src/Pure/drule.ML
author wenzelm
Wed Feb 15 23:19:30 2012 +0100 (2012-02-15)
changeset 46497 89ccf66aa73d
parent 46496 b8920f3fd259
child 47022 8eac39af4ec0
permissions -rw-r--r--
renamed Thm.capply to Thm.apply, and Thm.cabs to Thm.lambda in conformance with similar operations in structure Term and Logic;
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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 legacy_freeze_thaw: thm -> thm * (thm -> thm)
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  val legacy_freeze_thaw_robust: thm -> thm * (int -> 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 symmetric_fun: 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 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 swap_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 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 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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(*Convert all Vars in a theorem to Frees.  Also return a function for
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  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.*)
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fun legacy_freeze_thaw_robust th =
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 let val fth = Thm.legacy_freezeT th
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   307
     val thy = Thm.theory_of_thm fth
paulson@15495
   308
 in
wenzelm@44117
   309
   case Thm.fold_terms Term.add_vars fth [] of
paulson@15495
   310
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   311
     | vars =>
wenzelm@44117
   312
         let fun newName (ix,_) = (ix, legacy_gensym (string_of_indexname ix))
paulson@19753
   313
             val alist = map newName vars
wenzelm@44117
   314
             fun mk_inst (v,T) =
wenzelm@16425
   315
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   316
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   317
             val insts = map mk_inst vars
paulson@15495
   318
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   319
                 th' |> forall_intr_list (map #2 insts)
wenzelm@22906
   320
                     |> forall_elim_list (map (Thm.incr_indexes_cterm i o #1) insts)
paulson@15495
   321
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   322
 end;
paulson@15495
   323
paulson@15495
   324
(*Basic version of the function above. No option to rename Vars apart in thaw.
wenzelm@33832
   325
  The Frees created from Vars have nice names.*)
wenzelm@33832
   326
fun legacy_freeze_thaw th =
wenzelm@36615
   327
 let val fth = Thm.legacy_freezeT th
wenzelm@26627
   328
     val thy = Thm.theory_of_thm fth
paulson@7248
   329
 in
wenzelm@44117
   330
   case Thm.fold_terms Term.add_vars fth [] of
paulson@7248
   331
       [] => (fth, fn x => x)
paulson@7248
   332
     | vars =>
wenzelm@44117
   333
         let fun newName (ix, _) (pairs, used) =
wenzelm@43324
   334
                   let val v = singleton (Name.variant_list used) (string_of_indexname ix)
wenzelm@8328
   335
                   in  ((ix,v)::pairs, v::used)  end;
wenzelm@44117
   336
             val (alist, _) =
wenzelm@44117
   337
                 fold_rev newName vars ([], Thm.fold_terms Term.add_free_names fth [])
wenzelm@44117
   338
             fun mk_inst (v, T) =
wenzelm@16425
   339
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   340
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   341
             val insts = map mk_inst vars
wenzelm@8328
   342
             fun thaw th' =
wenzelm@8328
   343
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   344
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   345
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   346
 end;
paulson@4610
   347
paulson@7248
   348
(*Rotates a rule's premises to the left by k*)
wenzelm@23537
   349
fun rotate_prems 0 = I
wenzelm@31945
   350
  | rotate_prems k = Thm.permute_prems 0 k;
wenzelm@23537
   351
wenzelm@23423
   352
fun with_subgoal i f = rotate_prems (i - 1) #> f #> rotate_prems (1 - i);
paulson@4610
   353
wenzelm@31945
   354
(*Permute prems, where the i-th position in the argument list (counting from 0)
wenzelm@31945
   355
  gives the position within the original thm to be transferred to position i.
wenzelm@31945
   356
  Any remaining trailing positions are left unchanged.*)
wenzelm@31945
   357
val rearrange_prems =
wenzelm@31945
   358
  let
wenzelm@31945
   359
    fun rearr new [] thm = thm
wenzelm@31945
   360
      | rearr new (p :: ps) thm =
wenzelm@31945
   361
          rearr (new + 1)
wenzelm@31945
   362
            (map (fn q => if new <= q andalso q < p then q + 1 else q) ps)
wenzelm@31945
   363
            (Thm.permute_prems (new + 1) (new - p) (Thm.permute_prems new (p - new) thm))
oheimb@11163
   364
  in rearr 0 end;
paulson@4610
   365
wenzelm@252
   366
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   367
fun tha RSN (i,thb) =
wenzelm@31945
   368
  case Seq.chop 2 (Thm.biresolution false [(false,tha)] i thb) of
clasohm@0
   369
      ([th],_) => th
clasohm@0
   370
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   371
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   372
clasohm@0
   373
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   374
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   375
clasohm@0
   376
(*For joining lists of rules*)
wenzelm@252
   377
fun thas RLN (i,thbs) =
wenzelm@31945
   378
  let val resolve = Thm.biresolution false (map (pair false) thas) i
wenzelm@4270
   379
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   380
  in maps resb thbs end;
clasohm@0
   381
clasohm@0
   382
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   383
lcp@11
   384
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   385
  makes proof trees*)
wenzelm@252
   386
fun rls MRS bottom_rl =
lcp@11
   387
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   388
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   389
  in  rs_aux 1 rls  end;
lcp@11
   390
wenzelm@9288
   391
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   392
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   393
wenzelm@252
   394
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   395
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   396
  ALWAYS deletes premise i *)
wenzelm@252
   397
fun compose(tha,i,thb) =
wenzelm@31945
   398
    distinct Thm.eq_thm (Seq.list_of (Thm.bicompose false (false,tha,0) i thb));
clasohm@0
   399
wenzelm@6946
   400
fun compose_single (tha,i,thb) =
paulson@24426
   401
  case compose (tha,i,thb) of
wenzelm@6946
   402
    [th] => th
paulson@24426
   403
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]);
wenzelm@6946
   404
clasohm@0
   405
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   406
fun tha COMP thb =
paulson@24426
   407
    case compose(tha,1,thb) of
wenzelm@252
   408
        [th] => th
clasohm@0
   409
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   410
wenzelm@13105
   411
wenzelm@4016
   412
(** theorem equality **)
clasohm@0
   413
clasohm@0
   414
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   415
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   416
lcp@1194
   417
lcp@1194
   418
clasohm@0
   419
(*** Meta-Rewriting Rules ***)
clasohm@0
   420
wenzelm@33384
   421
val read_prop = certify o Simple_Syntax.read_prop;
wenzelm@26487
   422
wenzelm@26487
   423
fun store_thm name th =
wenzelm@39557
   424
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm (name, th)));
paulson@4610
   425
wenzelm@26487
   426
fun store_thm_open name th =
wenzelm@39557
   427
  Context.>>> (Context.map_theory_result (Global_Theory.store_thm_open (name, th)));
wenzelm@26487
   428
wenzelm@35021
   429
fun store_standard_thm name th = store_thm name (export_without_context th);
wenzelm@35021
   430
fun store_standard_thm_open name thm = store_thm_open name (export_without_context_open thm);
wenzelm@4016
   431
clasohm@0
   432
val reflexive_thm =
wenzelm@26487
   433
  let val cx = certify (Var(("x",0),TVar(("'a",0),[])))
wenzelm@33277
   434
  in store_standard_thm_open (Binding.name "reflexive") (Thm.reflexive cx) end;
clasohm@0
   435
clasohm@0
   436
val symmetric_thm =
wenzelm@33277
   437
  let
wenzelm@33277
   438
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   439
    val thm = Thm.implies_intr xy (Thm.symmetric (Thm.assume xy));
wenzelm@33277
   440
  in store_standard_thm_open (Binding.name "symmetric") thm end;
clasohm@0
   441
clasohm@0
   442
val transitive_thm =
wenzelm@33277
   443
  let
wenzelm@33277
   444
    val xy = read_prop "x::'a == y::'a";
wenzelm@33277
   445
    val yz = read_prop "y::'a == z::'a";
wenzelm@33277
   446
    val xythm = Thm.assume xy;
wenzelm@33277
   447
    val yzthm = Thm.assume yz;
wenzelm@33277
   448
    val thm = Thm.implies_intr yz (Thm.transitive xythm yzthm);
wenzelm@33277
   449
  in store_standard_thm_open (Binding.name "transitive") thm end;
clasohm@0
   450
nipkow@4679
   451
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   452
berghofe@11512
   453
fun extensional eq =
berghofe@11512
   454
  let val eq' =
wenzelm@36944
   455
    Thm.abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (cprop_of eq)))) eq
wenzelm@36944
   456
  in Thm.equal_elim (Thm.eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   457
wenzelm@18820
   458
val equals_cong =
wenzelm@33277
   459
  store_standard_thm_open (Binding.name "equals_cong")
wenzelm@33277
   460
    (Thm.reflexive (read_prop "x::'a == y::'a"));
wenzelm@18820
   461
berghofe@10414
   462
val imp_cong =
berghofe@10414
   463
  let
wenzelm@24241
   464
    val ABC = read_prop "A ==> B::prop == C::prop"
wenzelm@24241
   465
    val AB = read_prop "A ==> B"
wenzelm@24241
   466
    val AC = read_prop "A ==> C"
wenzelm@24241
   467
    val A = read_prop "A"
berghofe@10414
   468
  in
wenzelm@36944
   469
    store_standard_thm_open (Binding.name "imp_cong") (Thm.implies_intr ABC (Thm.equal_intr
wenzelm@36944
   470
      (Thm.implies_intr AB (Thm.implies_intr A
wenzelm@36944
   471
        (Thm.equal_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A))
wenzelm@36944
   472
          (Thm.implies_elim (Thm.assume AB) (Thm.assume A)))))
wenzelm@36944
   473
      (Thm.implies_intr AC (Thm.implies_intr A
wenzelm@36944
   474
        (Thm.equal_elim (Thm.symmetric (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)))
wenzelm@36944
   475
          (Thm.implies_elim (Thm.assume AC) (Thm.assume A)))))))
berghofe@10414
   476
  end;
berghofe@10414
   477
berghofe@10414
   478
val swap_prems_eq =
berghofe@10414
   479
  let
wenzelm@24241
   480
    val ABC = read_prop "A ==> B ==> C"
wenzelm@24241
   481
    val BAC = read_prop "B ==> A ==> C"
wenzelm@24241
   482
    val A = read_prop "A"
wenzelm@24241
   483
    val B = read_prop "B"
berghofe@10414
   484
  in
wenzelm@33277
   485
    store_standard_thm_open (Binding.name "swap_prems_eq")
wenzelm@36944
   486
      (Thm.equal_intr
wenzelm@36944
   487
        (Thm.implies_intr ABC (Thm.implies_intr B (Thm.implies_intr A
wenzelm@36944
   488
          (Thm.implies_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)) (Thm.assume B)))))
wenzelm@36944
   489
        (Thm.implies_intr BAC (Thm.implies_intr A (Thm.implies_intr B
wenzelm@36944
   490
          (Thm.implies_elim (Thm.implies_elim (Thm.assume BAC) (Thm.assume B)) (Thm.assume A))))))
berghofe@10414
   491
  end;
lcp@229
   492
wenzelm@22938
   493
val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
wenzelm@22938
   494
wenzelm@23537
   495
fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM in LCF/HOL*)
wenzelm@23537
   496
fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM in LCF/HOL*)
wenzelm@23568
   497
fun binop_cong_rule ct th1 th2 = Thm.combination (arg_cong_rule ct th1) th2;
clasohm@0
   498
skalberg@15001
   499
local
wenzelm@22906
   500
  val dest_eq = Thm.dest_equals o cprop_of
skalberg@15001
   501
  val rhs_of = snd o dest_eq
skalberg@15001
   502
in
skalberg@15001
   503
fun beta_eta_conversion t =
wenzelm@36944
   504
  let val thm = Thm.beta_conversion true t
wenzelm@36944
   505
  in Thm.transitive thm (Thm.eta_conversion (rhs_of thm)) end
skalberg@15001
   506
end;
skalberg@15001
   507
wenzelm@36944
   508
fun eta_long_conversion ct =
wenzelm@36944
   509
  Thm.transitive
wenzelm@36944
   510
    (beta_eta_conversion ct)
wenzelm@36944
   511
    (Thm.symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   512
paulson@20861
   513
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   514
fun eta_contraction_rule th =
wenzelm@36944
   515
  Thm.equal_elim (Thm.eta_conversion (cprop_of th)) th;
paulson@20861
   516
wenzelm@24947
   517
wenzelm@24947
   518
(* abs_def *)
wenzelm@24947
   519
wenzelm@24947
   520
(*
wenzelm@24947
   521
   f ?x1 ... ?xn == u
wenzelm@24947
   522
  --------------------
wenzelm@24947
   523
   f == %x1 ... xn. u
wenzelm@24947
   524
*)
wenzelm@24947
   525
wenzelm@24947
   526
local
wenzelm@24947
   527
wenzelm@24947
   528
fun contract_lhs th =
wenzelm@24947
   529
  Thm.transitive (Thm.symmetric (beta_eta_conversion
wenzelm@24947
   530
    (fst (Thm.dest_equals (cprop_of th))))) th;
wenzelm@24947
   531
wenzelm@24947
   532
fun var_args ct =
wenzelm@24947
   533
  (case try Thm.dest_comb ct of
wenzelm@24947
   534
    SOME (f, arg) =>
wenzelm@24947
   535
      (case Thm.term_of arg of
wenzelm@24947
   536
        Var ((x, _), _) => update (eq_snd (op aconvc)) (x, arg) (var_args f)
wenzelm@24947
   537
      | _ => [])
wenzelm@24947
   538
  | NONE => []);
wenzelm@24947
   539
wenzelm@24947
   540
in
wenzelm@24947
   541
wenzelm@24947
   542
fun abs_def th =
wenzelm@18337
   543
  let
wenzelm@24947
   544
    val th' = contract_lhs th;
wenzelm@24947
   545
    val args = var_args (Thm.lhs_of th');
wenzelm@24947
   546
  in contract_lhs (fold (uncurry Thm.abstract_rule) args th') end;
wenzelm@24947
   547
wenzelm@24947
   548
end;
wenzelm@24947
   549
wenzelm@18337
   550
wenzelm@18468
   551
wenzelm@15669
   552
(*** Some useful meta-theorems ***)
clasohm@0
   553
clasohm@0
   554
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@33277
   555
val asm_rl = store_standard_thm_open (Binding.name "asm_rl") (Thm.trivial (read_prop "?psi"));
clasohm@0
   556
clasohm@0
   557
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   558
val cut_rl =
wenzelm@33277
   559
  store_standard_thm_open (Binding.name "cut_rl")
wenzelm@24241
   560
    (Thm.trivial (read_prop "?psi ==> ?theta"));
clasohm@0
   561
wenzelm@252
   562
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   563
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   564
val revcut_rl =
wenzelm@33277
   565
  let
wenzelm@33277
   566
    val V = read_prop "V";
wenzelm@33277
   567
    val VW = read_prop "V ==> W";
wenzelm@4016
   568
  in
wenzelm@33277
   569
    store_standard_thm_open (Binding.name "revcut_rl")
wenzelm@36944
   570
      (Thm.implies_intr V (Thm.implies_intr VW (Thm.implies_elim (Thm.assume VW) (Thm.assume V))))
clasohm@0
   571
  end;
clasohm@0
   572
lcp@668
   573
(*for deleting an unwanted assumption*)
lcp@668
   574
val thin_rl =
wenzelm@33277
   575
  let
wenzelm@33277
   576
    val V = read_prop "V";
wenzelm@33277
   577
    val W = read_prop "W";
wenzelm@36944
   578
    val thm = Thm.implies_intr V (Thm.implies_intr W (Thm.assume W));
wenzelm@33277
   579
  in store_standard_thm_open (Binding.name "thin_rl") thm end;
lcp@668
   580
clasohm@0
   581
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   582
val triv_forall_equality =
wenzelm@33277
   583
  let
wenzelm@33277
   584
    val V = read_prop "V";
wenzelm@33277
   585
    val QV = read_prop "!!x::'a. V";
wenzelm@33277
   586
    val x = certify (Free ("x", Term.aT []));
wenzelm@4016
   587
  in
wenzelm@33277
   588
    store_standard_thm_open (Binding.name "triv_forall_equality")
wenzelm@36944
   589
      (Thm.equal_intr (Thm.implies_intr QV (Thm.forall_elim x (Thm.assume QV)))
wenzelm@36944
   590
        (Thm.implies_intr V (Thm.forall_intr x (Thm.assume V))))
clasohm@0
   591
  end;
clasohm@0
   592
wenzelm@19051
   593
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   594
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   595
*)
wenzelm@19051
   596
val distinct_prems_rl =
wenzelm@19051
   597
  let
wenzelm@33277
   598
    val AAB = read_prop "Phi ==> Phi ==> Psi";
wenzelm@24241
   599
    val A = read_prop "Phi";
wenzelm@19051
   600
  in
wenzelm@33277
   601
    store_standard_thm_open (Binding.name "distinct_prems_rl")
wenzelm@36944
   602
      (implies_intr_list [AAB, A] (implies_elim_list (Thm.assume AAB) [Thm.assume A, Thm.assume A]))
wenzelm@19051
   603
  end;
wenzelm@19051
   604
nipkow@1756
   605
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   606
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   607
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   608
*)
nipkow@1756
   609
val swap_prems_rl =
wenzelm@33277
   610
  let
wenzelm@33277
   611
    val cmajor = read_prop "PhiA ==> PhiB ==> Psi";
wenzelm@36944
   612
    val major = Thm.assume cmajor;
wenzelm@33277
   613
    val cminor1 = read_prop "PhiA";
wenzelm@36944
   614
    val minor1 = Thm.assume cminor1;
wenzelm@33277
   615
    val cminor2 = read_prop "PhiB";
wenzelm@36944
   616
    val minor2 = Thm.assume cminor2;
wenzelm@33277
   617
  in
wenzelm@33277
   618
    store_standard_thm_open (Binding.name "swap_prems_rl")
wenzelm@36944
   619
      (Thm.implies_intr cmajor (Thm.implies_intr cminor2 (Thm.implies_intr cminor1
wenzelm@36944
   620
        (Thm.implies_elim (Thm.implies_elim major minor1) minor2))))
nipkow@1756
   621
  end;
nipkow@1756
   622
nipkow@3653
   623
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   624
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   625
   Introduction rule for == as a meta-theorem.
nipkow@3653
   626
*)
nipkow@3653
   627
val equal_intr_rule =
wenzelm@33277
   628
  let
wenzelm@33277
   629
    val PQ = read_prop "phi ==> psi";
wenzelm@33277
   630
    val QP = read_prop "psi ==> phi";
wenzelm@4016
   631
  in
wenzelm@33277
   632
    store_standard_thm_open (Binding.name "equal_intr_rule")
wenzelm@36944
   633
      (Thm.implies_intr PQ (Thm.implies_intr QP (Thm.equal_intr (Thm.assume PQ) (Thm.assume QP))))
nipkow@3653
   634
  end;
nipkow@3653
   635
wenzelm@19421
   636
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   637
val equal_elim_rule1 =
wenzelm@33277
   638
  let
wenzelm@33277
   639
    val eq = read_prop "phi::prop == psi::prop";
wenzelm@33277
   640
    val P = read_prop "phi";
wenzelm@33277
   641
  in
wenzelm@33277
   642
    store_standard_thm_open (Binding.name "equal_elim_rule1")
wenzelm@36944
   643
      (Thm.equal_elim (Thm.assume eq) (Thm.assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   644
  end;
wenzelm@4285
   645
wenzelm@19421
   646
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   647
val equal_elim_rule2 =
wenzelm@33277
   648
  store_standard_thm_open (Binding.name "equal_elim_rule2")
wenzelm@33277
   649
    (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   650
wenzelm@28618
   651
(* PROP ?phi ==> PROP ?phi ==> PROP ?psi ==> PROP ?psi *)
wenzelm@12297
   652
val remdups_rl =
wenzelm@33277
   653
  let
wenzelm@33277
   654
    val P = read_prop "phi";
wenzelm@33277
   655
    val Q = read_prop "psi";
wenzelm@33277
   656
    val thm = implies_intr_list [P, P, Q] (Thm.assume Q);
wenzelm@33277
   657
  in store_standard_thm_open (Binding.name "remdups_rl") thm end;
wenzelm@12297
   658
wenzelm@12297
   659
wenzelm@28618
   660
wenzelm@28618
   661
(** embedded terms and types **)
wenzelm@28618
   662
wenzelm@28618
   663
local
wenzelm@28618
   664
  val A = certify (Free ("A", propT));
wenzelm@35845
   665
  val axiom = Thm.unvarify_global o Thm.axiom (Context.the_theory (Context.the_thread_data ()));
wenzelm@28674
   666
  val prop_def = axiom "Pure.prop_def";
wenzelm@28674
   667
  val term_def = axiom "Pure.term_def";
wenzelm@28674
   668
  val sort_constraint_def = axiom "Pure.sort_constraint_def";
wenzelm@28618
   669
  val C = Thm.lhs_of sort_constraint_def;
wenzelm@28618
   670
  val T = Thm.dest_arg C;
wenzelm@28618
   671
  val CA = mk_implies (C, A);
wenzelm@28618
   672
in
wenzelm@28618
   673
wenzelm@28618
   674
(* protect *)
wenzelm@28618
   675
wenzelm@46497
   676
val protect = Thm.apply (certify Logic.protectC);
wenzelm@28618
   677
wenzelm@33277
   678
val protectI =
wenzelm@35021
   679
  store_standard_thm (Binding.conceal (Binding.name "protectI"))
wenzelm@35021
   680
    (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A));
wenzelm@28618
   681
wenzelm@33277
   682
val protectD =
wenzelm@35021
   683
  store_standard_thm (Binding.conceal (Binding.name "protectD"))
wenzelm@35021
   684
    (Thm.equal_elim prop_def (Thm.assume (protect A)));
wenzelm@28618
   685
wenzelm@33277
   686
val protect_cong =
wenzelm@33277
   687
  store_standard_thm_open (Binding.name "protect_cong") (Thm.reflexive (protect A));
wenzelm@28618
   688
wenzelm@28618
   689
fun implies_intr_protected asms th =
wenzelm@28618
   690
  let val asms' = map protect asms in
wenzelm@28618
   691
    implies_elim_list
wenzelm@28618
   692
      (implies_intr_list asms th)
wenzelm@28618
   693
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@28618
   694
    |> implies_intr_list asms'
wenzelm@28618
   695
  end;
wenzelm@28618
   696
wenzelm@28618
   697
wenzelm@28618
   698
(* term *)
wenzelm@28618
   699
wenzelm@33277
   700
val termI =
wenzelm@35021
   701
  store_standard_thm (Binding.conceal (Binding.name "termI"))
wenzelm@35021
   702
    (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)));
wenzelm@9554
   703
wenzelm@28618
   704
fun mk_term ct =
wenzelm@28618
   705
  let
wenzelm@28618
   706
    val thy = Thm.theory_of_cterm ct;
wenzelm@28618
   707
    val cert = Thm.cterm_of thy;
wenzelm@28618
   708
    val certT = Thm.ctyp_of thy;
wenzelm@28618
   709
    val T = Thm.typ_of (Thm.ctyp_of_term ct);
wenzelm@28618
   710
    val a = certT (TVar (("'a", 0), []));
wenzelm@28618
   711
    val x = cert (Var (("x", 0), T));
wenzelm@28618
   712
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@28618
   713
wenzelm@28618
   714
fun dest_term th =
wenzelm@28618
   715
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@28618
   716
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@28618
   717
      Thm.dest_arg cprop
wenzelm@28618
   718
    else raise THM ("dest_term", 0, [th])
wenzelm@28618
   719
  end;
wenzelm@28618
   720
wenzelm@28618
   721
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@28618
   722
wenzelm@45156
   723
val dummy_thm = mk_term (certify Term.dummy_prop);
wenzelm@28618
   724
wenzelm@28618
   725
wenzelm@28618
   726
(* sort_constraint *)
wenzelm@28618
   727
wenzelm@33277
   728
val sort_constraintI =
wenzelm@35021
   729
  store_standard_thm (Binding.conceal (Binding.name "sort_constraintI"))
wenzelm@35021
   730
    (Thm.equal_elim (Thm.symmetric sort_constraint_def) (mk_term T));
wenzelm@28618
   731
wenzelm@33277
   732
val sort_constraint_eq =
wenzelm@35021
   733
  store_standard_thm (Binding.conceal (Binding.name "sort_constraint_eq"))
wenzelm@35021
   734
    (Thm.equal_intr
wenzelm@35845
   735
      (Thm.implies_intr CA (Thm.implies_elim (Thm.assume CA)
wenzelm@35845
   736
        (Thm.unvarify_global sort_constraintI)))
wenzelm@35021
   737
      (implies_intr_list [A, C] (Thm.assume A)));
wenzelm@28618
   738
wenzelm@28618
   739
end;
wenzelm@28618
   740
wenzelm@28618
   741
wenzelm@28618
   742
(* HHF normalization *)
wenzelm@28618
   743
wenzelm@46214
   744
(* (PROP ?phi ==> (!!x. PROP ?psi x)) == (!!x. PROP ?phi ==> PROP ?psi x) *)
wenzelm@9554
   745
val norm_hhf_eq =
wenzelm@9554
   746
  let
wenzelm@14854
   747
    val aT = TFree ("'a", []);
wenzelm@9554
   748
    val x = Free ("x", aT);
wenzelm@9554
   749
    val phi = Free ("phi", propT);
wenzelm@9554
   750
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   751
wenzelm@26487
   752
    val cx = certify x;
wenzelm@26487
   753
    val cphi = certify phi;
wenzelm@46214
   754
    val lhs = certify (Logic.mk_implies (phi, Logic.all x (psi $ x)));
wenzelm@46214
   755
    val rhs = certify (Logic.all x (Logic.mk_implies (phi, psi $ x)));
wenzelm@9554
   756
  in
wenzelm@9554
   757
    Thm.equal_intr
wenzelm@9554
   758
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   759
        |> Thm.forall_elim cx
wenzelm@9554
   760
        |> Thm.implies_intr cphi
wenzelm@9554
   761
        |> Thm.forall_intr cx
wenzelm@9554
   762
        |> Thm.implies_intr lhs)
wenzelm@9554
   763
      (Thm.implies_elim
wenzelm@9554
   764
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   765
        |> Thm.forall_intr cx
wenzelm@9554
   766
        |> Thm.implies_intr cphi
wenzelm@9554
   767
        |> Thm.implies_intr rhs)
wenzelm@33277
   768
    |> store_standard_thm_open (Binding.name "norm_hhf_eq")
wenzelm@9554
   769
  end;
wenzelm@9554
   770
wenzelm@18179
   771
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@28618
   772
val norm_hhf_eqs = [norm_hhf_eq, sort_constraint_eq];
wenzelm@18179
   773
wenzelm@30553
   774
fun is_norm_hhf (Const ("Pure.sort_constraint", _)) = false
wenzelm@30553
   775
  | is_norm_hhf (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@30553
   776
  | is_norm_hhf (Abs _ $ _) = false
wenzelm@30553
   777
  | is_norm_hhf (t $ u) = is_norm_hhf t andalso is_norm_hhf u
wenzelm@30553
   778
  | is_norm_hhf (Abs (_, _, t)) = is_norm_hhf t
wenzelm@30553
   779
  | is_norm_hhf _ = true;
wenzelm@12800
   780
wenzelm@16425
   781
fun norm_hhf thy t =
wenzelm@12800
   782
  if is_norm_hhf t then t
wenzelm@18179
   783
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   784
wenzelm@20298
   785
fun norm_hhf_cterm ct =
wenzelm@20298
   786
  if is_norm_hhf (Thm.term_of ct) then ct
wenzelm@20298
   787
  else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
wenzelm@20298
   788
wenzelm@12800
   789
wenzelm@21603
   790
(* var indexes *)
wenzelm@21603
   791
wenzelm@21603
   792
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   793
wenzelm@21603
   794
fun incr_indexes2 th1 th2 =
wenzelm@21603
   795
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   796
wenzelm@21603
   797
fun th1 INCR_COMP th2 = incr_indexes th2 th1 COMP th2;
wenzelm@21603
   798
fun th1 COMP_INCR th2 = th1 COMP incr_indexes th1 th2;
wenzelm@21603
   799
wenzelm@29344
   800
fun comp_no_flatten (th, n) i rule =
wenzelm@29344
   801
  (case distinct Thm.eq_thm (Seq.list_of
wenzelm@29344
   802
      (Thm.compose_no_flatten false (th, n) i (incr_indexes th rule))) of
wenzelm@29344
   803
    [th'] => th'
wenzelm@29344
   804
  | [] => raise THM ("comp_no_flatten", i, [th, rule])
wenzelm@29344
   805
  | _ => raise THM ("comp_no_flatten: unique result expected", i, [th, rule]));
wenzelm@29344
   806
wenzelm@29344
   807
wenzelm@9554
   808
wenzelm@45348
   809
(** variations on Thm.instantiate **)
paulson@8129
   810
wenzelm@43333
   811
fun instantiate_normalize instpair th =
wenzelm@21603
   812
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   813
wenzelm@45347
   814
(*Left-to-right replacements: tpairs = [..., (vi, ti), ...].
wenzelm@45347
   815
  Instantiates distinct Vars by terms, inferring type instantiations.*)
paulson@8129
   816
local
wenzelm@45347
   817
  fun add_types (ct, cu) (thy, tye, maxidx) =
wenzelm@26627
   818
    let
wenzelm@45347
   819
      val {t, T, maxidx = maxt, ...} = Thm.rep_cterm ct;
wenzelm@45347
   820
      val {t = u, T = U, maxidx = maxu, ...} = Thm.rep_cterm cu;
wenzelm@45347
   821
      val maxi = Int.max (maxidx, Int.max (maxt, maxu));
wenzelm@45347
   822
      val thy' = Theory.merge (thy, Theory.merge (Thm.theory_of_cterm ct, Thm.theory_of_cterm cu));
wenzelm@45347
   823
      val (tye', maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@45347
   824
        handle Type.TUNIFY => raise TYPE ("Ill-typed instantiation:\nType\n" ^
wenzelm@45347
   825
          Syntax.string_of_typ_global thy' (Envir.norm_type tye T) ^
wenzelm@45347
   826
          "\nof variable " ^
wenzelm@45347
   827
          Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) t) ^
wenzelm@45347
   828
          "\ncannot be unified with type\n" ^
wenzelm@45347
   829
          Syntax.string_of_typ_global thy' (Envir.norm_type tye U) ^ "\nof term " ^
wenzelm@45347
   830
          Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) u),
wenzelm@45347
   831
          [T, U], [t, u])
wenzelm@45347
   832
    in (thy', tye', maxi') end;
paulson@8129
   833
in
wenzelm@45347
   834
paulson@22561
   835
fun cterm_instantiate [] th = th
wenzelm@45348
   836
  | cterm_instantiate ctpairs th =
wenzelm@45347
   837
      let
wenzelm@45348
   838
        val (thy, tye, _) = fold_rev add_types ctpairs (Thm.theory_of_thm th, Vartab.empty, 0);
wenzelm@45347
   839
        val certT = ctyp_of thy;
wenzelm@45348
   840
        val instT =
wenzelm@45348
   841
          Vartab.fold (fn (xi, (S, T)) =>
wenzelm@45348
   842
            cons (certT (TVar (xi, S)), certT (Envir.norm_type tye T))) tye [];
wenzelm@45348
   843
        val inst = map (pairself (Thm.instantiate_cterm (instT, []))) ctpairs;
wenzelm@45348
   844
      in instantiate_normalize (instT, inst) th end
wenzelm@45348
   845
      handle TERM (msg, _) => raise THM (msg, 0, [th])
wenzelm@45347
   846
        | TYPE (msg, _, _) => raise THM (msg, 0, [th]);
paulson@8129
   847
end;
paulson@8129
   848
paulson@8129
   849
wenzelm@4285
   850
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   851
wenzelm@4285
   852
fun instantiate' cTs cts thm =
wenzelm@4285
   853
  let
wenzelm@4285
   854
    fun err msg =
wenzelm@4285
   855
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   856
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   857
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   858
wenzelm@4285
   859
    fun inst_of (v, ct) =
wenzelm@16425
   860
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   861
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   862
berghofe@15797
   863
    fun tyinst_of (v, cT) =
wenzelm@16425
   864
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   865
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   866
wenzelm@20298
   867
    fun zip_vars xs ys =
wenzelm@40722
   868
      zip_options xs ys handle ListPair.UnequalLengths =>
wenzelm@20298
   869
        err "more instantiations than variables in thm";
wenzelm@4285
   870
wenzelm@4285
   871
    (*instantiate types first!*)
wenzelm@4285
   872
    val thm' =
wenzelm@4285
   873
      if forall is_none cTs then thm
wenzelm@20298
   874
      else Thm.instantiate
wenzelm@22695
   875
        (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
wenzelm@20579
   876
    val thm'' =
wenzelm@4285
   877
      if forall is_none cts then thm'
wenzelm@20298
   878
      else Thm.instantiate
wenzelm@22695
   879
        ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
wenzelm@20298
   880
    in thm'' end;
wenzelm@4285
   881
wenzelm@4285
   882
berghofe@14081
   883
berghofe@14081
   884
(** renaming of bound variables **)
berghofe@14081
   885
berghofe@14081
   886
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   887
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   888
berghofe@14081
   889
fun rename_bvars [] thm = thm
berghofe@14081
   890
  | rename_bvars vs thm =
wenzelm@26627
   891
      let
wenzelm@26627
   892
        val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   893
        fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
wenzelm@26627
   894
          | ren (t $ u) = ren t $ ren u
wenzelm@26627
   895
          | ren t = t;
wenzelm@36944
   896
      in Thm.equal_elim (Thm.reflexive (cert (ren (Thm.prop_of thm)))) thm end;
berghofe@14081
   897
berghofe@14081
   898
berghofe@14081
   899
(* renaming in left-to-right order *)
berghofe@14081
   900
berghofe@14081
   901
fun rename_bvars' xs thm =
berghofe@14081
   902
  let
wenzelm@26627
   903
    val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   904
    val prop = Thm.prop_of thm;
berghofe@14081
   905
    fun rename [] t = ([], t)
berghofe@14081
   906
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   907
          let val (xs', t') = rename xs t
wenzelm@18929
   908
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
   909
      | rename xs (t $ u) =
berghofe@14081
   910
          let
berghofe@14081
   911
            val (xs', t') = rename xs t;
berghofe@14081
   912
            val (xs'', u') = rename xs' u
berghofe@14081
   913
          in (xs'', t' $ u') end
berghofe@14081
   914
      | rename xs t = (xs, t);
berghofe@14081
   915
  in case rename xs prop of
wenzelm@36944
   916
      ([], prop') => Thm.equal_elim (Thm.reflexive (cert prop')) thm
berghofe@14081
   917
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   918
  end;
berghofe@14081
   919
berghofe@14081
   920
wenzelm@11975
   921
wenzelm@18225
   922
(** multi_resolve **)
wenzelm@18225
   923
wenzelm@18225
   924
local
wenzelm@18225
   925
wenzelm@18225
   926
fun res th i rule =
wenzelm@18225
   927
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
   928
wenzelm@18225
   929
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
   930
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
   931
wenzelm@18225
   932
in
wenzelm@18225
   933
wenzelm@18225
   934
val multi_resolve = multi_res 1;
wenzelm@18225
   935
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
   936
wenzelm@18225
   937
end;
wenzelm@18225
   938
wenzelm@11975
   939
end;
wenzelm@5903
   940
wenzelm@35021
   941
structure Basic_Drule: BASIC_DRULE = Drule;
wenzelm@35021
   942
open Basic_Drule;