _) = fold infer args (Vartab.empty, 0);
wenzelm@60794
   777
        val instT =
wenzelm@60794
   778
          Vartab.fold (fn (xi, (S, T)) =>
wenzelm@60794
   779
            cons ((xi, S), Thm.ctyp_of ctxt (Envir.norm_type tyenv T))) tyenv [];
wenzelm@60794
   780
        val inst = args |> map (fn ((xi, T), cu) =>
wenzelm@60794
   781
          ((xi, Envir.norm_type tyenv T),
wenzelm@60794
   782
            Thm.instantiate_cterm (instT, []) (Thm.transfer_cterm thy cu)));
wenzelm@60794
   783
      in instantiate_normalize (instT, inst) th end
wenzelm@60798
   784
      handle CTERM (msg, _) => raise THM (msg, 0, [raw_th])
wenzelm@60798
   785
        | TERM (msg, _) => raise THM (msg, 0, [raw_th])
wenzelm@60798
   786
        | TYPE (msg, _, _) => raise THM (msg, 0, [raw_th]);
wenzelm@60794
   787
wenzelm@60778
   788
fun infer_instantiate _ [] th = th
wenzelm@60778
   789
  | infer_instantiate ctxt args th =
wenzelm@60778
   790
      let
wenzelm@60778
   791
        val vars = Term.add_vars (Thm.full_prop_of th) [];
wenzelm@60778
   792
        val dups = duplicates (eq_fst op =) vars;
wenzelm@60778
   793
        val _ = null dups orelse
wenzelm@60778
   794
          raise THM ("infer_instantiate: inconsistent types for variables " ^
wenzelm@60778
   795
            commas_quote (map (Syntax.string_of_term (Config.put show_types true ctxt) o Var) dups),
wenzelm@60778
   796
            0, [th]);
wenzelm@60794
   797
        val args' = args |> map_filter (fn (xi, cu) =>
wenzelm@60794
   798
          AList.lookup (op =) vars xi |> Option.map (fn T => ((xi, T), cu)));
wenzelm@60795
   799
      in infer_instantiate_types ctxt args' th end;
wenzelm@60778
   800
wenzelm@60783
   801
fun infer_instantiate' ctxt args th =
wenzelm@60783
   802
  let
wenzelm@60794
   803
    val vars = rev (Term.add_vars (Thm.full_prop_of th) []);
wenzelm@60783
   804
    val args' = zip_options vars args
wenzelm@60783
   805
      handle ListPair.UnequalLengths =>
wenzelm@60783
   806
        raise THM ("infer_instantiate': more instantiations than variables in thm", 0, [th]);
wenzelm@60795
   807
  in infer_instantiate_types ctxt args' th end;
wenzelm@4285
   808
wenzelm@4285
   809
berghofe@14081
   810
berghofe@14081
   811
(** renaming of bound variables **)
berghofe@14081
   812
berghofe@14081
   813
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   814
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   815
berghofe@14081
   816
fun rename_bvars [] thm = thm
berghofe@14081
   817
  | rename_bvars vs thm =
wenzelm@26627
   818
      let
wenzelm@60313
   819
        fun rename (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, rename t)
wenzelm@60313
   820
          | rename (t $ u) = rename t $ rename u
wenzelm@60313
   821
          | rename a = a;
wenzelm@60313
   822
      in Thm.renamed_prop (rename (Thm.prop_of thm)) thm end;
berghofe@14081
   823
berghofe@14081
   824
berghofe@14081
   825
(* renaming in left-to-right order *)
berghofe@14081
   826
berghofe@14081
   827
fun rename_bvars' xs thm =
berghofe@14081
   828
  let
berghofe@14081
   829
    fun rename [] t = ([], t)
berghofe@14081
   830
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   831
          let val (xs', t') = rename xs t
wenzelm@18929
   832
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
   833
      | rename xs (t $ u) =
berghofe@14081
   834
          let
berghofe@14081
   835
            val (xs', t') = rename xs t;
wenzelm@60313
   836
            val (xs'', u') = rename xs' u;
berghofe@14081
   837
          in (xs'', t' $ u') end
wenzelm@60320
   838
      | rename xs a = (xs, a);
wenzelm@59616
   839
  in
wenzelm@60313
   840
    (case rename xs (Thm.prop_of thm) of
wenzelm@60313
   841
      ([], prop') => Thm.renamed_prop prop' thm
wenzelm@59616
   842
    | _ => error "More names than abstractions in theorem")
berghofe@14081
   843
  end;
berghofe@14081
   844
wenzelm@11975
   845
end;
wenzelm@5903
   846
wenzelm@35021
   847
structure Basic_Drule: BASIC_DRULE = Drule;
wenzelm@35021
   848
open Basic_Drule;