src/Pure/drule.ML
author wenzelm
Sat May 30 22:04:15 2015 +0200 (2015-05-30)
changeset 60316 e487b83a9885
parent 60315 c08adefc98ea
child 60319 127c2f00ca94
permissions -rw-r--r--
tuned;
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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 cterm_fun: (term -> term) -> (cterm -> cterm)
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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 gen_all: int -> thm -> thm
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  val lift_all: 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: (ctyp * ctyp) list * (cterm * cterm) 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 cterm_instantiate: (cterm * cterm) list -> 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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  val instantiate': ctyp option list -> cterm option list -> thm -> 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 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_long_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 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 cterm_fun f ct = Thm.global_cterm_of (Thm.theory_of_cterm ct) (f (Thm.term_of ct));
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fun certify t = Thm.global_cterm_of (Context.the_theory (Context.the_thread_data ())) 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 =
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  fold Thm.forall_intr
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    (map (Thm.global_cterm_of (Thm.theory_of_thm th) o Var) (Thm.fold_terms Term.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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(*generalize outermost parameters*)
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fun gen_all maxidx0 th =
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  let
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    val thy = Thm.theory_of_thm th;
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    val maxidx = Thm.maxidx_thm th maxidx0;
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    val prop = Thm.prop_of th;
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    fun elim (x, T) =
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      Thm.forall_elim (Thm.global_cterm_of thy (Var ((x, maxidx + 1), T)));
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  in fold elim (outer_params prop) th 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 goal th =
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  let
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    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm 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), Term.list_comb (Var (xi, Ts ---> T), ps)));
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  in
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    th
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    |> Thm.instantiate (Thm.certify_inst thy ([], inst))
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    |> fold_rev (Thm.forall_intr o Thm.global_cterm_of thy) 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 thy = Theory.merge_list (map Thm.theory_of_thm ths);
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        val inst =
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          Term_Subst.zero_var_indexes_inst (map Thm.full_prop_of ths)
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          |> Thm.certify_inst thy;
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      in map (Thm.adjust_maxidx_thm ~1 o Thm.instantiate 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 =
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  fold Thm.implies_intr (#hyps (Thm.crep_thm 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
   313
  | ([], _) => raise THM ("RSN: no unifiers", i, [tha, thb])
wenzelm@47427
   314
  | _ => raise THM ("RSN: multiple unifiers", i, [tha, thb]));
wenzelm@47427
   315
wenzelm@47427
   316
(*Resolution: P==>Q, Q==>R gives P==>R*)
clasohm@0
   317
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   318
clasohm@0
   319
(*For joining lists of rules*)
wenzelm@47427
   320
fun thas RLN (i, thbs) =
wenzelm@59773
   321
  let
wenzelm@59773
   322
    val resolve = Thm.biresolution NONE false (map (pair false) thas) i
wenzelm@59773
   323
    fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   324
  in maps resb thbs end;
clasohm@0
   325
wenzelm@47427
   326
fun thas RL thbs = thas RLN (1, thbs);
wenzelm@47427
   327
wenzelm@47427
   328
(*Isar-style multi-resolution*)
wenzelm@47427
   329
fun bottom_rl OF rls =
wenzelm@58950
   330
  (case Seq.chop 2 (multi_resolve NONE rls bottom_rl) of
wenzelm@47427
   331
    ([th], _) => th
wenzelm@47427
   332
  | ([], _) => raise THM ("OF: no unifiers", 0, bottom_rl :: rls)
wenzelm@47427
   333
  | _ => raise THM ("OF: multiple unifiers", 0, bottom_rl :: rls));
clasohm@0
   334
lcp@11
   335
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   336
  makes proof trees*)
wenzelm@47427
   337
fun rls MRS bottom_rl = bottom_rl OF rls;
wenzelm@9288
   338
wenzelm@252
   339
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   340
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   341
  ALWAYS deletes premise i *)
wenzelm@52467
   342
fun compose (tha, i, thb) =
wenzelm@58950
   343
  Thm.bicompose NONE {flatten = true, match = false, incremented = false} (false, tha, 0) i thb
wenzelm@52467
   344
  |> Seq.list_of |> distinct Thm.eq_thm
wenzelm@52467
   345
  |> (fn [th] => th | _ => raise THM ("compose: unique result expected", i, [tha, thb]));
wenzelm@6946
   346
wenzelm@13105
   347
wenzelm@4016
   348
(** theorem equality **)
clasohm@0
   349
clasohm@0
   350
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   351
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   352
lcp@1194
   353
lcp@1194
   354
clasohm@0
   355
(*** Meta-Rewriting Rules ***)
clasohm@0
   356
wenzelm@33384
   357
val read_prop = certify o Simple_Syntax.read_prop;
wenzelm@26487
   358
wenzelm@26487
   359
fun store_thm name th =
wenzelm@39557
   360
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm (name, th)));
paulson@4610
   361
wenzelm@26487
   362
fun store_thm_open name th =
wenzelm@39557
   363
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm_open (name, th)));
wenzelm@26487
   364
wenzelm@35021
   365
fun store_standard_thm name th = store_thm name (export_without_context th);
wenzelm@35021
   366
fun store_standard_thm_open name thm = store_thm_open name (export_without_context_open thm);
wenzelm@4016
   367
clasohm@0
   368
val reflexive_thm =
wenzelm@26487
   369
  let val cx = certify (Var(("x",0),TVar(("'a",0),[])))
wenzelm@56436
   370
  in store_standard_thm_open (Binding.make ("reflexive", @{here})) (Thm.reflexive cx) end;
clasohm@0
   371
clasohm@0
   372
val symmetric_thm =
wenzelm@33277
   373
  let
wenzelm@33277
   374
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   375
    val thm = Thm.implies_intr xy (Thm.symmetric (Thm.assume xy));
wenzelm@56436
   376
  in store_standard_thm_open (Binding.make ("symmetric", @{here})) thm end;
clasohm@0
   377
clasohm@0
   378
val transitive_thm =
wenzelm@33277
   379
  let
wenzelm@33277
   380
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   381
    val yz = read_prop "y::'a == z::'a";
wenzelm@33277
   382
    val xythm = Thm.assume xy;
wenzelm@33277
   383
    val yzthm = Thm.assume yz;
wenzelm@33277
   384
    val thm = Thm.implies_intr yz (Thm.transitive xythm yzthm);
wenzelm@56436
   385
  in store_standard_thm_open (Binding.make ("transitive", @{here})) thm end;
clasohm@0
   386
berghofe@11512
   387
fun extensional eq =
berghofe@11512
   388
  let val eq' =
wenzelm@59582
   389
    Thm.abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (Thm.cprop_of eq)))) eq
wenzelm@59582
   390
  in Thm.equal_elim (Thm.eta_conversion (Thm.cprop_of eq')) eq' end;
berghofe@11512
   391
wenzelm@18820
   392
val equals_cong =
wenzelm@56436
   393
  store_standard_thm_open (Binding.make ("equals_cong", @{here}))
wenzelm@33277
   394
    (Thm.reflexive (read_prop "x::'a == y::'a"));
wenzelm@18820
   395
berghofe@10414
   396
val imp_cong =
berghofe@10414
   397
  let
wenzelm@24241
   398
    val ABC = read_prop "A ==> B::prop == C::prop"
wenzelm@24241
   399
    val AB = read_prop "A ==> B"
wenzelm@24241
   400
    val AC = read_prop "A ==> C"
wenzelm@24241
   401
    val A = read_prop "A"
berghofe@10414
   402
  in
wenzelm@56436
   403
    store_standard_thm_open (Binding.make ("imp_cong", @{here}))
wenzelm@56436
   404
      (Thm.implies_intr ABC (Thm.equal_intr
wenzelm@56436
   405
        (Thm.implies_intr AB (Thm.implies_intr A
wenzelm@56436
   406
          (Thm.equal_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A))
wenzelm@56436
   407
            (Thm.implies_elim (Thm.assume AB) (Thm.assume A)))))
wenzelm@56436
   408
        (Thm.implies_intr AC (Thm.implies_intr A
wenzelm@56436
   409
          (Thm.equal_elim (Thm.symmetric (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)))
wenzelm@56436
   410
            (Thm.implies_elim (Thm.assume AC) (Thm.assume A)))))))
berghofe@10414
   411
  end;
berghofe@10414
   412
berghofe@10414
   413
val swap_prems_eq =
berghofe@10414
   414
  let
wenzelm@24241
   415
    val ABC = read_prop "A ==> B ==> C"
wenzelm@24241
   416
    val BAC = read_prop "B ==> A ==> C"
wenzelm@24241
   417
    val A = read_prop "A"
wenzelm@24241
   418
    val B = read_prop "B"
berghofe@10414
   419
  in
wenzelm@56436
   420
    store_standard_thm_open (Binding.make ("swap_prems_eq", @{here}))
wenzelm@36944
   421
      (Thm.equal_intr
wenzelm@36944
   422
        (Thm.implies_intr ABC (Thm.implies_intr B (Thm.implies_intr A
wenzelm@36944
   423
          (Thm.implies_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)) (Thm.assume B)))))
wenzelm@36944
   424
        (Thm.implies_intr BAC (Thm.implies_intr A (Thm.implies_intr B
wenzelm@36944
   425
          (Thm.implies_elim (Thm.implies_elim (Thm.assume BAC) (Thm.assume B)) (Thm.assume A))))))
berghofe@10414
   426
  end;
lcp@229
   427
wenzelm@22938
   428
val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
wenzelm@22938
   429
wenzelm@23537
   430
fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM in LCF/HOL*)
wenzelm@23537
   431
fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM in LCF/HOL*)
wenzelm@23568
   432
fun binop_cong_rule ct th1 th2 = Thm.combination (arg_cong_rule ct th1) th2;
clasohm@0
   433
wenzelm@60316
   434
fun beta_eta_conversion ct =
wenzelm@60316
   435
  let val thm = Thm.beta_conversion true ct
wenzelm@60316
   436
  in Thm.transitive thm (Thm.eta_conversion (Thm.rhs_of thm)) end;
skalberg@15001
   437
wenzelm@36944
   438
fun eta_long_conversion ct =
wenzelm@36944
   439
  Thm.transitive
wenzelm@36944
   440
    (beta_eta_conversion ct)
wenzelm@52131
   441
    (Thm.symmetric (beta_eta_conversion (cterm_fun (Envir.eta_long []) ct)));
berghofe@15925
   442
paulson@20861
   443
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   444
fun eta_contraction_rule th =
wenzelm@59582
   445
  Thm.equal_elim (Thm.eta_conversion (Thm.cprop_of th)) th;
paulson@20861
   446
wenzelm@24947
   447
wenzelm@24947
   448
(* abs_def *)
wenzelm@24947
   449
wenzelm@24947
   450
(*
wenzelm@24947
   451
   f ?x1 ... ?xn == u
wenzelm@24947
   452
  --------------------
wenzelm@24947
   453
   f == %x1 ... xn. u
wenzelm@24947
   454
*)
wenzelm@24947
   455
wenzelm@24947
   456
local
wenzelm@24947
   457
wenzelm@24947
   458
fun contract_lhs th =
wenzelm@24947
   459
  Thm.transitive (Thm.symmetric (beta_eta_conversion
wenzelm@59582
   460
    (fst (Thm.dest_equals (Thm.cprop_of th))))) th;
wenzelm@24947
   461
wenzelm@24947
   462
fun var_args ct =
wenzelm@24947
   463
  (case try Thm.dest_comb ct of
wenzelm@24947
   464
    SOME (f, arg) =>
wenzelm@24947
   465
      (case Thm.term_of arg of
wenzelm@24947
   466
        Var ((x, _), _) => update (eq_snd (op aconvc)) (x, arg) (var_args f)
wenzelm@24947
   467
      | _ => [])
wenzelm@24947
   468
  | NONE => []);
wenzelm@24947
   469
wenzelm@24947
   470
in
wenzelm@24947
   471
wenzelm@24947
   472
fun abs_def th =
wenzelm@18337
   473
  let
wenzelm@24947
   474
    val th' = contract_lhs th;
wenzelm@24947
   475
    val args = var_args (Thm.lhs_of th');
wenzelm@24947
   476
  in contract_lhs (fold (uncurry Thm.abstract_rule) args th') end;
wenzelm@24947
   477
wenzelm@24947
   478
end;
wenzelm@24947
   479
wenzelm@18337
   480
wenzelm@18468
   481
wenzelm@15669
   482
(*** Some useful meta-theorems ***)
clasohm@0
   483
clasohm@0
   484
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@56436
   485
val asm_rl =
wenzelm@56436
   486
  store_standard_thm_open (Binding.make ("asm_rl", @{here}))
wenzelm@56436
   487
    (Thm.trivial (read_prop "?psi"));
clasohm@0
   488
clasohm@0
   489
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   490
val cut_rl =
wenzelm@56436
   491
  store_standard_thm_open (Binding.make ("cut_rl", @{here}))
wenzelm@24241
   492
    (Thm.trivial (read_prop "?psi ==> ?theta"));
clasohm@0
   493
wenzelm@252
   494
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   495
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   496
val revcut_rl =
wenzelm@33277
   497
  let
wenzelm@33277
   498
    val V = read_prop "V";
wenzelm@33277
   499
    val VW = read_prop "V ==> W";
wenzelm@4016
   500
  in
wenzelm@56436
   501
    store_standard_thm_open (Binding.make ("revcut_rl", @{here}))
wenzelm@56436
   502
      (Thm.implies_intr V
wenzelm@56436
   503
        (Thm.implies_intr VW (Thm.implies_elim (Thm.assume VW) (Thm.assume V))))
clasohm@0
   504
  end;
clasohm@0
   505
lcp@668
   506
(*for deleting an unwanted assumption*)
lcp@668
   507
val thin_rl =
wenzelm@33277
   508
  let
wenzelm@33277
   509
    val V = read_prop "V";
wenzelm@33277
   510
    val W = read_prop "W";
wenzelm@36944
   511
    val thm = Thm.implies_intr V (Thm.implies_intr W (Thm.assume W));
wenzelm@56436
   512
  in store_standard_thm_open (Binding.make ("thin_rl", @{here})) thm end;
lcp@668
   513
clasohm@0
   514
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   515
val triv_forall_equality =
wenzelm@33277
   516
  let
wenzelm@33277
   517
    val V = read_prop "V";
wenzelm@33277
   518
    val QV = read_prop "!!x::'a. V";
wenzelm@33277
   519
    val x = certify (Free ("x", Term.aT []));
wenzelm@4016
   520
  in
wenzelm@56436
   521
    store_standard_thm_open (Binding.make ("triv_forall_equality", @{here}))
wenzelm@36944
   522
      (Thm.equal_intr (Thm.implies_intr QV (Thm.forall_elim x (Thm.assume QV)))
wenzelm@36944
   523
        (Thm.implies_intr V (Thm.forall_intr x (Thm.assume V))))
clasohm@0
   524
  end;
clasohm@0
   525
wenzelm@19051
   526
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   527
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   528
*)
wenzelm@19051
   529
val distinct_prems_rl =
wenzelm@19051
   530
  let
wenzelm@33277
   531
    val AAB = read_prop "Phi ==> Phi ==> Psi";
wenzelm@24241
   532
    val A = read_prop "Phi";
wenzelm@19051
   533
  in
wenzelm@56436
   534
    store_standard_thm_open (Binding.make ("distinct_prems_rl", @{here}))
wenzelm@56436
   535
      (implies_intr_list [AAB, A]
wenzelm@56436
   536
        (implies_elim_list (Thm.assume AAB) [Thm.assume A, Thm.assume A]))
wenzelm@19051
   537
  end;
wenzelm@19051
   538
nipkow@3653
   539
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   540
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   541
   Introduction rule for == as a meta-theorem.
nipkow@3653
   542
*)
nipkow@3653
   543
val equal_intr_rule =
wenzelm@33277
   544
  let
wenzelm@33277
   545
    val PQ = read_prop "phi ==> psi";
wenzelm@33277
   546
    val QP = read_prop "psi ==> phi";
wenzelm@4016
   547
  in
wenzelm@56436
   548
    store_standard_thm_open (Binding.make ("equal_intr_rule", @{here}))
wenzelm@56436
   549
      (Thm.implies_intr PQ
wenzelm@56436
   550
        (Thm.implies_intr QP (Thm.equal_intr (Thm.assume PQ) (Thm.assume QP))))
nipkow@3653
   551
  end;
nipkow@3653
   552
wenzelm@19421
   553
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   554
val equal_elim_rule1 =
wenzelm@33277
   555
  let
wenzelm@33277
   556
    val eq = read_prop "phi::prop == psi::prop";
wenzelm@33277
   557
    val P = read_prop "phi";
wenzelm@33277
   558
  in
wenzelm@56436
   559
    store_standard_thm_open (Binding.make ("equal_elim_rule1", @{here}))
wenzelm@36944
   560
      (Thm.equal_elim (Thm.assume eq) (Thm.assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   561
  end;
wenzelm@4285
   562
wenzelm@19421
   563
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   564
val equal_elim_rule2 =
wenzelm@56436
   565
  store_standard_thm_open (Binding.make ("equal_elim_rule2", @{here}))
wenzelm@33277
   566
    (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   567
wenzelm@28618
   568
(* PROP ?phi ==> PROP ?phi ==> PROP ?psi ==> PROP ?psi *)
wenzelm@12297
   569
val remdups_rl =
wenzelm@33277
   570
  let
wenzelm@33277
   571
    val P = read_prop "phi";
wenzelm@33277
   572
    val Q = read_prop "psi";
wenzelm@33277
   573
    val thm = implies_intr_list [P, P, Q] (Thm.assume Q);
wenzelm@56436
   574
  in store_standard_thm_open (Binding.make ("remdups_rl", @{here})) thm end;
wenzelm@12297
   575
wenzelm@12297
   576
wenzelm@28618
   577
wenzelm@28618
   578
(** embedded terms and types **)
wenzelm@28618
   579
wenzelm@28618
   580
local
wenzelm@28618
   581
  val A = certify (Free ("A", propT));
wenzelm@35845
   582
  val axiom = Thm.unvarify_global o Thm.axiom (Context.the_theory (Context.the_thread_data ()));
wenzelm@28674
   583
  val prop_def = axiom "Pure.prop_def";
wenzelm@28674
   584
  val term_def = axiom "Pure.term_def";
wenzelm@28674
   585
  val sort_constraint_def = axiom "Pure.sort_constraint_def";
wenzelm@28618
   586
  val C = Thm.lhs_of sort_constraint_def;
wenzelm@28618
   587
  val T = Thm.dest_arg C;
wenzelm@28618
   588
  val CA = mk_implies (C, A);
wenzelm@28618
   589
in
wenzelm@28618
   590
wenzelm@28618
   591
(* protect *)
wenzelm@28618
   592
wenzelm@46497
   593
val protect = Thm.apply (certify Logic.protectC);
wenzelm@28618
   594
wenzelm@33277
   595
val protectI =
wenzelm@59859
   596
  store_standard_thm (Binding.concealed (Binding.make ("protectI", @{here})))
wenzelm@35021
   597
    (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A));
wenzelm@28618
   598
wenzelm@33277
   599
val protectD =
wenzelm@59859
   600
  store_standard_thm (Binding.concealed (Binding.make ("protectD", @{here})))
wenzelm@35021
   601
    (Thm.equal_elim prop_def (Thm.assume (protect A)));
wenzelm@28618
   602
wenzelm@33277
   603
val protect_cong =
wenzelm@56436
   604
  store_standard_thm_open (Binding.make ("protect_cong", @{here}))
wenzelm@56436
   605
    (Thm.reflexive (protect A));
wenzelm@28618
   606
wenzelm@28618
   607
fun implies_intr_protected asms th =
wenzelm@28618
   608
  let val asms' = map protect asms in
wenzelm@28618
   609
    implies_elim_list
wenzelm@28618
   610
      (implies_intr_list asms th)
wenzelm@28618
   611
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@28618
   612
    |> implies_intr_list asms'
wenzelm@28618
   613
  end;
wenzelm@28618
   614
wenzelm@28618
   615
wenzelm@28618
   616
(* term *)
wenzelm@28618
   617
wenzelm@33277
   618
val termI =
wenzelm@59859
   619
  store_standard_thm (Binding.concealed (Binding.make ("termI", @{here})))
wenzelm@35021
   620
    (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)));
wenzelm@9554
   621
wenzelm@28618
   622
fun mk_term ct =
wenzelm@28618
   623
  let
wenzelm@28618
   624
    val thy = Thm.theory_of_cterm ct;
wenzelm@59586
   625
    val T = Thm.typ_of_cterm ct;
wenzelm@59995
   626
    val instT = apply2 (Thm.global_ctyp_of thy) (TVar (("'a", 0), []), T);
wenzelm@59621
   627
    val x = Thm.global_cterm_of thy (Var (("x", 0), T));
wenzelm@59995
   628
  in Thm.instantiate ([instT], [(x, ct)]) termI end;
wenzelm@28618
   629
wenzelm@28618
   630
fun dest_term th =
wenzelm@28618
   631
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@28618
   632
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@28618
   633
      Thm.dest_arg cprop
wenzelm@28618
   634
    else raise THM ("dest_term", 0, [th])
wenzelm@28618
   635
  end;
wenzelm@28618
   636
wenzelm@28618
   637
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@28618
   638
wenzelm@45156
   639
val dummy_thm = mk_term (certify Term.dummy_prop);
wenzelm@28618
   640
wenzelm@28618
   641
wenzelm@28618
   642
(* sort_constraint *)
wenzelm@28618
   643
wenzelm@60240
   644
fun is_sort_constraint (Const ("Pure.sort_constraint", _) $ Const ("Pure.type", _)) = true
wenzelm@60240
   645
  | is_sort_constraint _ = false;
wenzelm@60240
   646
wenzelm@33277
   647
val sort_constraintI =
wenzelm@59859
   648
  store_standard_thm (Binding.concealed (Binding.make ("sort_constraintI", @{here})))
wenzelm@35021
   649
    (Thm.equal_elim (Thm.symmetric sort_constraint_def) (mk_term T));
wenzelm@28618
   650
wenzelm@33277
   651
val sort_constraint_eq =
wenzelm@59859
   652
  store_standard_thm (Binding.concealed (Binding.make ("sort_constraint_eq", @{here})))
wenzelm@35021
   653
    (Thm.equal_intr
wenzelm@35845
   654
      (Thm.implies_intr CA (Thm.implies_elim (Thm.assume CA)
wenzelm@35845
   655
        (Thm.unvarify_global sort_constraintI)))
wenzelm@35021
   656
      (implies_intr_list [A, C] (Thm.assume A)));
wenzelm@28618
   657
wenzelm@28618
   658
end;
wenzelm@28618
   659
wenzelm@28618
   660
wenzelm@28618
   661
(* HHF normalization *)
wenzelm@28618
   662
wenzelm@46214
   663
(* (PROP ?phi ==> (!!x. PROP ?psi x)) == (!!x. PROP ?phi ==> PROP ?psi x) *)
wenzelm@9554
   664
val norm_hhf_eq =
wenzelm@9554
   665
  let
wenzelm@14854
   666
    val aT = TFree ("'a", []);
wenzelm@9554
   667
    val x = Free ("x", aT);
wenzelm@9554
   668
    val phi = Free ("phi", propT);
wenzelm@9554
   669
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   670
wenzelm@26487
   671
    val cx = certify x;
wenzelm@26487
   672
    val cphi = certify phi;
wenzelm@46214
   673
    val lhs = certify (Logic.mk_implies (phi, Logic.all x (psi $ x)));
wenzelm@46214
   674
    val rhs = certify (Logic.all x (Logic.mk_implies (phi, psi $ x)));
wenzelm@9554
   675
  in
wenzelm@9554
   676
    Thm.equal_intr
wenzelm@9554
   677
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   678
        |> Thm.forall_elim cx
wenzelm@9554
   679
        |> Thm.implies_intr cphi
wenzelm@9554
   680
        |> Thm.forall_intr cx
wenzelm@9554
   681
        |> Thm.implies_intr lhs)
wenzelm@9554
   682
      (Thm.implies_elim
wenzelm@9554
   683
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   684
        |> Thm.forall_intr cx
wenzelm@9554
   685
        |> Thm.implies_intr cphi
wenzelm@9554
   686
        |> Thm.implies_intr rhs)
wenzelm@56436
   687
    |> store_standard_thm_open (Binding.make ("norm_hhf_eq", @{here}))
wenzelm@9554
   688
  end;
wenzelm@9554
   689
wenzelm@18179
   690
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@28618
   691
val norm_hhf_eqs = [norm_hhf_eq, sort_constraint_eq];
wenzelm@18179
   692
wenzelm@30553
   693
fun is_norm_hhf (Const ("Pure.sort_constraint", _)) = false
wenzelm@56245
   694
  | is_norm_hhf (Const ("Pure.imp", _) $ _ $ (Const ("Pure.all", _) $ _)) = false
wenzelm@30553
   695
  | is_norm_hhf (Abs _ $ _) = false
wenzelm@30553
   696
  | is_norm_hhf (t $ u) = is_norm_hhf t andalso is_norm_hhf u
wenzelm@30553
   697
  | is_norm_hhf (Abs (_, _, t)) = is_norm_hhf t
wenzelm@30553
   698
  | is_norm_hhf _ = true;
wenzelm@12800
   699
wenzelm@16425
   700
fun norm_hhf thy t =
wenzelm@12800
   701
  if is_norm_hhf t then t
wenzelm@18179
   702
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   703
wenzelm@60315
   704
fun norm_hhf_cterm ctxt raw_ct =
wenzelm@60315
   705
  let
wenzelm@60315
   706
    val thy = Proof_Context.theory_of ctxt;
wenzelm@60315
   707
    val ct = Thm.transfer_cterm thy raw_ct;
wenzelm@60315
   708
    val t = Thm.term_of ct;
wenzelm@60315
   709
  in if is_norm_hhf t then ct else Thm.cterm_of ctxt (norm_hhf thy t) end;
wenzelm@20298
   710
wenzelm@12800
   711
wenzelm@21603
   712
(* var indexes *)
wenzelm@21603
   713
wenzelm@21603
   714
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   715
wenzelm@21603
   716
fun incr_indexes2 th1 th2 =
wenzelm@21603
   717
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   718
wenzelm@52224
   719
local
wenzelm@52224
   720
wenzelm@52224
   721
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
wenzelm@52224
   722
fun comp incremented th1 th2 =
wenzelm@59773
   723
  Thm.bicompose NONE {flatten = true, match = false, incremented = incremented}
wenzelm@59773
   724
    (false, th1, 0) 1 th2
wenzelm@52224
   725
  |> Seq.list_of |> distinct Thm.eq_thm
wenzelm@52224
   726
  |> (fn [th] => th | _ => raise THM ("COMP", 1, [th1, th2]));
wenzelm@52224
   727
wenzelm@52224
   728
in
wenzelm@52224
   729
wenzelm@52224
   730
fun th1 COMP th2 = comp false th1 th2;
wenzelm@52224
   731
fun th1 INCR_COMP th2 = comp true (incr_indexes th2 th1) th2;
wenzelm@52224
   732
fun th1 COMP_INCR th2 = comp true th1 (incr_indexes th1 th2);
wenzelm@52224
   733
wenzelm@52224
   734
end;
wenzelm@21603
   735
wenzelm@29344
   736
fun comp_no_flatten (th, n) i rule =
wenzelm@29344
   737
  (case distinct Thm.eq_thm (Seq.list_of
wenzelm@58950
   738
      (Thm.bicompose NONE {flatten = false, match = false, incremented = true}
wenzelm@52223
   739
        (false, th, n) i (incr_indexes th rule))) of
wenzelm@29344
   740
    [th'] => th'
wenzelm@29344
   741
  | [] => raise THM ("comp_no_flatten", i, [th, rule])
wenzelm@29344
   742
  | _ => raise THM ("comp_no_flatten: unique result expected", i, [th, rule]));
wenzelm@29344
   743
wenzelm@29344
   744
wenzelm@9554
   745
wenzelm@45348
   746
(** variations on Thm.instantiate **)
paulson@8129
   747
wenzelm@43333
   748
fun instantiate_normalize instpair th =
wenzelm@21603
   749
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   750
wenzelm@45347
   751
(*Left-to-right replacements: tpairs = [..., (vi, ti), ...].
wenzelm@45347
   752
  Instantiates distinct Vars by terms, inferring type instantiations.*)
paulson@8129
   753
local
wenzelm@45347
   754
  fun add_types (ct, cu) (thy, tye, maxidx) =
wenzelm@26627
   755
    let
wenzelm@59591
   756
      val t = Thm.term_of ct and T = Thm.typ_of_cterm ct;
wenzelm@59591
   757
      val u = Thm.term_of cu and U = Thm.typ_of_cterm cu;
wenzelm@59591
   758
      val maxi = Int.max (maxidx, Int.max (apply2 Thm.maxidx_of_cterm (ct, cu)));
wenzelm@59591
   759
      val thy' = Theory.merge (thy, Theory.merge (apply2 Thm.theory_of_cterm (ct, cu)));
wenzelm@45347
   760
      val (tye', maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@45347
   761
        handle Type.TUNIFY => raise TYPE ("Ill-typed instantiation:\nType\n" ^
wenzelm@45347
   762
          Syntax.string_of_typ_global thy' (Envir.norm_type tye T) ^
wenzelm@45347
   763
          "\nof variable " ^
wenzelm@45347
   764
          Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) t) ^
wenzelm@45347
   765
          "\ncannot be unified with type\n" ^
wenzelm@45347
   766
          Syntax.string_of_typ_global thy' (Envir.norm_type tye U) ^ "\nof term " ^
wenzelm@45347
   767
          Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) u),
wenzelm@59773
   768
          [T, U], [t, u]);
wenzelm@45347
   769
    in (thy', tye', maxi') end;
paulson@8129
   770
in
wenzelm@45347
   771
paulson@22561
   772
fun cterm_instantiate [] th = th
wenzelm@45348
   773
  | cterm_instantiate ctpairs th =
wenzelm@45347
   774
      let
wenzelm@45348
   775
        val (thy, tye, _) = fold_rev add_types ctpairs (Thm.theory_of_thm th, Vartab.empty, 0);
wenzelm@45348
   776
        val instT =
wenzelm@45348
   777
          Vartab.fold (fn (xi, (S, T)) =>
wenzelm@59773
   778
            cons (apply2 (Thm.global_ctyp_of thy) (TVar (xi, S), Envir.norm_type tye T))) tye [];
wenzelm@59058
   779
        val inst = map (apply2 (Thm.instantiate_cterm (instT, []))) ctpairs;
wenzelm@45348
   780
      in instantiate_normalize (instT, inst) th end
wenzelm@45348
   781
      handle TERM (msg, _) => raise THM (msg, 0, [th])
wenzelm@45347
   782
        | TYPE (msg, _, _) => raise THM (msg, 0, [th]);
paulson@8129
   783
end;
paulson@8129
   784
paulson@8129
   785
wenzelm@4285
   786
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   787
wenzelm@4285
   788
fun instantiate' cTs cts thm =
wenzelm@4285
   789
  let
wenzelm@4285
   790
    fun err msg =
wenzelm@4285
   791
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   792
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   793
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   794
wenzelm@4285
   795
    fun inst_of (v, ct) =
wenzelm@59621
   796
      (Thm.global_cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   797
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   798
berghofe@15797
   799
    fun tyinst_of (v, cT) =
wenzelm@59621
   800
      (Thm.global_ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   801
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   802
wenzelm@20298
   803
    fun zip_vars xs ys =
wenzelm@40722
   804
      zip_options xs ys handle ListPair.UnequalLengths =>
wenzelm@20298
   805
        err "more instantiations than variables in thm";
wenzelm@4285
   806
wenzelm@4285
   807
    (*instantiate types first!*)
wenzelm@4285
   808
    val thm' =
wenzelm@4285
   809
      if forall is_none cTs then thm
wenzelm@20298
   810
      else Thm.instantiate
wenzelm@22695
   811
        (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
wenzelm@20579
   812
    val thm'' =
wenzelm@4285
   813
      if forall is_none cts then thm'
wenzelm@20298
   814
      else Thm.instantiate
wenzelm@22695
   815
        ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
wenzelm@20298
   816
    in thm'' end;
wenzelm@4285
   817
wenzelm@4285
   818
berghofe@14081
   819
berghofe@14081
   820
(** renaming of bound variables **)
berghofe@14081
   821
berghofe@14081
   822
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   823
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   824
berghofe@14081
   825
fun rename_bvars [] thm = thm
berghofe@14081
   826
  | rename_bvars vs thm =
wenzelm@26627
   827
      let
wenzelm@60313
   828
        fun rename (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, rename t)
wenzelm@60313
   829
          | rename (t $ u) = rename t $ rename u
wenzelm@60313
   830
          | rename a = a;
wenzelm@60313
   831
      in Thm.renamed_prop (rename (Thm.prop_of thm)) thm end;
berghofe@14081
   832
berghofe@14081
   833
berghofe@14081
   834
(* renaming in left-to-right order *)
berghofe@14081
   835
berghofe@14081
   836
fun rename_bvars' xs thm =
berghofe@14081
   837
  let
berghofe@14081
   838
    fun rename [] t = ([], t)
berghofe@14081
   839
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   840
          let val (xs', t') = rename xs t
wenzelm@18929
   841
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
   842
      | rename xs (t $ u) =
berghofe@14081
   843
          let
berghofe@14081
   844
            val (xs', t') = rename xs t;
wenzelm@60313
   845
            val (xs'', u') = rename xs' u;
berghofe@14081
   846
          in (xs'', t' $ u') end
berghofe@14081
   847
      | rename xs t = (xs, t);
wenzelm@59616
   848
  in
wenzelm@60313
   849
    (case rename xs (Thm.prop_of thm) of
wenzelm@60313
   850
      ([], prop') => Thm.renamed_prop prop' thm
wenzelm@59616
   851
    | _ => error "More names than abstractions in theorem")
berghofe@14081
   852
  end;
berghofe@14081
   853
wenzelm@11975
   854
end;
wenzelm@5903
   855
wenzelm@35021
   856
structure Basic_Drule: BASIC_DRULE = Drule;
wenzelm@35021
   857
open Basic_Drule;