src/Pure/drule.ML
author wenzelm
Thu May 10 00:39:52 2007 +0200 (2007-05-10)
changeset 22906 195b7515911a
parent 22695 17073e9b94f2
child 22938 454f1678bf5f
permissions -rw-r--r--
moved some operations to more_thm.ML and conv.ML;
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(*  Title:      Pure/drule.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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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 read_insts: theory -> (indexname -> typ option) * (indexname -> sort option) ->
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    (indexname -> typ option) * (indexname -> sort option) -> string list ->
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    (indexname * string) list -> (ctyp * ctyp) list * (cterm * cterm) list
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  val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
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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 forall_elim_var: int -> thm -> thm
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  val forall_elim_vars: int -> 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 read_instantiate_sg: theory -> (string*string)list -> thm -> thm
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  val read_instantiate: (string*string)list -> 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 add_used: thm -> string list -> string list
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  val flexflex_unique: thm -> thm
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  val close_derivation: thm -> 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 add_rule: thm -> thm list -> thm list
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  val del_rule: thm -> thm list -> thm list
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  val merge_rules: thm list * thm list -> thm list
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  val imp_cong_rule: thm -> thm -> 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 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 unvarify: thm -> thm
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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 sort_triv: theory -> typ * sort -> thm list
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  val unconstrainTs: 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 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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  val read_instantiate_sg': theory -> (indexname * string) list -> thm -> thm
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  val read_instantiate': (indexname * string) list -> 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 =
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  let val {t, thy, ...} = Thm.rep_cterm ct
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  in Thm.cterm_of thy (f t) end;
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fun ctyp_fun f cT =
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  let val {T, thy, ...} = Thm.rep_ctyp cT
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  in Thm.ctyp_of thy (f T) end;
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val cert = cterm_of ProtoPure.thy;
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val implies = cert Term.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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(** reading of instantiations **)
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fun absent ixn =
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  error("No such variable in term: " ^ Term.string_of_vname ixn);
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fun inst_failure ixn =
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  error("Instantiation of " ^ Term.string_of_vname ixn ^ " fails");
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fun read_insts thy (rtypes,rsorts) (types,sorts) used insts =
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let
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    fun is_tv ((a, _), _) =
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      (case Symbol.explode a of "'" :: _ => true | _ => false);
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    val (tvs, vs) = List.partition is_tv insts;
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    fun sort_of ixn = case rsorts ixn of SOME S => S | NONE => absent ixn;
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    fun readT (ixn, st) =
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        let val S = sort_of ixn;
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            val T = Sign.read_def_typ (thy,sorts) st;
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        in if Sign.typ_instance thy (T, TVar(ixn,S)) then (ixn,T)
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           else inst_failure ixn
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        end
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    val tye = map readT tvs;
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    fun mkty(ixn,st) = (case rtypes ixn of
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                          SOME T => (ixn,(st,typ_subst_TVars tye T))
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                        | NONE => absent ixn);
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    val ixnsTs = map mkty vs;
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    val ixns = map fst ixnsTs
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    and sTs  = map snd ixnsTs
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    val (cts,tye2) = Thm.read_def_cterms(thy,types,sorts) used false sTs;
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    fun mkcVar(ixn,T) =
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        let val U = typ_subst_TVars tye2 T
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        in cterm_of thy (Var(ixn,U)) end
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    val ixnTs = ListPair.zip(ixns, map snd sTs)
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in (map (fn (ixn, T) => (ctyp_of thy (TVar (ixn, sort_of ixn)),
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      ctyp_of thy T)) (tye2 @ tye),
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    ListPair.zip(map mkcVar ixnTs,cts))
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end;
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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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val add_used =
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  (Thm.fold_terms o fold_types o fold_atyps)
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    (fn TFree (a, _) => insert (op =) a
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      | TVar ((a, _), _) => insert (op =) a
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      | _ => I);
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(** Standardization of rules **)
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(* type classes and sorts *)
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fun sort_triv thy (T, S) =
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  let
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    val certT = Thm.ctyp_of thy;
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    val cT = certT T;
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    fun class_triv c =
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      Thm.class_triv thy c
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      |> Thm.instantiate ([(certT (TVar (("'a", 0), [c])), cT)], []);
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  in map class_triv S end;
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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 {prop, hyps, tpairs, thy,...} = 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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val forall_elim_var = PureThy.forall_elim_var;
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val forall_elim_vars = PureThy.forall_elim_vars;
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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, prop, maxidx, ...} = Thm.rep_thm th;
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    val cert = Thm.cterm_of thy;
wenzelm@18025
   308
    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
wenzelm@18025
   309
  in fold elim (outer_params prop) th end;
wenzelm@18025
   310
wenzelm@18025
   311
(*lift vars wrt. outermost goal parameters
wenzelm@18118
   312
  -- reverses the effect of gen_all modulo higher-order unification*)
wenzelm@18025
   313
fun lift_all goal th =
wenzelm@18025
   314
  let
wenzelm@18025
   315
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   316
    val cert = Thm.cterm_of thy;
wenzelm@19421
   317
    val maxidx = Thm.maxidx_of th;
wenzelm@18025
   318
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   319
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   320
    val Ts = map Term.fastype_of ps;
wenzelm@22695
   321
    val inst = Thm.fold_terms Term.add_vars th [] |> map (fn (xi, T) =>
wenzelm@18025
   322
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   323
  in
wenzelm@18025
   324
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   325
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   326
  end;
wenzelm@18025
   327
wenzelm@19999
   328
(*direct generalization*)
wenzelm@19999
   329
fun generalize names th = Thm.generalize names (Thm.maxidx_of th + 1) th;
wenzelm@9554
   330
wenzelm@16949
   331
(*specialization over a list of cterms*)
wenzelm@16949
   332
val forall_elim_list = fold forall_elim;
clasohm@0
   333
wenzelm@16949
   334
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   335
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   336
wenzelm@16949
   337
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
skalberg@15570
   338
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   339
clasohm@0
   340
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@21603
   341
fun zero_var_indexes_list [] = []
wenzelm@21603
   342
  | zero_var_indexes_list ths =
wenzelm@21603
   343
      let
wenzelm@21603
   344
        val thy = Theory.merge_list (map Thm.theory_of_thm ths);
wenzelm@21603
   345
        val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@21603
   346
        val (instT, inst) = TermSubst.zero_var_indexes_inst (map Thm.full_prop_of ths);
wenzelm@21603
   347
        val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@21603
   348
        val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@21603
   349
      in map (Thm.adjust_maxidx_thm ~1 o Thm.instantiate (cinstT, cinst)) ths end;
wenzelm@21603
   350
wenzelm@21603
   351
val zero_var_indexes = singleton zero_var_indexes_list;
clasohm@0
   352
clasohm@0
   353
paulson@14394
   354
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   355
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   356
wenzelm@16595
   357
(*Discharge all hypotheses.*)
wenzelm@16595
   358
fun implies_intr_hyps th =
wenzelm@16595
   359
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   360
paulson@14394
   361
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   362
  This step can lose information.*)
paulson@14387
   363
fun flexflex_unique th =
berghofe@17713
   364
  if null (tpairs_of th) then th else
wenzelm@19861
   365
    case Seq.chop 2 (flexflex_rule th) of
paulson@14387
   366
      ([th],_) => th
paulson@14387
   367
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   368
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   369
wenzelm@10515
   370
fun close_derivation thm =
wenzelm@21646
   371
  if Thm.get_name thm = "" then Thm.put_name "" thm
wenzelm@10515
   372
  else thm;
wenzelm@10515
   373
wenzelm@21603
   374
wenzelm@21603
   375
(* legacy standard operations *)
wenzelm@21603
   376
wenzelm@16949
   377
val standard' =
wenzelm@16949
   378
  implies_intr_hyps
wenzelm@16949
   379
  #> forall_intr_frees
wenzelm@19421
   380
  #> `Thm.maxidx_of
wenzelm@16949
   381
  #-> (fn maxidx =>
wenzelm@16949
   382
    forall_elim_vars (maxidx + 1)
wenzelm@20904
   383
    #> Thm.strip_shyps
wenzelm@16949
   384
    #> zero_var_indexes
wenzelm@16949
   385
    #> Thm.varifyT
wenzelm@21600
   386
    #> Thm.compress);
wenzelm@1218
   387
wenzelm@16949
   388
val standard =
wenzelm@21600
   389
  flexflex_unique
wenzelm@16949
   390
  #> standard'
wenzelm@16949
   391
  #> close_derivation;
berghofe@11512
   392
clasohm@0
   393
wenzelm@8328
   394
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   395
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   396
  Similar code in type/freeze_thaw*)
paulson@15495
   397
paulson@15495
   398
fun freeze_thaw_robust th =
wenzelm@19878
   399
 let val fth = Thm.freezeT th
wenzelm@16425
   400
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@15495
   401
 in
skalberg@15574
   402
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   403
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   404
     | vars =>
paulson@19753
   405
         let fun newName (Var(ix,_)) = (ix, gensym (string_of_indexname ix))
paulson@19753
   406
             val alist = map newName vars
paulson@15495
   407
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   408
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   409
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   410
             val insts = map mk_inst vars
paulson@15495
   411
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   412
                 th' |> forall_intr_list (map #2 insts)
wenzelm@22906
   413
                     |> forall_elim_list (map (Thm.incr_indexes_cterm i o #1) insts)
paulson@15495
   414
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   415
 end;
paulson@15495
   416
paulson@15495
   417
(*Basic version of the function above. No option to rename Vars apart in thaw.
wenzelm@19999
   418
  The Frees created from Vars have nice names. FIXME: does not check for
paulson@19753
   419
  clashes with variables in the assumptions, so delete and use freeze_thaw_robust instead?*)
paulson@4610
   420
fun freeze_thaw th =
wenzelm@19878
   421
 let val fth = Thm.freezeT th
wenzelm@16425
   422
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@7248
   423
 in
skalberg@15574
   424
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   425
       [] => (fth, fn x => x)
paulson@7248
   426
     | vars =>
wenzelm@8328
   427
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@20077
   428
                   let val v = Name.variant used (string_of_indexname ix)
wenzelm@8328
   429
                   in  ((ix,v)::pairs, v::used)  end;
skalberg@15574
   430
             val (alist, _) = foldr newName ([], Library.foldr add_term_names
skalberg@15574
   431
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   432
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   433
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   434
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   435
             val insts = map mk_inst vars
wenzelm@8328
   436
             fun thaw th' =
wenzelm@8328
   437
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   438
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   439
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   440
 end;
paulson@4610
   441
paulson@7248
   442
(*Rotates a rule's premises to the left by k*)
paulson@7248
   443
val rotate_prems = permute_prems 0;
paulson@4610
   444
oheimb@11163
   445
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   446
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   447
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   448
val rearrange_prems = let
oheimb@11163
   449
  fun rearr new []      thm = thm
wenzelm@11815
   450
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   451
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   452
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   453
  in rearr 0 end;
paulson@4610
   454
wenzelm@252
   455
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   456
fun tha RSN (i,thb) =
wenzelm@19861
   457
  case Seq.chop 2 (biresolution false [(false,tha)] i thb) of
clasohm@0
   458
      ([th],_) => th
clasohm@0
   459
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   460
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   461
clasohm@0
   462
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   463
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   464
clasohm@0
   465
(*For joining lists of rules*)
wenzelm@252
   466
fun thas RLN (i,thbs) =
clasohm@0
   467
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   468
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   469
  in maps resb thbs end;
clasohm@0
   470
clasohm@0
   471
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   472
lcp@11
   473
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   474
  makes proof trees*)
wenzelm@252
   475
fun rls MRS bottom_rl =
lcp@11
   476
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   477
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   478
  in  rs_aux 1 rls  end;
lcp@11
   479
lcp@11
   480
(*As above, but for rule lists*)
wenzelm@252
   481
fun rlss MRL bottom_rls =
lcp@11
   482
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   483
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   484
  in  rs_aux 1 rlss  end;
lcp@11
   485
wenzelm@9288
   486
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   487
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   488
wenzelm@252
   489
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   490
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   491
  ALWAYS deletes premise i *)
wenzelm@252
   492
fun compose(tha,i,thb) =
wenzelm@4270
   493
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   494
wenzelm@6946
   495
fun compose_single (tha,i,thb) =
wenzelm@6946
   496
  (case compose (tha,i,thb) of
wenzelm@6946
   497
    [th] => th
wenzelm@6946
   498
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   499
clasohm@0
   500
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   501
fun tha COMP thb =
wenzelm@22360
   502
    case distinct Thm.eq_thm (compose(tha,1,thb)) of
wenzelm@252
   503
        [th] => th
clasohm@0
   504
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   505
wenzelm@13105
   506
wenzelm@4016
   507
(** theorem equality **)
clasohm@0
   508
clasohm@0
   509
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   510
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   511
wenzelm@9829
   512
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@22360
   513
val del_rule = remove Thm.eq_thm_prop;
wenzelm@18922
   514
fun add_rule th = cons th o del_rule th;
wenzelm@22360
   515
val merge_rules = Library.merge Thm.eq_thm_prop;
wenzelm@9829
   516
lcp@1194
   517
lcp@1194
   518
clasohm@0
   519
(*** Meta-Rewriting Rules ***)
clasohm@0
   520
wenzelm@22681
   521
fun read_prop s = Thm.read_cterm ProtoPure.thy (s, propT);
paulson@4610
   522
wenzelm@9455
   523
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   524
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   525
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   526
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   527
clasohm@0
   528
val reflexive_thm =
wenzelm@19421
   529
  let val cx = cert (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   530
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   531
clasohm@0
   532
val symmetric_thm =
wenzelm@14854
   533
  let val xy = read_prop "x == y"
wenzelm@16595
   534
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   535
clasohm@0
   536
val transitive_thm =
wenzelm@14854
   537
  let val xy = read_prop "x == y"
wenzelm@14854
   538
      val yz = read_prop "y == z"
clasohm@0
   539
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   540
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   541
nipkow@4679
   542
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   543
berghofe@11512
   544
fun extensional eq =
berghofe@11512
   545
  let val eq' =
wenzelm@22906
   546
    abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (cprop_of eq)))) eq
berghofe@11512
   547
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   548
wenzelm@18820
   549
val equals_cong =
wenzelm@18820
   550
  store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x == y"));
wenzelm@18820
   551
berghofe@10414
   552
val imp_cong =
berghofe@10414
   553
  let
berghofe@10414
   554
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   555
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   556
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   557
    val A = read_prop "PROP A"
berghofe@10414
   558
  in
wenzelm@12135
   559
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   560
      (implies_intr AB (implies_intr A
berghofe@10414
   561
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   562
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   563
      (implies_intr AC (implies_intr A
berghofe@10414
   564
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   565
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   566
  end;
berghofe@10414
   567
berghofe@10414
   568
val swap_prems_eq =
berghofe@10414
   569
  let
berghofe@10414
   570
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   571
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   572
    val A = read_prop "PROP A"
berghofe@10414
   573
    val B = read_prop "PROP B"
berghofe@10414
   574
  in
wenzelm@12135
   575
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   576
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   577
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   578
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   579
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   580
  end;
lcp@229
   581
wenzelm@18468
   582
val imp_cong_rule = combination o combination (reflexive implies);
clasohm@0
   583
skalberg@15001
   584
local
wenzelm@22906
   585
  val dest_eq = Thm.dest_equals o cprop_of
skalberg@15001
   586
  val rhs_of = snd o dest_eq
skalberg@15001
   587
in
skalberg@15001
   588
fun beta_eta_conversion t =
skalberg@15001
   589
  let val thm = beta_conversion true t
skalberg@15001
   590
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   591
end;
skalberg@15001
   592
berghofe@15925
   593
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   594
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   595
paulson@20861
   596
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   597
fun eta_contraction_rule th =
paulson@20861
   598
  equal_elim (eta_conversion (cprop_of th)) th;
paulson@20861
   599
wenzelm@18337
   600
val abs_def =
wenzelm@18337
   601
  let
wenzelm@18337
   602
    fun contract_lhs th =
wenzelm@22906
   603
      Thm.transitive (Thm.symmetric (beta_eta_conversion
wenzelm@22906
   604
        (fst (Thm.dest_equals (cprop_of th))))) th;
wenzelm@18777
   605
    fun abstract cx th = Thm.abstract_rule
wenzelm@18777
   606
        (case Thm.term_of cx of Var ((x, _), _) => x | Free (x, _) => x | _ => "x") cx th
wenzelm@18777
   607
      handle THM _ => raise THM ("Malformed definitional equation", 0, [th]);
wenzelm@18337
   608
  in
wenzelm@18337
   609
    contract_lhs
wenzelm@22906
   610
    #> `(snd o strip_comb o fst o Thm.dest_equals o cprop_of)
wenzelm@18337
   611
    #-> fold_rev abstract
wenzelm@18337
   612
    #> contract_lhs
wenzelm@18337
   613
  end;
wenzelm@18337
   614
wenzelm@18468
   615
wenzelm@15669
   616
(*** Some useful meta-theorems ***)
clasohm@0
   617
clasohm@0
   618
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   619
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   620
val _ = store_thm "_" asm_rl;
clasohm@0
   621
clasohm@0
   622
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   623
val cut_rl =
wenzelm@12135
   624
  store_standard_thm_open "cut_rl"
wenzelm@9455
   625
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   626
wenzelm@252
   627
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   628
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   629
val revcut_rl =
paulson@4610
   630
  let val V = read_prop "PROP V"
paulson@4610
   631
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   632
  in
wenzelm@12135
   633
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   634
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   635
  end;
clasohm@0
   636
lcp@668
   637
(*for deleting an unwanted assumption*)
lcp@668
   638
val thin_rl =
paulson@4610
   639
  let val V = read_prop "PROP V"
paulson@4610
   640
      and W = read_prop "PROP W";
wenzelm@12135
   641
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   642
clasohm@0
   643
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   644
val triv_forall_equality =
paulson@4610
   645
  let val V  = read_prop "PROP V"
paulson@4610
   646
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@19421
   647
      and x  = cert (Free ("x", Term.aT []));
wenzelm@4016
   648
  in
wenzelm@12135
   649
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   650
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   651
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   652
  end;
clasohm@0
   653
wenzelm@19051
   654
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   655
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   656
*)
wenzelm@19051
   657
val distinct_prems_rl =
wenzelm@19051
   658
  let
wenzelm@19051
   659
    val AAB = read_prop "PROP Phi ==> PROP Phi ==> PROP Psi"
wenzelm@19051
   660
    val A = read_prop "PROP Phi";
wenzelm@19051
   661
  in
wenzelm@19051
   662
    store_standard_thm_open "distinct_prems_rl"
wenzelm@19051
   663
      (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
wenzelm@19051
   664
  end;
wenzelm@19051
   665
nipkow@1756
   666
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   667
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   668
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   669
*)
nipkow@1756
   670
val swap_prems_rl =
paulson@4610
   671
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   672
      val major = assume cmajor;
paulson@4610
   673
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   674
      val minor1 = assume cminor1;
paulson@4610
   675
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   676
      val minor2 = assume cminor2;
wenzelm@12135
   677
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   678
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   679
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   680
  end;
nipkow@1756
   681
nipkow@3653
   682
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   683
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   684
   Introduction rule for == as a meta-theorem.
nipkow@3653
   685
*)
nipkow@3653
   686
val equal_intr_rule =
paulson@4610
   687
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   688
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   689
  in
wenzelm@12135
   690
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   691
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   692
  end;
nipkow@3653
   693
wenzelm@19421
   694
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   695
val equal_elim_rule1 =
wenzelm@13368
   696
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   697
      and P = read_prop "PROP phi"
wenzelm@13368
   698
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   699
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   700
  end;
wenzelm@4285
   701
wenzelm@19421
   702
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   703
val equal_elim_rule2 =
wenzelm@19421
   704
  store_standard_thm_open "equal_elim_rule2" (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   705
wenzelm@12297
   706
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   707
val remdups_rl =
wenzelm@12297
   708
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   709
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   710
wenzelm@12297
   711
wenzelm@9554
   712
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   713
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   714
wenzelm@9554
   715
val norm_hhf_eq =
wenzelm@9554
   716
  let
wenzelm@14854
   717
    val aT = TFree ("'a", []);
wenzelm@9554
   718
    val all = Term.all aT;
wenzelm@9554
   719
    val x = Free ("x", aT);
wenzelm@9554
   720
    val phi = Free ("phi", propT);
wenzelm@9554
   721
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   722
wenzelm@9554
   723
    val cx = cert x;
wenzelm@9554
   724
    val cphi = cert phi;
wenzelm@9554
   725
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   726
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   727
  in
wenzelm@9554
   728
    Thm.equal_intr
wenzelm@9554
   729
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   730
        |> Thm.forall_elim cx
wenzelm@9554
   731
        |> Thm.implies_intr cphi
wenzelm@9554
   732
        |> Thm.forall_intr cx
wenzelm@9554
   733
        |> Thm.implies_intr lhs)
wenzelm@9554
   734
      (Thm.implies_elim
wenzelm@9554
   735
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   736
        |> Thm.forall_intr cx
wenzelm@9554
   737
        |> Thm.implies_intr cphi
wenzelm@9554
   738
        |> Thm.implies_intr rhs)
wenzelm@12135
   739
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   740
  end;
wenzelm@9554
   741
wenzelm@18179
   742
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@18179
   743
wenzelm@12800
   744
fun is_norm_hhf tm =
wenzelm@12800
   745
  let
wenzelm@12800
   746
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   747
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   748
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   749
      | is_norm _ = true;
wenzelm@18929
   750
  in is_norm (Envir.beta_eta_contract tm) end;
wenzelm@12800
   751
wenzelm@16425
   752
fun norm_hhf thy t =
wenzelm@12800
   753
  if is_norm_hhf t then t
wenzelm@18179
   754
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   755
wenzelm@20298
   756
fun norm_hhf_cterm ct =
wenzelm@20298
   757
  if is_norm_hhf (Thm.term_of ct) then ct
wenzelm@20298
   758
  else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
wenzelm@20298
   759
wenzelm@12800
   760
wenzelm@21603
   761
(* var indexes *)
wenzelm@21603
   762
wenzelm@21603
   763
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   764
wenzelm@21603
   765
fun incr_indexes2 th1 th2 =
wenzelm@21603
   766
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   767
wenzelm@21603
   768
fun th1 INCR_COMP th2 = incr_indexes th2 th1 COMP th2;
wenzelm@21603
   769
fun th1 COMP_INCR th2 = th1 COMP incr_indexes th1 th2;
wenzelm@21603
   770
wenzelm@9554
   771
wenzelm@16425
   772
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   773
paulson@8129
   774
(*Version that normalizes the result: Thm.instantiate no longer does that*)
wenzelm@21603
   775
fun instantiate instpair th =
wenzelm@21603
   776
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   777
wenzelm@16425
   778
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   779
    let val ts = types_sorts th;
wenzelm@15669
   780
        val used = add_used th [];
wenzelm@16425
   781
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   782
wenzelm@16425
   783
fun read_instantiate_sg thy sinsts th =
wenzelm@20298
   784
  read_instantiate_sg' thy (map (apfst Syntax.read_indexname) sinsts) th;
paulson@8129
   785
paulson@8129
   786
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   787
fun read_instantiate sinsts th =
wenzelm@16425
   788
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   789
berghofe@15797
   790
fun read_instantiate' sinsts th =
wenzelm@16425
   791
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   792
paulson@8129
   793
paulson@8129
   794
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   795
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   796
local
wenzelm@16425
   797
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@16425
   798
    let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
wenzelm@16425
   799
        and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   800
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   801
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   802
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@10403
   803
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
wenzelm@16425
   804
    in  (thy', tye', maxi')  end;
paulson@8129
   805
in
paulson@22561
   806
fun cterm_instantiate [] th = th
paulson@22561
   807
  | cterm_instantiate ctpairs0 th =
wenzelm@16425
   808
  let val (thy,tye,_) = foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   809
      fun instT(ct,cu) =
paulson@22287
   810
        let val inst = cterm_of thy o Term.map_types (Envir.norm_type tye) o term_of
paulson@14340
   811
        in (inst ct, inst cu) end
paulson@22307
   812
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy (Envir.norm_type tye T))
berghofe@8406
   813
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   814
  handle TERM _ =>
wenzelm@16425
   815
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   816
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   817
end;
paulson@8129
   818
paulson@8129
   819
wenzelm@19878
   820
(* global schematic variables *)
wenzelm@19878
   821
wenzelm@19878
   822
fun unvarify th =
wenzelm@19878
   823
  let
wenzelm@19878
   824
    val thy = Thm.theory_of_thm th;
wenzelm@19878
   825
    val cert = Thm.cterm_of thy;
wenzelm@19878
   826
    val certT = Thm.ctyp_of thy;
wenzelm@19878
   827
wenzelm@19878
   828
    val prop = Thm.full_prop_of th;
wenzelm@19878
   829
    val _ = map Logic.unvarify (prop :: Thm.hyps_of th)
wenzelm@19878
   830
      handle TERM (msg, _) => raise THM (msg, 0, [th]);
wenzelm@19878
   831
wenzelm@19878
   832
    val instT0 = rev (Term.add_tvars prop []) |> map (fn v as ((a, _), S) => (v, TFree (a, S)));
wenzelm@19878
   833
    val instT = map (fn (v, T) => (certT (TVar v), certT T)) instT0;
wenzelm@19878
   834
    val inst = rev (Term.add_vars prop []) |> map (fn ((a, i), T) =>
wenzelm@20509
   835
      let val T' = TermSubst.instantiateT instT0 T
wenzelm@19878
   836
      in (cert (Var ((a, i), T')), cert (Free ((a, T')))) end);
wenzelm@19878
   837
  in Thm.instantiate (instT, inst) th end;
wenzelm@19878
   838
wenzelm@19878
   839
wenzelm@19775
   840
(** protected propositions and embedded terms **)
wenzelm@4789
   841
wenzelm@4789
   842
local
wenzelm@18025
   843
  val A = cert (Free ("A", propT));
wenzelm@19878
   844
  val prop_def = unvarify ProtoPure.prop_def;
wenzelm@19878
   845
  val term_def = unvarify ProtoPure.term_def;
wenzelm@4789
   846
in
wenzelm@18025
   847
  val protect = Thm.capply (cert Logic.protectC);
wenzelm@21437
   848
  val protectI = store_thm "protectI" (PureThy.kind_rule Thm.internalK (standard
wenzelm@18025
   849
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@21437
   850
  val protectD = store_thm "protectD" (PureThy.kind_rule Thm.internalK (standard
wenzelm@18025
   851
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@18179
   852
  val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@19775
   853
wenzelm@21437
   854
  val termI = store_thm "termI" (PureThy.kind_rule Thm.internalK (standard
wenzelm@19775
   855
      (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)))));
wenzelm@4789
   856
end;
wenzelm@4789
   857
wenzelm@18025
   858
fun implies_intr_protected asms th =
wenzelm@18118
   859
  let val asms' = map protect asms in
wenzelm@18118
   860
    implies_elim_list
wenzelm@18118
   861
      (implies_intr_list asms th)
wenzelm@18118
   862
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@18118
   863
    |> implies_intr_list asms'
wenzelm@18118
   864
  end;
wenzelm@11815
   865
wenzelm@19775
   866
fun mk_term ct =
wenzelm@19775
   867
  let
wenzelm@19775
   868
    val {thy, T, ...} = Thm.rep_cterm ct;
wenzelm@19775
   869
    val cert = Thm.cterm_of thy;
wenzelm@19775
   870
    val certT = Thm.ctyp_of thy;
wenzelm@19775
   871
    val a = certT (TVar (("'a", 0), []));
wenzelm@19775
   872
    val x = cert (Var (("x", 0), T));
wenzelm@19775
   873
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@19775
   874
wenzelm@19775
   875
fun dest_term th =
wenzelm@21566
   876
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@19775
   877
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@20579
   878
      Thm.dest_arg cprop
wenzelm@19775
   879
    else raise THM ("dest_term", 0, [th])
wenzelm@19775
   880
  end;
wenzelm@19775
   881
wenzelm@21519
   882
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@21519
   883
fun term_rule thy f t = Thm.term_of (cterm_rule f (Thm.cterm_of thy t));
wenzelm@20881
   884
wenzelm@19775
   885
wenzelm@4789
   886
wenzelm@5688
   887
(** variations on instantiate **)
wenzelm@4285
   888
wenzelm@4285
   889
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   890
wenzelm@4285
   891
fun instantiate' cTs cts thm =
wenzelm@4285
   892
  let
wenzelm@4285
   893
    fun err msg =
wenzelm@4285
   894
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   895
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   896
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   897
wenzelm@4285
   898
    fun inst_of (v, ct) =
wenzelm@16425
   899
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   900
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   901
berghofe@15797
   902
    fun tyinst_of (v, cT) =
wenzelm@16425
   903
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   904
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   905
wenzelm@20298
   906
    fun zip_vars xs ys =
wenzelm@20298
   907
      zip_options xs ys handle Library.UnequalLengths =>
wenzelm@20298
   908
        err "more instantiations than variables in thm";
wenzelm@4285
   909
wenzelm@4285
   910
    (*instantiate types first!*)
wenzelm@4285
   911
    val thm' =
wenzelm@4285
   912
      if forall is_none cTs then thm
wenzelm@20298
   913
      else Thm.instantiate
wenzelm@22695
   914
        (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
wenzelm@20579
   915
    val thm'' =
wenzelm@4285
   916
      if forall is_none cts then thm'
wenzelm@20298
   917
      else Thm.instantiate
wenzelm@22695
   918
        ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
wenzelm@20298
   919
    in thm'' end;
wenzelm@4285
   920
wenzelm@4285
   921
berghofe@14081
   922
berghofe@14081
   923
(** renaming of bound variables **)
berghofe@14081
   924
berghofe@14081
   925
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   926
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   927
berghofe@14081
   928
fun rename_bvars [] thm = thm
berghofe@14081
   929
  | rename_bvars vs thm =
berghofe@14081
   930
    let
wenzelm@16425
   931
      val {thy, prop, ...} = rep_thm thm;
haftmann@17325
   932
      fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
berghofe@14081
   933
        | ren (t $ u) = ren t $ ren u
berghofe@14081
   934
        | ren t = t;
wenzelm@16425
   935
    in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
berghofe@14081
   936
berghofe@14081
   937
berghofe@14081
   938
(* renaming in left-to-right order *)
berghofe@14081
   939
berghofe@14081
   940
fun rename_bvars' xs thm =
berghofe@14081
   941
  let
wenzelm@16425
   942
    val {thy, prop, ...} = rep_thm thm;
berghofe@14081
   943
    fun rename [] t = ([], t)
berghofe@14081
   944
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   945
          let val (xs', t') = rename xs t
wenzelm@18929
   946
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
   947
      | rename xs (t $ u) =
berghofe@14081
   948
          let
berghofe@14081
   949
            val (xs', t') = rename xs t;
berghofe@14081
   950
            val (xs'', u') = rename xs' u
berghofe@14081
   951
          in (xs'', t' $ u') end
berghofe@14081
   952
      | rename xs t = (xs, t);
berghofe@14081
   953
  in case rename xs prop of
wenzelm@16425
   954
      ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
berghofe@14081
   955
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   956
  end;
berghofe@14081
   957
berghofe@14081
   958
wenzelm@11975
   959
wenzelm@18225
   960
(** multi_resolve **)
wenzelm@18225
   961
wenzelm@18225
   962
local
wenzelm@18225
   963
wenzelm@18225
   964
fun res th i rule =
wenzelm@18225
   965
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
   966
wenzelm@18225
   967
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
   968
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
   969
wenzelm@18225
   970
in
wenzelm@18225
   971
wenzelm@18225
   972
val multi_resolve = multi_res 1;
wenzelm@18225
   973
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
   974
wenzelm@18225
   975
end;
wenzelm@18225
   976
wenzelm@11975
   977
end;
wenzelm@5903
   978
wenzelm@5903
   979
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
   980
open BasicDrule;