src/Pure/drule.ML
author wenzelm
Sat Mar 04 21:10:07 2006 +0100 (2006-03-04)
changeset 19183 3421668ae316
parent 19124 d9ac560a7bc8
child 19421 1051bde222db
permissions -rw-r--r--
added mk_conjunction;
tuned conj_curry;
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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;
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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 dest_implies: cterm -> cterm * cterm
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  val dest_equals: cterm -> 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 strip_shyps_warning: thm -> thm
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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: 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 assume_ax: theory -> string -> 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 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 eq_thm_thy: thm * thm -> bool
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  val eq_thm_prop: thm * thm -> bool
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  val weak_eq_thm: thm * thm -> bool
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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 equal_abs_elim: cterm  -> thm -> thm
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  val equal_abs_elim_list: cterm list -> thm -> thm
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  val asm_rl: thm
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  val cut_rl: thm
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  val revcut_rl: thm
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  val thin_rl: thm
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  val 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 inst: string -> string -> thm -> 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 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 plain_prop_of: thm -> term
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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 local_standard: 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 forall_conv: int -> (cterm -> thm) -> cterm -> thm
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  val concl_conv: int -> (cterm -> thm) -> cterm -> thm
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  val prems_conv: int -> (int -> cterm -> thm) -> cterm -> thm
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  val mk_conjunction: cterm * cterm -> cterm
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  val conjunction_cong: thm -> thm -> thm
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  val conjunction_conv: int -> (int -> cterm -> thm) -> cterm -> thm
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  val goals_conv: (int -> bool) -> (cterm -> thm) -> cterm -> thm
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  val fconv_rule: (cterm -> thm) -> 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 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 freeze_all: thm -> thm
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  val tvars_of_terms: term list -> (indexname * sort) list
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  val vars_of_terms: term list -> (indexname * typ) list
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  val tvars_of: thm -> (indexname * sort) list
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  val vars_of: thm -> (indexname * typ) list
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  val tfrees_of: thm -> (string * sort) list
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  val frees_of: thm -> (string * typ) list
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  val fold_terms: (term -> 'a -> 'a) -> thm -> 'a -> 'a
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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 unvarifyT: thm -> thm
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  val unvarify: thm -> thm
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  val tvars_intr_list: string list -> thm -> (string * (indexname * sort)) list * 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 conjunctionD1: thm
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  val conjunctionD2: thm
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  val conjunctionI: thm
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  val conj_intr: thm -> thm -> thm
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  val conj_intr_list: thm list -> thm
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  val conj_elim: thm -> thm * thm
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  val conj_elim_list: thm -> thm list
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  val conj_elim_precise: int list -> thm -> thm list list
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  val conj_uncurry: int -> thm -> thm
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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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fun dest_binop ct =
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  let val (ct1, ct2) = Thm.dest_comb ct
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  in (#2 (Thm.dest_comb ct1), ct2) end;
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fun dest_implies ct =
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  (case Thm.term_of ct of
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    (Const ("==>", _) $ _ $ _) => dest_binop ct
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  | _ => raise TERM ("dest_implies", [term_of ct]));
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fun dest_equals ct =
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  (case Thm.term_of ct of
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    (Const ("==", _) $ _ $ _) => dest_binop ct
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    | _ => raise TERM ("dest_equals", [term_of ct]));
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fun dest_conjunction ct =
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  (case Thm.term_of ct of
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    (Const ("ProtoPure.conjunction", _) $ _ $ _) => dest_binop ct
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  | _ => raise TERM ("dest_conjunction", [term_of ct]));
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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) = 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 term_of ct of (Const("==>", _) $ _ $ _) =>
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        strip_imp_concl (#2 (Thm.dest_comb 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 conjunction = cterm_of ProtoPure.thy Logic.conjunction;
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val implies = cterm_of ProtoPure.thy Term.implies;
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fun mk_implies (A, B) = Thm.capply (Thm.capply implies A) B;
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fun mk_conjunction (A, B) = Thm.capply (Thm.capply conjunction 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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    #2 (Thm.dest_comb (cprop_of (Thm.beta_conversion false (Thm.capply x y))));
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fun plain_prop_of raw_thm =
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  let
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    val thm = Thm.strip_shyps raw_thm;
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    fun err msg = raise THM ("plain_prop_of: " ^ msg, 0, [thm]);
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    val {hyps, prop, tpairs, ...} = Thm.rep_thm thm;
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  in
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    if not (null hyps) then
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      err "theorem may not contain hypotheses"
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    else if not (null (Thm.extra_shyps thm)) then
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      err "theorem may not contain sort hypotheses"
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    else if not (null tpairs) then
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      err "theorem may not contain flex-flex pairs"
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    else prop
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  end;
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lcp@708
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(** reading of instantiations **)
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fun absent ixn =
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  error("No such variable in term: " ^ Syntax.string_of_vname ixn);
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fun inst_failure ixn =
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  error("Instantiation of " ^ Syntax.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_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) = 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 val {prop, hyps, tpairs, ...} = Thm.rep_thm thm;
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        (* bogus term! *)
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        val big = Term.list_comb
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                    (Term.list_comb (prop, hyps), Thm.terms_of_tpairs tpairs);
wenzelm@252
   303
        val vars = map dest_Var (term_vars big);
wenzelm@252
   304
        val frees = map dest_Free (term_frees big);
wenzelm@252
   305
        val tvars = term_tvars big;
wenzelm@252
   306
        val tfrees = term_tfrees big;
haftmann@17325
   307
        fun typ(a,i) = if i<0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a,i);
haftmann@17325
   308
        fun sort(a,i) = if i<0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a,i);
clasohm@0
   309
    in (typ,sort) end;
clasohm@0
   310
wenzelm@15669
   311
fun add_used thm used =
wenzelm@15669
   312
  let val {prop, hyps, tpairs, ...} = Thm.rep_thm thm in
wenzelm@15669
   313
    add_term_tvarnames (prop, used)
wenzelm@15669
   314
    |> fold (curry add_term_tvarnames) hyps
wenzelm@15669
   315
    |> fold (curry add_term_tvarnames) (Thm.terms_of_tpairs tpairs)
wenzelm@15669
   316
  end;
wenzelm@15669
   317
wenzelm@7636
   318
wenzelm@9455
   319
clasohm@0
   320
(** Standardization of rules **)
clasohm@0
   321
wenzelm@18025
   322
(*vars in left-to-right order*)
wenzelm@18025
   323
fun tvars_of_terms ts = rev (fold Term.add_tvars ts []);
wenzelm@18025
   324
fun vars_of_terms ts = rev (fold Term.add_vars ts []);
wenzelm@18025
   325
fun tvars_of thm = tvars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   326
fun vars_of thm = vars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   327
wenzelm@18129
   328
fun fold_terms f th =
wenzelm@18129
   329
  let val {hyps, tpairs, prop, ...} = Thm.rep_thm th
wenzelm@18129
   330
  in f prop #> fold (fn (t, u) => f t #> f u) tpairs #> fold f hyps end;
wenzelm@18129
   331
wenzelm@18129
   332
fun tfrees_of th = rev (fold_terms Term.add_tfrees th []);
wenzelm@18129
   333
fun frees_of th = rev (fold_terms Term.add_frees th []);
wenzelm@18129
   334
wenzelm@7636
   335
(*Strip extraneous shyps as far as possible*)
wenzelm@7636
   336
fun strip_shyps_warning thm =
wenzelm@7636
   337
  let
wenzelm@16425
   338
    val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.theory_of_thm thm);
wenzelm@7636
   339
    val thm' = Thm.strip_shyps thm;
wenzelm@7636
   340
    val xshyps = Thm.extra_shyps thm';
wenzelm@7636
   341
  in
wenzelm@7636
   342
    if null xshyps then ()
wenzelm@7636
   343
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   344
    thm'
wenzelm@7636
   345
  end;
wenzelm@7636
   346
clasohm@0
   347
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   348
fun forall_intr_list [] th = th
clasohm@0
   349
  | forall_intr_list (y::ys) th =
wenzelm@252
   350
        let val gth = forall_intr_list ys th
wenzelm@252
   351
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   352
clasohm@0
   353
(*Generalization over all suitable Free variables*)
clasohm@0
   354
fun forall_intr_frees th =
wenzelm@16425
   355
    let val {prop,thy,...} = rep_thm th
clasohm@0
   356
    in  forall_intr_list
wenzelm@16983
   357
         (map (cterm_of thy) (sort Term.term_ord (term_frees prop)))
clasohm@0
   358
         th
clasohm@0
   359
    end;
clasohm@0
   360
wenzelm@18535
   361
(*Generalization over Vars -- canonical order*)
wenzelm@18535
   362
fun forall_intr_vars th =
wenzelm@18535
   363
  let val cert = Thm.cterm_of (Thm.theory_of_thm th)
wenzelm@18535
   364
  in forall_intr_list (map (cert o Var) (vars_of th)) th end;
wenzelm@18535
   365
wenzelm@7898
   366
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   367
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   368
wenzelm@18025
   369
fun outer_params t =
wenzelm@18025
   370
  let
wenzelm@18025
   371
    val vs = Term.strip_all_vars t;
wenzelm@18375
   372
    val xs = Term.variantlist (map (perhaps (try Syntax.dest_skolem) o #1) vs, []);
wenzelm@18025
   373
  in xs ~~ map #2 vs end;
wenzelm@18025
   374
wenzelm@18025
   375
(*generalize outermost parameters*)
wenzelm@18025
   376
fun gen_all th =
wenzelm@12719
   377
  let
wenzelm@18025
   378
    val {thy, prop, maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   379
    val cert = Thm.cterm_of thy;
wenzelm@18025
   380
    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
wenzelm@18025
   381
  in fold elim (outer_params prop) th end;
wenzelm@18025
   382
wenzelm@18025
   383
(*lift vars wrt. outermost goal parameters
wenzelm@18118
   384
  -- reverses the effect of gen_all modulo higher-order unification*)
wenzelm@18025
   385
fun lift_all goal th =
wenzelm@18025
   386
  let
wenzelm@18025
   387
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   388
    val cert = Thm.cterm_of thy;
wenzelm@18025
   389
    val {maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   390
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   391
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   392
    val Ts = map Term.fastype_of ps;
wenzelm@18025
   393
    val inst = vars_of th |> map (fn (xi, T) =>
wenzelm@18025
   394
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   395
  in
wenzelm@18025
   396
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   397
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   398
  end;
wenzelm@18025
   399
wenzelm@9554
   400
wenzelm@16949
   401
(*specialization over a list of cterms*)
wenzelm@16949
   402
val forall_elim_list = fold forall_elim;
clasohm@0
   403
wenzelm@16949
   404
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   405
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   406
wenzelm@16949
   407
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
skalberg@15570
   408
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   409
clasohm@0
   410
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   411
fun zero_var_indexes th =
wenzelm@16949
   412
  let
wenzelm@16949
   413
    val thy = Thm.theory_of_thm th;
wenzelm@16949
   414
    val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@16949
   415
    val (instT, inst) = Term.zero_var_indexes_inst (Thm.full_prop_of th);
wenzelm@16949
   416
    val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@16949
   417
    val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@16949
   418
  in Thm.adjust_maxidx_thm (Thm.instantiate (cinstT, cinst) th) end;
clasohm@0
   419
clasohm@0
   420
paulson@14394
   421
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   422
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   423
wenzelm@16595
   424
(*Discharge all hypotheses.*)
wenzelm@16595
   425
fun implies_intr_hyps th =
wenzelm@16595
   426
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   427
paulson@14394
   428
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   429
  This step can lose information.*)
paulson@14387
   430
fun flexflex_unique th =
berghofe@17713
   431
  if null (tpairs_of th) then th else
paulson@14387
   432
    case Seq.chop (2, flexflex_rule th) of
paulson@14387
   433
      ([th],_) => th
paulson@14387
   434
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   435
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   436
wenzelm@10515
   437
fun close_derivation thm =
wenzelm@10515
   438
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   439
  else thm;
wenzelm@10515
   440
wenzelm@16949
   441
val standard' =
wenzelm@16949
   442
  implies_intr_hyps
wenzelm@16949
   443
  #> forall_intr_frees
wenzelm@16949
   444
  #> `(#maxidx o Thm.rep_thm)
wenzelm@16949
   445
  #-> (fn maxidx =>
wenzelm@16949
   446
    forall_elim_vars (maxidx + 1)
wenzelm@16949
   447
    #> strip_shyps_warning
wenzelm@16949
   448
    #> zero_var_indexes
wenzelm@16949
   449
    #> Thm.varifyT
wenzelm@16949
   450
    #> Thm.compress);
wenzelm@1218
   451
wenzelm@16949
   452
val standard =
wenzelm@16949
   453
  flexflex_unique
wenzelm@16949
   454
  #> standard'
wenzelm@16949
   455
  #> close_derivation;
berghofe@11512
   456
wenzelm@16949
   457
val local_standard =
wenzelm@16949
   458
  strip_shyps
wenzelm@16949
   459
  #> zero_var_indexes
wenzelm@16949
   460
  #> Thm.compress
wenzelm@16949
   461
  #> close_derivation;
wenzelm@12005
   462
clasohm@0
   463
wenzelm@8328
   464
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   465
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   466
  Similar code in type/freeze_thaw*)
paulson@15495
   467
paulson@15495
   468
fun freeze_thaw_robust th =
paulson@15495
   469
 let val fth = freezeT th
wenzelm@16425
   470
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@15495
   471
 in
skalberg@15574
   472
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   473
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   474
     | vars =>
paulson@15495
   475
         let fun newName (Var(ix,_), pairs) =
paulson@15495
   476
                   let val v = gensym (string_of_indexname ix)
paulson@15495
   477
                   in  ((ix,v)::pairs)  end;
skalberg@15574
   478
             val alist = foldr newName [] vars
paulson@15495
   479
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   480
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   481
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   482
             val insts = map mk_inst vars
paulson@15495
   483
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   484
                 th' |> forall_intr_list (map #2 insts)
paulson@15495
   485
                     |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
paulson@15495
   486
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   487
 end;
paulson@15495
   488
paulson@15495
   489
(*Basic version of the function above. No option to rename Vars apart in thaw.
paulson@15495
   490
  The Frees created from Vars have nice names.*)
paulson@4610
   491
fun freeze_thaw th =
paulson@7248
   492
 let val fth = freezeT th
wenzelm@16425
   493
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@7248
   494
 in
skalberg@15574
   495
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   496
       [] => (fth, fn x => x)
paulson@7248
   497
     | vars =>
wenzelm@8328
   498
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   499
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   500
                   in  ((ix,v)::pairs, v::used)  end;
skalberg@15574
   501
             val (alist, _) = foldr newName ([], Library.foldr add_term_names
skalberg@15574
   502
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   503
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   504
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   505
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   506
             val insts = map mk_inst vars
wenzelm@8328
   507
             fun thaw th' =
wenzelm@8328
   508
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   509
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   510
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   511
 end;
paulson@4610
   512
paulson@7248
   513
(*Rotates a rule's premises to the left by k*)
paulson@7248
   514
val rotate_prems = permute_prems 0;
paulson@4610
   515
oheimb@11163
   516
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   517
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   518
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   519
val rearrange_prems = let
oheimb@11163
   520
  fun rearr new []      thm = thm
wenzelm@11815
   521
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   522
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   523
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   524
  in rearr 0 end;
paulson@4610
   525
wenzelm@252
   526
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   527
  Generalizes over Free variables,
clasohm@0
   528
  creates the assumption, and then strips quantifiers.
clasohm@0
   529
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   530
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   531
fun assume_ax thy sP =
wenzelm@16425
   532
  let val prop = Logic.close_form (term_of (read_cterm thy (sP, propT)))
wenzelm@16425
   533
  in forall_elim_vars 0 (Thm.assume (cterm_of thy prop)) end;
clasohm@0
   534
wenzelm@252
   535
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   536
fun tha RSN (i,thb) =
wenzelm@4270
   537
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   538
      ([th],_) => th
clasohm@0
   539
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   540
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   541
clasohm@0
   542
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   543
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   544
clasohm@0
   545
(*For joining lists of rules*)
wenzelm@252
   546
fun thas RLN (i,thbs) =
clasohm@0
   547
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   548
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   549
  in  List.concat (map resb thbs)  end;
clasohm@0
   550
clasohm@0
   551
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   552
lcp@11
   553
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   554
  makes proof trees*)
wenzelm@252
   555
fun rls MRS bottom_rl =
lcp@11
   556
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   557
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   558
  in  rs_aux 1 rls  end;
lcp@11
   559
lcp@11
   560
(*As above, but for rule lists*)
wenzelm@252
   561
fun rlss MRL bottom_rls =
lcp@11
   562
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   563
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   564
  in  rs_aux 1 rlss  end;
lcp@11
   565
wenzelm@9288
   566
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   567
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   568
wenzelm@252
   569
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   570
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   571
  ALWAYS deletes premise i *)
wenzelm@252
   572
fun compose(tha,i,thb) =
wenzelm@4270
   573
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   574
wenzelm@6946
   575
fun compose_single (tha,i,thb) =
wenzelm@6946
   576
  (case compose (tha,i,thb) of
wenzelm@6946
   577
    [th] => th
wenzelm@6946
   578
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   579
clasohm@0
   580
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   581
fun tha COMP thb =
clasohm@0
   582
    case compose(tha,1,thb) of
wenzelm@252
   583
        [th] => th
clasohm@0
   584
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   585
wenzelm@13105
   586
wenzelm@4016
   587
(** theorem equality **)
clasohm@0
   588
wenzelm@16425
   589
(*True if the two theorems have the same theory.*)
wenzelm@16425
   590
val eq_thm_thy = eq_thy o pairself Thm.theory_of_thm;
paulson@13650
   591
paulson@13650
   592
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@16720
   593
val eq_thm_prop = op aconv o pairself Thm.full_prop_of;
clasohm@0
   594
clasohm@0
   595
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   596
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   597
wenzelm@9829
   598
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@18922
   599
val del_rule = remove eq_thm_prop;
wenzelm@18922
   600
fun add_rule th = cons th o del_rule th;
wenzelm@18922
   601
val merge_rules = Library.merge eq_thm_prop;
wenzelm@9829
   602
wenzelm@18535
   603
(*weak_eq_thm: ignores variable renaming and (some) type variable renaming*)
wenzelm@13105
   604
val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
lcp@1194
   605
lcp@1194
   606
clasohm@0
   607
(*** Meta-Rewriting Rules ***)
clasohm@0
   608
wenzelm@16425
   609
fun read_prop s = read_cterm ProtoPure.thy (s, propT);
paulson@4610
   610
wenzelm@9455
   611
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   612
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   613
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   614
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   615
clasohm@0
   616
val reflexive_thm =
wenzelm@16425
   617
  let val cx = cterm_of ProtoPure.thy (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   618
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   619
clasohm@0
   620
val symmetric_thm =
wenzelm@14854
   621
  let val xy = read_prop "x == y"
wenzelm@16595
   622
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   623
clasohm@0
   624
val transitive_thm =
wenzelm@14854
   625
  let val xy = read_prop "x == y"
wenzelm@14854
   626
      val yz = read_prop "y == z"
clasohm@0
   627
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   628
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   629
nipkow@4679
   630
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   631
berghofe@11512
   632
fun extensional eq =
berghofe@11512
   633
  let val eq' =
berghofe@11512
   634
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   635
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   636
wenzelm@18820
   637
val equals_cong =
wenzelm@18820
   638
  store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x == y"));
wenzelm@18820
   639
berghofe@10414
   640
val imp_cong =
berghofe@10414
   641
  let
berghofe@10414
   642
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   643
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   644
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   645
    val A = read_prop "PROP A"
berghofe@10414
   646
  in
wenzelm@12135
   647
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   648
      (implies_intr AB (implies_intr A
berghofe@10414
   649
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   650
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   651
      (implies_intr AC (implies_intr A
berghofe@10414
   652
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   653
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   654
  end;
berghofe@10414
   655
berghofe@10414
   656
val swap_prems_eq =
berghofe@10414
   657
  let
berghofe@10414
   658
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   659
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   660
    val A = read_prop "PROP A"
berghofe@10414
   661
    val B = read_prop "PROP B"
berghofe@10414
   662
  in
wenzelm@12135
   663
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   664
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   665
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   666
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   667
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   668
  end;
lcp@229
   669
wenzelm@18468
   670
val imp_cong_rule = combination o combination (reflexive implies);
clasohm@0
   671
skalberg@15001
   672
local
skalberg@15001
   673
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   674
  val rhs_of = snd o dest_eq
skalberg@15001
   675
in
skalberg@15001
   676
fun beta_eta_conversion t =
skalberg@15001
   677
  let val thm = beta_conversion true t
skalberg@15001
   678
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   679
end;
skalberg@15001
   680
berghofe@15925
   681
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   682
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   683
wenzelm@18337
   684
val abs_def =
wenzelm@18337
   685
  let
wenzelm@18337
   686
    fun contract_lhs th =
wenzelm@18337
   687
      Thm.transitive (Thm.symmetric (beta_eta_conversion (fst (dest_equals (cprop_of th))))) th;
wenzelm@18777
   688
    fun abstract cx th = Thm.abstract_rule
wenzelm@18777
   689
        (case Thm.term_of cx of Var ((x, _), _) => x | Free (x, _) => x | _ => "x") cx th
wenzelm@18777
   690
      handle THM _ => raise THM ("Malformed definitional equation", 0, [th]);
wenzelm@18337
   691
  in
wenzelm@18337
   692
    contract_lhs
wenzelm@18337
   693
    #> `(snd o strip_comb o fst o dest_equals o cprop_of)
wenzelm@18337
   694
    #-> fold_rev abstract
wenzelm@18337
   695
    #> contract_lhs
wenzelm@18337
   696
  end;
wenzelm@18337
   697
wenzelm@18468
   698
(*rewrite B in !!x1 ... xn. B*)
wenzelm@18251
   699
fun forall_conv 0 cv ct = cv ct
wenzelm@18251
   700
  | forall_conv n cv ct =
wenzelm@18468
   701
      (case try Thm.dest_comb ct of
wenzelm@18468
   702
        NONE => cv ct
wenzelm@18468
   703
      | SOME (A, B) =>
wenzelm@18468
   704
          (case (term_of A, term_of B) of
wenzelm@18468
   705
            (Const ("all", _), Abs (x, _, _)) =>
wenzelm@18468
   706
              let val (v, B') = Thm.dest_abs (SOME (gensym "all_")) B in
wenzelm@18468
   707
                Thm.combination (Thm.reflexive A)
wenzelm@18468
   708
                  (Thm.abstract_rule x v (forall_conv (n - 1) cv B'))
wenzelm@18468
   709
              end
wenzelm@18468
   710
          | _ => cv ct));
wenzelm@18468
   711
wenzelm@18468
   712
(*rewrite B in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   713
fun concl_conv 0 cv ct = cv ct
wenzelm@18468
   714
  | concl_conv n cv ct =
wenzelm@18468
   715
      (case try dest_implies ct of
wenzelm@18468
   716
        NONE => cv ct
wenzelm@18468
   717
      | SOME (A, B) => imp_cong_rule (reflexive A) (concl_conv (n - 1) cv B));
skalberg@15001
   718
wenzelm@18468
   719
(*rewrite the A's in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   720
fun prems_conv 0 _ = reflexive
wenzelm@18468
   721
  | prems_conv n cv =
wenzelm@18468
   722
      let
wenzelm@18468
   723
        fun conv i ct =
wenzelm@18468
   724
          if i = n + 1 then reflexive ct
wenzelm@18468
   725
          else
wenzelm@18468
   726
            (case try dest_implies ct of
wenzelm@18468
   727
              NONE => reflexive ct
wenzelm@18468
   728
            | SOME (A, B) => imp_cong_rule (cv i A) (conv (i + 1) B));
wenzelm@18468
   729
  in conv 1 end;
wenzelm@18468
   730
wenzelm@19124
   731
wenzelm@18468
   732
(*rewrite the A's in A1 && ... && An*)
wenzelm@19124
   733
wenzelm@19183
   734
val conjunction_cong = Thm.combination o Thm.combination (Thm.reflexive conjunction);
wenzelm@19124
   735
wenzelm@18468
   736
fun conjunction_conv 0 _ = reflexive
wenzelm@18468
   737
  | conjunction_conv n cv =
wenzelm@18468
   738
      let
wenzelm@18468
   739
        fun conv i ct =
wenzelm@19124
   740
          if i = n then cv i ct
wenzelm@19124
   741
          else
wenzelm@19124
   742
            (case try dest_conjunction ct of
wenzelm@19124
   743
              NONE => cv i ct
wenzelm@19124
   744
            | SOME (A, B) => conjunction_cong (cv i A) (conv (i + 1) B));
wenzelm@18468
   745
      in conv 1 end;
wenzelm@18468
   746
wenzelm@18468
   747
wenzelm@18468
   748
fun goals_conv pred cv = prems_conv ~1 (fn i => if pred i then cv else reflexive);
skalberg@15001
   749
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   750
wenzelm@18468
   751
wenzelm@15669
   752
(*** Some useful meta-theorems ***)
clasohm@0
   753
clasohm@0
   754
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   755
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   756
val _ = store_thm "_" asm_rl;
clasohm@0
   757
clasohm@0
   758
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   759
val cut_rl =
wenzelm@12135
   760
  store_standard_thm_open "cut_rl"
wenzelm@9455
   761
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   762
wenzelm@252
   763
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   764
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   765
val revcut_rl =
paulson@4610
   766
  let val V = read_prop "PROP V"
paulson@4610
   767
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   768
  in
wenzelm@12135
   769
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   770
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   771
  end;
clasohm@0
   772
lcp@668
   773
(*for deleting an unwanted assumption*)
lcp@668
   774
val thin_rl =
paulson@4610
   775
  let val V = read_prop "PROP V"
paulson@4610
   776
      and W = read_prop "PROP W";
wenzelm@12135
   777
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   778
clasohm@0
   779
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   780
val triv_forall_equality =
paulson@4610
   781
  let val V  = read_prop "PROP V"
paulson@4610
   782
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@16425
   783
      and x  = read_cterm ProtoPure.thy ("x", TypeInfer.logicT);
wenzelm@4016
   784
  in
wenzelm@12135
   785
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   786
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   787
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   788
  end;
clasohm@0
   789
wenzelm@19051
   790
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   791
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   792
*)
wenzelm@19051
   793
val distinct_prems_rl =
wenzelm@19051
   794
  let
wenzelm@19051
   795
    val AAB = read_prop "PROP Phi ==> PROP Phi ==> PROP Psi"
wenzelm@19051
   796
    val A = read_prop "PROP Phi";
wenzelm@19051
   797
  in
wenzelm@19051
   798
    store_standard_thm_open "distinct_prems_rl"
wenzelm@19051
   799
      (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
wenzelm@19051
   800
  end;
wenzelm@19051
   801
nipkow@1756
   802
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   803
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   804
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   805
*)
nipkow@1756
   806
val swap_prems_rl =
paulson@4610
   807
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   808
      val major = assume cmajor;
paulson@4610
   809
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   810
      val minor1 = assume cminor1;
paulson@4610
   811
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   812
      val minor2 = assume cminor2;
wenzelm@12135
   813
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   814
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   815
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   816
  end;
nipkow@1756
   817
nipkow@3653
   818
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   819
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   820
   Introduction rule for == as a meta-theorem.
nipkow@3653
   821
*)
nipkow@3653
   822
val equal_intr_rule =
paulson@4610
   823
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   824
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   825
  in
wenzelm@12135
   826
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   827
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   828
  end;
nipkow@3653
   829
wenzelm@13368
   830
(* [| PROP ?phi == PROP ?psi; PROP ?phi |] ==> PROP ?psi *)
wenzelm@13368
   831
val equal_elim_rule1 =
wenzelm@13368
   832
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   833
      and P = read_prop "PROP phi"
wenzelm@13368
   834
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   835
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   836
  end;
wenzelm@4285
   837
wenzelm@12297
   838
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   839
wenzelm@12297
   840
val remdups_rl =
wenzelm@12297
   841
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   842
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   843
wenzelm@12297
   844
wenzelm@9554
   845
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   846
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   847
wenzelm@9554
   848
val norm_hhf_eq =
wenzelm@9554
   849
  let
wenzelm@16425
   850
    val cert = Thm.cterm_of ProtoPure.thy;
wenzelm@14854
   851
    val aT = TFree ("'a", []);
wenzelm@9554
   852
    val all = Term.all aT;
wenzelm@9554
   853
    val x = Free ("x", aT);
wenzelm@9554
   854
    val phi = Free ("phi", propT);
wenzelm@9554
   855
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   856
wenzelm@9554
   857
    val cx = cert x;
wenzelm@9554
   858
    val cphi = cert phi;
wenzelm@9554
   859
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   860
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   861
  in
wenzelm@9554
   862
    Thm.equal_intr
wenzelm@9554
   863
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   864
        |> Thm.forall_elim cx
wenzelm@9554
   865
        |> Thm.implies_intr cphi
wenzelm@9554
   866
        |> Thm.forall_intr cx
wenzelm@9554
   867
        |> Thm.implies_intr lhs)
wenzelm@9554
   868
      (Thm.implies_elim
wenzelm@9554
   869
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   870
        |> Thm.forall_intr cx
wenzelm@9554
   871
        |> Thm.implies_intr cphi
wenzelm@9554
   872
        |> Thm.implies_intr rhs)
wenzelm@12135
   873
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   874
  end;
wenzelm@9554
   875
wenzelm@18179
   876
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@18179
   877
wenzelm@12800
   878
fun is_norm_hhf tm =
wenzelm@12800
   879
  let
wenzelm@12800
   880
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   881
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   882
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   883
      | is_norm _ = true;
wenzelm@18929
   884
  in is_norm (Envir.beta_eta_contract tm) end;
wenzelm@12800
   885
wenzelm@16425
   886
fun norm_hhf thy t =
wenzelm@12800
   887
  if is_norm_hhf t then t
wenzelm@18179
   888
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   889
wenzelm@12800
   890
wenzelm@9554
   891
wenzelm@16425
   892
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   893
paulson@8129
   894
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   895
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   896
wenzelm@16425
   897
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   898
    let val ts = types_sorts th;
wenzelm@15669
   899
        val used = add_used th [];
wenzelm@16425
   900
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   901
wenzelm@16425
   902
fun read_instantiate_sg thy sinsts th =
wenzelm@16425
   903
  read_instantiate_sg' thy (map (apfst Syntax.indexname) sinsts) th;
paulson@8129
   904
paulson@8129
   905
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   906
fun read_instantiate sinsts th =
wenzelm@16425
   907
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   908
berghofe@15797
   909
fun read_instantiate' sinsts th =
wenzelm@16425
   910
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   911
paulson@8129
   912
paulson@8129
   913
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   914
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   915
local
wenzelm@16425
   916
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@16425
   917
    let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
wenzelm@16425
   918
        and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   919
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   920
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   921
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@10403
   922
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
wenzelm@16425
   923
    in  (thy', tye', maxi')  end;
paulson@8129
   924
in
paulson@8129
   925
fun cterm_instantiate ctpairs0 th =
wenzelm@16425
   926
  let val (thy,tye,_) = foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   927
      fun instT(ct,cu) =
wenzelm@16425
   928
        let val inst = cterm_of thy o Envir.subst_TVars tye o term_of
paulson@14340
   929
        in (inst ct, inst cu) end
wenzelm@16425
   930
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy T)
berghofe@8406
   931
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   932
  handle TERM _ =>
wenzelm@16425
   933
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   934
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   935
end;
paulson@8129
   936
paulson@8129
   937
paulson@8129
   938
(** Derived rules mainly for METAHYPS **)
paulson@8129
   939
paulson@8129
   940
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   941
fun equal_abs_elim ca eqth =
wenzelm@16425
   942
  let val {thy=thya, t=a, ...} = rep_cterm ca
paulson@8129
   943
      and combth = combination eqth (reflexive ca)
wenzelm@16425
   944
      val {thy,prop,...} = rep_thm eqth
paulson@8129
   945
      val (abst,absu) = Logic.dest_equals prop
wenzelm@16425
   946
      val cterm = cterm_of (Theory.merge (thy,thya))
berghofe@10414
   947
  in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
berghofe@10414
   948
           (transitive combth (beta_conversion false (cterm (absu$a))))
paulson@8129
   949
  end
paulson@8129
   950
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   951
paulson@8129
   952
(*Calling equal_abs_elim with multiple terms*)
skalberg@15574
   953
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) th (rev cts);
paulson@8129
   954
paulson@8129
   955
wenzelm@18025
   956
(** protected propositions **)
wenzelm@4789
   957
wenzelm@4789
   958
local
wenzelm@16425
   959
  val cert = Thm.cterm_of ProtoPure.thy;
wenzelm@18025
   960
  val A = cert (Free ("A", propT));
wenzelm@18025
   961
  val prop_def = #1 (freeze_thaw ProtoPure.prop_def);
wenzelm@4789
   962
in
wenzelm@18025
   963
  val protect = Thm.capply (cert Logic.protectC);
wenzelm@18799
   964
  val protectI = store_thm "protectI" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@18025
   965
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@18799
   966
  val protectD = store_thm "protectD" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@18025
   967
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@18179
   968
  val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@4789
   969
end;
wenzelm@4789
   970
wenzelm@18025
   971
fun implies_intr_protected asms th =
wenzelm@18118
   972
  let val asms' = map protect asms in
wenzelm@18118
   973
    implies_elim_list
wenzelm@18118
   974
      (implies_intr_list asms th)
wenzelm@18118
   975
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@18118
   976
    |> implies_intr_list asms'
wenzelm@18118
   977
  end;
wenzelm@11815
   978
wenzelm@4789
   979
wenzelm@5688
   980
(** variations on instantiate **)
wenzelm@4285
   981
paulson@8550
   982
(*shorthand for instantiating just one variable in the current theory*)
wenzelm@16425
   983
fun inst x t = read_instantiate_sg (the_context()) [(x,t)];
paulson@8550
   984
paulson@8550
   985
wenzelm@4285
   986
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   987
wenzelm@4285
   988
fun instantiate' cTs cts thm =
wenzelm@4285
   989
  let
wenzelm@4285
   990
    fun err msg =
wenzelm@4285
   991
      raise TYPE ("instantiate': " ^ msg,
skalberg@15570
   992
        List.mapPartial (Option.map Thm.typ_of) cTs,
skalberg@15570
   993
        List.mapPartial (Option.map Thm.term_of) cts);
wenzelm@4285
   994
wenzelm@4285
   995
    fun inst_of (v, ct) =
wenzelm@16425
   996
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   997
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   998
berghofe@15797
   999
    fun tyinst_of (v, cT) =
wenzelm@16425
  1000
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
  1001
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
  1002
wenzelm@4285
  1003
    fun zip_vars _ [] = []
skalberg@15531
  1004
      | zip_vars (_ :: vs) (NONE :: opt_ts) = zip_vars vs opt_ts
skalberg@15531
  1005
      | zip_vars (v :: vs) (SOME t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
  1006
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
  1007
wenzelm@4285
  1008
    (*instantiate types first!*)
wenzelm@4285
  1009
    val thm' =
wenzelm@4285
  1010
      if forall is_none cTs then thm
berghofe@15797
  1011
      else Thm.instantiate (map tyinst_of (zip_vars (tvars_of thm) cTs), []) thm;
wenzelm@4285
  1012
    in
wenzelm@4285
  1013
      if forall is_none cts then thm'
wenzelm@4285
  1014
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
  1015
    end;
wenzelm@4285
  1016
wenzelm@4285
  1017
berghofe@14081
  1018
berghofe@14081
  1019
(** renaming of bound variables **)
berghofe@14081
  1020
berghofe@14081
  1021
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
  1022
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
  1023
berghofe@14081
  1024
fun rename_bvars [] thm = thm
berghofe@14081
  1025
  | rename_bvars vs thm =
berghofe@14081
  1026
    let
wenzelm@16425
  1027
      val {thy, prop, ...} = rep_thm thm;
haftmann@17325
  1028
      fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
berghofe@14081
  1029
        | ren (t $ u) = ren t $ ren u
berghofe@14081
  1030
        | ren t = t;
wenzelm@16425
  1031
    in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
berghofe@14081
  1032
berghofe@14081
  1033
berghofe@14081
  1034
(* renaming in left-to-right order *)
berghofe@14081
  1035
berghofe@14081
  1036
fun rename_bvars' xs thm =
berghofe@14081
  1037
  let
wenzelm@16425
  1038
    val {thy, prop, ...} = rep_thm thm;
berghofe@14081
  1039
    fun rename [] t = ([], t)
berghofe@14081
  1040
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
  1041
          let val (xs', t') = rename xs t
wenzelm@18929
  1042
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
  1043
      | rename xs (t $ u) =
berghofe@14081
  1044
          let
berghofe@14081
  1045
            val (xs', t') = rename xs t;
berghofe@14081
  1046
            val (xs'', u') = rename xs' u
berghofe@14081
  1047
          in (xs'', t' $ u') end
berghofe@14081
  1048
      | rename xs t = (xs, t);
berghofe@14081
  1049
  in case rename xs prop of
wenzelm@16425
  1050
      ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
berghofe@14081
  1051
    | _ => error "More names than abstractions in theorem"
berghofe@14081
  1052
  end;
berghofe@14081
  1053
berghofe@14081
  1054
berghofe@14081
  1055
wenzelm@5688
  1056
(* unvarify(T) *)
wenzelm@5688
  1057
wenzelm@5688
  1058
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
  1059
wenzelm@5688
  1060
fun unvarifyT thm =
wenzelm@5688
  1061
  let
wenzelm@16425
  1062
    val cT = Thm.ctyp_of (Thm.theory_of_thm thm);
skalberg@15531
  1063
    val tfrees = map (fn ((x, _), S) => SOME (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
  1064
  in instantiate' tfrees [] thm end;
wenzelm@5688
  1065
wenzelm@5688
  1066
fun unvarify raw_thm =
wenzelm@5688
  1067
  let
wenzelm@5688
  1068
    val thm = unvarifyT raw_thm;
wenzelm@16425
  1069
    val ct = Thm.cterm_of (Thm.theory_of_thm thm);
skalberg@15531
  1070
    val frees = map (fn ((x, _), T) => SOME (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
  1071
  in instantiate' [] frees thm end;
wenzelm@5688
  1072
wenzelm@5688
  1073
wenzelm@8605
  1074
(* tvars_intr_list *)
wenzelm@8605
  1075
wenzelm@8605
  1076
fun tvars_intr_list tfrees thm =
wenzelm@18129
  1077
  apfst (map (fn ((s, S), ixn) => (s, (ixn, S)))) (Thm.varifyT'
berghofe@15797
  1078
    (gen_rems (op = o apfst fst) (tfrees_of thm, tfrees)) thm);
wenzelm@8605
  1079
wenzelm@8605
  1080
wenzelm@6435
  1081
(* increment var indexes *)
wenzelm@6435
  1082
wenzelm@18025
  1083
fun incr_indexes th = Thm.incr_indexes (#maxidx (Thm.rep_thm th) + 1);
wenzelm@18025
  1084
wenzelm@19124
  1085
fun incr_indexes2 th1 th2 =
wenzelm@19124
  1086
  Thm.incr_indexes (Int.max (#maxidx (Thm.rep_thm th1), #maxidx (Thm.rep_thm th2)) + 1);
wenzelm@6435
  1087
wenzelm@6435
  1088
wenzelm@8328
  1089
(* freeze_all *)
wenzelm@8328
  1090
wenzelm@8328
  1091
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
  1092
wenzelm@8328
  1093
fun freeze_all_TVars thm =
wenzelm@8328
  1094
  (case tvars_of thm of
wenzelm@8328
  1095
    [] => thm
wenzelm@8328
  1096
  | tvars =>
wenzelm@16425
  1097
      let val cert = Thm.ctyp_of (Thm.theory_of_thm thm)
skalberg@15531
  1098
      in instantiate' (map (fn ((x, _), S) => SOME (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
  1099
wenzelm@8328
  1100
fun freeze_all_Vars thm =
wenzelm@8328
  1101
  (case vars_of thm of
wenzelm@8328
  1102
    [] => thm
wenzelm@8328
  1103
  | vars =>
wenzelm@16425
  1104
      let val cert = Thm.cterm_of (Thm.theory_of_thm thm)
skalberg@15531
  1105
      in instantiate' [] (map (fn ((x, _), T) => SOME (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
  1106
wenzelm@8328
  1107
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
  1108
wenzelm@8328
  1109
wenzelm@11975
  1110
wenzelm@18225
  1111
(** multi_resolve **)
wenzelm@18225
  1112
wenzelm@18225
  1113
local
wenzelm@18225
  1114
wenzelm@18225
  1115
fun res th i rule =
wenzelm@18225
  1116
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
  1117
wenzelm@18225
  1118
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
  1119
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
  1120
wenzelm@18225
  1121
in
wenzelm@18225
  1122
wenzelm@18225
  1123
val multi_resolve = multi_res 1;
wenzelm@18225
  1124
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
  1125
wenzelm@18225
  1126
end;
wenzelm@18225
  1127
wenzelm@18225
  1128
wenzelm@18225
  1129
wenzelm@11975
  1130
(** meta-level conjunction **)
wenzelm@11975
  1131
wenzelm@11975
  1132
local
wenzelm@11975
  1133
  val A = read_prop "PROP A";
wenzelm@11975
  1134
  val B = read_prop "PROP B";
wenzelm@11975
  1135
  val C = read_prop "PROP C";
wenzelm@11975
  1136
  val ABC = read_prop "PROP A ==> PROP B ==> PROP C";
wenzelm@19124
  1137
  val A_B = read_prop "PROP ProtoPure.conjunction(A, B)"
wenzelm@11975
  1138
wenzelm@19124
  1139
  val conjunction_def = #1 (freeze_thaw ProtoPure.conjunction_def);
wenzelm@11975
  1140
wenzelm@19124
  1141
  fun conjunctionD which =
wenzelm@19124
  1142
    implies_intr_list [A, B] (Thm.assume (which (A, B))) COMP
wenzelm@19124
  1143
    forall_elim_vars 0 (Thm.equal_elim conjunction_def (Thm.assume A_B));
wenzelm@11975
  1144
in
wenzelm@11975
  1145
wenzelm@19124
  1146
val conjunctionD1 = store_standard_thm "conjunctionD1" (conjunctionD #1);
wenzelm@19124
  1147
val conjunctionD2 = store_standard_thm "conjunctionD2" (conjunctionD #2);
wenzelm@19124
  1148
wenzelm@19124
  1149
val conjunctionI = store_standard_thm "conjunctionI"
wenzelm@19124
  1150
  (implies_intr_list [A, B]
wenzelm@19124
  1151
    (Thm.equal_elim
wenzelm@19124
  1152
      (Thm.symmetric conjunction_def)
wenzelm@19124
  1153
      (Thm.forall_intr C (Thm.implies_intr ABC
wenzelm@19124
  1154
        (implies_elim_list (Thm.assume ABC) [Thm.assume A, Thm.assume B])))));
wenzelm@19124
  1155
wenzelm@19124
  1156
fun conj_intr tha thb = thb COMP (tha COMP incr_indexes2 tha thb conjunctionI);
wenzelm@12756
  1157
wenzelm@12756
  1158
fun conj_intr_list [] = asm_rl
wenzelm@12756
  1159
  | conj_intr_list ths = foldr1 (uncurry conj_intr) ths;
wenzelm@11975
  1160
wenzelm@11975
  1161
fun conj_elim th =
wenzelm@19124
  1162
 (th COMP incr_indexes th conjunctionD1,
wenzelm@19124
  1163
  th COMP incr_indexes th conjunctionD2);
wenzelm@11975
  1164
wenzelm@18498
  1165
(*((A && B) && C) && D && E -- flat*)
wenzelm@11975
  1166
fun conj_elim_list th =
wenzelm@11975
  1167
  let val (th1, th2) = conj_elim th
wenzelm@11975
  1168
  in conj_elim_list th1 @ conj_elim_list th2 end handle THM _ => [th];
wenzelm@11975
  1169
wenzelm@18498
  1170
(*(A1 && B1 && C1) && (A2 && B2 && C2 && D2) && A3 && B3 -- improper*)
wenzelm@18498
  1171
fun conj_elim_precise spans =
wenzelm@18498
  1172
  let
wenzelm@18498
  1173
    fun elim 0 _ = []
wenzelm@18498
  1174
      | elim 1 th = [th]
wenzelm@18498
  1175
      | elim n th =
wenzelm@18498
  1176
          let val (th1, th2) = conj_elim th
wenzelm@18498
  1177
          in th1 :: elim (n - 1) th2 end;
wenzelm@18498
  1178
    fun elims (0 :: ns) ths = [] :: elims ns ths
wenzelm@18498
  1179
      | elims (n :: ns) (th :: ths) = elim n th :: elims ns ths
wenzelm@18498
  1180
      | elims _ _ = [];
wenzelm@18498
  1181
  in elims spans o elim (length (filter_out (equal 0) spans)) end;
wenzelm@12135
  1182
wenzelm@18206
  1183
end;
wenzelm@18179
  1184
wenzelm@19183
  1185
(*
wenzelm@19183
  1186
  A1 ==> ... ==> An ==> B
wenzelm@19183
  1187
  -----------------------
wenzelm@19183
  1188
   A1 && ... && An ==> B
wenzelm@19183
  1189
*)
wenzelm@19183
  1190
fun conj_uncurry n th =
wenzelm@18206
  1191
  let
wenzelm@18206
  1192
    val {thy, maxidx, ...} = Thm.rep_thm th;
wenzelm@19183
  1193
    val m = if n = ~1 then Thm.nprems_of th else Int.min (n, Thm.nprems_of th);
wenzelm@18206
  1194
  in
wenzelm@19183
  1195
    if m < 2 then th
wenzelm@18206
  1196
    else
wenzelm@18206
  1197
      let
wenzelm@18206
  1198
        val cert = Thm.cterm_of thy;
wenzelm@19183
  1199
        val As = map (fn i => Free ("A" ^ string_of_int i, propT)) (1 upto m);
wenzelm@18206
  1200
        val B = Free ("B", propT);
wenzelm@18206
  1201
        val C = cert (Logic.mk_conjunction_list As);
wenzelm@18206
  1202
        val D = cert (Logic.list_implies (As, B));
wenzelm@18206
  1203
        val rule =
wenzelm@18206
  1204
          implies_elim_list (Thm.assume D) (conj_elim_list (Thm.assume C))
wenzelm@18206
  1205
          |> implies_intr_list [D, C]
wenzelm@18206
  1206
          |> forall_intr_frees
wenzelm@18206
  1207
          |> forall_elim_vars (maxidx + 1)
wenzelm@18206
  1208
      in Thm.adjust_maxidx_thm (th COMP rule) end
wenzelm@18206
  1209
  end;
wenzelm@252
  1210
wenzelm@11975
  1211
end;
wenzelm@5903
  1212
wenzelm@5903
  1213
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1214
open BasicDrule;