src/Pure/drule.ML
author wenzelm
Thu Oct 01 23:27:05 2009 +0200 (2009-10-01)
changeset 32843 c8f5a7c8353f
parent 31977 e03059ae2d82
child 32958 3228627994d9
permissions -rw-r--r--
moved cache_conv to src/Pure/conv.ML, use Thm.cterm_cache;
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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 MRL 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_frees: 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 freeze_thaw: thm -> thm * (thm -> thm)
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  val 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: (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 standard: thm -> thm
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  val standard': 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 MRL: thm list list * thm list -> thm list
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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 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 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 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 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 get_def: theory -> xstring -> thm
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  val store_thm: bstring -> thm -> thm
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  val store_standard_thm: bstring -> thm -> thm
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  val store_thm_open: bstring -> thm -> thm
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  val store_standard_thm_open: bstring -> thm -> thm
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  val compose_single: thm * int * thm -> 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 term_rule: theory -> (thm -> thm) -> term -> term
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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 unconstrainTs: thm -> 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_type_indexes: int -> 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 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.capply (Thm.capply 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.capply 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.capply 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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(* type classes and sorts *)
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fun unconstrainTs th =
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  fold (Thm.unconstrainT o Thm.ctyp_of (Thm.theory_of_thm th) o TVar)
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    (Thm.fold_terms Term.add_tvars th []) th;
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(*Generalization over a list of variables*)
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val forall_intr_list = fold_rev forall_intr;
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(*Generalization over all suitable Free variables*)
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fun forall_intr_frees th =
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    let
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      val thy = Thm.theory_of_thm th;
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      val {prop, hyps, tpairs, ...} = rep_thm th;
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      val fixed = fold Term.add_frees (Thm.terms_of_tpairs tpairs @ hyps) [];
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      val frees = Term.fold_aterms (fn Free v =>
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        if member (op =) fixed v then I else insert (op =) v | _ => I) prop [];
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    in fold (forall_intr o cterm_of thy o Free) frees th end;
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(*Generalization over Vars -- canonical order*)
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fun forall_intr_vars th =
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  fold 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 forall_elim;
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(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
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val implies_intr_list = fold_rev 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 (tpairs_of th) then th else
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    case distinct Thm.eq_thm (Seq.list_of (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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   303
    |  _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   304
wenzelm@21603
   305
wenzelm@21603
   306
(* legacy standard operations *)
wenzelm@21603
   307
wenzelm@16949
   308
val standard' =
wenzelm@16949
   309
  implies_intr_hyps
wenzelm@16949
   310
  #> forall_intr_frees
wenzelm@19421
   311
  #> `Thm.maxidx_of
wenzelm@16949
   312
  #-> (fn maxidx =>
wenzelm@26653
   313
    Thm.forall_elim_vars (maxidx + 1)
wenzelm@20904
   314
    #> Thm.strip_shyps
wenzelm@16949
   315
    #> zero_var_indexes
wenzelm@26627
   316
    #> Thm.varifyT);
wenzelm@1218
   317
wenzelm@16949
   318
val standard =
wenzelm@21600
   319
  flexflex_unique
wenzelm@16949
   320
  #> standard'
wenzelm@26627
   321
  #> Thm.close_derivation;
berghofe@11512
   322
clasohm@0
   323
wenzelm@8328
   324
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   325
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   326
  Similar code in type/freeze_thaw*)
paulson@15495
   327
paulson@15495
   328
fun freeze_thaw_robust th =
wenzelm@19878
   329
 let val fth = Thm.freezeT th
wenzelm@26627
   330
     val thy = Thm.theory_of_thm fth
wenzelm@26627
   331
     val {prop, tpairs, ...} = rep_thm fth
paulson@15495
   332
 in
wenzelm@29265
   333
   case List.foldr OldTerm.add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   334
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   335
     | vars =>
paulson@19753
   336
         let fun newName (Var(ix,_)) = (ix, gensym (string_of_indexname ix))
paulson@19753
   337
             val alist = map newName vars
paulson@15495
   338
             fun mk_inst (Var(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)))
paulson@15495
   341
             val insts = map mk_inst vars
paulson@15495
   342
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   343
                 th' |> forall_intr_list (map #2 insts)
wenzelm@22906
   344
                     |> forall_elim_list (map (Thm.incr_indexes_cterm i o #1) insts)
paulson@15495
   345
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   346
 end;
paulson@15495
   347
paulson@15495
   348
(*Basic version of the function above. No option to rename Vars apart in thaw.
wenzelm@19999
   349
  The Frees created from Vars have nice names. FIXME: does not check for
paulson@19753
   350
  clashes with variables in the assumptions, so delete and use freeze_thaw_robust instead?*)
paulson@4610
   351
fun freeze_thaw th =
wenzelm@19878
   352
 let val fth = Thm.freezeT th
wenzelm@26627
   353
     val thy = Thm.theory_of_thm fth
wenzelm@26627
   354
     val {prop, tpairs, ...} = rep_thm fth
paulson@7248
   355
 in
wenzelm@29265
   356
   case List.foldr OldTerm.add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   357
       [] => (fth, fn x => x)
paulson@7248
   358
     | vars =>
wenzelm@8328
   359
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@20077
   360
                   let val v = Name.variant used (string_of_indexname ix)
wenzelm@8328
   361
                   in  ((ix,v)::pairs, v::used)  end;
wenzelm@29270
   362
             val (alist, _) = List.foldr newName ([], Library.foldr OldTerm.add_term_names
skalberg@15574
   363
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   364
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   365
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   366
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   367
             val insts = map mk_inst vars
wenzelm@8328
   368
             fun thaw th' =
wenzelm@8328
   369
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   370
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   371
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   372
 end;
paulson@4610
   373
paulson@7248
   374
(*Rotates a rule's premises to the left by k*)
wenzelm@23537
   375
fun rotate_prems 0 = I
wenzelm@31945
   376
  | rotate_prems k = Thm.permute_prems 0 k;
wenzelm@23537
   377
wenzelm@23423
   378
fun with_subgoal i f = rotate_prems (i - 1) #> f #> rotate_prems (1 - i);
paulson@4610
   379
wenzelm@31945
   380
(*Permute prems, where the i-th position in the argument list (counting from 0)
wenzelm@31945
   381
  gives the position within the original thm to be transferred to position i.
wenzelm@31945
   382
  Any remaining trailing positions are left unchanged.*)
wenzelm@31945
   383
val rearrange_prems =
wenzelm@31945
   384
  let
wenzelm@31945
   385
    fun rearr new [] thm = thm
wenzelm@31945
   386
      | rearr new (p :: ps) thm =
wenzelm@31945
   387
          rearr (new + 1)
wenzelm@31945
   388
            (map (fn q => if new <= q andalso q < p then q + 1 else q) ps)
wenzelm@31945
   389
            (Thm.permute_prems (new + 1) (new - p) (Thm.permute_prems new (p - new) thm))
oheimb@11163
   390
  in rearr 0 end;
paulson@4610
   391
wenzelm@252
   392
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   393
fun tha RSN (i,thb) =
wenzelm@31945
   394
  case Seq.chop 2 (Thm.biresolution false [(false,tha)] i thb) of
clasohm@0
   395
      ([th],_) => th
clasohm@0
   396
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   397
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   398
clasohm@0
   399
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   400
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   401
clasohm@0
   402
(*For joining lists of rules*)
wenzelm@252
   403
fun thas RLN (i,thbs) =
wenzelm@31945
   404
  let val resolve = Thm.biresolution false (map (pair false) thas) i
wenzelm@4270
   405
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   406
  in maps resb thbs end;
clasohm@0
   407
clasohm@0
   408
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   409
lcp@11
   410
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   411
  makes proof trees*)
wenzelm@252
   412
fun rls MRS bottom_rl =
lcp@11
   413
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   414
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   415
  in  rs_aux 1 rls  end;
lcp@11
   416
lcp@11
   417
(*As above, but for rule lists*)
wenzelm@252
   418
fun rlss MRL bottom_rls =
lcp@11
   419
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   420
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   421
  in  rs_aux 1 rlss  end;
lcp@11
   422
wenzelm@9288
   423
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   424
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   425
wenzelm@252
   426
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   427
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   428
  ALWAYS deletes premise i *)
wenzelm@252
   429
fun compose(tha,i,thb) =
wenzelm@31945
   430
    distinct Thm.eq_thm (Seq.list_of (Thm.bicompose false (false,tha,0) i thb));
clasohm@0
   431
wenzelm@6946
   432
fun compose_single (tha,i,thb) =
paulson@24426
   433
  case compose (tha,i,thb) of
wenzelm@6946
   434
    [th] => th
paulson@24426
   435
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]);
wenzelm@6946
   436
clasohm@0
   437
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   438
fun tha COMP thb =
paulson@24426
   439
    case compose(tha,1,thb) of
wenzelm@252
   440
        [th] => th
clasohm@0
   441
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   442
wenzelm@13105
   443
wenzelm@4016
   444
(** theorem equality **)
clasohm@0
   445
clasohm@0
   446
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   447
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   448
lcp@1194
   449
lcp@1194
   450
clasohm@0
   451
(*** Meta-Rewriting Rules ***)
clasohm@0
   452
wenzelm@26487
   453
val read_prop = certify o SimpleSyntax.read_prop;
wenzelm@26487
   454
wenzelm@30342
   455
fun get_def thy = Thm.axiom thy o NameSpace.intern (Theory.axiom_space thy) o Thm.def_name;
wenzelm@30342
   456
wenzelm@26487
   457
fun store_thm name th =
haftmann@29579
   458
  Context.>>> (Context.map_theory_result (PureThy.store_thm (Binding.name name, th)));
paulson@4610
   459
wenzelm@26487
   460
fun store_thm_open name th =
haftmann@29579
   461
  Context.>>> (Context.map_theory_result (PureThy.store_thm_open (Binding.name name, th)));
wenzelm@26487
   462
wenzelm@26487
   463
fun store_standard_thm name th = store_thm name (standard th);
wenzelm@12135
   464
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   465
clasohm@0
   466
val reflexive_thm =
wenzelm@26487
   467
  let val cx = certify (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   468
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   469
clasohm@0
   470
val symmetric_thm =
wenzelm@24241
   471
  let val xy = read_prop "x::'a == y::'a"
wenzelm@16595
   472
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   473
clasohm@0
   474
val transitive_thm =
wenzelm@24241
   475
  let val xy = read_prop "x::'a == y::'a"
wenzelm@24241
   476
      val yz = read_prop "y::'a == z::'a"
clasohm@0
   477
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   478
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   479
nipkow@4679
   480
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   481
berghofe@11512
   482
fun extensional eq =
berghofe@11512
   483
  let val eq' =
wenzelm@22906
   484
    abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (cprop_of eq)))) eq
berghofe@11512
   485
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   486
wenzelm@18820
   487
val equals_cong =
wenzelm@24241
   488
  store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x::'a == y::'a"));
wenzelm@18820
   489
berghofe@10414
   490
val imp_cong =
berghofe@10414
   491
  let
wenzelm@24241
   492
    val ABC = read_prop "A ==> B::prop == C::prop"
wenzelm@24241
   493
    val AB = read_prop "A ==> B"
wenzelm@24241
   494
    val AC = read_prop "A ==> C"
wenzelm@24241
   495
    val A = read_prop "A"
berghofe@10414
   496
  in
wenzelm@12135
   497
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   498
      (implies_intr AB (implies_intr A
berghofe@10414
   499
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   500
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   501
      (implies_intr AC (implies_intr A
berghofe@10414
   502
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   503
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   504
  end;
berghofe@10414
   505
berghofe@10414
   506
val swap_prems_eq =
berghofe@10414
   507
  let
wenzelm@24241
   508
    val ABC = read_prop "A ==> B ==> C"
wenzelm@24241
   509
    val BAC = read_prop "B ==> A ==> C"
wenzelm@24241
   510
    val A = read_prop "A"
wenzelm@24241
   511
    val B = read_prop "B"
berghofe@10414
   512
  in
wenzelm@12135
   513
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   514
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   515
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   516
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   517
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   518
  end;
lcp@229
   519
wenzelm@22938
   520
val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
wenzelm@22938
   521
wenzelm@23537
   522
fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM in LCF/HOL*)
wenzelm@23537
   523
fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM in LCF/HOL*)
wenzelm@23568
   524
fun binop_cong_rule ct th1 th2 = Thm.combination (arg_cong_rule ct th1) th2;
clasohm@0
   525
skalberg@15001
   526
local
wenzelm@22906
   527
  val dest_eq = Thm.dest_equals o cprop_of
skalberg@15001
   528
  val rhs_of = snd o dest_eq
skalberg@15001
   529
in
skalberg@15001
   530
fun beta_eta_conversion t =
skalberg@15001
   531
  let val thm = beta_conversion true t
skalberg@15001
   532
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   533
end;
skalberg@15001
   534
berghofe@15925
   535
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   536
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   537
paulson@20861
   538
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   539
fun eta_contraction_rule th =
paulson@20861
   540
  equal_elim (eta_conversion (cprop_of th)) th;
paulson@20861
   541
wenzelm@24947
   542
wenzelm@24947
   543
(* abs_def *)
wenzelm@24947
   544
wenzelm@24947
   545
(*
wenzelm@24947
   546
   f ?x1 ... ?xn == u
wenzelm@24947
   547
  --------------------
wenzelm@24947
   548
   f == %x1 ... xn. u
wenzelm@24947
   549
*)
wenzelm@24947
   550
wenzelm@24947
   551
local
wenzelm@24947
   552
wenzelm@24947
   553
fun contract_lhs th =
wenzelm@24947
   554
  Thm.transitive (Thm.symmetric (beta_eta_conversion
wenzelm@24947
   555
    (fst (Thm.dest_equals (cprop_of th))))) th;
wenzelm@24947
   556
wenzelm@24947
   557
fun var_args ct =
wenzelm@24947
   558
  (case try Thm.dest_comb ct of
wenzelm@24947
   559
    SOME (f, arg) =>
wenzelm@24947
   560
      (case Thm.term_of arg of
wenzelm@24947
   561
        Var ((x, _), _) => update (eq_snd (op aconvc)) (x, arg) (var_args f)
wenzelm@24947
   562
      | _ => [])
wenzelm@24947
   563
  | NONE => []);
wenzelm@24947
   564
wenzelm@24947
   565
in
wenzelm@24947
   566
wenzelm@24947
   567
fun abs_def th =
wenzelm@18337
   568
  let
wenzelm@24947
   569
    val th' = contract_lhs th;
wenzelm@24947
   570
    val args = var_args (Thm.lhs_of th');
wenzelm@24947
   571
  in contract_lhs (fold (uncurry Thm.abstract_rule) args th') end;
wenzelm@24947
   572
wenzelm@24947
   573
end;
wenzelm@24947
   574
wenzelm@18337
   575
wenzelm@18468
   576
wenzelm@15669
   577
(*** Some useful meta-theorems ***)
clasohm@0
   578
clasohm@0
   579
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@24241
   580
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "?psi"));
berghofe@28713
   581
val _ = store_thm_open "_" asm_rl;
clasohm@0
   582
clasohm@0
   583
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   584
val cut_rl =
wenzelm@12135
   585
  store_standard_thm_open "cut_rl"
wenzelm@24241
   586
    (Thm.trivial (read_prop "?psi ==> ?theta"));
clasohm@0
   587
wenzelm@252
   588
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   589
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   590
val revcut_rl =
wenzelm@24241
   591
  let val V = read_prop "V"
wenzelm@24241
   592
      and VW = read_prop "V ==> W";
wenzelm@4016
   593
  in
wenzelm@12135
   594
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   595
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   596
  end;
clasohm@0
   597
lcp@668
   598
(*for deleting an unwanted assumption*)
lcp@668
   599
val thin_rl =
wenzelm@24241
   600
  let val V = read_prop "V"
wenzelm@24241
   601
      and W = read_prop "W";
wenzelm@12135
   602
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   603
clasohm@0
   604
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   605
val triv_forall_equality =
wenzelm@24241
   606
  let val V  = read_prop "V"
wenzelm@24241
   607
      and QV = read_prop "!!x::'a. V"
wenzelm@26487
   608
      and x  = certify (Free ("x", Term.aT []));
wenzelm@4016
   609
  in
wenzelm@12135
   610
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   611
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   612
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   613
  end;
clasohm@0
   614
wenzelm@19051
   615
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   616
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   617
*)
wenzelm@19051
   618
val distinct_prems_rl =
wenzelm@19051
   619
  let
wenzelm@24241
   620
    val AAB = read_prop "Phi ==> Phi ==> Psi"
wenzelm@24241
   621
    val A = read_prop "Phi";
wenzelm@19051
   622
  in
wenzelm@19051
   623
    store_standard_thm_open "distinct_prems_rl"
wenzelm@19051
   624
      (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
wenzelm@19051
   625
  end;
wenzelm@19051
   626
nipkow@1756
   627
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   628
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   629
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   630
*)
nipkow@1756
   631
val swap_prems_rl =
wenzelm@24241
   632
  let val cmajor = read_prop "PhiA ==> PhiB ==> Psi";
nipkow@1756
   633
      val major = assume cmajor;
wenzelm@24241
   634
      val cminor1 = read_prop "PhiA";
nipkow@1756
   635
      val minor1 = assume cminor1;
wenzelm@24241
   636
      val cminor2 = read_prop "PhiB";
nipkow@1756
   637
      val minor2 = assume cminor2;
wenzelm@12135
   638
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   639
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   640
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   641
  end;
nipkow@1756
   642
nipkow@3653
   643
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   644
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   645
   Introduction rule for == as a meta-theorem.
nipkow@3653
   646
*)
nipkow@3653
   647
val equal_intr_rule =
wenzelm@24241
   648
  let val PQ = read_prop "phi ==> psi"
wenzelm@24241
   649
      and QP = read_prop "psi ==> phi"
wenzelm@4016
   650
  in
wenzelm@12135
   651
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   652
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   653
  end;
nipkow@3653
   654
wenzelm@19421
   655
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   656
val equal_elim_rule1 =
wenzelm@24241
   657
  let val eq = read_prop "phi::prop == psi::prop"
wenzelm@24241
   658
      and P = read_prop "phi"
wenzelm@13368
   659
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   660
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   661
  end;
wenzelm@4285
   662
wenzelm@19421
   663
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   664
val equal_elim_rule2 =
wenzelm@19421
   665
  store_standard_thm_open "equal_elim_rule2" (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   666
wenzelm@28618
   667
(* PROP ?phi ==> PROP ?phi ==> PROP ?psi ==> PROP ?psi *)
wenzelm@12297
   668
val remdups_rl =
wenzelm@24241
   669
  let val P = read_prop "phi" and Q = read_prop "psi";
wenzelm@12297
   670
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   671
wenzelm@12297
   672
wenzelm@28618
   673
wenzelm@28618
   674
(** embedded terms and types **)
wenzelm@28618
   675
wenzelm@28618
   676
local
wenzelm@28618
   677
  val A = certify (Free ("A", propT));
wenzelm@28674
   678
  val axiom = Thm.unvarify o Thm.axiom (Context.the_theory (Context.the_thread_data ()));
wenzelm@28674
   679
  val prop_def = axiom "Pure.prop_def";
wenzelm@28674
   680
  val term_def = axiom "Pure.term_def";
wenzelm@28674
   681
  val sort_constraint_def = axiom "Pure.sort_constraint_def";
wenzelm@28618
   682
  val C = Thm.lhs_of sort_constraint_def;
wenzelm@28618
   683
  val T = Thm.dest_arg C;
wenzelm@28618
   684
  val CA = mk_implies (C, A);
wenzelm@28618
   685
in
wenzelm@28618
   686
wenzelm@28618
   687
(* protect *)
wenzelm@28618
   688
wenzelm@28618
   689
val protect = Thm.capply (certify Logic.protectC);
wenzelm@28618
   690
wenzelm@28618
   691
val protectI = store_thm "protectI" (Thm.kind_rule Thm.internalK (standard
wenzelm@28618
   692
    (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@28618
   693
wenzelm@28618
   694
val protectD = store_thm "protectD" (Thm.kind_rule Thm.internalK (standard
wenzelm@28618
   695
    (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@28618
   696
wenzelm@28618
   697
val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@28618
   698
wenzelm@28618
   699
fun implies_intr_protected asms th =
wenzelm@28618
   700
  let val asms' = map protect asms in
wenzelm@28618
   701
    implies_elim_list
wenzelm@28618
   702
      (implies_intr_list asms th)
wenzelm@28618
   703
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@28618
   704
    |> implies_intr_list asms'
wenzelm@28618
   705
  end;
wenzelm@28618
   706
wenzelm@28618
   707
wenzelm@28618
   708
(* term *)
wenzelm@28618
   709
wenzelm@28618
   710
val termI = store_thm "termI" (Thm.kind_rule Thm.internalK (standard
wenzelm@28618
   711
    (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)))));
wenzelm@9554
   712
wenzelm@28618
   713
fun mk_term ct =
wenzelm@28618
   714
  let
wenzelm@28618
   715
    val thy = Thm.theory_of_cterm ct;
wenzelm@28618
   716
    val cert = Thm.cterm_of thy;
wenzelm@28618
   717
    val certT = Thm.ctyp_of thy;
wenzelm@28618
   718
    val T = Thm.typ_of (Thm.ctyp_of_term ct);
wenzelm@28618
   719
    val a = certT (TVar (("'a", 0), []));
wenzelm@28618
   720
    val x = cert (Var (("x", 0), T));
wenzelm@28618
   721
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@28618
   722
wenzelm@28618
   723
fun dest_term th =
wenzelm@28618
   724
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@28618
   725
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@28618
   726
      Thm.dest_arg cprop
wenzelm@28618
   727
    else raise THM ("dest_term", 0, [th])
wenzelm@28618
   728
  end;
wenzelm@28618
   729
wenzelm@28618
   730
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@28618
   731
fun term_rule thy f t = Thm.term_of (cterm_rule f (Thm.cterm_of thy t));
wenzelm@28618
   732
wenzelm@28618
   733
val dummy_thm = mk_term (certify (Term.dummy_pattern propT));
wenzelm@28618
   734
wenzelm@28618
   735
wenzelm@28618
   736
(* sort_constraint *)
wenzelm@28618
   737
wenzelm@28618
   738
val sort_constraintI = store_thm "sort_constraintI" (Thm.kind_rule Thm.internalK (standard
wenzelm@28618
   739
  (Thm.equal_elim (Thm.symmetric sort_constraint_def) (mk_term T))));
wenzelm@28618
   740
wenzelm@28618
   741
val sort_constraint_eq = store_thm "sort_constraint_eq" (Thm.kind_rule Thm.internalK (standard
wenzelm@28618
   742
  (Thm.equal_intr
wenzelm@28618
   743
    (Thm.implies_intr CA (Thm.implies_elim (Thm.assume CA) (Thm.unvarify sort_constraintI)))
wenzelm@28618
   744
    (implies_intr_list [A, C] (Thm.assume A)))));
wenzelm@28618
   745
wenzelm@28618
   746
end;
wenzelm@28618
   747
wenzelm@28618
   748
wenzelm@28618
   749
(* HHF normalization *)
wenzelm@28618
   750
wenzelm@28618
   751
(* (PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x)) *)
wenzelm@9554
   752
val norm_hhf_eq =
wenzelm@9554
   753
  let
wenzelm@14854
   754
    val aT = TFree ("'a", []);
wenzelm@9554
   755
    val all = Term.all aT;
wenzelm@9554
   756
    val x = Free ("x", aT);
wenzelm@9554
   757
    val phi = Free ("phi", propT);
wenzelm@9554
   758
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   759
wenzelm@26487
   760
    val cx = certify x;
wenzelm@26487
   761
    val cphi = certify phi;
wenzelm@26487
   762
    val lhs = certify (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@26487
   763
    val rhs = certify (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   764
  in
wenzelm@9554
   765
    Thm.equal_intr
wenzelm@9554
   766
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   767
        |> Thm.forall_elim cx
wenzelm@9554
   768
        |> Thm.implies_intr cphi
wenzelm@9554
   769
        |> Thm.forall_intr cx
wenzelm@9554
   770
        |> Thm.implies_intr lhs)
wenzelm@9554
   771
      (Thm.implies_elim
wenzelm@9554
   772
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   773
        |> Thm.forall_intr cx
wenzelm@9554
   774
        |> Thm.implies_intr cphi
wenzelm@9554
   775
        |> Thm.implies_intr rhs)
wenzelm@12135
   776
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   777
  end;
wenzelm@9554
   778
wenzelm@18179
   779
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@28618
   780
val norm_hhf_eqs = [norm_hhf_eq, sort_constraint_eq];
wenzelm@18179
   781
wenzelm@30553
   782
fun is_norm_hhf (Const ("Pure.sort_constraint", _)) = false
wenzelm@30553
   783
  | is_norm_hhf (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@30553
   784
  | is_norm_hhf (Abs _ $ _) = false
wenzelm@30553
   785
  | is_norm_hhf (t $ u) = is_norm_hhf t andalso is_norm_hhf u
wenzelm@30553
   786
  | is_norm_hhf (Abs (_, _, t)) = is_norm_hhf t
wenzelm@30553
   787
  | is_norm_hhf _ = true;
wenzelm@12800
   788
wenzelm@16425
   789
fun norm_hhf thy t =
wenzelm@12800
   790
  if is_norm_hhf t then t
wenzelm@18179
   791
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   792
wenzelm@20298
   793
fun norm_hhf_cterm ct =
wenzelm@20298
   794
  if is_norm_hhf (Thm.term_of ct) then ct
wenzelm@20298
   795
  else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
wenzelm@20298
   796
wenzelm@12800
   797
wenzelm@21603
   798
(* var indexes *)
wenzelm@21603
   799
paulson@24426
   800
(*Increment the indexes of only the type variables*)
paulson@24426
   801
fun incr_type_indexes inc th =
wenzelm@29270
   802
  let val tvs = OldTerm.term_tvars (prop_of th)
wenzelm@29270
   803
      and thy = Thm.theory_of_thm th
paulson@24426
   804
      fun inc_tvar ((a,i),s) = pairself (ctyp_of thy) (TVar ((a,i),s), TVar ((a,i+inc),s))
paulson@24426
   805
  in Thm.instantiate (map inc_tvar tvs, []) th end;
paulson@24426
   806
wenzelm@21603
   807
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   808
wenzelm@21603
   809
fun incr_indexes2 th1 th2 =
wenzelm@21603
   810
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   811
wenzelm@21603
   812
fun th1 INCR_COMP th2 = incr_indexes th2 th1 COMP th2;
wenzelm@21603
   813
fun th1 COMP_INCR th2 = th1 COMP incr_indexes th1 th2;
wenzelm@21603
   814
wenzelm@29344
   815
fun comp_no_flatten (th, n) i rule =
wenzelm@29344
   816
  (case distinct Thm.eq_thm (Seq.list_of
wenzelm@29344
   817
      (Thm.compose_no_flatten false (th, n) i (incr_indexes th rule))) of
wenzelm@29344
   818
    [th'] => th'
wenzelm@29344
   819
  | [] => raise THM ("comp_no_flatten", i, [th, rule])
wenzelm@29344
   820
  | _ => raise THM ("comp_no_flatten: unique result expected", i, [th, rule]));
wenzelm@29344
   821
wenzelm@29344
   822
wenzelm@9554
   823
wenzelm@16425
   824
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   825
paulson@8129
   826
(*Version that normalizes the result: Thm.instantiate no longer does that*)
wenzelm@21603
   827
fun instantiate instpair th =
wenzelm@21603
   828
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   829
paulson@8129
   830
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   831
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   832
local
wenzelm@16425
   833
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@26627
   834
    let
wenzelm@26627
   835
        val thyt = Thm.theory_of_cterm ct;
wenzelm@26627
   836
        val thyu = Thm.theory_of_cterm cu;
wenzelm@26627
   837
        val {t, T, maxidx = maxt, ...} = Thm.rep_cterm ct;
wenzelm@26627
   838
        val {t = u, T = U, maxidx = maxu, ...} = Thm.rep_cterm cu;
paulson@8129
   839
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   840
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   841
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
berghofe@25470
   842
          handle Type.TUNIFY => raise TYPE ("Ill-typed instantiation:\nType\n" ^
wenzelm@26939
   843
            Syntax.string_of_typ_global thy' (Envir.norm_type tye T) ^
berghofe@25470
   844
            "\nof variable " ^
wenzelm@26939
   845
            Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) t) ^
berghofe@25470
   846
            "\ncannot be unified with type\n" ^
wenzelm@26939
   847
            Syntax.string_of_typ_global thy' (Envir.norm_type tye U) ^ "\nof term " ^
wenzelm@26939
   848
            Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) u),
berghofe@25470
   849
            [T, U], [t, u])
wenzelm@16425
   850
    in  (thy', tye', maxi')  end;
paulson@8129
   851
in
paulson@22561
   852
fun cterm_instantiate [] th = th
paulson@22561
   853
  | cterm_instantiate ctpairs0 th =
wenzelm@23178
   854
  let val (thy,tye,_) = List.foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   855
      fun instT(ct,cu) =
paulson@22287
   856
        let val inst = cterm_of thy o Term.map_types (Envir.norm_type tye) o term_of
paulson@14340
   857
        in (inst ct, inst cu) end
paulson@22307
   858
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy (Envir.norm_type tye T))
berghofe@8406
   859
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   860
  handle TERM _ =>
wenzelm@16425
   861
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   862
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   863
end;
paulson@8129
   864
paulson@8129
   865
wenzelm@4789
   866
wenzelm@5688
   867
(** variations on instantiate **)
wenzelm@4285
   868
wenzelm@4285
   869
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   870
wenzelm@4285
   871
fun instantiate' cTs cts thm =
wenzelm@4285
   872
  let
wenzelm@4285
   873
    fun err msg =
wenzelm@4285
   874
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   875
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   876
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   877
wenzelm@4285
   878
    fun inst_of (v, ct) =
wenzelm@16425
   879
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   880
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   881
berghofe@15797
   882
    fun tyinst_of (v, cT) =
wenzelm@16425
   883
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   884
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   885
wenzelm@20298
   886
    fun zip_vars xs ys =
wenzelm@20298
   887
      zip_options xs ys handle Library.UnequalLengths =>
wenzelm@20298
   888
        err "more instantiations than variables in thm";
wenzelm@4285
   889
wenzelm@4285
   890
    (*instantiate types first!*)
wenzelm@4285
   891
    val thm' =
wenzelm@4285
   892
      if forall is_none cTs then thm
wenzelm@20298
   893
      else Thm.instantiate
wenzelm@22695
   894
        (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
wenzelm@20579
   895
    val thm'' =
wenzelm@4285
   896
      if forall is_none cts then thm'
wenzelm@20298
   897
      else Thm.instantiate
wenzelm@22695
   898
        ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
wenzelm@20298
   899
    in thm'' end;
wenzelm@4285
   900
wenzelm@4285
   901
berghofe@14081
   902
berghofe@14081
   903
(** renaming of bound variables **)
berghofe@14081
   904
berghofe@14081
   905
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   906
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   907
berghofe@14081
   908
fun rename_bvars [] thm = thm
berghofe@14081
   909
  | rename_bvars vs thm =
wenzelm@26627
   910
      let
wenzelm@26627
   911
        val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   912
        fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
wenzelm@26627
   913
          | ren (t $ u) = ren t $ ren u
wenzelm@26627
   914
          | ren t = t;
wenzelm@26627
   915
      in equal_elim (reflexive (cert (ren (Thm.prop_of thm)))) thm end;
berghofe@14081
   916
berghofe@14081
   917
berghofe@14081
   918
(* renaming in left-to-right order *)
berghofe@14081
   919
berghofe@14081
   920
fun rename_bvars' xs thm =
berghofe@14081
   921
  let
wenzelm@26627
   922
    val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   923
    val prop = Thm.prop_of thm;
berghofe@14081
   924
    fun rename [] t = ([], t)
berghofe@14081
   925
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   926
          let val (xs', t') = rename xs t
wenzelm@18929
   927
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
   928
      | rename xs (t $ u) =
berghofe@14081
   929
          let
berghofe@14081
   930
            val (xs', t') = rename xs t;
berghofe@14081
   931
            val (xs'', u') = rename xs' u
berghofe@14081
   932
          in (xs'', t' $ u') end
berghofe@14081
   933
      | rename xs t = (xs, t);
berghofe@14081
   934
  in case rename xs prop of
wenzelm@26627
   935
      ([], prop') => equal_elim (reflexive (cert prop')) thm
berghofe@14081
   936
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   937
  end;
berghofe@14081
   938
berghofe@14081
   939
wenzelm@11975
   940
wenzelm@18225
   941
(** multi_resolve **)
wenzelm@18225
   942
wenzelm@18225
   943
local
wenzelm@18225
   944
wenzelm@18225
   945
fun res th i rule =
wenzelm@18225
   946
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
   947
wenzelm@18225
   948
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
   949
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
   950
wenzelm@18225
   951
in
wenzelm@18225
   952
wenzelm@18225
   953
val multi_resolve = multi_res 1;
wenzelm@18225
   954
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
   955
wenzelm@18225
   956
end;
wenzelm@18225
   957
wenzelm@11975
   958
end;
wenzelm@5903
   959
wenzelm@5903
   960
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
   961
open BasicDrule;