src/Pure/drule.ML
author paulson
Wed Jun 20 17:32:53 2007 +0200 (2007-06-20 ago)
changeset 23439 8c7da8649f2f
parent 23423 b2d64f86d21b
child 23537 ecf487dce798
permissions -rw-r--r--
A more robust flexflex_unique
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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 arg_cong_rule: cterm -> 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 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 with_subgoal: int -> (thm -> thm) -> 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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   308
  let
wenzelm@18025
   309
    val {thy, prop, maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   310
    val cert = Thm.cterm_of thy;
wenzelm@18025
   311
    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
wenzelm@18025
   312
  in fold elim (outer_params prop) th end;
wenzelm@18025
   313
wenzelm@18025
   314
(*lift vars wrt. outermost goal parameters
wenzelm@18118
   315
  -- reverses the effect of gen_all modulo higher-order unification*)
wenzelm@18025
   316
fun lift_all goal th =
wenzelm@18025
   317
  let
wenzelm@18025
   318
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   319
    val cert = Thm.cterm_of thy;
wenzelm@19421
   320
    val maxidx = Thm.maxidx_of th;
wenzelm@18025
   321
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   322
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   323
    val Ts = map Term.fastype_of ps;
wenzelm@22695
   324
    val inst = Thm.fold_terms Term.add_vars th [] |> map (fn (xi, T) =>
wenzelm@18025
   325
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   326
  in
wenzelm@18025
   327
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   328
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   329
  end;
wenzelm@18025
   330
wenzelm@19999
   331
(*direct generalization*)
wenzelm@19999
   332
fun generalize names th = Thm.generalize names (Thm.maxidx_of th + 1) th;
wenzelm@9554
   333
wenzelm@16949
   334
(*specialization over a list of cterms*)
wenzelm@16949
   335
val forall_elim_list = fold forall_elim;
clasohm@0
   336
wenzelm@16949
   337
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   338
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   339
wenzelm@16949
   340
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
skalberg@15570
   341
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   342
clasohm@0
   343
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@21603
   344
fun zero_var_indexes_list [] = []
wenzelm@21603
   345
  | zero_var_indexes_list ths =
wenzelm@21603
   346
      let
wenzelm@21603
   347
        val thy = Theory.merge_list (map Thm.theory_of_thm ths);
wenzelm@21603
   348
        val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@21603
   349
        val (instT, inst) = TermSubst.zero_var_indexes_inst (map Thm.full_prop_of ths);
wenzelm@21603
   350
        val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@21603
   351
        val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@21603
   352
      in map (Thm.adjust_maxidx_thm ~1 o Thm.instantiate (cinstT, cinst)) ths end;
wenzelm@21603
   353
wenzelm@21603
   354
val zero_var_indexes = singleton zero_var_indexes_list;
clasohm@0
   355
clasohm@0
   356
paulson@14394
   357
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   358
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   359
wenzelm@16595
   360
(*Discharge all hypotheses.*)
wenzelm@16595
   361
fun implies_intr_hyps th =
wenzelm@16595
   362
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   363
paulson@14394
   364
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   365
  This step can lose information.*)
paulson@14387
   366
fun flexflex_unique th =
berghofe@17713
   367
  if null (tpairs_of th) then th else
paulson@23439
   368
    case distinct Thm.eq_thm (Seq.list_of (flexflex_rule th)) of
paulson@23439
   369
      [th] => th
paulson@23439
   370
    | []   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@23439
   371
    |  _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   372
wenzelm@10515
   373
fun close_derivation thm =
wenzelm@21646
   374
  if Thm.get_name thm = "" then Thm.put_name "" thm
wenzelm@10515
   375
  else thm;
wenzelm@10515
   376
wenzelm@21603
   377
wenzelm@21603
   378
(* legacy standard operations *)
wenzelm@21603
   379
wenzelm@16949
   380
val standard' =
wenzelm@16949
   381
  implies_intr_hyps
wenzelm@16949
   382
  #> forall_intr_frees
wenzelm@19421
   383
  #> `Thm.maxidx_of
wenzelm@16949
   384
  #-> (fn maxidx =>
wenzelm@16949
   385
    forall_elim_vars (maxidx + 1)
wenzelm@20904
   386
    #> Thm.strip_shyps
wenzelm@16949
   387
    #> zero_var_indexes
wenzelm@16949
   388
    #> Thm.varifyT
wenzelm@21600
   389
    #> Thm.compress);
wenzelm@1218
   390
wenzelm@16949
   391
val standard =
wenzelm@21600
   392
  flexflex_unique
wenzelm@16949
   393
  #> standard'
wenzelm@16949
   394
  #> close_derivation;
berghofe@11512
   395
clasohm@0
   396
wenzelm@8328
   397
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   398
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   399
  Similar code in type/freeze_thaw*)
paulson@15495
   400
paulson@15495
   401
fun freeze_thaw_robust th =
wenzelm@19878
   402
 let val fth = Thm.freezeT th
wenzelm@16425
   403
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@15495
   404
 in
wenzelm@23178
   405
   case List.foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   406
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   407
     | vars =>
paulson@19753
   408
         let fun newName (Var(ix,_)) = (ix, gensym (string_of_indexname ix))
paulson@19753
   409
             val alist = map newName vars
paulson@15495
   410
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   411
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   412
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   413
             val insts = map mk_inst vars
paulson@15495
   414
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   415
                 th' |> forall_intr_list (map #2 insts)
wenzelm@22906
   416
                     |> forall_elim_list (map (Thm.incr_indexes_cterm i o #1) insts)
paulson@15495
   417
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   418
 end;
paulson@15495
   419
paulson@15495
   420
(*Basic version of the function above. No option to rename Vars apart in thaw.
wenzelm@19999
   421
  The Frees created from Vars have nice names. FIXME: does not check for
paulson@19753
   422
  clashes with variables in the assumptions, so delete and use freeze_thaw_robust instead?*)
paulson@4610
   423
fun freeze_thaw th =
wenzelm@19878
   424
 let val fth = Thm.freezeT th
wenzelm@16425
   425
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@7248
   426
 in
wenzelm@23178
   427
   case List.foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   428
       [] => (fth, fn x => x)
paulson@7248
   429
     | vars =>
wenzelm@8328
   430
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@20077
   431
                   let val v = Name.variant used (string_of_indexname ix)
wenzelm@8328
   432
                   in  ((ix,v)::pairs, v::used)  end;
wenzelm@23178
   433
             val (alist, _) = List.foldr newName ([], Library.foldr add_term_names
skalberg@15574
   434
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   435
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   436
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   437
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   438
             val insts = map mk_inst vars
wenzelm@8328
   439
             fun thaw th' =
wenzelm@8328
   440
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   441
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   442
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   443
 end;
paulson@4610
   444
paulson@7248
   445
(*Rotates a rule's premises to the left by k*)
paulson@7248
   446
val rotate_prems = permute_prems 0;
wenzelm@23423
   447
fun with_subgoal i f = rotate_prems (i - 1) #> f #> rotate_prems (1 - i);
paulson@4610
   448
oheimb@11163
   449
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   450
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   451
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   452
val rearrange_prems = let
oheimb@11163
   453
  fun rearr new []      thm = thm
wenzelm@11815
   454
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   455
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   456
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   457
  in rearr 0 end;
paulson@4610
   458
wenzelm@252
   459
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   460
fun tha RSN (i,thb) =
wenzelm@19861
   461
  case Seq.chop 2 (biresolution false [(false,tha)] i thb) of
clasohm@0
   462
      ([th],_) => th
clasohm@0
   463
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   464
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   465
clasohm@0
   466
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   467
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   468
clasohm@0
   469
(*For joining lists of rules*)
wenzelm@252
   470
fun thas RLN (i,thbs) =
clasohm@0
   471
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   472
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   473
  in maps resb thbs end;
clasohm@0
   474
clasohm@0
   475
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   476
lcp@11
   477
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   478
  makes proof trees*)
wenzelm@252
   479
fun rls MRS bottom_rl =
lcp@11
   480
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   481
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   482
  in  rs_aux 1 rls  end;
lcp@11
   483
lcp@11
   484
(*As above, but for rule lists*)
wenzelm@252
   485
fun rlss MRL bottom_rls =
lcp@11
   486
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   487
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   488
  in  rs_aux 1 rlss  end;
lcp@11
   489
wenzelm@9288
   490
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   491
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   492
wenzelm@252
   493
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   494
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   495
  ALWAYS deletes premise i *)
wenzelm@252
   496
fun compose(tha,i,thb) =
wenzelm@4270
   497
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   498
wenzelm@6946
   499
fun compose_single (tha,i,thb) =
wenzelm@6946
   500
  (case compose (tha,i,thb) of
wenzelm@6946
   501
    [th] => th
wenzelm@6946
   502
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   503
clasohm@0
   504
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   505
fun tha COMP thb =
wenzelm@22360
   506
    case distinct Thm.eq_thm (compose(tha,1,thb)) of
wenzelm@252
   507
        [th] => th
clasohm@0
   508
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   509
wenzelm@13105
   510
wenzelm@4016
   511
(** theorem equality **)
clasohm@0
   512
clasohm@0
   513
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   514
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   515
wenzelm@9829
   516
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@22360
   517
val del_rule = remove Thm.eq_thm_prop;
wenzelm@18922
   518
fun add_rule th = cons th o del_rule th;
wenzelm@22360
   519
val merge_rules = Library.merge Thm.eq_thm_prop;
wenzelm@9829
   520
lcp@1194
   521
lcp@1194
   522
clasohm@0
   523
(*** Meta-Rewriting Rules ***)
clasohm@0
   524
wenzelm@22681
   525
fun read_prop s = Thm.read_cterm ProtoPure.thy (s, propT);
paulson@4610
   526
wenzelm@9455
   527
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   528
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   529
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   530
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   531
clasohm@0
   532
val reflexive_thm =
wenzelm@19421
   533
  let val cx = cert (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   534
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   535
clasohm@0
   536
val symmetric_thm =
wenzelm@14854
   537
  let val xy = read_prop "x == y"
wenzelm@16595
   538
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   539
clasohm@0
   540
val transitive_thm =
wenzelm@14854
   541
  let val xy = read_prop "x == y"
wenzelm@14854
   542
      val yz = read_prop "y == z"
clasohm@0
   543
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   544
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   545
nipkow@4679
   546
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   547
berghofe@11512
   548
fun extensional eq =
berghofe@11512
   549
  let val eq' =
wenzelm@22906
   550
    abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (cprop_of eq)))) eq
berghofe@11512
   551
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   552
wenzelm@18820
   553
val equals_cong =
wenzelm@18820
   554
  store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x == y"));
wenzelm@18820
   555
berghofe@10414
   556
val imp_cong =
berghofe@10414
   557
  let
berghofe@10414
   558
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   559
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   560
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   561
    val A = read_prop "PROP A"
berghofe@10414
   562
  in
wenzelm@12135
   563
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   564
      (implies_intr AB (implies_intr A
berghofe@10414
   565
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   566
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   567
      (implies_intr AC (implies_intr A
berghofe@10414
   568
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   569
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   570
  end;
berghofe@10414
   571
berghofe@10414
   572
val swap_prems_eq =
berghofe@10414
   573
  let
berghofe@10414
   574
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   575
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   576
    val A = read_prop "PROP A"
berghofe@10414
   577
    val B = read_prop "PROP B"
berghofe@10414
   578
  in
wenzelm@12135
   579
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   580
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   581
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   582
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   583
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   584
  end;
lcp@229
   585
wenzelm@22938
   586
val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
wenzelm@22938
   587
wenzelm@22938
   588
fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM*)
wenzelm@22938
   589
fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM*)
clasohm@0
   590
skalberg@15001
   591
local
wenzelm@22906
   592
  val dest_eq = Thm.dest_equals o cprop_of
skalberg@15001
   593
  val rhs_of = snd o dest_eq
skalberg@15001
   594
in
skalberg@15001
   595
fun beta_eta_conversion t =
skalberg@15001
   596
  let val thm = beta_conversion true t
skalberg@15001
   597
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   598
end;
skalberg@15001
   599
berghofe@15925
   600
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   601
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   602
paulson@20861
   603
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   604
fun eta_contraction_rule th =
paulson@20861
   605
  equal_elim (eta_conversion (cprop_of th)) th;
paulson@20861
   606
wenzelm@18337
   607
val abs_def =
wenzelm@18337
   608
  let
wenzelm@18337
   609
    fun contract_lhs th =
wenzelm@22906
   610
      Thm.transitive (Thm.symmetric (beta_eta_conversion
wenzelm@22906
   611
        (fst (Thm.dest_equals (cprop_of th))))) th;
wenzelm@18777
   612
    fun abstract cx th = Thm.abstract_rule
wenzelm@18777
   613
        (case Thm.term_of cx of Var ((x, _), _) => x | Free (x, _) => x | _ => "x") cx th
wenzelm@18777
   614
      handle THM _ => raise THM ("Malformed definitional equation", 0, [th]);
wenzelm@18337
   615
  in
wenzelm@18337
   616
    contract_lhs
wenzelm@22906
   617
    #> `(snd o strip_comb o fst o Thm.dest_equals o cprop_of)
wenzelm@18337
   618
    #-> fold_rev abstract
wenzelm@18337
   619
    #> contract_lhs
wenzelm@18337
   620
  end;
wenzelm@18337
   621
wenzelm@18468
   622
wenzelm@15669
   623
(*** Some useful meta-theorems ***)
clasohm@0
   624
clasohm@0
   625
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   626
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   627
val _ = store_thm "_" asm_rl;
clasohm@0
   628
clasohm@0
   629
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   630
val cut_rl =
wenzelm@12135
   631
  store_standard_thm_open "cut_rl"
wenzelm@9455
   632
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   633
wenzelm@252
   634
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   635
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   636
val revcut_rl =
paulson@4610
   637
  let val V = read_prop "PROP V"
paulson@4610
   638
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   639
  in
wenzelm@12135
   640
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   641
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   642
  end;
clasohm@0
   643
lcp@668
   644
(*for deleting an unwanted assumption*)
lcp@668
   645
val thin_rl =
paulson@4610
   646
  let val V = read_prop "PROP V"
paulson@4610
   647
      and W = read_prop "PROP W";
wenzelm@12135
   648
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   649
clasohm@0
   650
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   651
val triv_forall_equality =
paulson@4610
   652
  let val V  = read_prop "PROP V"
paulson@4610
   653
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@19421
   654
      and x  = cert (Free ("x", Term.aT []));
wenzelm@4016
   655
  in
wenzelm@12135
   656
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   657
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   658
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   659
  end;
clasohm@0
   660
wenzelm@19051
   661
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   662
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   663
*)
wenzelm@19051
   664
val distinct_prems_rl =
wenzelm@19051
   665
  let
wenzelm@19051
   666
    val AAB = read_prop "PROP Phi ==> PROP Phi ==> PROP Psi"
wenzelm@19051
   667
    val A = read_prop "PROP Phi";
wenzelm@19051
   668
  in
wenzelm@19051
   669
    store_standard_thm_open "distinct_prems_rl"
wenzelm@19051
   670
      (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
wenzelm@19051
   671
  end;
wenzelm@19051
   672
nipkow@1756
   673
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   674
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   675
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   676
*)
nipkow@1756
   677
val swap_prems_rl =
paulson@4610
   678
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   679
      val major = assume cmajor;
paulson@4610
   680
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   681
      val minor1 = assume cminor1;
paulson@4610
   682
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   683
      val minor2 = assume cminor2;
wenzelm@12135
   684
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   685
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   686
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   687
  end;
nipkow@1756
   688
nipkow@3653
   689
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   690
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   691
   Introduction rule for == as a meta-theorem.
nipkow@3653
   692
*)
nipkow@3653
   693
val equal_intr_rule =
paulson@4610
   694
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   695
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   696
  in
wenzelm@12135
   697
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   698
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   699
  end;
nipkow@3653
   700
wenzelm@19421
   701
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   702
val equal_elim_rule1 =
wenzelm@13368
   703
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   704
      and P = read_prop "PROP phi"
wenzelm@13368
   705
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   706
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   707
  end;
wenzelm@4285
   708
wenzelm@19421
   709
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   710
val equal_elim_rule2 =
wenzelm@19421
   711
  store_standard_thm_open "equal_elim_rule2" (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   712
wenzelm@12297
   713
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   714
val remdups_rl =
wenzelm@12297
   715
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   716
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   717
wenzelm@12297
   718
wenzelm@9554
   719
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   720
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   721
wenzelm@9554
   722
val norm_hhf_eq =
wenzelm@9554
   723
  let
wenzelm@14854
   724
    val aT = TFree ("'a", []);
wenzelm@9554
   725
    val all = Term.all aT;
wenzelm@9554
   726
    val x = Free ("x", aT);
wenzelm@9554
   727
    val phi = Free ("phi", propT);
wenzelm@9554
   728
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   729
wenzelm@9554
   730
    val cx = cert x;
wenzelm@9554
   731
    val cphi = cert phi;
wenzelm@9554
   732
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   733
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   734
  in
wenzelm@9554
   735
    Thm.equal_intr
wenzelm@9554
   736
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   737
        |> Thm.forall_elim cx
wenzelm@9554
   738
        |> Thm.implies_intr cphi
wenzelm@9554
   739
        |> Thm.forall_intr cx
wenzelm@9554
   740
        |> Thm.implies_intr lhs)
wenzelm@9554
   741
      (Thm.implies_elim
wenzelm@9554
   742
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   743
        |> Thm.forall_intr cx
wenzelm@9554
   744
        |> Thm.implies_intr cphi
wenzelm@9554
   745
        |> Thm.implies_intr rhs)
wenzelm@12135
   746
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   747
  end;
wenzelm@9554
   748
wenzelm@18179
   749
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@18179
   750
wenzelm@12800
   751
fun is_norm_hhf tm =
wenzelm@12800
   752
  let
wenzelm@12800
   753
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   754
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   755
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   756
      | is_norm _ = true;
wenzelm@18929
   757
  in is_norm (Envir.beta_eta_contract tm) end;
wenzelm@12800
   758
wenzelm@16425
   759
fun norm_hhf thy t =
wenzelm@12800
   760
  if is_norm_hhf t then t
wenzelm@18179
   761
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   762
wenzelm@20298
   763
fun norm_hhf_cterm ct =
wenzelm@20298
   764
  if is_norm_hhf (Thm.term_of ct) then ct
wenzelm@20298
   765
  else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
wenzelm@20298
   766
wenzelm@12800
   767
wenzelm@21603
   768
(* var indexes *)
wenzelm@21603
   769
wenzelm@21603
   770
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   771
wenzelm@21603
   772
fun incr_indexes2 th1 th2 =
wenzelm@21603
   773
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   774
wenzelm@21603
   775
fun th1 INCR_COMP th2 = incr_indexes th2 th1 COMP th2;
wenzelm@21603
   776
fun th1 COMP_INCR th2 = th1 COMP incr_indexes th1 th2;
wenzelm@21603
   777
wenzelm@9554
   778
wenzelm@16425
   779
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   780
paulson@8129
   781
(*Version that normalizes the result: Thm.instantiate no longer does that*)
wenzelm@21603
   782
fun instantiate instpair th =
wenzelm@21603
   783
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   784
wenzelm@16425
   785
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   786
    let val ts = types_sorts th;
wenzelm@15669
   787
        val used = add_used th [];
wenzelm@16425
   788
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   789
wenzelm@16425
   790
fun read_instantiate_sg thy sinsts th =
wenzelm@20298
   791
  read_instantiate_sg' thy (map (apfst Syntax.read_indexname) sinsts) th;
paulson@8129
   792
paulson@8129
   793
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   794
fun read_instantiate sinsts th =
wenzelm@16425
   795
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   796
berghofe@15797
   797
fun read_instantiate' sinsts th =
wenzelm@16425
   798
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   799
paulson@8129
   800
paulson@8129
   801
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   802
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   803
local
wenzelm@16425
   804
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@16425
   805
    let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
wenzelm@16425
   806
        and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   807
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   808
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   809
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@10403
   810
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
wenzelm@16425
   811
    in  (thy', tye', maxi')  end;
paulson@8129
   812
in
paulson@22561
   813
fun cterm_instantiate [] th = th
paulson@22561
   814
  | cterm_instantiate ctpairs0 th =
wenzelm@23178
   815
  let val (thy,tye,_) = List.foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   816
      fun instT(ct,cu) =
paulson@22287
   817
        let val inst = cterm_of thy o Term.map_types (Envir.norm_type tye) o term_of
paulson@14340
   818
        in (inst ct, inst cu) end
paulson@22307
   819
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy (Envir.norm_type tye T))
berghofe@8406
   820
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   821
  handle TERM _ =>
wenzelm@16425
   822
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   823
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   824
end;
paulson@8129
   825
paulson@8129
   826
wenzelm@19878
   827
(* global schematic variables *)
wenzelm@19878
   828
wenzelm@19878
   829
fun unvarify th =
wenzelm@19878
   830
  let
wenzelm@19878
   831
    val thy = Thm.theory_of_thm th;
wenzelm@19878
   832
    val cert = Thm.cterm_of thy;
wenzelm@19878
   833
    val certT = Thm.ctyp_of thy;
wenzelm@19878
   834
wenzelm@19878
   835
    val prop = Thm.full_prop_of th;
wenzelm@19878
   836
    val _ = map Logic.unvarify (prop :: Thm.hyps_of th)
wenzelm@19878
   837
      handle TERM (msg, _) => raise THM (msg, 0, [th]);
wenzelm@19878
   838
wenzelm@19878
   839
    val instT0 = rev (Term.add_tvars prop []) |> map (fn v as ((a, _), S) => (v, TFree (a, S)));
wenzelm@19878
   840
    val instT = map (fn (v, T) => (certT (TVar v), certT T)) instT0;
wenzelm@19878
   841
    val inst = rev (Term.add_vars prop []) |> map (fn ((a, i), T) =>
wenzelm@20509
   842
      let val T' = TermSubst.instantiateT instT0 T
wenzelm@19878
   843
      in (cert (Var ((a, i), T')), cert (Free ((a, T')))) end);
wenzelm@19878
   844
  in Thm.instantiate (instT, inst) th end;
wenzelm@19878
   845
wenzelm@19878
   846
wenzelm@19775
   847
(** protected propositions and embedded terms **)
wenzelm@4789
   848
wenzelm@4789
   849
local
wenzelm@18025
   850
  val A = cert (Free ("A", propT));
wenzelm@19878
   851
  val prop_def = unvarify ProtoPure.prop_def;
wenzelm@19878
   852
  val term_def = unvarify ProtoPure.term_def;
wenzelm@4789
   853
in
wenzelm@18025
   854
  val protect = Thm.capply (cert Logic.protectC);
wenzelm@21437
   855
  val protectI = store_thm "protectI" (PureThy.kind_rule Thm.internalK (standard
wenzelm@18025
   856
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@21437
   857
  val protectD = store_thm "protectD" (PureThy.kind_rule Thm.internalK (standard
wenzelm@18025
   858
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@18179
   859
  val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@19775
   860
wenzelm@21437
   861
  val termI = store_thm "termI" (PureThy.kind_rule Thm.internalK (standard
wenzelm@19775
   862
      (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)))));
wenzelm@4789
   863
end;
wenzelm@4789
   864
wenzelm@18025
   865
fun implies_intr_protected asms th =
wenzelm@18118
   866
  let val asms' = map protect asms in
wenzelm@18118
   867
    implies_elim_list
wenzelm@18118
   868
      (implies_intr_list asms th)
wenzelm@18118
   869
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@18118
   870
    |> implies_intr_list asms'
wenzelm@18118
   871
  end;
wenzelm@11815
   872
wenzelm@19775
   873
fun mk_term ct =
wenzelm@19775
   874
  let
wenzelm@19775
   875
    val {thy, T, ...} = Thm.rep_cterm ct;
wenzelm@19775
   876
    val cert = Thm.cterm_of thy;
wenzelm@19775
   877
    val certT = Thm.ctyp_of thy;
wenzelm@19775
   878
    val a = certT (TVar (("'a", 0), []));
wenzelm@19775
   879
    val x = cert (Var (("x", 0), T));
wenzelm@19775
   880
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@19775
   881
wenzelm@19775
   882
fun dest_term th =
wenzelm@21566
   883
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@19775
   884
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@20579
   885
      Thm.dest_arg cprop
wenzelm@19775
   886
    else raise THM ("dest_term", 0, [th])
wenzelm@19775
   887
  end;
wenzelm@19775
   888
wenzelm@21519
   889
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@21519
   890
fun term_rule thy f t = Thm.term_of (cterm_rule f (Thm.cterm_of thy t));
wenzelm@20881
   891
wenzelm@19775
   892
wenzelm@4789
   893
wenzelm@5688
   894
(** variations on instantiate **)
wenzelm@4285
   895
wenzelm@4285
   896
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   897
wenzelm@4285
   898
fun instantiate' cTs cts thm =
wenzelm@4285
   899
  let
wenzelm@4285
   900
    fun err msg =
wenzelm@4285
   901
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   902
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   903
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   904
wenzelm@4285
   905
    fun inst_of (v, ct) =
wenzelm@16425
   906
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   907
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   908
berghofe@15797
   909
    fun tyinst_of (v, cT) =
wenzelm@16425
   910
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   911
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   912
wenzelm@20298
   913
    fun zip_vars xs ys =
wenzelm@20298
   914
      zip_options xs ys handle Library.UnequalLengths =>
wenzelm@20298
   915
        err "more instantiations than variables in thm";
wenzelm@4285
   916
wenzelm@4285
   917
    (*instantiate types first!*)
wenzelm@4285
   918
    val thm' =
wenzelm@4285
   919
      if forall is_none cTs then thm
wenzelm@20298
   920
      else Thm.instantiate
wenzelm@22695
   921
        (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
wenzelm@20579
   922
    val thm'' =
wenzelm@4285
   923
      if forall is_none cts then thm'
wenzelm@20298
   924
      else Thm.instantiate
wenzelm@22695
   925
        ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
wenzelm@20298
   926
    in thm'' end;
wenzelm@4285
   927
wenzelm@4285
   928
berghofe@14081
   929
berghofe@14081
   930
(** renaming of bound variables **)
berghofe@14081
   931
berghofe@14081
   932
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   933
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   934
berghofe@14081
   935
fun rename_bvars [] thm = thm
berghofe@14081
   936
  | rename_bvars vs thm =
berghofe@14081
   937
    let
wenzelm@16425
   938
      val {thy, prop, ...} = rep_thm thm;
haftmann@17325
   939
      fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
berghofe@14081
   940
        | ren (t $ u) = ren t $ ren u
berghofe@14081
   941
        | ren t = t;
wenzelm@16425
   942
    in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
berghofe@14081
   943
berghofe@14081
   944
berghofe@14081
   945
(* renaming in left-to-right order *)
berghofe@14081
   946
berghofe@14081
   947
fun rename_bvars' xs thm =
berghofe@14081
   948
  let
wenzelm@16425
   949
    val {thy, prop, ...} = rep_thm thm;
berghofe@14081
   950
    fun rename [] t = ([], t)
berghofe@14081
   951
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   952
          let val (xs', t') = rename xs t
wenzelm@18929
   953
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
   954
      | rename xs (t $ u) =
berghofe@14081
   955
          let
berghofe@14081
   956
            val (xs', t') = rename xs t;
berghofe@14081
   957
            val (xs'', u') = rename xs' u
berghofe@14081
   958
          in (xs'', t' $ u') end
berghofe@14081
   959
      | rename xs t = (xs, t);
berghofe@14081
   960
  in case rename xs prop of
wenzelm@16425
   961
      ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
berghofe@14081
   962
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   963
  end;
berghofe@14081
   964
berghofe@14081
   965
wenzelm@11975
   966
wenzelm@18225
   967
(** multi_resolve **)
wenzelm@18225
   968
wenzelm@18225
   969
local
wenzelm@18225
   970
wenzelm@18225
   971
fun res th i rule =
wenzelm@18225
   972
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
   973
wenzelm@18225
   974
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
   975
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
   976
wenzelm@18225
   977
in
wenzelm@18225
   978
wenzelm@18225
   979
val multi_resolve = multi_res 1;
wenzelm@18225
   980
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
   981
wenzelm@18225
   982
end;
wenzelm@18225
   983
wenzelm@11975
   984
end;
wenzelm@5903
   985
wenzelm@5903
   986
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
   987
open BasicDrule;