src/Pure/drule.ML
author wenzelm
Fri May 26 22:20:05 2006 +0200 (2006-05-26 ago)
changeset 19730 8abecd308e60
parent 19523 0531e5abf680
child 19753 b345d4e70ca9
permissions -rw-r--r--
forall_intr_list: do not ignore errors;
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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 equal_elim_rule2: 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 dest_binop: cterm -> cterm * cterm
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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 store_thm: bstring -> thm -> thm
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  val store_standard_thm: bstring -> thm -> thm
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  val store_thm_open: bstring -> thm -> thm
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  val store_standard_thm_open: bstring -> thm -> thm
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  val compose_single: thm * int * thm -> thm
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  val add_rule: thm -> thm list -> thm list
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  val del_rule: thm -> thm list -> thm list
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  val merge_rules: thm list * thm list -> thm list
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  val imp_cong_rule: thm -> thm -> thm
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  val beta_eta_conversion: cterm -> thm
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  val eta_long_conversion: cterm -> thm
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  val 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 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 sort_triv: theory -> typ * sort -> thm list
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  val unconstrainTs: thm -> thm
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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 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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(* 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 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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    #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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(** 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);
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        val vars = map dest_Var (term_vars big);
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        val frees = map dest_Free (term_frees big);
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        val tvars = term_tvars big;
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        val tfrees = term_tfrees big;
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        fun typ(a,i) = if i<0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a,i);
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        fun sort(a,i) = if i<0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a,i);
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    in (typ,sort) end;
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fun add_used thm used =
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   302
  let val {prop, hyps, tpairs, ...} = Thm.rep_thm thm in
wenzelm@15669
   303
    add_term_tvarnames (prop, used)
wenzelm@15669
   304
    |> fold (curry add_term_tvarnames) hyps
wenzelm@15669
   305
    |> fold (curry add_term_tvarnames) (Thm.terms_of_tpairs tpairs)
wenzelm@15669
   306
  end;
wenzelm@15669
   307
wenzelm@7636
   308
wenzelm@9455
   309
clasohm@0
   310
(** Standardization of rules **)
clasohm@0
   311
wenzelm@18025
   312
(*vars in left-to-right order*)
wenzelm@18025
   313
fun tvars_of_terms ts = rev (fold Term.add_tvars ts []);
wenzelm@18025
   314
fun vars_of_terms ts = rev (fold Term.add_vars ts []);
wenzelm@18025
   315
fun tvars_of thm = tvars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   316
fun vars_of thm = vars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   317
wenzelm@18129
   318
fun fold_terms f th =
wenzelm@18129
   319
  let val {hyps, tpairs, prop, ...} = Thm.rep_thm th
wenzelm@18129
   320
  in f prop #> fold (fn (t, u) => f t #> f u) tpairs #> fold f hyps end;
wenzelm@18129
   321
wenzelm@18129
   322
fun tfrees_of th = rev (fold_terms Term.add_tfrees th []);
wenzelm@18129
   323
fun frees_of th = rev (fold_terms Term.add_frees th []);
wenzelm@18129
   324
wenzelm@19523
   325
wenzelm@19523
   326
(* type classes and sorts *)
wenzelm@19523
   327
wenzelm@19523
   328
fun sort_triv thy (T, S) =
wenzelm@19523
   329
  let
wenzelm@19523
   330
    val certT = Thm.ctyp_of thy;
wenzelm@19523
   331
    val cT = certT T;
wenzelm@19523
   332
    fun class_triv c =
wenzelm@19523
   333
      Thm.class_triv thy c
wenzelm@19523
   334
      |> Thm.instantiate ([(certT (TVar (("'a", 0), [c])), cT)], []);
wenzelm@19523
   335
  in map class_triv S end;
wenzelm@19523
   336
wenzelm@19504
   337
fun unconstrainTs th =
wenzelm@19504
   338
  fold_rev (Thm.unconstrainT o Thm.ctyp_of (Thm.theory_of_thm th) o TVar) (tvars_of th) th;
wenzelm@19504
   339
wenzelm@7636
   340
fun strip_shyps_warning thm =
wenzelm@7636
   341
  let
wenzelm@16425
   342
    val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.theory_of_thm thm);
wenzelm@7636
   343
    val thm' = Thm.strip_shyps thm;
wenzelm@7636
   344
    val xshyps = Thm.extra_shyps thm';
wenzelm@7636
   345
  in
wenzelm@7636
   346
    if null xshyps then ()
wenzelm@7636
   347
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   348
    thm'
wenzelm@7636
   349
  end;
wenzelm@7636
   350
wenzelm@19730
   351
(*Generalization over a list of variables*)
wenzelm@19730
   352
val forall_intr_list = fold_rev forall_intr;
clasohm@0
   353
clasohm@0
   354
(*Generalization over all suitable Free variables*)
clasohm@0
   355
fun forall_intr_frees th =
wenzelm@19730
   356
    let
wenzelm@19730
   357
      val {prop, hyps, tpairs, thy,...} = rep_thm th;
wenzelm@19730
   358
      val fixed = fold Term.add_frees (Thm.terms_of_tpairs tpairs @ hyps) [];
wenzelm@19730
   359
      val frees = Term.fold_aterms (fn Free v =>
wenzelm@19730
   360
        if member (op =) fixed v then I else insert (op =) v | _ => I) prop [];
wenzelm@19730
   361
    in fold (forall_intr o cterm_of thy o Free) frees th end;
clasohm@0
   362
wenzelm@18535
   363
(*Generalization over Vars -- canonical order*)
wenzelm@18535
   364
fun forall_intr_vars th =
wenzelm@18535
   365
  let val cert = Thm.cterm_of (Thm.theory_of_thm th)
wenzelm@18535
   366
  in forall_intr_list (map (cert o Var) (vars_of th)) th end;
wenzelm@18535
   367
wenzelm@7898
   368
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   369
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   370
wenzelm@18025
   371
fun outer_params t =
wenzelm@18025
   372
  let
wenzelm@18025
   373
    val vs = Term.strip_all_vars t;
wenzelm@18375
   374
    val xs = Term.variantlist (map (perhaps (try Syntax.dest_skolem) o #1) vs, []);
wenzelm@18025
   375
  in xs ~~ map #2 vs end;
wenzelm@18025
   376
wenzelm@18025
   377
(*generalize outermost parameters*)
wenzelm@18025
   378
fun gen_all th =
wenzelm@12719
   379
  let
wenzelm@18025
   380
    val {thy, prop, maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   381
    val cert = Thm.cterm_of thy;
wenzelm@18025
   382
    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
wenzelm@18025
   383
  in fold elim (outer_params prop) th end;
wenzelm@18025
   384
wenzelm@18025
   385
(*lift vars wrt. outermost goal parameters
wenzelm@18118
   386
  -- reverses the effect of gen_all modulo higher-order unification*)
wenzelm@18025
   387
fun lift_all goal th =
wenzelm@18025
   388
  let
wenzelm@18025
   389
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   390
    val cert = Thm.cterm_of thy;
wenzelm@19421
   391
    val maxidx = Thm.maxidx_of th;
wenzelm@18025
   392
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   393
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   394
    val Ts = map Term.fastype_of ps;
wenzelm@18025
   395
    val inst = vars_of th |> map (fn (xi, T) =>
wenzelm@18025
   396
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   397
  in
wenzelm@18025
   398
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   399
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   400
  end;
wenzelm@18025
   401
wenzelm@9554
   402
wenzelm@16949
   403
(*specialization over a list of cterms*)
wenzelm@16949
   404
val forall_elim_list = fold forall_elim;
clasohm@0
   405
wenzelm@16949
   406
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   407
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   408
wenzelm@16949
   409
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
skalberg@15570
   410
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   411
clasohm@0
   412
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   413
fun zero_var_indexes th =
wenzelm@16949
   414
  let
wenzelm@16949
   415
    val thy = Thm.theory_of_thm th;
wenzelm@16949
   416
    val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@16949
   417
    val (instT, inst) = Term.zero_var_indexes_inst (Thm.full_prop_of th);
wenzelm@16949
   418
    val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@16949
   419
    val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@16949
   420
  in Thm.adjust_maxidx_thm (Thm.instantiate (cinstT, cinst) th) end;
clasohm@0
   421
clasohm@0
   422
paulson@14394
   423
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   424
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   425
wenzelm@16595
   426
(*Discharge all hypotheses.*)
wenzelm@16595
   427
fun implies_intr_hyps th =
wenzelm@16595
   428
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   429
paulson@14394
   430
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   431
  This step can lose information.*)
paulson@14387
   432
fun flexflex_unique th =
berghofe@17713
   433
  if null (tpairs_of th) then th else
paulson@14387
   434
    case Seq.chop (2, flexflex_rule th) of
paulson@14387
   435
      ([th],_) => th
paulson@14387
   436
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   437
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   438
wenzelm@10515
   439
fun close_derivation thm =
wenzelm@10515
   440
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   441
  else thm;
wenzelm@10515
   442
wenzelm@16949
   443
val standard' =
wenzelm@16949
   444
  implies_intr_hyps
wenzelm@16949
   445
  #> forall_intr_frees
wenzelm@19421
   446
  #> `Thm.maxidx_of
wenzelm@16949
   447
  #-> (fn maxidx =>
wenzelm@16949
   448
    forall_elim_vars (maxidx + 1)
wenzelm@16949
   449
    #> strip_shyps_warning
wenzelm@16949
   450
    #> zero_var_indexes
wenzelm@16949
   451
    #> Thm.varifyT
wenzelm@16949
   452
    #> Thm.compress);
wenzelm@1218
   453
wenzelm@16949
   454
val standard =
wenzelm@16949
   455
  flexflex_unique
wenzelm@16949
   456
  #> standard'
wenzelm@16949
   457
  #> close_derivation;
berghofe@11512
   458
wenzelm@16949
   459
val local_standard =
wenzelm@16949
   460
  strip_shyps
wenzelm@16949
   461
  #> zero_var_indexes
wenzelm@16949
   462
  #> Thm.compress
wenzelm@16949
   463
  #> close_derivation;
wenzelm@12005
   464
clasohm@0
   465
wenzelm@8328
   466
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   467
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   468
  Similar code in type/freeze_thaw*)
paulson@15495
   469
paulson@15495
   470
fun freeze_thaw_robust th =
paulson@15495
   471
 let val fth = freezeT th
wenzelm@16425
   472
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@15495
   473
 in
skalberg@15574
   474
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   475
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   476
     | vars =>
paulson@15495
   477
         let fun newName (Var(ix,_), pairs) =
paulson@15495
   478
                   let val v = gensym (string_of_indexname ix)
paulson@15495
   479
                   in  ((ix,v)::pairs)  end;
skalberg@15574
   480
             val alist = foldr newName [] vars
paulson@15495
   481
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   482
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   483
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   484
             val insts = map mk_inst vars
paulson@15495
   485
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   486
                 th' |> forall_intr_list (map #2 insts)
paulson@15495
   487
                     |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
paulson@15495
   488
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   489
 end;
paulson@15495
   490
paulson@15495
   491
(*Basic version of the function above. No option to rename Vars apart in thaw.
paulson@15495
   492
  The Frees created from Vars have nice names.*)
paulson@4610
   493
fun freeze_thaw th =
paulson@7248
   494
 let val fth = freezeT th
wenzelm@16425
   495
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@7248
   496
 in
skalberg@15574
   497
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   498
       [] => (fth, fn x => x)
paulson@7248
   499
     | vars =>
wenzelm@8328
   500
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   501
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   502
                   in  ((ix,v)::pairs, v::used)  end;
skalberg@15574
   503
             val (alist, _) = foldr newName ([], Library.foldr add_term_names
skalberg@15574
   504
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   505
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   506
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   507
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   508
             val insts = map mk_inst vars
wenzelm@8328
   509
             fun thaw th' =
wenzelm@8328
   510
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   511
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   512
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   513
 end;
paulson@4610
   514
paulson@7248
   515
(*Rotates a rule's premises to the left by k*)
paulson@7248
   516
val rotate_prems = permute_prems 0;
paulson@4610
   517
oheimb@11163
   518
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   519
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   520
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   521
val rearrange_prems = let
oheimb@11163
   522
  fun rearr new []      thm = thm
wenzelm@11815
   523
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   524
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   525
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   526
  in rearr 0 end;
paulson@4610
   527
wenzelm@252
   528
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   529
  Generalizes over Free variables,
clasohm@0
   530
  creates the assumption, and then strips quantifiers.
clasohm@0
   531
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   532
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   533
fun assume_ax thy sP =
wenzelm@16425
   534
  let val prop = Logic.close_form (term_of (read_cterm thy (sP, propT)))
wenzelm@16425
   535
  in forall_elim_vars 0 (Thm.assume (cterm_of thy prop)) end;
clasohm@0
   536
wenzelm@252
   537
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   538
fun tha RSN (i,thb) =
wenzelm@4270
   539
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   540
      ([th],_) => th
clasohm@0
   541
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   542
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   543
clasohm@0
   544
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   545
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   546
clasohm@0
   547
(*For joining lists of rules*)
wenzelm@252
   548
fun thas RLN (i,thbs) =
clasohm@0
   549
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   550
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   551
  in maps resb thbs end;
clasohm@0
   552
clasohm@0
   553
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   554
lcp@11
   555
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   556
  makes proof trees*)
wenzelm@252
   557
fun rls MRS bottom_rl =
lcp@11
   558
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   559
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   560
  in  rs_aux 1 rls  end;
lcp@11
   561
lcp@11
   562
(*As above, but for rule lists*)
wenzelm@252
   563
fun rlss MRL bottom_rls =
lcp@11
   564
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   565
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   566
  in  rs_aux 1 rlss  end;
lcp@11
   567
wenzelm@9288
   568
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   569
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   570
wenzelm@252
   571
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   572
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   573
  ALWAYS deletes premise i *)
wenzelm@252
   574
fun compose(tha,i,thb) =
wenzelm@4270
   575
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   576
wenzelm@6946
   577
fun compose_single (tha,i,thb) =
wenzelm@6946
   578
  (case compose (tha,i,thb) of
wenzelm@6946
   579
    [th] => th
wenzelm@6946
   580
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   581
clasohm@0
   582
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   583
fun tha COMP thb =
clasohm@0
   584
    case compose(tha,1,thb) of
wenzelm@252
   585
        [th] => th
clasohm@0
   586
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   587
wenzelm@13105
   588
wenzelm@4016
   589
(** theorem equality **)
clasohm@0
   590
wenzelm@16425
   591
(*True if the two theorems have the same theory.*)
wenzelm@16425
   592
val eq_thm_thy = eq_thy o pairself Thm.theory_of_thm;
paulson@13650
   593
paulson@13650
   594
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@16720
   595
val eq_thm_prop = op aconv o pairself Thm.full_prop_of;
clasohm@0
   596
clasohm@0
   597
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   598
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   599
wenzelm@9829
   600
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@18922
   601
val del_rule = remove eq_thm_prop;
wenzelm@18922
   602
fun add_rule th = cons th o del_rule th;
wenzelm@18922
   603
val merge_rules = Library.merge eq_thm_prop;
wenzelm@9829
   604
wenzelm@18535
   605
(*weak_eq_thm: ignores variable renaming and (some) type variable renaming*)
wenzelm@13105
   606
val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
lcp@1194
   607
lcp@1194
   608
clasohm@0
   609
(*** Meta-Rewriting Rules ***)
clasohm@0
   610
wenzelm@16425
   611
fun read_prop s = read_cterm ProtoPure.thy (s, propT);
paulson@4610
   612
wenzelm@9455
   613
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   614
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   615
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   616
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   617
clasohm@0
   618
val reflexive_thm =
wenzelm@19421
   619
  let val cx = cert (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   620
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   621
clasohm@0
   622
val symmetric_thm =
wenzelm@14854
   623
  let val xy = read_prop "x == y"
wenzelm@16595
   624
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   625
clasohm@0
   626
val transitive_thm =
wenzelm@14854
   627
  let val xy = read_prop "x == y"
wenzelm@14854
   628
      val yz = read_prop "y == z"
clasohm@0
   629
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   630
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   631
nipkow@4679
   632
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   633
berghofe@11512
   634
fun extensional eq =
berghofe@11512
   635
  let val eq' =
berghofe@11512
   636
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   637
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   638
wenzelm@18820
   639
val equals_cong =
wenzelm@18820
   640
  store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x == y"));
wenzelm@18820
   641
berghofe@10414
   642
val imp_cong =
berghofe@10414
   643
  let
berghofe@10414
   644
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   645
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   646
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   647
    val A = read_prop "PROP A"
berghofe@10414
   648
  in
wenzelm@12135
   649
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   650
      (implies_intr AB (implies_intr A
berghofe@10414
   651
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   652
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   653
      (implies_intr AC (implies_intr A
berghofe@10414
   654
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   655
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   656
  end;
berghofe@10414
   657
berghofe@10414
   658
val swap_prems_eq =
berghofe@10414
   659
  let
berghofe@10414
   660
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   661
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   662
    val A = read_prop "PROP A"
berghofe@10414
   663
    val B = read_prop "PROP B"
berghofe@10414
   664
  in
wenzelm@12135
   665
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   666
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   667
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   668
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   669
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   670
  end;
lcp@229
   671
wenzelm@18468
   672
val imp_cong_rule = combination o combination (reflexive implies);
clasohm@0
   673
skalberg@15001
   674
local
skalberg@15001
   675
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   676
  val rhs_of = snd o dest_eq
skalberg@15001
   677
in
skalberg@15001
   678
fun beta_eta_conversion t =
skalberg@15001
   679
  let val thm = beta_conversion true t
skalberg@15001
   680
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   681
end;
skalberg@15001
   682
berghofe@15925
   683
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   684
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   685
wenzelm@18337
   686
val abs_def =
wenzelm@18337
   687
  let
wenzelm@18337
   688
    fun contract_lhs th =
wenzelm@18337
   689
      Thm.transitive (Thm.symmetric (beta_eta_conversion (fst (dest_equals (cprop_of th))))) th;
wenzelm@18777
   690
    fun abstract cx th = Thm.abstract_rule
wenzelm@18777
   691
        (case Thm.term_of cx of Var ((x, _), _) => x | Free (x, _) => x | _ => "x") cx th
wenzelm@18777
   692
      handle THM _ => raise THM ("Malformed definitional equation", 0, [th]);
wenzelm@18337
   693
  in
wenzelm@18337
   694
    contract_lhs
wenzelm@18337
   695
    #> `(snd o strip_comb o fst o dest_equals o cprop_of)
wenzelm@18337
   696
    #-> fold_rev abstract
wenzelm@18337
   697
    #> contract_lhs
wenzelm@18337
   698
  end;
wenzelm@18337
   699
wenzelm@18468
   700
(*rewrite B in !!x1 ... xn. B*)
wenzelm@18251
   701
fun forall_conv 0 cv ct = cv ct
wenzelm@18251
   702
  | forall_conv n cv ct =
wenzelm@18468
   703
      (case try Thm.dest_comb ct of
wenzelm@18468
   704
        NONE => cv ct
wenzelm@18468
   705
      | SOME (A, B) =>
wenzelm@18468
   706
          (case (term_of A, term_of B) of
wenzelm@18468
   707
            (Const ("all", _), Abs (x, _, _)) =>
wenzelm@18468
   708
              let val (v, B') = Thm.dest_abs (SOME (gensym "all_")) B in
wenzelm@18468
   709
                Thm.combination (Thm.reflexive A)
wenzelm@18468
   710
                  (Thm.abstract_rule x v (forall_conv (n - 1) cv B'))
wenzelm@18468
   711
              end
wenzelm@18468
   712
          | _ => cv ct));
wenzelm@18468
   713
wenzelm@18468
   714
(*rewrite B in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   715
fun concl_conv 0 cv ct = cv ct
wenzelm@18468
   716
  | concl_conv n cv ct =
wenzelm@18468
   717
      (case try dest_implies ct of
wenzelm@18468
   718
        NONE => cv ct
wenzelm@18468
   719
      | SOME (A, B) => imp_cong_rule (reflexive A) (concl_conv (n - 1) cv B));
skalberg@15001
   720
wenzelm@18468
   721
(*rewrite the A's in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   722
fun prems_conv 0 _ = reflexive
wenzelm@18468
   723
  | prems_conv n cv =
wenzelm@18468
   724
      let
wenzelm@18468
   725
        fun conv i ct =
wenzelm@18468
   726
          if i = n + 1 then reflexive ct
wenzelm@18468
   727
          else
wenzelm@18468
   728
            (case try dest_implies ct of
wenzelm@18468
   729
              NONE => reflexive ct
wenzelm@18468
   730
            | SOME (A, B) => imp_cong_rule (cv i A) (conv (i + 1) B));
wenzelm@18468
   731
  in conv 1 end;
wenzelm@18468
   732
wenzelm@18468
   733
fun goals_conv pred cv = prems_conv ~1 (fn i => if pred i then cv else reflexive);
skalberg@15001
   734
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   735
wenzelm@18468
   736
wenzelm@15669
   737
(*** Some useful meta-theorems ***)
clasohm@0
   738
clasohm@0
   739
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   740
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   741
val _ = store_thm "_" asm_rl;
clasohm@0
   742
clasohm@0
   743
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   744
val cut_rl =
wenzelm@12135
   745
  store_standard_thm_open "cut_rl"
wenzelm@9455
   746
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   747
wenzelm@252
   748
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   749
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   750
val revcut_rl =
paulson@4610
   751
  let val V = read_prop "PROP V"
paulson@4610
   752
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   753
  in
wenzelm@12135
   754
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   755
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   756
  end;
clasohm@0
   757
lcp@668
   758
(*for deleting an unwanted assumption*)
lcp@668
   759
val thin_rl =
paulson@4610
   760
  let val V = read_prop "PROP V"
paulson@4610
   761
      and W = read_prop "PROP W";
wenzelm@12135
   762
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   763
clasohm@0
   764
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   765
val triv_forall_equality =
paulson@4610
   766
  let val V  = read_prop "PROP V"
paulson@4610
   767
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@19421
   768
      and x  = cert (Free ("x", Term.aT []));
wenzelm@4016
   769
  in
wenzelm@12135
   770
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   771
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   772
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   773
  end;
clasohm@0
   774
wenzelm@19051
   775
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   776
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   777
*)
wenzelm@19051
   778
val distinct_prems_rl =
wenzelm@19051
   779
  let
wenzelm@19051
   780
    val AAB = read_prop "PROP Phi ==> PROP Phi ==> PROP Psi"
wenzelm@19051
   781
    val A = read_prop "PROP Phi";
wenzelm@19051
   782
  in
wenzelm@19051
   783
    store_standard_thm_open "distinct_prems_rl"
wenzelm@19051
   784
      (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
wenzelm@19051
   785
  end;
wenzelm@19051
   786
nipkow@1756
   787
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   788
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   789
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   790
*)
nipkow@1756
   791
val swap_prems_rl =
paulson@4610
   792
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   793
      val major = assume cmajor;
paulson@4610
   794
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   795
      val minor1 = assume cminor1;
paulson@4610
   796
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   797
      val minor2 = assume cminor2;
wenzelm@12135
   798
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   799
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   800
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   801
  end;
nipkow@1756
   802
nipkow@3653
   803
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   804
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   805
   Introduction rule for == as a meta-theorem.
nipkow@3653
   806
*)
nipkow@3653
   807
val equal_intr_rule =
paulson@4610
   808
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   809
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   810
  in
wenzelm@12135
   811
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   812
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   813
  end;
nipkow@3653
   814
wenzelm@19421
   815
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   816
val equal_elim_rule1 =
wenzelm@13368
   817
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   818
      and P = read_prop "PROP phi"
wenzelm@13368
   819
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   820
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   821
  end;
wenzelm@4285
   822
wenzelm@19421
   823
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   824
val equal_elim_rule2 =
wenzelm@19421
   825
  store_standard_thm_open "equal_elim_rule2" (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   826
wenzelm@12297
   827
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   828
val remdups_rl =
wenzelm@12297
   829
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   830
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   831
wenzelm@12297
   832
wenzelm@9554
   833
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   834
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   835
wenzelm@9554
   836
val norm_hhf_eq =
wenzelm@9554
   837
  let
wenzelm@14854
   838
    val aT = TFree ("'a", []);
wenzelm@9554
   839
    val all = Term.all aT;
wenzelm@9554
   840
    val x = Free ("x", aT);
wenzelm@9554
   841
    val phi = Free ("phi", propT);
wenzelm@9554
   842
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   843
wenzelm@9554
   844
    val cx = cert x;
wenzelm@9554
   845
    val cphi = cert phi;
wenzelm@9554
   846
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   847
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   848
  in
wenzelm@9554
   849
    Thm.equal_intr
wenzelm@9554
   850
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   851
        |> Thm.forall_elim cx
wenzelm@9554
   852
        |> Thm.implies_intr cphi
wenzelm@9554
   853
        |> Thm.forall_intr cx
wenzelm@9554
   854
        |> Thm.implies_intr lhs)
wenzelm@9554
   855
      (Thm.implies_elim
wenzelm@9554
   856
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   857
        |> Thm.forall_intr cx
wenzelm@9554
   858
        |> Thm.implies_intr cphi
wenzelm@9554
   859
        |> Thm.implies_intr rhs)
wenzelm@12135
   860
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   861
  end;
wenzelm@9554
   862
wenzelm@18179
   863
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@18179
   864
wenzelm@12800
   865
fun is_norm_hhf tm =
wenzelm@12800
   866
  let
wenzelm@12800
   867
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   868
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   869
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   870
      | is_norm _ = true;
wenzelm@18929
   871
  in is_norm (Envir.beta_eta_contract tm) end;
wenzelm@12800
   872
wenzelm@16425
   873
fun norm_hhf thy t =
wenzelm@12800
   874
  if is_norm_hhf t then t
wenzelm@18179
   875
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   876
wenzelm@12800
   877
wenzelm@9554
   878
wenzelm@16425
   879
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   880
paulson@8129
   881
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   882
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   883
wenzelm@16425
   884
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   885
    let val ts = types_sorts th;
wenzelm@15669
   886
        val used = add_used th [];
wenzelm@16425
   887
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   888
wenzelm@16425
   889
fun read_instantiate_sg thy sinsts th =
wenzelm@16425
   890
  read_instantiate_sg' thy (map (apfst Syntax.indexname) sinsts) th;
paulson@8129
   891
paulson@8129
   892
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   893
fun read_instantiate sinsts th =
wenzelm@16425
   894
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   895
berghofe@15797
   896
fun read_instantiate' sinsts th =
wenzelm@16425
   897
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   898
paulson@8129
   899
paulson@8129
   900
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   901
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   902
local
wenzelm@16425
   903
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@16425
   904
    let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
wenzelm@16425
   905
        and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   906
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   907
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   908
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@10403
   909
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
wenzelm@16425
   910
    in  (thy', tye', maxi')  end;
paulson@8129
   911
in
paulson@8129
   912
fun cterm_instantiate ctpairs0 th =
wenzelm@16425
   913
  let val (thy,tye,_) = foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   914
      fun instT(ct,cu) =
wenzelm@16425
   915
        let val inst = cterm_of thy o Envir.subst_TVars tye o term_of
paulson@14340
   916
        in (inst ct, inst cu) end
wenzelm@16425
   917
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy T)
berghofe@8406
   918
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   919
  handle TERM _ =>
wenzelm@16425
   920
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   921
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   922
end;
paulson@8129
   923
paulson@8129
   924
paulson@8129
   925
(** Derived rules mainly for METAHYPS **)
paulson@8129
   926
paulson@8129
   927
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   928
fun equal_abs_elim ca eqth =
wenzelm@16425
   929
  let val {thy=thya, t=a, ...} = rep_cterm ca
paulson@8129
   930
      and combth = combination eqth (reflexive ca)
wenzelm@16425
   931
      val {thy,prop,...} = rep_thm eqth
paulson@8129
   932
      val (abst,absu) = Logic.dest_equals prop
wenzelm@19421
   933
      val cert = cterm_of (Theory.merge (thy,thya))
wenzelm@19421
   934
  in  transitive (symmetric (beta_conversion false (cert (abst$a))))
wenzelm@19421
   935
           (transitive combth (beta_conversion false (cert (absu$a))))
paulson@8129
   936
  end
paulson@8129
   937
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   938
paulson@8129
   939
(*Calling equal_abs_elim with multiple terms*)
skalberg@15574
   940
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) th (rev cts);
paulson@8129
   941
paulson@8129
   942
wenzelm@18025
   943
(** protected propositions **)
wenzelm@4789
   944
wenzelm@4789
   945
local
wenzelm@18025
   946
  val A = cert (Free ("A", propT));
wenzelm@18025
   947
  val prop_def = #1 (freeze_thaw ProtoPure.prop_def);
wenzelm@4789
   948
in
wenzelm@18025
   949
  val protect = Thm.capply (cert Logic.protectC);
wenzelm@18799
   950
  val protectI = store_thm "protectI" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@18025
   951
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@18799
   952
  val protectD = store_thm "protectD" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@18025
   953
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@18179
   954
  val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@4789
   955
end;
wenzelm@4789
   956
wenzelm@18025
   957
fun implies_intr_protected asms th =
wenzelm@18118
   958
  let val asms' = map protect asms in
wenzelm@18118
   959
    implies_elim_list
wenzelm@18118
   960
      (implies_intr_list asms th)
wenzelm@18118
   961
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@18118
   962
    |> implies_intr_list asms'
wenzelm@18118
   963
  end;
wenzelm@11815
   964
wenzelm@4789
   965
wenzelm@5688
   966
(** variations on instantiate **)
wenzelm@4285
   967
paulson@8550
   968
(*shorthand for instantiating just one variable in the current theory*)
wenzelm@16425
   969
fun inst x t = read_instantiate_sg (the_context()) [(x,t)];
paulson@8550
   970
paulson@8550
   971
wenzelm@4285
   972
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   973
wenzelm@4285
   974
fun instantiate' cTs cts thm =
wenzelm@4285
   975
  let
wenzelm@4285
   976
    fun err msg =
wenzelm@4285
   977
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   978
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   979
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   980
wenzelm@4285
   981
    fun inst_of (v, ct) =
wenzelm@16425
   982
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   983
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   984
berghofe@15797
   985
    fun tyinst_of (v, cT) =
wenzelm@16425
   986
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   987
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   988
wenzelm@4285
   989
    fun zip_vars _ [] = []
skalberg@15531
   990
      | zip_vars (_ :: vs) (NONE :: opt_ts) = zip_vars vs opt_ts
skalberg@15531
   991
      | zip_vars (v :: vs) (SOME t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
   992
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
   993
wenzelm@4285
   994
    (*instantiate types first!*)
wenzelm@4285
   995
    val thm' =
wenzelm@4285
   996
      if forall is_none cTs then thm
berghofe@15797
   997
      else Thm.instantiate (map tyinst_of (zip_vars (tvars_of thm) cTs), []) thm;
wenzelm@4285
   998
    in
wenzelm@4285
   999
      if forall is_none cts then thm'
wenzelm@4285
  1000
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
  1001
    end;
wenzelm@4285
  1002
wenzelm@4285
  1003
berghofe@14081
  1004
berghofe@14081
  1005
(** renaming of bound variables **)
berghofe@14081
  1006
berghofe@14081
  1007
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
  1008
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
  1009
berghofe@14081
  1010
fun rename_bvars [] thm = thm
berghofe@14081
  1011
  | rename_bvars vs thm =
berghofe@14081
  1012
    let
wenzelm@16425
  1013
      val {thy, prop, ...} = rep_thm thm;
haftmann@17325
  1014
      fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
berghofe@14081
  1015
        | ren (t $ u) = ren t $ ren u
berghofe@14081
  1016
        | ren t = t;
wenzelm@16425
  1017
    in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
berghofe@14081
  1018
berghofe@14081
  1019
berghofe@14081
  1020
(* renaming in left-to-right order *)
berghofe@14081
  1021
berghofe@14081
  1022
fun rename_bvars' xs thm =
berghofe@14081
  1023
  let
wenzelm@16425
  1024
    val {thy, prop, ...} = rep_thm thm;
berghofe@14081
  1025
    fun rename [] t = ([], t)
berghofe@14081
  1026
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
  1027
          let val (xs', t') = rename xs t
wenzelm@18929
  1028
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
  1029
      | rename xs (t $ u) =
berghofe@14081
  1030
          let
berghofe@14081
  1031
            val (xs', t') = rename xs t;
berghofe@14081
  1032
            val (xs'', u') = rename xs' u
berghofe@14081
  1033
          in (xs'', t' $ u') end
berghofe@14081
  1034
      | rename xs t = (xs, t);
berghofe@14081
  1035
  in case rename xs prop of
wenzelm@16425
  1036
      ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
berghofe@14081
  1037
    | _ => error "More names than abstractions in theorem"
berghofe@14081
  1038
  end;
berghofe@14081
  1039
berghofe@14081
  1040
berghofe@14081
  1041
wenzelm@5688
  1042
(* unvarify(T) *)
wenzelm@5688
  1043
wenzelm@5688
  1044
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
  1045
wenzelm@5688
  1046
fun unvarifyT thm =
wenzelm@5688
  1047
  let
wenzelm@16425
  1048
    val cT = Thm.ctyp_of (Thm.theory_of_thm thm);
skalberg@15531
  1049
    val tfrees = map (fn ((x, _), S) => SOME (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
  1050
  in instantiate' tfrees [] thm end;
wenzelm@5688
  1051
wenzelm@5688
  1052
fun unvarify raw_thm =
wenzelm@5688
  1053
  let
wenzelm@5688
  1054
    val thm = unvarifyT raw_thm;
wenzelm@16425
  1055
    val ct = Thm.cterm_of (Thm.theory_of_thm thm);
skalberg@15531
  1056
    val frees = map (fn ((x, _), T) => SOME (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
  1057
  in instantiate' [] frees thm end;
wenzelm@5688
  1058
wenzelm@5688
  1059
wenzelm@8605
  1060
(* tvars_intr_list *)
wenzelm@8605
  1061
wenzelm@8605
  1062
fun tvars_intr_list tfrees thm =
wenzelm@18129
  1063
  apfst (map (fn ((s, S), ixn) => (s, (ixn, S)))) (Thm.varifyT'
berghofe@15797
  1064
    (gen_rems (op = o apfst fst) (tfrees_of thm, tfrees)) thm);
wenzelm@8605
  1065
wenzelm@8605
  1066
wenzelm@6435
  1067
(* increment var indexes *)
wenzelm@6435
  1068
wenzelm@19421
  1069
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@18025
  1070
wenzelm@19124
  1071
fun incr_indexes2 th1 th2 =
wenzelm@19421
  1072
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@6435
  1073
wenzelm@6435
  1074
wenzelm@8328
  1075
(* freeze_all *)
wenzelm@8328
  1076
wenzelm@8328
  1077
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
  1078
wenzelm@8328
  1079
fun freeze_all_TVars thm =
wenzelm@8328
  1080
  (case tvars_of thm of
wenzelm@8328
  1081
    [] => thm
wenzelm@8328
  1082
  | tvars =>
wenzelm@16425
  1083
      let val cert = Thm.ctyp_of (Thm.theory_of_thm thm)
skalberg@15531
  1084
      in instantiate' (map (fn ((x, _), S) => SOME (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
  1085
wenzelm@8328
  1086
fun freeze_all_Vars thm =
wenzelm@8328
  1087
  (case vars_of thm of
wenzelm@8328
  1088
    [] => thm
wenzelm@8328
  1089
  | vars =>
wenzelm@16425
  1090
      let val cert = Thm.cterm_of (Thm.theory_of_thm thm)
skalberg@15531
  1091
      in instantiate' [] (map (fn ((x, _), T) => SOME (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
  1092
wenzelm@8328
  1093
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
  1094
wenzelm@8328
  1095
wenzelm@11975
  1096
wenzelm@18225
  1097
(** multi_resolve **)
wenzelm@18225
  1098
wenzelm@18225
  1099
local
wenzelm@18225
  1100
wenzelm@18225
  1101
fun res th i rule =
wenzelm@18225
  1102
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
  1103
wenzelm@18225
  1104
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
  1105
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
  1106
wenzelm@18225
  1107
in
wenzelm@18225
  1108
wenzelm@18225
  1109
val multi_resolve = multi_res 1;
wenzelm@18225
  1110
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
  1111
wenzelm@18225
  1112
end;
wenzelm@18225
  1113
wenzelm@11975
  1114
end;
wenzelm@5903
  1115
wenzelm@5903
  1116
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1117
open BasicDrule;