src/Pure/drule.ML
author wenzelm
Thu Jun 27 17:06:22 2013 +0200 (2013-06-27)
changeset 52467 24c6ddb48cb8
parent 52465 4970437fe092
child 56245 84fc7dfa3cd4
permissions -rw-r--r--
tuned signature;
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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 ctyp_fun: (typ -> typ) -> (ctyp -> ctyp)
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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: 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 types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
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  val flexflex_unique: 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: thm list -> thm -> thm Seq.seq
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  val multi_resolves: 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: 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 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 ("==>", _) $ _ $ _ => 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 cprop_of;
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fun cterm_fun f ct = Thm.cterm_of (Thm.theory_of_cterm ct) (f (Thm.term_of ct));
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fun ctyp_fun f cT = Thm.ctyp_of (Thm.theory_of_ctyp cT) (f (Thm.typ_of cT));
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fun certify t = Thm.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 (cprop_of (Thm.beta_conversion false (Thm.apply x y)));
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(*** Find the type (sort) associated with a (T)Var or (T)Free in a term
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     Used for establishing default types (of variables) and sorts (of
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     type variables) when reading another term.
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     Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
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***)
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fun types_sorts thm =
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  let
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    val vars = Thm.fold_terms Term.add_vars thm [];
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    val frees = Thm.fold_terms Term.add_frees thm [];
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    val tvars = Thm.fold_terms Term.add_tvars thm [];
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    val tfrees = Thm.fold_terms Term.add_tfrees thm [];
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    fun types (a, i) =
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      if i < 0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a, i);
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    fun sorts (a, i) =
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      if i < 0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a, i);
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  in (types, sorts) end;
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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.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 th =
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  let
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    val thy = Thm.theory_of_thm th;
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    val {prop, maxidx, ...} = Thm.rep_thm th;
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    val cert = Thm.cterm_of thy;
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    fun elim (x, T) = Thm.forall_elim (cert (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 cert = Thm.cterm_of thy;
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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 = Thm.fold_terms Term.add_vars th [] |> map (fn (xi, T) =>
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      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
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  in
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    th |> Thm.instantiate ([], inst)
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    |> fold_rev (Thm.forall_intr o cert) 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 certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
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        val (instT, inst) = Term_Subst.zero_var_indexes_inst (map Thm.full_prop_of ths);
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        val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
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        val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
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      in map (Thm.adjust_maxidx_thm ~1 o Thm.instantiate (cinstT, cinst)) 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 th =
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  if null (Thm.tpairs_of th) then th else
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    case distinct Thm.eq_thm (Seq.list_of (Thm.flexflex_rule 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
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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)
wenzelm@31945
   311
            (map (fn q => if new <= q andalso q < p then q + 1 else q) ps)
wenzelm@31945
   312
            (Thm.permute_prems (new + 1) (new - p) (Thm.permute_prems new (p - new) thm))
oheimb@11163
   313
  in rearr 0 end;
paulson@4610
   314
wenzelm@47427
   315
wenzelm@47427
   316
(*Resolution: multiple arguments, multiple results*)
wenzelm@47427
   317
local
wenzelm@47427
   318
  fun res th i rule =
wenzelm@47427
   319
    Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
clasohm@0
   320
wenzelm@47427
   321
  fun multi_res _ [] rule = Seq.single rule
wenzelm@47427
   322
    | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@47427
   323
in
wenzelm@47427
   324
  val multi_resolve = multi_res 1;
wenzelm@47427
   325
  fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@47427
   326
end;
wenzelm@47427
   327
wenzelm@47427
   328
(*Resolution: exactly one resolvent must be produced*)
wenzelm@47427
   329
fun tha RSN (i, thb) =
wenzelm@47427
   330
  (case Seq.chop 2 (Thm.biresolution false [(false, tha)] i thb) of
wenzelm@47427
   331
    ([th], _) => th
wenzelm@47427
   332
  | ([], _) => raise THM ("RSN: no unifiers", i, [tha, thb])
wenzelm@47427
   333
  | _ => raise THM ("RSN: multiple unifiers", i, [tha, thb]));
wenzelm@47427
   334
wenzelm@47427
   335
(*Resolution: P==>Q, Q==>R gives P==>R*)
clasohm@0
   336
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   337
clasohm@0
   338
(*For joining lists of rules*)
wenzelm@47427
   339
fun thas RLN (i, thbs) =
wenzelm@31945
   340
  let val resolve = Thm.biresolution false (map (pair false) thas) i
wenzelm@4270
   341
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   342
  in maps resb thbs end;
clasohm@0
   343
wenzelm@47427
   344
fun thas RL thbs = thas RLN (1, thbs);
wenzelm@47427
   345
wenzelm@47427
   346
(*Isar-style multi-resolution*)
wenzelm@47427
   347
fun bottom_rl OF rls =
wenzelm@47427
   348
  (case Seq.chop 2 (multi_resolve rls bottom_rl) of
wenzelm@47427
   349
    ([th], _) => th
wenzelm@47427
   350
  | ([], _) => raise THM ("OF: no unifiers", 0, bottom_rl :: rls)
wenzelm@47427
   351
  | _ => raise THM ("OF: multiple unifiers", 0, bottom_rl :: rls));
clasohm@0
   352
lcp@11
   353
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   354
  makes proof trees*)
wenzelm@47427
   355
fun rls MRS bottom_rl = bottom_rl OF rls;
wenzelm@9288
   356
wenzelm@252
   357
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   358
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   359
  ALWAYS deletes premise i *)
wenzelm@52467
   360
fun compose (tha, i, thb) =
wenzelm@52467
   361
  Thm.bicompose {flatten = true, match = false, incremented = false} (false, tha, 0) i thb
wenzelm@52467
   362
  |> Seq.list_of |> distinct Thm.eq_thm
wenzelm@52467
   363
  |> (fn [th] => th | _ => raise THM ("compose: unique result expected", i, [tha, thb]));
wenzelm@6946
   364
wenzelm@13105
   365
wenzelm@4016
   366
(** theorem equality **)
clasohm@0
   367
clasohm@0
   368
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   369
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   370
lcp@1194
   371
lcp@1194
   372
clasohm@0
   373
(*** Meta-Rewriting Rules ***)
clasohm@0
   374
wenzelm@33384
   375
val read_prop = certify o Simple_Syntax.read_prop;
wenzelm@26487
   376
wenzelm@26487
   377
fun store_thm name th =
wenzelm@39557
   378
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm (name, th)));
paulson@4610
   379
wenzelm@26487
   380
fun store_thm_open name th =
wenzelm@39557
   381
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm_open (name, th)));
wenzelm@26487
   382
wenzelm@35021
   383
fun store_standard_thm name th = store_thm name (export_without_context th);
wenzelm@35021
   384
fun store_standard_thm_open name thm = store_thm_open name (export_without_context_open thm);
wenzelm@4016
   385
clasohm@0
   386
val reflexive_thm =
wenzelm@26487
   387
  let val cx = certify (Var(("x",0),TVar(("'a",0),[])))
wenzelm@33277
   388
  in store_standard_thm_open (Binding.name "reflexive") (Thm.reflexive cx) end;
clasohm@0
   389
clasohm@0
   390
val symmetric_thm =
wenzelm@33277
   391
  let
wenzelm@33277
   392
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   393
    val thm = Thm.implies_intr xy (Thm.symmetric (Thm.assume xy));
wenzelm@33277
   394
  in store_standard_thm_open (Binding.name "symmetric") thm end;
clasohm@0
   395
clasohm@0
   396
val transitive_thm =
wenzelm@33277
   397
  let
wenzelm@33277
   398
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   399
    val yz = read_prop "y::'a == z::'a";
wenzelm@33277
   400
    val xythm = Thm.assume xy;
wenzelm@33277
   401
    val yzthm = Thm.assume yz;
wenzelm@33277
   402
    val thm = Thm.implies_intr yz (Thm.transitive xythm yzthm);
wenzelm@33277
   403
  in store_standard_thm_open (Binding.name "transitive") thm end;
clasohm@0
   404
berghofe@11512
   405
fun extensional eq =
berghofe@11512
   406
  let val eq' =
wenzelm@36944
   407
    Thm.abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (cprop_of eq)))) eq
wenzelm@36944
   408
  in Thm.equal_elim (Thm.eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   409
wenzelm@18820
   410
val equals_cong =
wenzelm@33277
   411
  store_standard_thm_open (Binding.name "equals_cong")
wenzelm@33277
   412
    (Thm.reflexive (read_prop "x::'a == y::'a"));
wenzelm@18820
   413
berghofe@10414
   414
val imp_cong =
berghofe@10414
   415
  let
wenzelm@24241
   416
    val ABC = read_prop "A ==> B::prop == C::prop"
wenzelm@24241
   417
    val AB = read_prop "A ==> B"
wenzelm@24241
   418
    val AC = read_prop "A ==> C"
wenzelm@24241
   419
    val A = read_prop "A"
berghofe@10414
   420
  in
wenzelm@36944
   421
    store_standard_thm_open (Binding.name "imp_cong") (Thm.implies_intr ABC (Thm.equal_intr
wenzelm@36944
   422
      (Thm.implies_intr AB (Thm.implies_intr A
wenzelm@36944
   423
        (Thm.equal_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A))
wenzelm@36944
   424
          (Thm.implies_elim (Thm.assume AB) (Thm.assume A)))))
wenzelm@36944
   425
      (Thm.implies_intr AC (Thm.implies_intr A
wenzelm@36944
   426
        (Thm.equal_elim (Thm.symmetric (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)))
wenzelm@36944
   427
          (Thm.implies_elim (Thm.assume AC) (Thm.assume A)))))))
berghofe@10414
   428
  end;
berghofe@10414
   429
berghofe@10414
   430
val swap_prems_eq =
berghofe@10414
   431
  let
wenzelm@24241
   432
    val ABC = read_prop "A ==> B ==> C"
wenzelm@24241
   433
    val BAC = read_prop "B ==> A ==> C"
wenzelm@24241
   434
    val A = read_prop "A"
wenzelm@24241
   435
    val B = read_prop "B"
berghofe@10414
   436
  in
wenzelm@33277
   437
    store_standard_thm_open (Binding.name "swap_prems_eq")
wenzelm@36944
   438
      (Thm.equal_intr
wenzelm@36944
   439
        (Thm.implies_intr ABC (Thm.implies_intr B (Thm.implies_intr A
wenzelm@36944
   440
          (Thm.implies_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)) (Thm.assume B)))))
wenzelm@36944
   441
        (Thm.implies_intr BAC (Thm.implies_intr A (Thm.implies_intr B
wenzelm@36944
   442
          (Thm.implies_elim (Thm.implies_elim (Thm.assume BAC) (Thm.assume B)) (Thm.assume A))))))
berghofe@10414
   443
  end;
lcp@229
   444
wenzelm@22938
   445
val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
wenzelm@22938
   446
wenzelm@23537
   447
fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM in LCF/HOL*)
wenzelm@23537
   448
fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM in LCF/HOL*)
wenzelm@23568
   449
fun binop_cong_rule ct th1 th2 = Thm.combination (arg_cong_rule ct th1) th2;
clasohm@0
   450
skalberg@15001
   451
local
wenzelm@22906
   452
  val dest_eq = Thm.dest_equals o cprop_of
skalberg@15001
   453
  val rhs_of = snd o dest_eq
skalberg@15001
   454
in
skalberg@15001
   455
fun beta_eta_conversion t =
wenzelm@36944
   456
  let val thm = Thm.beta_conversion true t
wenzelm@36944
   457
  in Thm.transitive thm (Thm.eta_conversion (rhs_of thm)) end
skalberg@15001
   458
end;
skalberg@15001
   459
wenzelm@36944
   460
fun eta_long_conversion ct =
wenzelm@36944
   461
  Thm.transitive
wenzelm@36944
   462
    (beta_eta_conversion ct)
wenzelm@52131
   463
    (Thm.symmetric (beta_eta_conversion (cterm_fun (Envir.eta_long []) ct)));
berghofe@15925
   464
paulson@20861
   465
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   466
fun eta_contraction_rule th =
wenzelm@36944
   467
  Thm.equal_elim (Thm.eta_conversion (cprop_of th)) th;
paulson@20861
   468
wenzelm@24947
   469
wenzelm@24947
   470
(* abs_def *)
wenzelm@24947
   471
wenzelm@24947
   472
(*
wenzelm@24947
   473
   f ?x1 ... ?xn == u
wenzelm@24947
   474
  --------------------
wenzelm@24947
   475
   f == %x1 ... xn. u
wenzelm@24947
   476
*)
wenzelm@24947
   477
wenzelm@24947
   478
local
wenzelm@24947
   479
wenzelm@24947
   480
fun contract_lhs th =
wenzelm@24947
   481
  Thm.transitive (Thm.symmetric (beta_eta_conversion
wenzelm@24947
   482
    (fst (Thm.dest_equals (cprop_of th))))) th;
wenzelm@24947
   483
wenzelm@24947
   484
fun var_args ct =
wenzelm@24947
   485
  (case try Thm.dest_comb ct of
wenzelm@24947
   486
    SOME (f, arg) =>
wenzelm@24947
   487
      (case Thm.term_of arg of
wenzelm@24947
   488
        Var ((x, _), _) => update (eq_snd (op aconvc)) (x, arg) (var_args f)
wenzelm@24947
   489
      | _ => [])
wenzelm@24947
   490
  | NONE => []);
wenzelm@24947
   491
wenzelm@24947
   492
in
wenzelm@24947
   493
wenzelm@24947
   494
fun abs_def th =
wenzelm@18337
   495
  let
wenzelm@24947
   496
    val th' = contract_lhs th;
wenzelm@24947
   497
    val args = var_args (Thm.lhs_of th');
wenzelm@24947
   498
  in contract_lhs (fold (uncurry Thm.abstract_rule) args th') end;
wenzelm@24947
   499
wenzelm@24947
   500
end;
wenzelm@24947
   501
wenzelm@18337
   502
wenzelm@18468
   503
wenzelm@15669
   504
(*** Some useful meta-theorems ***)
clasohm@0
   505
clasohm@0
   506
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@33277
   507
val asm_rl = store_standard_thm_open (Binding.name "asm_rl") (Thm.trivial (read_prop "?psi"));
clasohm@0
   508
clasohm@0
   509
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   510
val cut_rl =
wenzelm@33277
   511
  store_standard_thm_open (Binding.name "cut_rl")
wenzelm@24241
   512
    (Thm.trivial (read_prop "?psi ==> ?theta"));
clasohm@0
   513
wenzelm@252
   514
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   515
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   516
val revcut_rl =
wenzelm@33277
   517
  let
wenzelm@33277
   518
    val V = read_prop "V";
wenzelm@33277
   519
    val VW = read_prop "V ==> W";
wenzelm@4016
   520
  in
wenzelm@33277
   521
    store_standard_thm_open (Binding.name "revcut_rl")
wenzelm@36944
   522
      (Thm.implies_intr V (Thm.implies_intr VW (Thm.implies_elim (Thm.assume VW) (Thm.assume V))))
clasohm@0
   523
  end;
clasohm@0
   524
lcp@668
   525
(*for deleting an unwanted assumption*)
lcp@668
   526
val thin_rl =
wenzelm@33277
   527
  let
wenzelm@33277
   528
    val V = read_prop "V";
wenzelm@33277
   529
    val W = read_prop "W";
wenzelm@36944
   530
    val thm = Thm.implies_intr V (Thm.implies_intr W (Thm.assume W));
wenzelm@33277
   531
  in store_standard_thm_open (Binding.name "thin_rl") thm end;
lcp@668
   532
clasohm@0
   533
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   534
val triv_forall_equality =
wenzelm@33277
   535
  let
wenzelm@33277
   536
    val V = read_prop "V";
wenzelm@33277
   537
    val QV = read_prop "!!x::'a. V";
wenzelm@33277
   538
    val x = certify (Free ("x", Term.aT []));
wenzelm@4016
   539
  in
wenzelm@33277
   540
    store_standard_thm_open (Binding.name "triv_forall_equality")
wenzelm@36944
   541
      (Thm.equal_intr (Thm.implies_intr QV (Thm.forall_elim x (Thm.assume QV)))
wenzelm@36944
   542
        (Thm.implies_intr V (Thm.forall_intr x (Thm.assume V))))
clasohm@0
   543
  end;
clasohm@0
   544
wenzelm@19051
   545
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   546
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   547
*)
wenzelm@19051
   548
val distinct_prems_rl =
wenzelm@19051
   549
  let
wenzelm@33277
   550
    val AAB = read_prop "Phi ==> Phi ==> Psi";
wenzelm@24241
   551
    val A = read_prop "Phi";
wenzelm@19051
   552
  in
wenzelm@33277
   553
    store_standard_thm_open (Binding.name "distinct_prems_rl")
wenzelm@36944
   554
      (implies_intr_list [AAB, A] (implies_elim_list (Thm.assume AAB) [Thm.assume A, Thm.assume A]))
wenzelm@19051
   555
  end;
wenzelm@19051
   556
nipkow@3653
   557
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   558
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   559
   Introduction rule for == as a meta-theorem.
nipkow@3653
   560
*)
nipkow@3653
   561
val equal_intr_rule =
wenzelm@33277
   562
  let
wenzelm@33277
   563
    val PQ = read_prop "phi ==> psi";
wenzelm@33277
   564
    val QP = read_prop "psi ==> phi";
wenzelm@4016
   565
  in
wenzelm@33277
   566
    store_standard_thm_open (Binding.name "equal_intr_rule")
wenzelm@36944
   567
      (Thm.implies_intr PQ (Thm.implies_intr QP (Thm.equal_intr (Thm.assume PQ) (Thm.assume QP))))
nipkow@3653
   568
  end;
nipkow@3653
   569
wenzelm@19421
   570
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   571
val equal_elim_rule1 =
wenzelm@33277
   572
  let
wenzelm@33277
   573
    val eq = read_prop "phi::prop == psi::prop";
wenzelm@33277
   574
    val P = read_prop "phi";
wenzelm@33277
   575
  in
wenzelm@33277
   576
    store_standard_thm_open (Binding.name "equal_elim_rule1")
wenzelm@36944
   577
      (Thm.equal_elim (Thm.assume eq) (Thm.assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   578
  end;
wenzelm@4285
   579
wenzelm@19421
   580
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   581
val equal_elim_rule2 =
wenzelm@33277
   582
  store_standard_thm_open (Binding.name "equal_elim_rule2")
wenzelm@33277
   583
    (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   584
wenzelm@28618
   585
(* PROP ?phi ==> PROP ?phi ==> PROP ?psi ==> PROP ?psi *)
wenzelm@12297
   586
val remdups_rl =
wenzelm@33277
   587
  let
wenzelm@33277
   588
    val P = read_prop "phi";
wenzelm@33277
   589
    val Q = read_prop "psi";
wenzelm@33277
   590
    val thm = implies_intr_list [P, P, Q] (Thm.assume Q);
wenzelm@33277
   591
  in store_standard_thm_open (Binding.name "remdups_rl") thm end;
wenzelm@12297
   592
wenzelm@12297
   593
wenzelm@28618
   594
wenzelm@28618
   595
(** embedded terms and types **)
wenzelm@28618
   596
wenzelm@28618
   597
local
wenzelm@28618
   598
  val A = certify (Free ("A", propT));
wenzelm@35845
   599
  val axiom = Thm.unvarify_global o Thm.axiom (Context.the_theory (Context.the_thread_data ()));
wenzelm@28674
   600
  val prop_def = axiom "Pure.prop_def";
wenzelm@28674
   601
  val term_def = axiom "Pure.term_def";
wenzelm@28674
   602
  val sort_constraint_def = axiom "Pure.sort_constraint_def";
wenzelm@28618
   603
  val C = Thm.lhs_of sort_constraint_def;
wenzelm@28618
   604
  val T = Thm.dest_arg C;
wenzelm@28618
   605
  val CA = mk_implies (C, A);
wenzelm@28618
   606
in
wenzelm@28618
   607
wenzelm@28618
   608
(* protect *)
wenzelm@28618
   609
wenzelm@46497
   610
val protect = Thm.apply (certify Logic.protectC);
wenzelm@28618
   611
wenzelm@33277
   612
val protectI =
wenzelm@35021
   613
  store_standard_thm (Binding.conceal (Binding.name "protectI"))
wenzelm@35021
   614
    (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A));
wenzelm@28618
   615
wenzelm@33277
   616
val protectD =
wenzelm@35021
   617
  store_standard_thm (Binding.conceal (Binding.name "protectD"))
wenzelm@35021
   618
    (Thm.equal_elim prop_def (Thm.assume (protect A)));
wenzelm@28618
   619
wenzelm@33277
   620
val protect_cong =
wenzelm@33277
   621
  store_standard_thm_open (Binding.name "protect_cong") (Thm.reflexive (protect A));
wenzelm@28618
   622
wenzelm@28618
   623
fun implies_intr_protected asms th =
wenzelm@28618
   624
  let val asms' = map protect asms in
wenzelm@28618
   625
    implies_elim_list
wenzelm@28618
   626
      (implies_intr_list asms th)
wenzelm@28618
   627
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@28618
   628
    |> implies_intr_list asms'
wenzelm@28618
   629
  end;
wenzelm@28618
   630
wenzelm@28618
   631
wenzelm@28618
   632
(* term *)
wenzelm@28618
   633
wenzelm@33277
   634
val termI =
wenzelm@35021
   635
  store_standard_thm (Binding.conceal (Binding.name "termI"))
wenzelm@35021
   636
    (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)));
wenzelm@9554
   637
wenzelm@28618
   638
fun mk_term ct =
wenzelm@28618
   639
  let
wenzelm@28618
   640
    val thy = Thm.theory_of_cterm ct;
wenzelm@28618
   641
    val cert = Thm.cterm_of thy;
wenzelm@28618
   642
    val certT = Thm.ctyp_of thy;
wenzelm@28618
   643
    val T = Thm.typ_of (Thm.ctyp_of_term ct);
wenzelm@28618
   644
    val a = certT (TVar (("'a", 0), []));
wenzelm@28618
   645
    val x = cert (Var (("x", 0), T));
wenzelm@28618
   646
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@28618
   647
wenzelm@28618
   648
fun dest_term th =
wenzelm@28618
   649
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@28618
   650
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@28618
   651
      Thm.dest_arg cprop
wenzelm@28618
   652
    else raise THM ("dest_term", 0, [th])
wenzelm@28618
   653
  end;
wenzelm@28618
   654
wenzelm@28618
   655
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@28618
   656
wenzelm@45156
   657
val dummy_thm = mk_term (certify Term.dummy_prop);
wenzelm@28618
   658
wenzelm@28618
   659
wenzelm@28618
   660
(* sort_constraint *)
wenzelm@28618
   661
wenzelm@33277
   662
val sort_constraintI =
wenzelm@35021
   663
  store_standard_thm (Binding.conceal (Binding.name "sort_constraintI"))
wenzelm@35021
   664
    (Thm.equal_elim (Thm.symmetric sort_constraint_def) (mk_term T));
wenzelm@28618
   665
wenzelm@33277
   666
val sort_constraint_eq =
wenzelm@35021
   667
  store_standard_thm (Binding.conceal (Binding.name "sort_constraint_eq"))
wenzelm@35021
   668
    (Thm.equal_intr
wenzelm@35845
   669
      (Thm.implies_intr CA (Thm.implies_elim (Thm.assume CA)
wenzelm@35845
   670
        (Thm.unvarify_global sort_constraintI)))
wenzelm@35021
   671
      (implies_intr_list [A, C] (Thm.assume A)));
wenzelm@28618
   672
wenzelm@28618
   673
end;
wenzelm@28618
   674
wenzelm@28618
   675
wenzelm@28618
   676
(* HHF normalization *)
wenzelm@28618
   677
wenzelm@46214
   678
(* (PROP ?phi ==> (!!x. PROP ?psi x)) == (!!x. PROP ?phi ==> PROP ?psi x) *)
wenzelm@9554
   679
val norm_hhf_eq =
wenzelm@9554
   680
  let
wenzelm@14854
   681
    val aT = TFree ("'a", []);
wenzelm@9554
   682
    val x = Free ("x", aT);
wenzelm@9554
   683
    val phi = Free ("phi", propT);
wenzelm@9554
   684
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   685
wenzelm@26487
   686
    val cx = certify x;
wenzelm@26487
   687
    val cphi = certify phi;
wenzelm@46214
   688
    val lhs = certify (Logic.mk_implies (phi, Logic.all x (psi $ x)));
wenzelm@46214
   689
    val rhs = certify (Logic.all x (Logic.mk_implies (phi, psi $ x)));
wenzelm@9554
   690
  in
wenzelm@9554
   691
    Thm.equal_intr
wenzelm@9554
   692
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   693
        |> Thm.forall_elim cx
wenzelm@9554
   694
        |> Thm.implies_intr cphi
wenzelm@9554
   695
        |> Thm.forall_intr cx
wenzelm@9554
   696
        |> Thm.implies_intr lhs)
wenzelm@9554
   697
      (Thm.implies_elim
wenzelm@9554
   698
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   699
        |> Thm.forall_intr cx
wenzelm@9554
   700
        |> Thm.implies_intr cphi
wenzelm@9554
   701
        |> Thm.implies_intr rhs)
wenzelm@33277
   702
    |> store_standard_thm_open (Binding.name "norm_hhf_eq")
wenzelm@9554
   703
  end;
wenzelm@9554
   704
wenzelm@18179
   705
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@28618
   706
val norm_hhf_eqs = [norm_hhf_eq, sort_constraint_eq];
wenzelm@18179
   707
wenzelm@30553
   708
fun is_norm_hhf (Const ("Pure.sort_constraint", _)) = false
wenzelm@30553
   709
  | is_norm_hhf (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@30553
   710
  | is_norm_hhf (Abs _ $ _) = false
wenzelm@30553
   711
  | is_norm_hhf (t $ u) = is_norm_hhf t andalso is_norm_hhf u
wenzelm@30553
   712
  | is_norm_hhf (Abs (_, _, t)) = is_norm_hhf t
wenzelm@30553
   713
  | is_norm_hhf _ = true;
wenzelm@12800
   714
wenzelm@16425
   715
fun norm_hhf thy t =
wenzelm@12800
   716
  if is_norm_hhf t then t
wenzelm@18179
   717
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   718
wenzelm@20298
   719
fun norm_hhf_cterm ct =
wenzelm@20298
   720
  if is_norm_hhf (Thm.term_of ct) then ct
wenzelm@20298
   721
  else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
wenzelm@20298
   722
wenzelm@12800
   723
wenzelm@21603
   724
(* var indexes *)
wenzelm@21603
   725
wenzelm@21603
   726
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   727
wenzelm@21603
   728
fun incr_indexes2 th1 th2 =
wenzelm@21603
   729
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   730
wenzelm@52224
   731
local
wenzelm@52224
   732
wenzelm@52224
   733
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
wenzelm@52224
   734
fun comp incremented th1 th2 =
wenzelm@52224
   735
  Thm.bicompose {flatten = true, match = false, incremented = incremented} (false, th1, 0) 1 th2
wenzelm@52224
   736
  |> Seq.list_of |> distinct Thm.eq_thm
wenzelm@52224
   737
  |> (fn [th] => th | _ => raise THM ("COMP", 1, [th1, th2]));
wenzelm@52224
   738
wenzelm@52224
   739
in
wenzelm@52224
   740
wenzelm@52224
   741
fun th1 COMP th2 = comp false th1 th2;
wenzelm@52224
   742
fun th1 INCR_COMP th2 = comp true (incr_indexes th2 th1) th2;
wenzelm@52224
   743
fun th1 COMP_INCR th2 = comp true th1 (incr_indexes th1 th2);
wenzelm@52224
   744
wenzelm@52224
   745
end;
wenzelm@21603
   746
wenzelm@29344
   747
fun comp_no_flatten (th, n) i rule =
wenzelm@29344
   748
  (case distinct Thm.eq_thm (Seq.list_of
wenzelm@52223
   749
      (Thm.bicompose {flatten = false, match = false, incremented = true}
wenzelm@52223
   750
        (false, th, n) i (incr_indexes th rule))) of
wenzelm@29344
   751
    [th'] => th'
wenzelm@29344
   752
  | [] => raise THM ("comp_no_flatten", i, [th, rule])
wenzelm@29344
   753
  | _ => raise THM ("comp_no_flatten: unique result expected", i, [th, rule]));
wenzelm@29344
   754
wenzelm@29344
   755
wenzelm@9554
   756
wenzelm@45348
   757
(** variations on Thm.instantiate **)
paulson@8129
   758
wenzelm@43333
   759
fun instantiate_normalize instpair th =
wenzelm@21603
   760
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   761
wenzelm@45347
   762
(*Left-to-right replacements: tpairs = [..., (vi, ti), ...].
wenzelm@45347
   763
  Instantiates distinct Vars by terms, inferring type instantiations.*)
paulson@8129
   764
local
wenzelm@45347
   765
  fun add_types (ct, cu) (thy, tye, maxidx) =
wenzelm@26627
   766
    let
wenzelm@45347
   767
      val {t, T, maxidx = maxt, ...} = Thm.rep_cterm ct;
wenzelm@45347
   768
      val {t = u, T = U, maxidx = maxu, ...} = Thm.rep_cterm cu;
wenzelm@45347
   769
      val maxi = Int.max (maxidx, Int.max (maxt, maxu));
wenzelm@45347
   770
      val thy' = Theory.merge (thy, Theory.merge (Thm.theory_of_cterm ct, Thm.theory_of_cterm cu));
wenzelm@45347
   771
      val (tye', maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@45347
   772
        handle Type.TUNIFY => raise TYPE ("Ill-typed instantiation:\nType\n" ^
wenzelm@45347
   773
          Syntax.string_of_typ_global thy' (Envir.norm_type tye T) ^
wenzelm@45347
   774
          "\nof variable " ^
wenzelm@45347
   775
          Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) t) ^
wenzelm@45347
   776
          "\ncannot be unified with type\n" ^
wenzelm@45347
   777
          Syntax.string_of_typ_global thy' (Envir.norm_type tye U) ^ "\nof term " ^
wenzelm@45347
   778
          Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) u),
wenzelm@45347
   779
          [T, U], [t, u])
wenzelm@45347
   780
    in (thy', tye', maxi') end;
paulson@8129
   781
in
wenzelm@45347
   782
paulson@22561
   783
fun cterm_instantiate [] th = th
wenzelm@45348
   784
  | cterm_instantiate ctpairs th =
wenzelm@45347
   785
      let
wenzelm@45348
   786
        val (thy, tye, _) = fold_rev add_types ctpairs (Thm.theory_of_thm th, Vartab.empty, 0);
wenzelm@45347
   787
        val certT = ctyp_of thy;
wenzelm@45348
   788
        val instT =
wenzelm@45348
   789
          Vartab.fold (fn (xi, (S, T)) =>
wenzelm@45348
   790
            cons (certT (TVar (xi, S)), certT (Envir.norm_type tye T))) tye [];
wenzelm@45348
   791
        val inst = map (pairself (Thm.instantiate_cterm (instT, []))) ctpairs;
wenzelm@45348
   792
      in instantiate_normalize (instT, inst) th end
wenzelm@45348
   793
      handle TERM (msg, _) => raise THM (msg, 0, [th])
wenzelm@45347
   794
        | TYPE (msg, _, _) => raise THM (msg, 0, [th]);
paulson@8129
   795
end;
paulson@8129
   796
paulson@8129
   797
wenzelm@4285
   798
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   799
wenzelm@4285
   800
fun instantiate' cTs cts thm =
wenzelm@4285
   801
  let
wenzelm@4285
   802
    fun err msg =
wenzelm@4285
   803
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   804
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   805
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   806
wenzelm@4285
   807
    fun inst_of (v, ct) =
wenzelm@16425
   808
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   809
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   810
berghofe@15797
   811
    fun tyinst_of (v, cT) =
wenzelm@16425
   812
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   813
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   814
wenzelm@20298
   815
    fun zip_vars xs ys =
wenzelm@40722
   816
      zip_options xs ys handle ListPair.UnequalLengths =>
wenzelm@20298
   817
        err "more instantiations than variables in thm";
wenzelm@4285
   818
wenzelm@4285
   819
    (*instantiate types first!*)
wenzelm@4285
   820
    val thm' =
wenzelm@4285
   821
      if forall is_none cTs then thm
wenzelm@20298
   822
      else Thm.instantiate
wenzelm@22695
   823
        (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
wenzelm@20579
   824
    val thm'' =
wenzelm@4285
   825
      if forall is_none cts then thm'
wenzelm@20298
   826
      else Thm.instantiate
wenzelm@22695
   827
        ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
wenzelm@20298
   828
    in thm'' end;
wenzelm@4285
   829
wenzelm@4285
   830
berghofe@14081
   831
berghofe@14081
   832
(** renaming of bound variables **)
berghofe@14081
   833
berghofe@14081
   834
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   835
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   836
berghofe@14081
   837
fun rename_bvars [] thm = thm
berghofe@14081
   838
  | rename_bvars vs thm =
wenzelm@26627
   839
      let
wenzelm@26627
   840
        val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   841
        fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
wenzelm@26627
   842
          | ren (t $ u) = ren t $ ren u
wenzelm@26627
   843
          | ren t = t;
wenzelm@36944
   844
      in Thm.equal_elim (Thm.reflexive (cert (ren (Thm.prop_of thm)))) thm end;
berghofe@14081
   845
berghofe@14081
   846
berghofe@14081
   847
(* renaming in left-to-right order *)
berghofe@14081
   848
berghofe@14081
   849
fun rename_bvars' xs thm =
berghofe@14081
   850
  let
wenzelm@26627
   851
    val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   852
    val prop = Thm.prop_of thm;
berghofe@14081
   853
    fun rename [] t = ([], t)
berghofe@14081
   854
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   855
          let val (xs', t') = rename xs t
wenzelm@18929
   856
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
   857
      | rename xs (t $ u) =
berghofe@14081
   858
          let
berghofe@14081
   859
            val (xs', t') = rename xs t;
berghofe@14081
   860
            val (xs'', u') = rename xs' u
berghofe@14081
   861
          in (xs'', t' $ u') end
berghofe@14081
   862
      | rename xs t = (xs, t);
berghofe@14081
   863
  in case rename xs prop of
wenzelm@36944
   864
      ([], prop') => Thm.equal_elim (Thm.reflexive (cert prop')) thm
berghofe@14081
   865
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   866
  end;
berghofe@14081
   867
wenzelm@11975
   868
end;
wenzelm@5903
   869
wenzelm@35021
   870
structure Basic_Drule: BASIC_DRULE = Drule;
wenzelm@35021
   871
open Basic_Drule;