src/Pure/drule.ML
author wenzelm
Wed Dec 12 23:36:07 2012 +0100 (2012-12-12 ago)
changeset 50499 f496b2b7bafb
parent 48127 d30957198bbb
child 52131 366fa32ee2a3
permissions -rw-r--r--
rendering of selected dialog_result as active_result_color, depending on dynamic command status in output panel, but not static popups etc.;
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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 compose: thm * int * thm -> thm list
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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_single: 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
wenzelm@31945
   309
    fun rearr new [] thm = thm
wenzelm@31945
   310
      | rearr new (p :: ps) thm =
wenzelm@31945
   311
          rearr (new + 1)
wenzelm@31945
   312
            (map (fn q => if new <= q andalso q < p then q + 1 else q) ps)
wenzelm@31945
   313
            (Thm.permute_prems (new + 1) (new - p) (Thm.permute_prems new (p - new) thm))
oheimb@11163
   314
  in rearr 0 end;
paulson@4610
   315
wenzelm@47427
   316
wenzelm@47427
   317
(*Resolution: multiple arguments, multiple results*)
wenzelm@47427
   318
local
wenzelm@47427
   319
  fun res th i rule =
wenzelm@47427
   320
    Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
clasohm@0
   321
wenzelm@47427
   322
  fun multi_res _ [] rule = Seq.single rule
wenzelm@47427
   323
    | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@47427
   324
in
wenzelm@47427
   325
  val multi_resolve = multi_res 1;
wenzelm@47427
   326
  fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@47427
   327
end;
wenzelm@47427
   328
wenzelm@47427
   329
(*Resolution: exactly one resolvent must be produced*)
wenzelm@47427
   330
fun tha RSN (i, thb) =
wenzelm@47427
   331
  (case Seq.chop 2 (Thm.biresolution false [(false, tha)] i thb) of
wenzelm@47427
   332
    ([th], _) => th
wenzelm@47427
   333
  | ([], _) => raise THM ("RSN: no unifiers", i, [tha, thb])
wenzelm@47427
   334
  | _ => raise THM ("RSN: multiple unifiers", i, [tha, thb]));
wenzelm@47427
   335
wenzelm@47427
   336
(*Resolution: P==>Q, Q==>R gives P==>R*)
clasohm@0
   337
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   338
clasohm@0
   339
(*For joining lists of rules*)
wenzelm@47427
   340
fun thas RLN (i, thbs) =
wenzelm@31945
   341
  let val resolve = Thm.biresolution false (map (pair false) thas) i
wenzelm@4270
   342
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   343
  in maps resb thbs end;
clasohm@0
   344
wenzelm@47427
   345
fun thas RL thbs = thas RLN (1, thbs);
wenzelm@47427
   346
wenzelm@47427
   347
(*Isar-style multi-resolution*)
wenzelm@47427
   348
fun bottom_rl OF rls =
wenzelm@47427
   349
  (case Seq.chop 2 (multi_resolve rls bottom_rl) of
wenzelm@47427
   350
    ([th], _) => th
wenzelm@47427
   351
  | ([], _) => raise THM ("OF: no unifiers", 0, bottom_rl :: rls)
wenzelm@47427
   352
  | _ => raise THM ("OF: multiple unifiers", 0, bottom_rl :: rls));
clasohm@0
   353
lcp@11
   354
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   355
  makes proof trees*)
wenzelm@47427
   356
fun rls MRS bottom_rl = bottom_rl OF rls;
wenzelm@9288
   357
wenzelm@252
   358
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   359
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   360
  ALWAYS deletes premise i *)
wenzelm@252
   361
fun compose(tha,i,thb) =
wenzelm@47427
   362
  distinct Thm.eq_thm (Seq.list_of (Thm.bicompose false (false,tha,0) i thb));
clasohm@0
   363
wenzelm@6946
   364
fun compose_single (tha,i,thb) =
wenzelm@47427
   365
  (case compose (tha,i,thb) of
wenzelm@6946
   366
    [th] => th
wenzelm@47427
   367
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   368
clasohm@0
   369
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   370
fun tha COMP thb =
wenzelm@47427
   371
  (case compose(tha, 1, thb) of
wenzelm@47427
   372
    [th] => th
wenzelm@47427
   373
  | _ => raise THM ("COMP", 1, [tha, thb]));
clasohm@0
   374
wenzelm@13105
   375
wenzelm@4016
   376
(** theorem equality **)
clasohm@0
   377
clasohm@0
   378
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   379
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   380
lcp@1194
   381
lcp@1194
   382
clasohm@0
   383
(*** Meta-Rewriting Rules ***)
clasohm@0
   384
wenzelm@33384
   385
val read_prop = certify o Simple_Syntax.read_prop;
wenzelm@26487
   386
wenzelm@26487
   387
fun store_thm name th =
wenzelm@39557
   388
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm (name, th)));
paulson@4610
   389
wenzelm@26487
   390
fun store_thm_open name th =
wenzelm@39557
   391
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm_open (name, th)));
wenzelm@26487
   392
wenzelm@35021
   393
fun store_standard_thm name th = store_thm name (export_without_context th);
wenzelm@35021
   394
fun store_standard_thm_open name thm = store_thm_open name (export_without_context_open thm);
wenzelm@4016
   395
clasohm@0
   396
val reflexive_thm =
wenzelm@26487
   397
  let val cx = certify (Var(("x",0),TVar(("'a",0),[])))
wenzelm@33277
   398
  in store_standard_thm_open (Binding.name "reflexive") (Thm.reflexive cx) end;
clasohm@0
   399
clasohm@0
   400
val symmetric_thm =
wenzelm@33277
   401
  let
wenzelm@33277
   402
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   403
    val thm = Thm.implies_intr xy (Thm.symmetric (Thm.assume xy));
wenzelm@33277
   404
  in store_standard_thm_open (Binding.name "symmetric") thm end;
clasohm@0
   405
clasohm@0
   406
val transitive_thm =
wenzelm@33277
   407
  let
wenzelm@33277
   408
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   409
    val yz = read_prop "y::'a == z::'a";
wenzelm@33277
   410
    val xythm = Thm.assume xy;
wenzelm@33277
   411
    val yzthm = Thm.assume yz;
wenzelm@33277
   412
    val thm = Thm.implies_intr yz (Thm.transitive xythm yzthm);
wenzelm@33277
   413
  in store_standard_thm_open (Binding.name "transitive") thm end;
clasohm@0
   414
berghofe@11512
   415
fun extensional eq =
berghofe@11512
   416
  let val eq' =
wenzelm@36944
   417
    Thm.abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (cprop_of eq)))) eq
wenzelm@36944
   418
  in Thm.equal_elim (Thm.eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   419
wenzelm@18820
   420
val equals_cong =
wenzelm@33277
   421
  store_standard_thm_open (Binding.name "equals_cong")
wenzelm@33277
   422
    (Thm.reflexive (read_prop "x::'a == y::'a"));
wenzelm@18820
   423
berghofe@10414
   424
val imp_cong =
berghofe@10414
   425
  let
wenzelm@24241
   426
    val ABC = read_prop "A ==> B::prop == C::prop"
wenzelm@24241
   427
    val AB = read_prop "A ==> B"
wenzelm@24241
   428
    val AC = read_prop "A ==> C"
wenzelm@24241
   429
    val A = read_prop "A"
berghofe@10414
   430
  in
wenzelm@36944
   431
    store_standard_thm_open (Binding.name "imp_cong") (Thm.implies_intr ABC (Thm.equal_intr
wenzelm@36944
   432
      (Thm.implies_intr AB (Thm.implies_intr A
wenzelm@36944
   433
        (Thm.equal_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A))
wenzelm@36944
   434
          (Thm.implies_elim (Thm.assume AB) (Thm.assume A)))))
wenzelm@36944
   435
      (Thm.implies_intr AC (Thm.implies_intr A
wenzelm@36944
   436
        (Thm.equal_elim (Thm.symmetric (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)))
wenzelm@36944
   437
          (Thm.implies_elim (Thm.assume AC) (Thm.assume A)))))))
berghofe@10414
   438
  end;
berghofe@10414
   439
berghofe@10414
   440
val swap_prems_eq =
berghofe@10414
   441
  let
wenzelm@24241
   442
    val ABC = read_prop "A ==> B ==> C"
wenzelm@24241
   443
    val BAC = read_prop "B ==> A ==> C"
wenzelm@24241
   444
    val A = read_prop "A"
wenzelm@24241
   445
    val B = read_prop "B"
berghofe@10414
   446
  in
wenzelm@33277
   447
    store_standard_thm_open (Binding.name "swap_prems_eq")
wenzelm@36944
   448
      (Thm.equal_intr
wenzelm@36944
   449
        (Thm.implies_intr ABC (Thm.implies_intr B (Thm.implies_intr A
wenzelm@36944
   450
          (Thm.implies_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)) (Thm.assume B)))))
wenzelm@36944
   451
        (Thm.implies_intr BAC (Thm.implies_intr A (Thm.implies_intr B
wenzelm@36944
   452
          (Thm.implies_elim (Thm.implies_elim (Thm.assume BAC) (Thm.assume B)) (Thm.assume A))))))
berghofe@10414
   453
  end;
lcp@229
   454
wenzelm@22938
   455
val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
wenzelm@22938
   456
wenzelm@23537
   457
fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM in LCF/HOL*)
wenzelm@23537
   458
fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM in LCF/HOL*)
wenzelm@23568
   459
fun binop_cong_rule ct th1 th2 = Thm.combination (arg_cong_rule ct th1) th2;
clasohm@0
   460
skalberg@15001
   461
local
wenzelm@22906
   462
  val dest_eq = Thm.dest_equals o cprop_of
skalberg@15001
   463
  val rhs_of = snd o dest_eq
skalberg@15001
   464
in
skalberg@15001
   465
fun beta_eta_conversion t =
wenzelm@36944
   466
  let val thm = Thm.beta_conversion true t
wenzelm@36944
   467
  in Thm.transitive thm (Thm.eta_conversion (rhs_of thm)) end
skalberg@15001
   468
end;
skalberg@15001
   469
wenzelm@36944
   470
fun eta_long_conversion ct =
wenzelm@36944
   471
  Thm.transitive
wenzelm@36944
   472
    (beta_eta_conversion ct)
wenzelm@36944
   473
    (Thm.symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   474
paulson@20861
   475
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   476
fun eta_contraction_rule th =
wenzelm@36944
   477
  Thm.equal_elim (Thm.eta_conversion (cprop_of th)) th;
paulson@20861
   478
wenzelm@24947
   479
wenzelm@24947
   480
(* abs_def *)
wenzelm@24947
   481
wenzelm@24947
   482
(*
wenzelm@24947
   483
   f ?x1 ... ?xn == u
wenzelm@24947
   484
  --------------------
wenzelm@24947
   485
   f == %x1 ... xn. u
wenzelm@24947
   486
*)
wenzelm@24947
   487
wenzelm@24947
   488
local
wenzelm@24947
   489
wenzelm@24947
   490
fun contract_lhs th =
wenzelm@24947
   491
  Thm.transitive (Thm.symmetric (beta_eta_conversion
wenzelm@24947
   492
    (fst (Thm.dest_equals (cprop_of th))))) th;
wenzelm@24947
   493
wenzelm@24947
   494
fun var_args ct =
wenzelm@24947
   495
  (case try Thm.dest_comb ct of
wenzelm@24947
   496
    SOME (f, arg) =>
wenzelm@24947
   497
      (case Thm.term_of arg of
wenzelm@24947
   498
        Var ((x, _), _) => update (eq_snd (op aconvc)) (x, arg) (var_args f)
wenzelm@24947
   499
      | _ => [])
wenzelm@24947
   500
  | NONE => []);
wenzelm@24947
   501
wenzelm@24947
   502
in
wenzelm@24947
   503
wenzelm@24947
   504
fun abs_def th =
wenzelm@18337
   505
  let
wenzelm@24947
   506
    val th' = contract_lhs th;
wenzelm@24947
   507
    val args = var_args (Thm.lhs_of th');
wenzelm@24947
   508
  in contract_lhs (fold (uncurry Thm.abstract_rule) args th') end;
wenzelm@24947
   509
wenzelm@24947
   510
end;
wenzelm@24947
   511
wenzelm@18337
   512
wenzelm@18468
   513
wenzelm@15669
   514
(*** Some useful meta-theorems ***)
clasohm@0
   515
clasohm@0
   516
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@33277
   517
val asm_rl = store_standard_thm_open (Binding.name "asm_rl") (Thm.trivial (read_prop "?psi"));
clasohm@0
   518
clasohm@0
   519
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   520
val cut_rl =
wenzelm@33277
   521
  store_standard_thm_open (Binding.name "cut_rl")
wenzelm@24241
   522
    (Thm.trivial (read_prop "?psi ==> ?theta"));
clasohm@0
   523
wenzelm@252
   524
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   525
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   526
val revcut_rl =
wenzelm@33277
   527
  let
wenzelm@33277
   528
    val V = read_prop "V";
wenzelm@33277
   529
    val VW = read_prop "V ==> W";
wenzelm@4016
   530
  in
wenzelm@33277
   531
    store_standard_thm_open (Binding.name "revcut_rl")
wenzelm@36944
   532
      (Thm.implies_intr V (Thm.implies_intr VW (Thm.implies_elim (Thm.assume VW) (Thm.assume V))))
clasohm@0
   533
  end;
clasohm@0
   534
lcp@668
   535
(*for deleting an unwanted assumption*)
lcp@668
   536
val thin_rl =
wenzelm@33277
   537
  let
wenzelm@33277
   538
    val V = read_prop "V";
wenzelm@33277
   539
    val W = read_prop "W";
wenzelm@36944
   540
    val thm = Thm.implies_intr V (Thm.implies_intr W (Thm.assume W));
wenzelm@33277
   541
  in store_standard_thm_open (Binding.name "thin_rl") thm end;
lcp@668
   542
clasohm@0
   543
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   544
val triv_forall_equality =
wenzelm@33277
   545
  let
wenzelm@33277
   546
    val V = read_prop "V";
wenzelm@33277
   547
    val QV = read_prop "!!x::'a. V";
wenzelm@33277
   548
    val x = certify (Free ("x", Term.aT []));
wenzelm@4016
   549
  in
wenzelm@33277
   550
    store_standard_thm_open (Binding.name "triv_forall_equality")
wenzelm@36944
   551
      (Thm.equal_intr (Thm.implies_intr QV (Thm.forall_elim x (Thm.assume QV)))
wenzelm@36944
   552
        (Thm.implies_intr V (Thm.forall_intr x (Thm.assume V))))
clasohm@0
   553
  end;
clasohm@0
   554
wenzelm@19051
   555
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   556
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   557
*)
wenzelm@19051
   558
val distinct_prems_rl =
wenzelm@19051
   559
  let
wenzelm@33277
   560
    val AAB = read_prop "Phi ==> Phi ==> Psi";
wenzelm@24241
   561
    val A = read_prop "Phi";
wenzelm@19051
   562
  in
wenzelm@33277
   563
    store_standard_thm_open (Binding.name "distinct_prems_rl")
wenzelm@36944
   564
      (implies_intr_list [AAB, A] (implies_elim_list (Thm.assume AAB) [Thm.assume A, Thm.assume A]))
wenzelm@19051
   565
  end;
wenzelm@19051
   566
nipkow@3653
   567
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   568
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   569
   Introduction rule for == as a meta-theorem.
nipkow@3653
   570
*)
nipkow@3653
   571
val equal_intr_rule =
wenzelm@33277
   572
  let
wenzelm@33277
   573
    val PQ = read_prop "phi ==> psi";
wenzelm@33277
   574
    val QP = read_prop "psi ==> phi";
wenzelm@4016
   575
  in
wenzelm@33277
   576
    store_standard_thm_open (Binding.name "equal_intr_rule")
wenzelm@36944
   577
      (Thm.implies_intr PQ (Thm.implies_intr QP (Thm.equal_intr (Thm.assume PQ) (Thm.assume QP))))
nipkow@3653
   578
  end;
nipkow@3653
   579
wenzelm@19421
   580
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   581
val equal_elim_rule1 =
wenzelm@33277
   582
  let
wenzelm@33277
   583
    val eq = read_prop "phi::prop == psi::prop";
wenzelm@33277
   584
    val P = read_prop "phi";
wenzelm@33277
   585
  in
wenzelm@33277
   586
    store_standard_thm_open (Binding.name "equal_elim_rule1")
wenzelm@36944
   587
      (Thm.equal_elim (Thm.assume eq) (Thm.assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   588
  end;
wenzelm@4285
   589
wenzelm@19421
   590
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   591
val equal_elim_rule2 =
wenzelm@33277
   592
  store_standard_thm_open (Binding.name "equal_elim_rule2")
wenzelm@33277
   593
    (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   594
wenzelm@28618
   595
(* PROP ?phi ==> PROP ?phi ==> PROP ?psi ==> PROP ?psi *)
wenzelm@12297
   596
val remdups_rl =
wenzelm@33277
   597
  let
wenzelm@33277
   598
    val P = read_prop "phi";
wenzelm@33277
   599
    val Q = read_prop "psi";
wenzelm@33277
   600
    val thm = implies_intr_list [P, P, Q] (Thm.assume Q);
wenzelm@33277
   601
  in store_standard_thm_open (Binding.name "remdups_rl") thm end;
wenzelm@12297
   602
wenzelm@12297
   603
wenzelm@28618
   604
wenzelm@28618
   605
(** embedded terms and types **)
wenzelm@28618
   606
wenzelm@28618
   607
local
wenzelm@28618
   608
  val A = certify (Free ("A", propT));
wenzelm@35845
   609
  val axiom = Thm.unvarify_global o Thm.axiom (Context.the_theory (Context.the_thread_data ()));
wenzelm@28674
   610
  val prop_def = axiom "Pure.prop_def";
wenzelm@28674
   611
  val term_def = axiom "Pure.term_def";
wenzelm@28674
   612
  val sort_constraint_def = axiom "Pure.sort_constraint_def";
wenzelm@28618
   613
  val C = Thm.lhs_of sort_constraint_def;
wenzelm@28618
   614
  val T = Thm.dest_arg C;
wenzelm@28618
   615
  val CA = mk_implies (C, A);
wenzelm@28618
   616
in
wenzelm@28618
   617
wenzelm@28618
   618
(* protect *)
wenzelm@28618
   619
wenzelm@46497
   620
val protect = Thm.apply (certify Logic.protectC);
wenzelm@28618
   621
wenzelm@33277
   622
val protectI =
wenzelm@35021
   623
  store_standard_thm (Binding.conceal (Binding.name "protectI"))
wenzelm@35021
   624
    (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A));
wenzelm@28618
   625
wenzelm@33277
   626
val protectD =
wenzelm@35021
   627
  store_standard_thm (Binding.conceal (Binding.name "protectD"))
wenzelm@35021
   628
    (Thm.equal_elim prop_def (Thm.assume (protect A)));
wenzelm@28618
   629
wenzelm@33277
   630
val protect_cong =
wenzelm@33277
   631
  store_standard_thm_open (Binding.name "protect_cong") (Thm.reflexive (protect A));
wenzelm@28618
   632
wenzelm@28618
   633
fun implies_intr_protected asms th =
wenzelm@28618
   634
  let val asms' = map protect asms in
wenzelm@28618
   635
    implies_elim_list
wenzelm@28618
   636
      (implies_intr_list asms th)
wenzelm@28618
   637
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@28618
   638
    |> implies_intr_list asms'
wenzelm@28618
   639
  end;
wenzelm@28618
   640
wenzelm@28618
   641
wenzelm@28618
   642
(* term *)
wenzelm@28618
   643
wenzelm@33277
   644
val termI =
wenzelm@35021
   645
  store_standard_thm (Binding.conceal (Binding.name "termI"))
wenzelm@35021
   646
    (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)));
wenzelm@9554
   647
wenzelm@28618
   648
fun mk_term ct =
wenzelm@28618
   649
  let
wenzelm@28618
   650
    val thy = Thm.theory_of_cterm ct;
wenzelm@28618
   651
    val cert = Thm.cterm_of thy;
wenzelm@28618
   652
    val certT = Thm.ctyp_of thy;
wenzelm@28618
   653
    val T = Thm.typ_of (Thm.ctyp_of_term ct);
wenzelm@28618
   654
    val a = certT (TVar (("'a", 0), []));
wenzelm@28618
   655
    val x = cert (Var (("x", 0), T));
wenzelm@28618
   656
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@28618
   657
wenzelm@28618
   658
fun dest_term th =
wenzelm@28618
   659
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@28618
   660
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@28618
   661
      Thm.dest_arg cprop
wenzelm@28618
   662
    else raise THM ("dest_term", 0, [th])
wenzelm@28618
   663
  end;
wenzelm@28618
   664
wenzelm@28618
   665
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@28618
   666
wenzelm@45156
   667
val dummy_thm = mk_term (certify Term.dummy_prop);
wenzelm@28618
   668
wenzelm@28618
   669
wenzelm@28618
   670
(* sort_constraint *)
wenzelm@28618
   671
wenzelm@33277
   672
val sort_constraintI =
wenzelm@35021
   673
  store_standard_thm (Binding.conceal (Binding.name "sort_constraintI"))
wenzelm@35021
   674
    (Thm.equal_elim (Thm.symmetric sort_constraint_def) (mk_term T));
wenzelm@28618
   675
wenzelm@33277
   676
val sort_constraint_eq =
wenzelm@35021
   677
  store_standard_thm (Binding.conceal (Binding.name "sort_constraint_eq"))
wenzelm@35021
   678
    (Thm.equal_intr
wenzelm@35845
   679
      (Thm.implies_intr CA (Thm.implies_elim (Thm.assume CA)
wenzelm@35845
   680
        (Thm.unvarify_global sort_constraintI)))
wenzelm@35021
   681
      (implies_intr_list [A, C] (Thm.assume A)));
wenzelm@28618
   682
wenzelm@28618
   683
end;
wenzelm@28618
   684
wenzelm@28618
   685
wenzelm@28618
   686
(* HHF normalization *)
wenzelm@28618
   687
wenzelm@46214
   688
(* (PROP ?phi ==> (!!x. PROP ?psi x)) == (!!x. PROP ?phi ==> PROP ?psi x) *)
wenzelm@9554
   689
val norm_hhf_eq =
wenzelm@9554
   690
  let
wenzelm@14854
   691
    val aT = TFree ("'a", []);
wenzelm@9554
   692
    val x = Free ("x", aT);
wenzelm@9554
   693
    val phi = Free ("phi", propT);
wenzelm@9554
   694
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   695
wenzelm@26487
   696
    val cx = certify x;
wenzelm@26487
   697
    val cphi = certify phi;
wenzelm@46214
   698
    val lhs = certify (Logic.mk_implies (phi, Logic.all x (psi $ x)));
wenzelm@46214
   699
    val rhs = certify (Logic.all x (Logic.mk_implies (phi, psi $ x)));
wenzelm@9554
   700
  in
wenzelm@9554
   701
    Thm.equal_intr
wenzelm@9554
   702
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   703
        |> Thm.forall_elim cx
wenzelm@9554
   704
        |> Thm.implies_intr cphi
wenzelm@9554
   705
        |> Thm.forall_intr cx
wenzelm@9554
   706
        |> Thm.implies_intr lhs)
wenzelm@9554
   707
      (Thm.implies_elim
wenzelm@9554
   708
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   709
        |> Thm.forall_intr cx
wenzelm@9554
   710
        |> Thm.implies_intr cphi
wenzelm@9554
   711
        |> Thm.implies_intr rhs)
wenzelm@33277
   712
    |> store_standard_thm_open (Binding.name "norm_hhf_eq")
wenzelm@9554
   713
  end;
wenzelm@9554
   714
wenzelm@18179
   715
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@28618
   716
val norm_hhf_eqs = [norm_hhf_eq, sort_constraint_eq];
wenzelm@18179
   717
wenzelm@30553
   718
fun is_norm_hhf (Const ("Pure.sort_constraint", _)) = false
wenzelm@30553
   719
  | is_norm_hhf (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@30553
   720
  | is_norm_hhf (Abs _ $ _) = false
wenzelm@30553
   721
  | is_norm_hhf (t $ u) = is_norm_hhf t andalso is_norm_hhf u
wenzelm@30553
   722
  | is_norm_hhf (Abs (_, _, t)) = is_norm_hhf t
wenzelm@30553
   723
  | is_norm_hhf _ = true;
wenzelm@12800
   724
wenzelm@16425
   725
fun norm_hhf thy t =
wenzelm@12800
   726
  if is_norm_hhf t then t
wenzelm@18179
   727
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   728
wenzelm@20298
   729
fun norm_hhf_cterm ct =
wenzelm@20298
   730
  if is_norm_hhf (Thm.term_of ct) then ct
wenzelm@20298
   731
  else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
wenzelm@20298
   732
wenzelm@12800
   733
wenzelm@21603
   734
(* var indexes *)
wenzelm@21603
   735
wenzelm@21603
   736
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   737
wenzelm@21603
   738
fun incr_indexes2 th1 th2 =
wenzelm@21603
   739
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   740
wenzelm@21603
   741
fun th1 INCR_COMP th2 = incr_indexes th2 th1 COMP th2;
wenzelm@21603
   742
fun th1 COMP_INCR th2 = th1 COMP incr_indexes th1 th2;
wenzelm@21603
   743
wenzelm@29344
   744
fun comp_no_flatten (th, n) i rule =
wenzelm@29344
   745
  (case distinct Thm.eq_thm (Seq.list_of
wenzelm@29344
   746
      (Thm.compose_no_flatten false (th, n) i (incr_indexes th rule))) of
wenzelm@29344
   747
    [th'] => th'
wenzelm@29344
   748
  | [] => raise THM ("comp_no_flatten", i, [th, rule])
wenzelm@29344
   749
  | _ => raise THM ("comp_no_flatten: unique result expected", i, [th, rule]));
wenzelm@29344
   750
wenzelm@29344
   751
wenzelm@9554
   752
wenzelm@45348
   753
(** variations on Thm.instantiate **)
paulson@8129
   754
wenzelm@43333
   755
fun instantiate_normalize instpair th =
wenzelm@21603
   756
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   757
wenzelm@45347
   758
(*Left-to-right replacements: tpairs = [..., (vi, ti), ...].
wenzelm@45347
   759
  Instantiates distinct Vars by terms, inferring type instantiations.*)
paulson@8129
   760
local
wenzelm@45347
   761
  fun add_types (ct, cu) (thy, tye, maxidx) =
wenzelm@26627
   762
    let
wenzelm@45347
   763
      val {t, T, maxidx = maxt, ...} = Thm.rep_cterm ct;
wenzelm@45347
   764
      val {t = u, T = U, maxidx = maxu, ...} = Thm.rep_cterm cu;
wenzelm@45347
   765
      val maxi = Int.max (maxidx, Int.max (maxt, maxu));
wenzelm@45347
   766
      val thy' = Theory.merge (thy, Theory.merge (Thm.theory_of_cterm ct, Thm.theory_of_cterm cu));
wenzelm@45347
   767
      val (tye', maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@45347
   768
        handle Type.TUNIFY => raise TYPE ("Ill-typed instantiation:\nType\n" ^
wenzelm@45347
   769
          Syntax.string_of_typ_global thy' (Envir.norm_type tye T) ^
wenzelm@45347
   770
          "\nof variable " ^
wenzelm@45347
   771
          Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) t) ^
wenzelm@45347
   772
          "\ncannot be unified with type\n" ^
wenzelm@45347
   773
          Syntax.string_of_typ_global thy' (Envir.norm_type tye U) ^ "\nof term " ^
wenzelm@45347
   774
          Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) u),
wenzelm@45347
   775
          [T, U], [t, u])
wenzelm@45347
   776
    in (thy', tye', maxi') end;
paulson@8129
   777
in
wenzelm@45347
   778
paulson@22561
   779
fun cterm_instantiate [] th = th
wenzelm@45348
   780
  | cterm_instantiate ctpairs th =
wenzelm@45347
   781
      let
wenzelm@45348
   782
        val (thy, tye, _) = fold_rev add_types ctpairs (Thm.theory_of_thm th, Vartab.empty, 0);
wenzelm@45347
   783
        val certT = ctyp_of thy;
wenzelm@45348
   784
        val instT =
wenzelm@45348
   785
          Vartab.fold (fn (xi, (S, T)) =>
wenzelm@45348
   786
            cons (certT (TVar (xi, S)), certT (Envir.norm_type tye T))) tye [];
wenzelm@45348
   787
        val inst = map (pairself (Thm.instantiate_cterm (instT, []))) ctpairs;
wenzelm@45348
   788
      in instantiate_normalize (instT, inst) th end
wenzelm@45348
   789
      handle TERM (msg, _) => raise THM (msg, 0, [th])
wenzelm@45347
   790
        | TYPE (msg, _, _) => raise THM (msg, 0, [th]);
paulson@8129
   791
end;
paulson@8129
   792
paulson@8129
   793
wenzelm@4285
   794
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   795
wenzelm@4285
   796
fun instantiate' cTs cts thm =
wenzelm@4285
   797
  let
wenzelm@4285
   798
    fun err msg =
wenzelm@4285
   799
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   800
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   801
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   802
wenzelm@4285
   803
    fun inst_of (v, ct) =
wenzelm@16425
   804
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   805
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   806
berghofe@15797
   807
    fun tyinst_of (v, cT) =
wenzelm@16425
   808
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   809
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   810
wenzelm@20298
   811
    fun zip_vars xs ys =
wenzelm@40722
   812
      zip_options xs ys handle ListPair.UnequalLengths =>
wenzelm@20298
   813
        err "more instantiations than variables in thm";
wenzelm@4285
   814
wenzelm@4285
   815
    (*instantiate types first!*)
wenzelm@4285
   816
    val thm' =
wenzelm@4285
   817
      if forall is_none cTs then thm
wenzelm@20298
   818
      else Thm.instantiate
wenzelm@22695
   819
        (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
wenzelm@20579
   820
    val thm'' =
wenzelm@4285
   821
      if forall is_none cts then thm'
wenzelm@20298
   822
      else Thm.instantiate
wenzelm@22695
   823
        ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
wenzelm@20298
   824
    in thm'' end;
wenzelm@4285
   825
wenzelm@4285
   826
berghofe@14081
   827
berghofe@14081
   828
(** renaming of bound variables **)
berghofe@14081
   829
berghofe@14081
   830
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   831
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   832
berghofe@14081
   833
fun rename_bvars [] thm = thm
berghofe@14081
   834
  | rename_bvars vs thm =
wenzelm@26627
   835
      let
wenzelm@26627
   836
        val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   837
        fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
wenzelm@26627
   838
          | ren (t $ u) = ren t $ ren u
wenzelm@26627
   839
          | ren t = t;
wenzelm@36944
   840
      in Thm.equal_elim (Thm.reflexive (cert (ren (Thm.prop_of thm)))) thm end;
berghofe@14081
   841
berghofe@14081
   842
berghofe@14081
   843
(* renaming in left-to-right order *)
berghofe@14081
   844
berghofe@14081
   845
fun rename_bvars' xs thm =
berghofe@14081
   846
  let
wenzelm@26627
   847
    val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   848
    val prop = Thm.prop_of thm;
berghofe@14081
   849
    fun rename [] t = ([], t)
berghofe@14081
   850
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   851
          let val (xs', t') = rename xs t
wenzelm@18929
   852
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
   853
      | rename xs (t $ u) =
berghofe@14081
   854
          let
berghofe@14081
   855
            val (xs', t') = rename xs t;
berghofe@14081
   856
            val (xs'', u') = rename xs' u
berghofe@14081
   857
          in (xs'', t' $ u') end
berghofe@14081
   858
      | rename xs t = (xs, t);
berghofe@14081
   859
  in case rename xs prop of
wenzelm@36944
   860
      ([], prop') => Thm.equal_elim (Thm.reflexive (cert prop')) thm
berghofe@14081
   861
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   862
  end;
berghofe@14081
   863
wenzelm@11975
   864
end;
wenzelm@5903
   865
wenzelm@35021
   866
structure Basic_Drule: BASIC_DRULE = Drule;
wenzelm@35021
   867
open Basic_Drule;