src/Pure/drule.ML
author wenzelm
Tue Jul 11 12:17:02 2006 +0200 (2006-07-11)
changeset 20077 4fc9a4fef219
parent 19999 9592df0c3176
child 20227 435601e8e53d
permissions -rw-r--r--
replaced Term.variant(list) by Name.variant(_list);
Name.clean;
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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 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 equiv_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 generalize: string list * string list -> thm -> thm
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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 unvarify: thm -> thm
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  val protect: cterm -> cterm
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  val protectI: thm
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  val protectD: thm
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  val protect_cong: thm
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  val implies_intr_protected: cterm list -> thm -> thm
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  val termI: thm
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  val mk_term: cterm -> thm
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  val dest_term: thm -> cterm
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  val 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 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 =
wenzelm@15669
   303
  let val {prop, hyps, tpairs, ...} = Thm.rep_thm thm in
wenzelm@15669
   304
    add_term_tvarnames (prop, used)
wenzelm@15669
   305
    |> fold (curry add_term_tvarnames) hyps
wenzelm@15669
   306
    |> fold (curry add_term_tvarnames) (Thm.terms_of_tpairs tpairs)
wenzelm@15669
   307
  end;
wenzelm@15669
   308
wenzelm@7636
   309
wenzelm@9455
   310
clasohm@0
   311
(** Standardization of rules **)
clasohm@0
   312
wenzelm@18025
   313
(*vars in left-to-right order*)
wenzelm@18025
   314
fun tvars_of_terms ts = rev (fold Term.add_tvars ts []);
wenzelm@18025
   315
fun vars_of_terms ts = rev (fold Term.add_vars ts []);
wenzelm@18025
   316
fun tvars_of thm = tvars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   317
fun vars_of thm = vars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   318
wenzelm@18129
   319
fun fold_terms f th =
wenzelm@18129
   320
  let val {hyps, tpairs, prop, ...} = Thm.rep_thm th
wenzelm@18129
   321
  in f prop #> fold (fn (t, u) => f t #> f u) tpairs #> fold f hyps end;
wenzelm@18129
   322
wenzelm@18129
   323
fun tfrees_of th = rev (fold_terms Term.add_tfrees th []);
wenzelm@18129
   324
fun frees_of th = rev (fold_terms Term.add_frees th []);
wenzelm@18129
   325
wenzelm@19523
   326
wenzelm@19523
   327
(* type classes and sorts *)
wenzelm@19523
   328
wenzelm@19523
   329
fun sort_triv thy (T, S) =
wenzelm@19523
   330
  let
wenzelm@19523
   331
    val certT = Thm.ctyp_of thy;
wenzelm@19523
   332
    val cT = certT T;
wenzelm@19523
   333
    fun class_triv c =
wenzelm@19523
   334
      Thm.class_triv thy c
wenzelm@19523
   335
      |> Thm.instantiate ([(certT (TVar (("'a", 0), [c])), cT)], []);
wenzelm@19523
   336
  in map class_triv S end;
wenzelm@19523
   337
wenzelm@19504
   338
fun unconstrainTs th =
wenzelm@19504
   339
  fold_rev (Thm.unconstrainT o Thm.ctyp_of (Thm.theory_of_thm th) o TVar) (tvars_of th) th;
wenzelm@19504
   340
wenzelm@7636
   341
fun strip_shyps_warning thm =
wenzelm@7636
   342
  let
wenzelm@16425
   343
    val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.theory_of_thm thm);
wenzelm@7636
   344
    val thm' = Thm.strip_shyps thm;
wenzelm@7636
   345
    val xshyps = Thm.extra_shyps thm';
wenzelm@7636
   346
  in
wenzelm@7636
   347
    if null xshyps then ()
wenzelm@7636
   348
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   349
    thm'
wenzelm@7636
   350
  end;
wenzelm@7636
   351
wenzelm@19730
   352
(*Generalization over a list of variables*)
wenzelm@19730
   353
val forall_intr_list = fold_rev forall_intr;
clasohm@0
   354
clasohm@0
   355
(*Generalization over all suitable Free variables*)
clasohm@0
   356
fun forall_intr_frees th =
wenzelm@19730
   357
    let
wenzelm@19730
   358
      val {prop, hyps, tpairs, thy,...} = rep_thm th;
wenzelm@19730
   359
      val fixed = fold Term.add_frees (Thm.terms_of_tpairs tpairs @ hyps) [];
wenzelm@19730
   360
      val frees = Term.fold_aterms (fn Free v =>
wenzelm@19730
   361
        if member (op =) fixed v then I else insert (op =) v | _ => I) prop [];
wenzelm@19730
   362
    in fold (forall_intr o cterm_of thy o Free) frees th end;
clasohm@0
   363
wenzelm@18535
   364
(*Generalization over Vars -- canonical order*)
wenzelm@18535
   365
fun forall_intr_vars th =
wenzelm@18535
   366
  let val cert = Thm.cterm_of (Thm.theory_of_thm th)
wenzelm@18535
   367
  in forall_intr_list (map (cert o Var) (vars_of th)) th end;
wenzelm@18535
   368
wenzelm@7898
   369
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   370
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   371
wenzelm@18025
   372
fun outer_params t =
wenzelm@20077
   373
  let val vs = Term.strip_all_vars t
wenzelm@20077
   374
  in Name.variant_list [] (map (Name.clean o #1) vs) ~~ map #2 vs end;
wenzelm@18025
   375
wenzelm@18025
   376
(*generalize outermost parameters*)
wenzelm@18025
   377
fun gen_all th =
wenzelm@12719
   378
  let
wenzelm@18025
   379
    val {thy, prop, maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   380
    val cert = Thm.cterm_of thy;
wenzelm@18025
   381
    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
wenzelm@18025
   382
  in fold elim (outer_params prop) th end;
wenzelm@18025
   383
wenzelm@18025
   384
(*lift vars wrt. outermost goal parameters
wenzelm@18118
   385
  -- reverses the effect of gen_all modulo higher-order unification*)
wenzelm@18025
   386
fun lift_all goal th =
wenzelm@18025
   387
  let
wenzelm@18025
   388
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   389
    val cert = Thm.cterm_of thy;
wenzelm@19421
   390
    val maxidx = Thm.maxidx_of th;
wenzelm@18025
   391
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   392
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   393
    val Ts = map Term.fastype_of ps;
wenzelm@18025
   394
    val inst = vars_of th |> map (fn (xi, T) =>
wenzelm@18025
   395
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   396
  in
wenzelm@18025
   397
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   398
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   399
  end;
wenzelm@18025
   400
wenzelm@19999
   401
(*direct generalization*)
wenzelm@19999
   402
fun generalize names th = Thm.generalize names (Thm.maxidx_of th + 1) th;
wenzelm@9554
   403
wenzelm@16949
   404
(*specialization over a list of cterms*)
wenzelm@16949
   405
val forall_elim_list = fold forall_elim;
clasohm@0
   406
wenzelm@16949
   407
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   408
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   409
wenzelm@16949
   410
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
skalberg@15570
   411
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   412
clasohm@0
   413
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   414
fun zero_var_indexes th =
wenzelm@16949
   415
  let
wenzelm@16949
   416
    val thy = Thm.theory_of_thm th;
wenzelm@16949
   417
    val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@16949
   418
    val (instT, inst) = Term.zero_var_indexes_inst (Thm.full_prop_of th);
wenzelm@16949
   419
    val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@16949
   420
    val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@16949
   421
  in Thm.adjust_maxidx_thm (Thm.instantiate (cinstT, cinst) th) end;
clasohm@0
   422
clasohm@0
   423
paulson@14394
   424
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   425
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   426
wenzelm@16595
   427
(*Discharge all hypotheses.*)
wenzelm@16595
   428
fun implies_intr_hyps th =
wenzelm@16595
   429
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   430
paulson@14394
   431
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   432
  This step can lose information.*)
paulson@14387
   433
fun flexflex_unique th =
berghofe@17713
   434
  if null (tpairs_of th) then th else
wenzelm@19861
   435
    case Seq.chop 2 (flexflex_rule th) of
paulson@14387
   436
      ([th],_) => th
paulson@14387
   437
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   438
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   439
wenzelm@10515
   440
fun close_derivation thm =
wenzelm@10515
   441
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   442
  else thm;
wenzelm@10515
   443
wenzelm@16949
   444
val standard' =
wenzelm@16949
   445
  implies_intr_hyps
wenzelm@16949
   446
  #> forall_intr_frees
wenzelm@19421
   447
  #> `Thm.maxidx_of
wenzelm@16949
   448
  #-> (fn maxidx =>
wenzelm@16949
   449
    forall_elim_vars (maxidx + 1)
wenzelm@16949
   450
    #> strip_shyps_warning
wenzelm@16949
   451
    #> zero_var_indexes
wenzelm@16949
   452
    #> Thm.varifyT
wenzelm@16949
   453
    #> Thm.compress);
wenzelm@1218
   454
wenzelm@16949
   455
val standard =
wenzelm@16949
   456
  flexflex_unique
wenzelm@16949
   457
  #> standard'
wenzelm@16949
   458
  #> close_derivation;
berghofe@11512
   459
wenzelm@16949
   460
val local_standard =
wenzelm@16949
   461
  strip_shyps
wenzelm@16949
   462
  #> zero_var_indexes
wenzelm@16949
   463
  #> Thm.compress
wenzelm@16949
   464
  #> close_derivation;
wenzelm@12005
   465
clasohm@0
   466
wenzelm@8328
   467
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   468
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   469
  Similar code in type/freeze_thaw*)
paulson@15495
   470
paulson@15495
   471
fun freeze_thaw_robust th =
wenzelm@19878
   472
 let val fth = Thm.freezeT th
wenzelm@16425
   473
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@15495
   474
 in
skalberg@15574
   475
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   476
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   477
     | vars =>
paulson@19753
   478
         let fun newName (Var(ix,_)) = (ix, gensym (string_of_indexname ix))
paulson@19753
   479
             val alist = map newName vars
paulson@15495
   480
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   481
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   482
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   483
             val insts = map mk_inst vars
paulson@15495
   484
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   485
                 th' |> forall_intr_list (map #2 insts)
paulson@15495
   486
                     |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
paulson@15495
   487
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   488
 end;
paulson@15495
   489
paulson@15495
   490
(*Basic version of the function above. No option to rename Vars apart in thaw.
wenzelm@19999
   491
  The Frees created from Vars have nice names. FIXME: does not check for
paulson@19753
   492
  clashes with variables in the assumptions, so delete and use freeze_thaw_robust instead?*)
paulson@4610
   493
fun freeze_thaw th =
wenzelm@19878
   494
 let val fth = Thm.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@20077
   501
                   let val v = Name.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
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   529
fun tha RSN (i,thb) =
wenzelm@19861
   530
  case Seq.chop 2 (biresolution false [(false,tha)] i thb) of
clasohm@0
   531
      ([th],_) => th
clasohm@0
   532
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   533
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   534
clasohm@0
   535
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   536
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   537
clasohm@0
   538
(*For joining lists of rules*)
wenzelm@252
   539
fun thas RLN (i,thbs) =
clasohm@0
   540
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   541
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   542
  in maps resb thbs end;
clasohm@0
   543
clasohm@0
   544
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   545
lcp@11
   546
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   547
  makes proof trees*)
wenzelm@252
   548
fun rls MRS bottom_rl =
lcp@11
   549
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   550
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   551
  in  rs_aux 1 rls  end;
lcp@11
   552
lcp@11
   553
(*As above, but for rule lists*)
wenzelm@252
   554
fun rlss MRL bottom_rls =
lcp@11
   555
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   556
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   557
  in  rs_aux 1 rlss  end;
lcp@11
   558
wenzelm@9288
   559
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   560
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   561
wenzelm@252
   562
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   563
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   564
  ALWAYS deletes premise i *)
wenzelm@252
   565
fun compose(tha,i,thb) =
wenzelm@4270
   566
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   567
wenzelm@6946
   568
fun compose_single (tha,i,thb) =
wenzelm@6946
   569
  (case compose (tha,i,thb) of
wenzelm@6946
   570
    [th] => th
wenzelm@6946
   571
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   572
clasohm@0
   573
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   574
fun tha COMP thb =
clasohm@0
   575
    case compose(tha,1,thb) of
wenzelm@252
   576
        [th] => th
clasohm@0
   577
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   578
wenzelm@13105
   579
wenzelm@4016
   580
(** theorem equality **)
clasohm@0
   581
wenzelm@16425
   582
(*True if the two theorems have the same theory.*)
wenzelm@16425
   583
val eq_thm_thy = eq_thy o pairself Thm.theory_of_thm;
paulson@13650
   584
paulson@13650
   585
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@16720
   586
val eq_thm_prop = op aconv o pairself Thm.full_prop_of;
clasohm@0
   587
clasohm@0
   588
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   589
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   590
wenzelm@9829
   591
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@18922
   592
val del_rule = remove eq_thm_prop;
wenzelm@18922
   593
fun add_rule th = cons th o del_rule th;
wenzelm@18922
   594
val merge_rules = Library.merge eq_thm_prop;
wenzelm@9829
   595
wenzelm@19878
   596
(*pattern equivalence*)
wenzelm@19878
   597
fun equiv_thm ths =
wenzelm@19878
   598
  Pattern.equiv (Theory.merge (pairself Thm.theory_of_thm ths)) (pairself Thm.full_prop_of ths);
lcp@1194
   599
lcp@1194
   600
clasohm@0
   601
(*** Meta-Rewriting Rules ***)
clasohm@0
   602
wenzelm@16425
   603
fun read_prop s = read_cterm ProtoPure.thy (s, propT);
paulson@4610
   604
wenzelm@9455
   605
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   606
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   607
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   608
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   609
clasohm@0
   610
val reflexive_thm =
wenzelm@19421
   611
  let val cx = cert (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   612
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   613
clasohm@0
   614
val symmetric_thm =
wenzelm@14854
   615
  let val xy = read_prop "x == y"
wenzelm@16595
   616
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   617
clasohm@0
   618
val transitive_thm =
wenzelm@14854
   619
  let val xy = read_prop "x == y"
wenzelm@14854
   620
      val yz = read_prop "y == z"
clasohm@0
   621
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   622
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   623
nipkow@4679
   624
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   625
berghofe@11512
   626
fun extensional eq =
berghofe@11512
   627
  let val eq' =
berghofe@11512
   628
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   629
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   630
wenzelm@18820
   631
val equals_cong =
wenzelm@18820
   632
  store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x == y"));
wenzelm@18820
   633
berghofe@10414
   634
val imp_cong =
berghofe@10414
   635
  let
berghofe@10414
   636
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   637
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   638
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   639
    val A = read_prop "PROP A"
berghofe@10414
   640
  in
wenzelm@12135
   641
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   642
      (implies_intr AB (implies_intr A
berghofe@10414
   643
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   644
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   645
      (implies_intr AC (implies_intr A
berghofe@10414
   646
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   647
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   648
  end;
berghofe@10414
   649
berghofe@10414
   650
val swap_prems_eq =
berghofe@10414
   651
  let
berghofe@10414
   652
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   653
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   654
    val A = read_prop "PROP A"
berghofe@10414
   655
    val B = read_prop "PROP B"
berghofe@10414
   656
  in
wenzelm@12135
   657
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   658
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   659
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   660
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   661
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   662
  end;
lcp@229
   663
wenzelm@18468
   664
val imp_cong_rule = combination o combination (reflexive implies);
clasohm@0
   665
skalberg@15001
   666
local
skalberg@15001
   667
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   668
  val rhs_of = snd o dest_eq
skalberg@15001
   669
in
skalberg@15001
   670
fun beta_eta_conversion t =
skalberg@15001
   671
  let val thm = beta_conversion true t
skalberg@15001
   672
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   673
end;
skalberg@15001
   674
berghofe@15925
   675
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   676
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   677
wenzelm@18337
   678
val abs_def =
wenzelm@18337
   679
  let
wenzelm@18337
   680
    fun contract_lhs th =
wenzelm@18337
   681
      Thm.transitive (Thm.symmetric (beta_eta_conversion (fst (dest_equals (cprop_of th))))) th;
wenzelm@18777
   682
    fun abstract cx th = Thm.abstract_rule
wenzelm@18777
   683
        (case Thm.term_of cx of Var ((x, _), _) => x | Free (x, _) => x | _ => "x") cx th
wenzelm@18777
   684
      handle THM _ => raise THM ("Malformed definitional equation", 0, [th]);
wenzelm@18337
   685
  in
wenzelm@18337
   686
    contract_lhs
wenzelm@18337
   687
    #> `(snd o strip_comb o fst o dest_equals o cprop_of)
wenzelm@18337
   688
    #-> fold_rev abstract
wenzelm@18337
   689
    #> contract_lhs
wenzelm@18337
   690
  end;
wenzelm@18337
   691
wenzelm@18468
   692
(*rewrite B in !!x1 ... xn. B*)
wenzelm@18251
   693
fun forall_conv 0 cv ct = cv ct
wenzelm@18251
   694
  | forall_conv n cv ct =
wenzelm@18468
   695
      (case try Thm.dest_comb ct of
wenzelm@18468
   696
        NONE => cv ct
wenzelm@18468
   697
      | SOME (A, B) =>
wenzelm@18468
   698
          (case (term_of A, term_of B) of
wenzelm@18468
   699
            (Const ("all", _), Abs (x, _, _)) =>
wenzelm@18468
   700
              let val (v, B') = Thm.dest_abs (SOME (gensym "all_")) B in
wenzelm@18468
   701
                Thm.combination (Thm.reflexive A)
wenzelm@18468
   702
                  (Thm.abstract_rule x v (forall_conv (n - 1) cv B'))
wenzelm@18468
   703
              end
wenzelm@18468
   704
          | _ => cv ct));
wenzelm@18468
   705
wenzelm@18468
   706
(*rewrite B in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   707
fun concl_conv 0 cv ct = cv ct
wenzelm@18468
   708
  | concl_conv n cv ct =
wenzelm@18468
   709
      (case try dest_implies ct of
wenzelm@18468
   710
        NONE => cv ct
wenzelm@18468
   711
      | SOME (A, B) => imp_cong_rule (reflexive A) (concl_conv (n - 1) cv B));
skalberg@15001
   712
wenzelm@18468
   713
(*rewrite the A's in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   714
fun prems_conv 0 _ = reflexive
wenzelm@18468
   715
  | prems_conv n cv =
wenzelm@18468
   716
      let
wenzelm@18468
   717
        fun conv i ct =
wenzelm@18468
   718
          if i = n + 1 then reflexive ct
wenzelm@18468
   719
          else
wenzelm@18468
   720
            (case try dest_implies ct of
wenzelm@18468
   721
              NONE => reflexive ct
wenzelm@18468
   722
            | SOME (A, B) => imp_cong_rule (cv i A) (conv (i + 1) B));
wenzelm@18468
   723
  in conv 1 end;
wenzelm@18468
   724
wenzelm@18468
   725
fun goals_conv pred cv = prems_conv ~1 (fn i => if pred i then cv else reflexive);
skalberg@15001
   726
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   727
wenzelm@18468
   728
wenzelm@15669
   729
(*** Some useful meta-theorems ***)
clasohm@0
   730
clasohm@0
   731
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   732
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   733
val _ = store_thm "_" asm_rl;
clasohm@0
   734
clasohm@0
   735
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   736
val cut_rl =
wenzelm@12135
   737
  store_standard_thm_open "cut_rl"
wenzelm@9455
   738
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   739
wenzelm@252
   740
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   741
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   742
val revcut_rl =
paulson@4610
   743
  let val V = read_prop "PROP V"
paulson@4610
   744
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   745
  in
wenzelm@12135
   746
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   747
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   748
  end;
clasohm@0
   749
lcp@668
   750
(*for deleting an unwanted assumption*)
lcp@668
   751
val thin_rl =
paulson@4610
   752
  let val V = read_prop "PROP V"
paulson@4610
   753
      and W = read_prop "PROP W";
wenzelm@12135
   754
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   755
clasohm@0
   756
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   757
val triv_forall_equality =
paulson@4610
   758
  let val V  = read_prop "PROP V"
paulson@4610
   759
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@19421
   760
      and x  = cert (Free ("x", Term.aT []));
wenzelm@4016
   761
  in
wenzelm@12135
   762
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   763
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   764
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   765
  end;
clasohm@0
   766
wenzelm@19051
   767
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   768
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   769
*)
wenzelm@19051
   770
val distinct_prems_rl =
wenzelm@19051
   771
  let
wenzelm@19051
   772
    val AAB = read_prop "PROP Phi ==> PROP Phi ==> PROP Psi"
wenzelm@19051
   773
    val A = read_prop "PROP Phi";
wenzelm@19051
   774
  in
wenzelm@19051
   775
    store_standard_thm_open "distinct_prems_rl"
wenzelm@19051
   776
      (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
wenzelm@19051
   777
  end;
wenzelm@19051
   778
nipkow@1756
   779
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   780
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   781
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   782
*)
nipkow@1756
   783
val swap_prems_rl =
paulson@4610
   784
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   785
      val major = assume cmajor;
paulson@4610
   786
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   787
      val minor1 = assume cminor1;
paulson@4610
   788
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   789
      val minor2 = assume cminor2;
wenzelm@12135
   790
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   791
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   792
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   793
  end;
nipkow@1756
   794
nipkow@3653
   795
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   796
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   797
   Introduction rule for == as a meta-theorem.
nipkow@3653
   798
*)
nipkow@3653
   799
val equal_intr_rule =
paulson@4610
   800
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   801
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   802
  in
wenzelm@12135
   803
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   804
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   805
  end;
nipkow@3653
   806
wenzelm@19421
   807
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   808
val equal_elim_rule1 =
wenzelm@13368
   809
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   810
      and P = read_prop "PROP phi"
wenzelm@13368
   811
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   812
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   813
  end;
wenzelm@4285
   814
wenzelm@19421
   815
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   816
val equal_elim_rule2 =
wenzelm@19421
   817
  store_standard_thm_open "equal_elim_rule2" (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   818
wenzelm@12297
   819
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   820
val remdups_rl =
wenzelm@12297
   821
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   822
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   823
wenzelm@12297
   824
wenzelm@9554
   825
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   826
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   827
wenzelm@9554
   828
val norm_hhf_eq =
wenzelm@9554
   829
  let
wenzelm@14854
   830
    val aT = TFree ("'a", []);
wenzelm@9554
   831
    val all = Term.all aT;
wenzelm@9554
   832
    val x = Free ("x", aT);
wenzelm@9554
   833
    val phi = Free ("phi", propT);
wenzelm@9554
   834
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   835
wenzelm@9554
   836
    val cx = cert x;
wenzelm@9554
   837
    val cphi = cert phi;
wenzelm@9554
   838
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   839
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   840
  in
wenzelm@9554
   841
    Thm.equal_intr
wenzelm@9554
   842
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   843
        |> Thm.forall_elim cx
wenzelm@9554
   844
        |> Thm.implies_intr cphi
wenzelm@9554
   845
        |> Thm.forall_intr cx
wenzelm@9554
   846
        |> Thm.implies_intr lhs)
wenzelm@9554
   847
      (Thm.implies_elim
wenzelm@9554
   848
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   849
        |> Thm.forall_intr cx
wenzelm@9554
   850
        |> Thm.implies_intr cphi
wenzelm@9554
   851
        |> Thm.implies_intr rhs)
wenzelm@12135
   852
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   853
  end;
wenzelm@9554
   854
wenzelm@18179
   855
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@18179
   856
wenzelm@12800
   857
fun is_norm_hhf tm =
wenzelm@12800
   858
  let
wenzelm@12800
   859
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   860
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   861
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   862
      | is_norm _ = true;
wenzelm@18929
   863
  in is_norm (Envir.beta_eta_contract tm) end;
wenzelm@12800
   864
wenzelm@16425
   865
fun norm_hhf thy t =
wenzelm@12800
   866
  if is_norm_hhf t then t
wenzelm@18179
   867
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   868
wenzelm@12800
   869
wenzelm@9554
   870
wenzelm@16425
   871
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   872
paulson@8129
   873
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   874
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   875
wenzelm@16425
   876
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   877
    let val ts = types_sorts th;
wenzelm@15669
   878
        val used = add_used th [];
wenzelm@16425
   879
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   880
wenzelm@16425
   881
fun read_instantiate_sg thy sinsts th =
wenzelm@16425
   882
  read_instantiate_sg' thy (map (apfst Syntax.indexname) sinsts) th;
paulson@8129
   883
paulson@8129
   884
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   885
fun read_instantiate sinsts th =
wenzelm@16425
   886
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   887
berghofe@15797
   888
fun read_instantiate' sinsts th =
wenzelm@16425
   889
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   890
paulson@8129
   891
paulson@8129
   892
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   893
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   894
local
wenzelm@16425
   895
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@16425
   896
    let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
wenzelm@16425
   897
        and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   898
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   899
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   900
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@10403
   901
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
wenzelm@16425
   902
    in  (thy', tye', maxi')  end;
paulson@8129
   903
in
paulson@8129
   904
fun cterm_instantiate ctpairs0 th =
wenzelm@16425
   905
  let val (thy,tye,_) = foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   906
      fun instT(ct,cu) =
wenzelm@16425
   907
        let val inst = cterm_of thy o Envir.subst_TVars tye o term_of
paulson@14340
   908
        in (inst ct, inst cu) end
wenzelm@16425
   909
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy T)
berghofe@8406
   910
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   911
  handle TERM _ =>
wenzelm@16425
   912
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   913
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   914
end;
paulson@8129
   915
paulson@8129
   916
paulson@8129
   917
(** Derived rules mainly for METAHYPS **)
paulson@8129
   918
paulson@8129
   919
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   920
fun equal_abs_elim ca eqth =
wenzelm@16425
   921
  let val {thy=thya, t=a, ...} = rep_cterm ca
paulson@8129
   922
      and combth = combination eqth (reflexive ca)
wenzelm@16425
   923
      val {thy,prop,...} = rep_thm eqth
paulson@8129
   924
      val (abst,absu) = Logic.dest_equals prop
wenzelm@19421
   925
      val cert = cterm_of (Theory.merge (thy,thya))
wenzelm@19421
   926
  in  transitive (symmetric (beta_conversion false (cert (abst$a))))
wenzelm@19421
   927
           (transitive combth (beta_conversion false (cert (absu$a))))
paulson@8129
   928
  end
paulson@8129
   929
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   930
paulson@8129
   931
(*Calling equal_abs_elim with multiple terms*)
skalberg@15574
   932
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) th (rev cts);
paulson@8129
   933
paulson@8129
   934
wenzelm@19878
   935
(* global schematic variables *)
wenzelm@19878
   936
wenzelm@19878
   937
fun unvarify th =
wenzelm@19878
   938
  let
wenzelm@19878
   939
    val thy = Thm.theory_of_thm th;
wenzelm@19878
   940
    val cert = Thm.cterm_of thy;
wenzelm@19878
   941
    val certT = Thm.ctyp_of thy;
wenzelm@19878
   942
wenzelm@19878
   943
    val prop = Thm.full_prop_of th;
wenzelm@19878
   944
    val _ = map Logic.unvarify (prop :: Thm.hyps_of th)
wenzelm@19878
   945
      handle TERM (msg, _) => raise THM (msg, 0, [th]);
wenzelm@19878
   946
wenzelm@19878
   947
    val instT0 = rev (Term.add_tvars prop []) |> map (fn v as ((a, _), S) => (v, TFree (a, S)));
wenzelm@19878
   948
    val instT = map (fn (v, T) => (certT (TVar v), certT T)) instT0;
wenzelm@19878
   949
    val inst = rev (Term.add_vars prop []) |> map (fn ((a, i), T) =>
wenzelm@19878
   950
      let val T' = Term.instantiateT instT0 T
wenzelm@19878
   951
      in (cert (Var ((a, i), T')), cert (Free ((a, T')))) end);
wenzelm@19878
   952
  in Thm.instantiate (instT, inst) th end;
wenzelm@19878
   953
wenzelm@19878
   954
wenzelm@19775
   955
(** protected propositions and embedded terms **)
wenzelm@4789
   956
wenzelm@4789
   957
local
wenzelm@18025
   958
  val A = cert (Free ("A", propT));
wenzelm@19878
   959
  val prop_def = unvarify ProtoPure.prop_def;
wenzelm@19878
   960
  val term_def = unvarify ProtoPure.term_def;
wenzelm@4789
   961
in
wenzelm@18025
   962
  val protect = Thm.capply (cert Logic.protectC);
wenzelm@18799
   963
  val protectI = store_thm "protectI" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@18025
   964
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@18799
   965
  val protectD = store_thm "protectD" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@18025
   966
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@18179
   967
  val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@19775
   968
wenzelm@19775
   969
  val termI = store_thm "termI" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@19775
   970
      (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)))));
wenzelm@4789
   971
end;
wenzelm@4789
   972
wenzelm@18025
   973
fun implies_intr_protected asms th =
wenzelm@18118
   974
  let val asms' = map protect asms in
wenzelm@18118
   975
    implies_elim_list
wenzelm@18118
   976
      (implies_intr_list asms th)
wenzelm@18118
   977
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@18118
   978
    |> implies_intr_list asms'
wenzelm@18118
   979
  end;
wenzelm@11815
   980
wenzelm@19775
   981
fun mk_term ct =
wenzelm@19775
   982
  let
wenzelm@19775
   983
    val {thy, T, ...} = Thm.rep_cterm ct;
wenzelm@19775
   984
    val cert = Thm.cterm_of thy;
wenzelm@19775
   985
    val certT = Thm.ctyp_of thy;
wenzelm@19775
   986
    val a = certT (TVar (("'a", 0), []));
wenzelm@19775
   987
    val x = cert (Var (("x", 0), T));
wenzelm@19775
   988
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@19775
   989
wenzelm@19775
   990
fun dest_term th =
wenzelm@19775
   991
  let val cprop = Thm.cprop_of th in
wenzelm@19775
   992
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@19775
   993
      #2 (Thm.dest_comb cprop)
wenzelm@19775
   994
    else raise THM ("dest_term", 0, [th])
wenzelm@19775
   995
  end;
wenzelm@19775
   996
wenzelm@19775
   997
wenzelm@4789
   998
wenzelm@5688
   999
(** variations on instantiate **)
wenzelm@4285
  1000
paulson@8550
  1001
(*shorthand for instantiating just one variable in the current theory*)
wenzelm@16425
  1002
fun inst x t = read_instantiate_sg (the_context()) [(x,t)];
paulson@8550
  1003
paulson@8550
  1004
wenzelm@4285
  1005
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
  1006
wenzelm@4285
  1007
fun instantiate' cTs cts thm =
wenzelm@4285
  1008
  let
wenzelm@4285
  1009
    fun err msg =
wenzelm@4285
  1010
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
  1011
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
  1012
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
  1013
wenzelm@4285
  1014
    fun inst_of (v, ct) =
wenzelm@16425
  1015
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
  1016
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
  1017
berghofe@15797
  1018
    fun tyinst_of (v, cT) =
wenzelm@16425
  1019
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
  1020
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
  1021
wenzelm@4285
  1022
    fun zip_vars _ [] = []
skalberg@15531
  1023
      | zip_vars (_ :: vs) (NONE :: opt_ts) = zip_vars vs opt_ts
skalberg@15531
  1024
      | zip_vars (v :: vs) (SOME t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
  1025
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
  1026
wenzelm@4285
  1027
    (*instantiate types first!*)
wenzelm@4285
  1028
    val thm' =
wenzelm@4285
  1029
      if forall is_none cTs then thm
berghofe@15797
  1030
      else Thm.instantiate (map tyinst_of (zip_vars (tvars_of thm) cTs), []) thm;
wenzelm@4285
  1031
    in
wenzelm@4285
  1032
      if forall is_none cts then thm'
wenzelm@4285
  1033
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
  1034
    end;
wenzelm@4285
  1035
wenzelm@4285
  1036
berghofe@14081
  1037
berghofe@14081
  1038
(** renaming of bound variables **)
berghofe@14081
  1039
berghofe@14081
  1040
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
  1041
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
  1042
berghofe@14081
  1043
fun rename_bvars [] thm = thm
berghofe@14081
  1044
  | rename_bvars vs thm =
berghofe@14081
  1045
    let
wenzelm@16425
  1046
      val {thy, prop, ...} = rep_thm thm;
haftmann@17325
  1047
      fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
berghofe@14081
  1048
        | ren (t $ u) = ren t $ ren u
berghofe@14081
  1049
        | ren t = t;
wenzelm@16425
  1050
    in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
berghofe@14081
  1051
berghofe@14081
  1052
berghofe@14081
  1053
(* renaming in left-to-right order *)
berghofe@14081
  1054
berghofe@14081
  1055
fun rename_bvars' xs thm =
berghofe@14081
  1056
  let
wenzelm@16425
  1057
    val {thy, prop, ...} = rep_thm thm;
berghofe@14081
  1058
    fun rename [] t = ([], t)
berghofe@14081
  1059
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
  1060
          let val (xs', t') = rename xs t
wenzelm@18929
  1061
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
  1062
      | rename xs (t $ u) =
berghofe@14081
  1063
          let
berghofe@14081
  1064
            val (xs', t') = rename xs t;
berghofe@14081
  1065
            val (xs'', u') = rename xs' u
berghofe@14081
  1066
          in (xs'', t' $ u') end
berghofe@14081
  1067
      | rename xs t = (xs, t);
berghofe@14081
  1068
  in case rename xs prop of
wenzelm@16425
  1069
      ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
berghofe@14081
  1070
    | _ => error "More names than abstractions in theorem"
berghofe@14081
  1071
  end;
berghofe@14081
  1072
berghofe@14081
  1073
wenzelm@19906
  1074
(* var indexes *)
wenzelm@6435
  1075
wenzelm@19421
  1076
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@18025
  1077
wenzelm@19124
  1078
fun incr_indexes2 th1 th2 =
wenzelm@19421
  1079
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@6435
  1080
wenzelm@6435
  1081
wenzelm@8328
  1082
(* freeze_all *)
wenzelm@8328
  1083
wenzelm@8328
  1084
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
  1085
wenzelm@8328
  1086
fun freeze_all_TVars thm =
wenzelm@8328
  1087
  (case tvars_of thm of
wenzelm@8328
  1088
    [] => thm
wenzelm@8328
  1089
  | tvars =>
wenzelm@16425
  1090
      let val cert = Thm.ctyp_of (Thm.theory_of_thm thm)
skalberg@15531
  1091
      in instantiate' (map (fn ((x, _), S) => SOME (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
  1092
wenzelm@8328
  1093
fun freeze_all_Vars thm =
wenzelm@8328
  1094
  (case vars_of thm of
wenzelm@8328
  1095
    [] => thm
wenzelm@8328
  1096
  | vars =>
wenzelm@16425
  1097
      let val cert = Thm.cterm_of (Thm.theory_of_thm thm)
skalberg@15531
  1098
      in instantiate' [] (map (fn ((x, _), T) => SOME (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
  1099
wenzelm@8328
  1100
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
  1101
wenzelm@8328
  1102
wenzelm@11975
  1103
wenzelm@18225
  1104
(** multi_resolve **)
wenzelm@18225
  1105
wenzelm@18225
  1106
local
wenzelm@18225
  1107
wenzelm@18225
  1108
fun res th i rule =
wenzelm@18225
  1109
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
  1110
wenzelm@18225
  1111
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
  1112
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
  1113
wenzelm@18225
  1114
in
wenzelm@18225
  1115
wenzelm@18225
  1116
val multi_resolve = multi_res 1;
wenzelm@18225
  1117
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
  1118
wenzelm@18225
  1119
end;
wenzelm@18225
  1120
wenzelm@11975
  1121
end;
wenzelm@5903
  1122
wenzelm@5903
  1123
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1124
open BasicDrule;