src/Pure/drule.ML
author wenzelm
Fri Oct 28 22:27:52 2005 +0200 (2005-10-28)
changeset 18025 7dac6858168d
parent 17964 6842ca6ecb87
child 18118 38316c575328
permissions -rw-r--r--
added incr_indexes;
added lift_all (approx. reverse of gen_all);
renamed Goal constant to prop, more general protect/unprotect interfaces;
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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        :
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          theory -> (indexname -> typ option) * (indexname -> sort option)
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                  -> (indexname -> typ option) * (indexname -> sort option)
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                  -> string list -> (indexname * string) list
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                  -> (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       :
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    (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 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 swap_prems_rl     : thm
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  val equal_intr_rule   : thm
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  val equal_elim_rule1  : thm
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  val inst              : string -> string -> thm -> thm
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  val instantiate'      : ctyp option list -> cterm option list -> thm -> thm
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  val incr_indexes      : thm -> thm -> thm
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  val incr_indexes_wrt  : int list -> ctyp list -> cterm list -> thm list -> thm -> thm
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end;
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signature DRULE =
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sig
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  include BASIC_DRULE
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  val list_comb: cterm * cterm list -> cterm
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  val strip_comb: cterm -> cterm * cterm list
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  val strip_type: ctyp -> ctyp list * ctyp
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  val beta_conv: cterm -> cterm -> cterm
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  val plain_prop_of: thm -> term
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  val add_used: thm -> string list -> string list
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  val rule_attribute: ('a -> thm -> thm) -> 'a attribute
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  val tag_rule: tag -> thm -> thm
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  val untag_rule: string -> thm -> thm
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  val tag: tag -> 'a attribute
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  val untag: string -> 'a attribute
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  val get_kind: thm -> string
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  val kind: string -> 'a attribute
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  val theoremK: string
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  val lemmaK: string
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  val corollaryK: string
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  val internalK: string
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  val kind_internal: 'a attribute
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  val has_internal: tag list -> bool
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  val impose_hyps: cterm list -> thm -> thm
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  val satisfy_hyps: thm list -> thm -> thm
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  val flexflex_unique: thm -> thm
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  val close_derivation: thm -> thm
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  val local_standard: thm -> thm
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  val compose_single: thm * int * thm -> thm
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  val add_rule: thm -> thm list -> thm list
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  val del_rule: thm -> thm list -> thm list
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  val add_rules: thm list -> thm list -> thm list
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  val del_rules: thm list -> thm list -> thm list
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  val merge_rules: thm list * thm list -> thm list
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  val imp_cong'         : 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 goals_conv        : (int -> bool) -> (cterm -> thm) -> cterm -> thm
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  val forall_conv       : (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 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 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 -> thm * (string * (indexname * sort)) list
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  val remdups_rl: thm
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  val conj_intr: thm -> thm -> thm
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  val conj_intr_list: thm list -> thm
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  val conj_elim: thm -> thm * thm
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  val conj_elim_list: thm -> thm list
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  val conj_elim_precise: int -> thm -> thm list
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  val conj_intr_thm: thm
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  val abs_def: thm -> thm
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  val read_instantiate_sg': theory -> (indexname * string) list -> thm -> thm
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  val read_instantiate': (indexname * string) list -> thm -> thm
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end;
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structure Drule: DRULE =
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struct
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(** some cterm->cterm operations: faster than calling cterm_of! **)
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(* FIXME exception CTERM (!?) *)
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fun dest_implies ct =
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  (case Thm.term_of ct of
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    (Const ("==>", _) $ _ $ _) =>
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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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  | _ => 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 ("==", _) $ _ $ _) =>
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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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    | _ => 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 implies = cterm_of ProtoPure.thy Term.implies;
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(*cterm version of mk_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);
wenzelm@252
   305
        val frees = map dest_Free (term_frees big);
wenzelm@252
   306
        val tvars = term_tvars big;
wenzelm@252
   307
        val tfrees = term_tfrees big;
haftmann@17325
   308
        fun typ(a,i) = if i<0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a,i);
haftmann@17325
   309
        fun sort(a,i) = if i<0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a,i);
clasohm@0
   310
    in (typ,sort) end;
clasohm@0
   311
wenzelm@15669
   312
fun add_used thm used =
wenzelm@15669
   313
  let val {prop, hyps, tpairs, ...} = Thm.rep_thm thm in
wenzelm@15669
   314
    add_term_tvarnames (prop, used)
wenzelm@15669
   315
    |> fold (curry add_term_tvarnames) hyps
wenzelm@15669
   316
    |> fold (curry add_term_tvarnames) (Thm.terms_of_tpairs tpairs)
wenzelm@15669
   317
  end;
wenzelm@15669
   318
wenzelm@7636
   319
wenzelm@9455
   320
wenzelm@9455
   321
(** basic attributes **)
wenzelm@9455
   322
wenzelm@9455
   323
(* dependent rules *)
wenzelm@9455
   324
wenzelm@9455
   325
fun rule_attribute f (x, thm) = (x, (f x thm));
wenzelm@9455
   326
wenzelm@9455
   327
wenzelm@9455
   328
(* add / delete tags *)
wenzelm@9455
   329
wenzelm@9455
   330
fun map_tags f thm =
wenzelm@9455
   331
  Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
wenzelm@9455
   332
wenzelm@9455
   333
fun tag_rule tg = map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]);
wenzelm@9455
   334
fun untag_rule s = map_tags (filter_out (equal s o #1));
wenzelm@9455
   335
wenzelm@9455
   336
fun tag tg x = rule_attribute (K (tag_rule tg)) x;
wenzelm@9455
   337
fun untag s x = rule_attribute (K (untag_rule s)) x;
wenzelm@9455
   338
wenzelm@9455
   339
fun simple_tag name x = tag (name, []) x;
wenzelm@9455
   340
wenzelm@11741
   341
wenzelm@11741
   342
(* theorem kinds *)
wenzelm@11741
   343
wenzelm@11741
   344
val theoremK = "theorem";
wenzelm@11741
   345
val lemmaK = "lemma";
wenzelm@11741
   346
val corollaryK = "corollary";
wenzelm@11741
   347
val internalK = "internal";
wenzelm@9455
   348
wenzelm@11741
   349
fun get_kind thm =
haftmann@17325
   350
  (case AList.lookup (op =) ((#2 o Thm.get_name_tags) thm) "kind" of
skalberg@15531
   351
    SOME (k :: _) => k
wenzelm@11741
   352
  | _ => "unknown");
wenzelm@11741
   353
wenzelm@11741
   354
fun kind_rule k = tag_rule ("kind", [k]) o untag_rule "kind";
wenzelm@12710
   355
fun kind k x = if k = "" then x else rule_attribute (K (kind_rule k)) x;
wenzelm@11741
   356
fun kind_internal x = kind internalK x;
wenzelm@11741
   357
fun has_internal tags = exists (equal internalK o fst) tags;
wenzelm@9455
   358
wenzelm@9455
   359
wenzelm@9455
   360
clasohm@0
   361
(** Standardization of rules **)
clasohm@0
   362
wenzelm@18025
   363
(*vars in left-to-right order*)
wenzelm@18025
   364
fun tvars_of_terms ts = rev (fold Term.add_tvars ts []);
wenzelm@18025
   365
fun vars_of_terms ts = rev (fold Term.add_vars ts []);
wenzelm@18025
   366
fun tvars_of thm = tvars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   367
fun vars_of thm = vars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   368
wenzelm@7636
   369
(*Strip extraneous shyps as far as possible*)
wenzelm@7636
   370
fun strip_shyps_warning thm =
wenzelm@7636
   371
  let
wenzelm@16425
   372
    val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.theory_of_thm thm);
wenzelm@7636
   373
    val thm' = Thm.strip_shyps thm;
wenzelm@7636
   374
    val xshyps = Thm.extra_shyps thm';
wenzelm@7636
   375
  in
wenzelm@7636
   376
    if null xshyps then ()
wenzelm@7636
   377
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   378
    thm'
wenzelm@7636
   379
  end;
wenzelm@7636
   380
clasohm@0
   381
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   382
fun forall_intr_list [] th = th
clasohm@0
   383
  | forall_intr_list (y::ys) th =
wenzelm@252
   384
        let val gth = forall_intr_list ys th
wenzelm@252
   385
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   386
clasohm@0
   387
(*Generalization over all suitable Free variables*)
clasohm@0
   388
fun forall_intr_frees th =
wenzelm@16425
   389
    let val {prop,thy,...} = rep_thm th
clasohm@0
   390
    in  forall_intr_list
wenzelm@16983
   391
         (map (cterm_of thy) (sort Term.term_ord (term_frees prop)))
clasohm@0
   392
         th
clasohm@0
   393
    end;
clasohm@0
   394
wenzelm@7898
   395
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   396
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   397
wenzelm@18025
   398
fun outer_params t =
wenzelm@18025
   399
  let
wenzelm@18025
   400
    val vs = Term.strip_all_vars t;
wenzelm@18025
   401
    val xs = Term.variantlist (map #1 vs, []);
wenzelm@18025
   402
  in xs ~~ map #2 vs end;
wenzelm@18025
   403
wenzelm@18025
   404
(*generalize outermost parameters*)
wenzelm@18025
   405
fun gen_all th =
wenzelm@12719
   406
  let
wenzelm@18025
   407
    val {thy, prop, maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   408
    val cert = Thm.cterm_of thy;
wenzelm@18025
   409
    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
wenzelm@18025
   410
  in fold elim (outer_params prop) th end;
wenzelm@18025
   411
wenzelm@18025
   412
(*lift vars wrt. outermost goal parameters
wenzelm@18025
   413
  -- reverses the effect of gen_all modulo HO unification*)
wenzelm@18025
   414
fun lift_all goal th =
wenzelm@18025
   415
  let
wenzelm@18025
   416
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   417
    val cert = Thm.cterm_of thy;
wenzelm@18025
   418
    val {maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   419
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   420
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   421
    val Ts = map Term.fastype_of ps;
wenzelm@18025
   422
    val inst = vars_of th |> map (fn (xi, T) =>
wenzelm@18025
   423
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   424
  in
wenzelm@18025
   425
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   426
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   427
  end;
wenzelm@18025
   428
wenzelm@9554
   429
wenzelm@16949
   430
(*specialization over a list of cterms*)
wenzelm@16949
   431
val forall_elim_list = fold forall_elim;
clasohm@0
   432
wenzelm@16949
   433
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   434
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   435
wenzelm@16949
   436
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
skalberg@15570
   437
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   438
wenzelm@16949
   439
(*maps |- B to A1,...,An |- B*)
wenzelm@16949
   440
val impose_hyps = fold Thm.weaken;
wenzelm@11960
   441
wenzelm@13389
   442
(* maps A1,...,An and A1,...,An |- B to |- B *)
wenzelm@13389
   443
fun satisfy_hyps ths th =
wenzelm@13389
   444
  implies_elim_list (implies_intr_list (map (#prop o Thm.crep_thm) ths) th) ths;
wenzelm@13389
   445
clasohm@0
   446
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   447
fun zero_var_indexes th =
wenzelm@16949
   448
  let
wenzelm@16949
   449
    val thy = Thm.theory_of_thm th;
wenzelm@16949
   450
    val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@16949
   451
    val (instT, inst) = Term.zero_var_indexes_inst (Thm.full_prop_of th);
wenzelm@16949
   452
    val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@16949
   453
    val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@16949
   454
  in Thm.adjust_maxidx_thm (Thm.instantiate (cinstT, cinst) th) end;
clasohm@0
   455
clasohm@0
   456
paulson@14394
   457
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   458
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   459
wenzelm@16595
   460
(*Discharge all hypotheses.*)
wenzelm@16595
   461
fun implies_intr_hyps th =
wenzelm@16595
   462
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   463
paulson@14394
   464
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   465
  This step can lose information.*)
paulson@14387
   466
fun flexflex_unique th =
berghofe@17713
   467
  if null (tpairs_of th) then th else
paulson@14387
   468
    case Seq.chop (2, flexflex_rule th) of
paulson@14387
   469
      ([th],_) => th
paulson@14387
   470
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   471
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   472
wenzelm@10515
   473
fun close_derivation thm =
wenzelm@10515
   474
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   475
  else thm;
wenzelm@10515
   476
wenzelm@16949
   477
val standard' =
wenzelm@16949
   478
  implies_intr_hyps
wenzelm@16949
   479
  #> forall_intr_frees
wenzelm@16949
   480
  #> `(#maxidx o Thm.rep_thm)
wenzelm@16949
   481
  #-> (fn maxidx =>
wenzelm@16949
   482
    forall_elim_vars (maxidx + 1)
wenzelm@16949
   483
    #> strip_shyps_warning
wenzelm@16949
   484
    #> zero_var_indexes
wenzelm@16949
   485
    #> Thm.varifyT
wenzelm@16949
   486
    #> Thm.compress);
wenzelm@1218
   487
wenzelm@16949
   488
val standard =
wenzelm@16949
   489
  flexflex_unique
wenzelm@16949
   490
  #> standard'
wenzelm@16949
   491
  #> close_derivation;
berghofe@11512
   492
wenzelm@16949
   493
val local_standard =
wenzelm@16949
   494
  strip_shyps
wenzelm@16949
   495
  #> zero_var_indexes
wenzelm@16949
   496
  #> Thm.compress
wenzelm@16949
   497
  #> close_derivation;
wenzelm@12005
   498
clasohm@0
   499
wenzelm@8328
   500
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   501
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   502
  Similar code in type/freeze_thaw*)
paulson@15495
   503
paulson@15495
   504
fun freeze_thaw_robust th =
paulson@15495
   505
 let val fth = freezeT th
wenzelm@16425
   506
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@15495
   507
 in
skalberg@15574
   508
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   509
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   510
     | vars =>
paulson@15495
   511
         let fun newName (Var(ix,_), pairs) =
paulson@15495
   512
                   let val v = gensym (string_of_indexname ix)
paulson@15495
   513
                   in  ((ix,v)::pairs)  end;
skalberg@15574
   514
             val alist = foldr newName [] vars
paulson@15495
   515
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   516
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   517
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   518
             val insts = map mk_inst vars
paulson@15495
   519
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   520
                 th' |> forall_intr_list (map #2 insts)
paulson@15495
   521
                     |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
paulson@15495
   522
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   523
 end;
paulson@15495
   524
paulson@15495
   525
(*Basic version of the function above. No option to rename Vars apart in thaw.
paulson@15495
   526
  The Frees created from Vars have nice names.*)
paulson@4610
   527
fun freeze_thaw th =
paulson@7248
   528
 let val fth = freezeT th
wenzelm@16425
   529
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@7248
   530
 in
skalberg@15574
   531
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   532
       [] => (fth, fn x => x)
paulson@7248
   533
     | vars =>
wenzelm@8328
   534
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   535
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   536
                   in  ((ix,v)::pairs, v::used)  end;
skalberg@15574
   537
             val (alist, _) = foldr newName ([], Library.foldr add_term_names
skalberg@15574
   538
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   539
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   540
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   541
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   542
             val insts = map mk_inst vars
wenzelm@8328
   543
             fun thaw th' =
wenzelm@8328
   544
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   545
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   546
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   547
 end;
paulson@4610
   548
paulson@7248
   549
(*Rotates a rule's premises to the left by k*)
paulson@7248
   550
val rotate_prems = permute_prems 0;
paulson@4610
   551
oheimb@11163
   552
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   553
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   554
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   555
val rearrange_prems = let
oheimb@11163
   556
  fun rearr new []      thm = thm
wenzelm@11815
   557
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   558
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   559
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   560
  in rearr 0 end;
paulson@4610
   561
wenzelm@252
   562
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   563
  Generalizes over Free variables,
clasohm@0
   564
  creates the assumption, and then strips quantifiers.
clasohm@0
   565
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   566
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   567
fun assume_ax thy sP =
wenzelm@16425
   568
  let val prop = Logic.close_form (term_of (read_cterm thy (sP, propT)))
wenzelm@16425
   569
  in forall_elim_vars 0 (Thm.assume (cterm_of thy prop)) end;
clasohm@0
   570
wenzelm@252
   571
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   572
fun tha RSN (i,thb) =
wenzelm@4270
   573
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   574
      ([th],_) => th
clasohm@0
   575
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   576
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   577
clasohm@0
   578
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   579
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   580
clasohm@0
   581
(*For joining lists of rules*)
wenzelm@252
   582
fun thas RLN (i,thbs) =
clasohm@0
   583
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   584
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   585
  in  List.concat (map resb thbs)  end;
clasohm@0
   586
clasohm@0
   587
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   588
lcp@11
   589
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   590
  makes proof trees*)
wenzelm@252
   591
fun rls MRS bottom_rl =
lcp@11
   592
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   593
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   594
  in  rs_aux 1 rls  end;
lcp@11
   595
lcp@11
   596
(*As above, but for rule lists*)
wenzelm@252
   597
fun rlss MRL bottom_rls =
lcp@11
   598
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   599
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   600
  in  rs_aux 1 rlss  end;
lcp@11
   601
wenzelm@9288
   602
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   603
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   604
wenzelm@252
   605
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   606
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   607
  ALWAYS deletes premise i *)
wenzelm@252
   608
fun compose(tha,i,thb) =
wenzelm@4270
   609
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   610
wenzelm@6946
   611
fun compose_single (tha,i,thb) =
wenzelm@6946
   612
  (case compose (tha,i,thb) of
wenzelm@6946
   613
    [th] => th
wenzelm@6946
   614
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   615
clasohm@0
   616
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   617
fun tha COMP thb =
clasohm@0
   618
    case compose(tha,1,thb) of
wenzelm@252
   619
        [th] => th
clasohm@0
   620
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   621
wenzelm@13105
   622
wenzelm@4016
   623
(** theorem equality **)
clasohm@0
   624
wenzelm@16425
   625
(*True if the two theorems have the same theory.*)
wenzelm@16425
   626
val eq_thm_thy = eq_thy o pairself Thm.theory_of_thm;
paulson@13650
   627
paulson@13650
   628
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@16720
   629
val eq_thm_prop = op aconv o pairself Thm.full_prop_of;
clasohm@0
   630
clasohm@0
   631
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   632
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   633
wenzelm@9829
   634
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@13105
   635
fun del_rules rs rules = Library.gen_rems eq_thm_prop (rules, rs);
wenzelm@9862
   636
fun add_rules rs rules = rs @ del_rules rs rules;
wenzelm@12373
   637
val del_rule = del_rules o single;
wenzelm@12373
   638
val add_rule = add_rules o single;
wenzelm@13105
   639
fun merge_rules (rules1, rules2) = gen_merge_lists' eq_thm_prop rules1 rules2;
wenzelm@9829
   640
lcp@1194
   641
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   642
    (some) type variable renaming **)
lcp@1194
   643
lcp@1194
   644
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   645
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   646
    in the term. *)
lcp@1194
   647
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   648
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   649
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   650
  | term_vars' _ = [];
lcp@1194
   651
lcp@1194
   652
fun forall_intr_vars th =
wenzelm@16425
   653
  let val {prop,thy,...} = rep_thm th;
lcp@1194
   654
      val vars = distinct (term_vars' prop);
wenzelm@16425
   655
  in forall_intr_list (map (cterm_of thy) vars) th end;
lcp@1194
   656
wenzelm@13105
   657
val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
lcp@1194
   658
lcp@1194
   659
clasohm@0
   660
(*** Meta-Rewriting Rules ***)
clasohm@0
   661
wenzelm@16425
   662
fun read_prop s = read_cterm ProtoPure.thy (s, propT);
paulson@4610
   663
wenzelm@9455
   664
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   665
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   666
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   667
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   668
clasohm@0
   669
val reflexive_thm =
wenzelm@16425
   670
  let val cx = cterm_of ProtoPure.thy (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   671
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   672
clasohm@0
   673
val symmetric_thm =
wenzelm@14854
   674
  let val xy = read_prop "x == y"
wenzelm@16595
   675
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   676
clasohm@0
   677
val transitive_thm =
wenzelm@14854
   678
  let val xy = read_prop "x == y"
wenzelm@14854
   679
      val yz = read_prop "y == z"
clasohm@0
   680
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   681
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   682
nipkow@4679
   683
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   684
berghofe@11512
   685
fun extensional eq =
berghofe@11512
   686
  let val eq' =
berghofe@11512
   687
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   688
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   689
berghofe@10414
   690
val imp_cong =
berghofe@10414
   691
  let
berghofe@10414
   692
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   693
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   694
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   695
    val A = read_prop "PROP A"
berghofe@10414
   696
  in
wenzelm@12135
   697
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   698
      (implies_intr AB (implies_intr A
berghofe@10414
   699
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   700
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   701
      (implies_intr AC (implies_intr A
berghofe@10414
   702
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   703
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   704
  end;
berghofe@10414
   705
berghofe@10414
   706
val swap_prems_eq =
berghofe@10414
   707
  let
berghofe@10414
   708
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   709
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   710
    val A = read_prop "PROP A"
berghofe@10414
   711
    val B = read_prop "PROP B"
berghofe@10414
   712
  in
wenzelm@12135
   713
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   714
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   715
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   716
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   717
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   718
  end;
lcp@229
   719
skalberg@15001
   720
val imp_cong' = combination o combination (reflexive implies)
clasohm@0
   721
berghofe@13325
   722
fun abs_def thm =
berghofe@13325
   723
  let
berghofe@13325
   724
    val (_, cvs) = strip_comb (fst (dest_equals (cprop_of thm)));
skalberg@15574
   725
    val thm' = foldr (fn (ct, thm) => Thm.abstract_rule
berghofe@13325
   726
      (case term_of ct of Var ((a, _), _) => a | Free (a, _) => a | _ => "x")
skalberg@15574
   727
        ct thm) thm cvs
berghofe@13325
   728
  in transitive
berghofe@13325
   729
    (symmetric (eta_conversion (fst (dest_equals (cprop_of thm'))))) thm'
berghofe@13325
   730
  end;
berghofe@13325
   731
clasohm@0
   732
skalberg@15001
   733
local
skalberg@15001
   734
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   735
  val rhs_of = snd o dest_eq
skalberg@15001
   736
in
skalberg@15001
   737
fun beta_eta_conversion t =
skalberg@15001
   738
  let val thm = beta_conversion true t
skalberg@15001
   739
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   740
end;
skalberg@15001
   741
berghofe@15925
   742
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   743
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   744
skalberg@15001
   745
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
skalberg@15001
   746
fun goals_conv pred cv =
skalberg@15001
   747
  let fun gconv i ct =
skalberg@15001
   748
        let val (A,B) = dest_implies ct
skalberg@15001
   749
        in imp_cong' (if pred i then cv A else reflexive A) (gconv (i+1) B) end
skalberg@15001
   750
        handle TERM _ => reflexive ct
skalberg@15001
   751
  in gconv 1 end
skalberg@15001
   752
skalberg@15001
   753
(* Rewrite A in !!x1,...,xn. A *)
skalberg@15001
   754
fun forall_conv cv ct =
skalberg@15001
   755
  let val p as (ct1, ct2) = Thm.dest_comb ct
skalberg@15001
   756
  in (case pairself term_of p of
skalberg@15001
   757
      (Const ("all", _), Abs (s, _, _)) =>
wenzelm@16682
   758
         let val (v, ct') = Thm.dest_abs (SOME (gensym "all_")) ct2;
skalberg@15001
   759
         in Thm.combination (Thm.reflexive ct1)
skalberg@15001
   760
           (Thm.abstract_rule s v (forall_conv cv ct'))
skalberg@15001
   761
         end
skalberg@15001
   762
    | _ => cv ct)
skalberg@15001
   763
  end handle TERM _ => cv ct;
skalberg@15001
   764
skalberg@15001
   765
(*Use a conversion to transform a theorem*)
skalberg@15001
   766
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   767
wenzelm@15669
   768
(*** Some useful meta-theorems ***)
clasohm@0
   769
clasohm@0
   770
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   771
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   772
val _ = store_thm "_" asm_rl;
clasohm@0
   773
clasohm@0
   774
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   775
val cut_rl =
wenzelm@12135
   776
  store_standard_thm_open "cut_rl"
wenzelm@9455
   777
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   778
wenzelm@252
   779
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   780
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   781
val revcut_rl =
paulson@4610
   782
  let val V = read_prop "PROP V"
paulson@4610
   783
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   784
  in
wenzelm@12135
   785
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   786
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   787
  end;
clasohm@0
   788
lcp@668
   789
(*for deleting an unwanted assumption*)
lcp@668
   790
val thin_rl =
paulson@4610
   791
  let val V = read_prop "PROP V"
paulson@4610
   792
      and W = read_prop "PROP W";
wenzelm@12135
   793
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   794
clasohm@0
   795
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   796
val triv_forall_equality =
paulson@4610
   797
  let val V  = read_prop "PROP V"
paulson@4610
   798
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@16425
   799
      and x  = read_cterm ProtoPure.thy ("x", TypeInfer.logicT);
wenzelm@4016
   800
  in
wenzelm@12135
   801
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   802
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   803
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   804
  end;
clasohm@0
   805
nipkow@1756
   806
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   807
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   808
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   809
*)
nipkow@1756
   810
val swap_prems_rl =
paulson@4610
   811
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   812
      val major = assume cmajor;
paulson@4610
   813
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   814
      val minor1 = assume cminor1;
paulson@4610
   815
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   816
      val minor2 = assume cminor2;
wenzelm@12135
   817
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   818
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   819
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   820
  end;
nipkow@1756
   821
nipkow@3653
   822
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   823
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   824
   Introduction rule for == as a meta-theorem.
nipkow@3653
   825
*)
nipkow@3653
   826
val equal_intr_rule =
paulson@4610
   827
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   828
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   829
  in
wenzelm@12135
   830
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   831
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   832
  end;
nipkow@3653
   833
wenzelm@13368
   834
(* [| PROP ?phi == PROP ?psi; PROP ?phi |] ==> PROP ?psi *)
wenzelm@13368
   835
val equal_elim_rule1 =
wenzelm@13368
   836
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   837
      and P = read_prop "PROP phi"
wenzelm@13368
   838
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   839
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   840
  end;
wenzelm@4285
   841
wenzelm@12297
   842
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   843
wenzelm@12297
   844
val remdups_rl =
wenzelm@12297
   845
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   846
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   847
wenzelm@12297
   848
wenzelm@9554
   849
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   850
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   851
wenzelm@9554
   852
val norm_hhf_eq =
wenzelm@9554
   853
  let
wenzelm@16425
   854
    val cert = Thm.cterm_of ProtoPure.thy;
wenzelm@14854
   855
    val aT = TFree ("'a", []);
wenzelm@9554
   856
    val all = Term.all aT;
wenzelm@9554
   857
    val x = Free ("x", aT);
wenzelm@9554
   858
    val phi = Free ("phi", propT);
wenzelm@9554
   859
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   860
wenzelm@9554
   861
    val cx = cert x;
wenzelm@9554
   862
    val cphi = cert phi;
wenzelm@9554
   863
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   864
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   865
  in
wenzelm@9554
   866
    Thm.equal_intr
wenzelm@9554
   867
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   868
        |> Thm.forall_elim cx
wenzelm@9554
   869
        |> Thm.implies_intr cphi
wenzelm@9554
   870
        |> Thm.forall_intr cx
wenzelm@9554
   871
        |> Thm.implies_intr lhs)
wenzelm@9554
   872
      (Thm.implies_elim
wenzelm@9554
   873
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   874
        |> Thm.forall_intr cx
wenzelm@9554
   875
        |> Thm.implies_intr cphi
wenzelm@9554
   876
        |> Thm.implies_intr rhs)
wenzelm@12135
   877
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   878
  end;
wenzelm@9554
   879
wenzelm@12800
   880
fun is_norm_hhf tm =
wenzelm@12800
   881
  let
wenzelm@12800
   882
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   883
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   884
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   885
      | is_norm _ = true;
wenzelm@12800
   886
  in is_norm (Pattern.beta_eta_contract tm) end;
wenzelm@12800
   887
wenzelm@16425
   888
fun norm_hhf thy t =
wenzelm@12800
   889
  if is_norm_hhf t then t
wenzelm@17203
   890
  else Pattern.rewrite_term thy [Logic.dest_equals (prop_of norm_hhf_eq)] [] t;
wenzelm@12800
   891
wenzelm@9554
   892
wenzelm@16425
   893
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   894
paulson@8129
   895
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   896
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   897
wenzelm@16425
   898
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   899
    let val ts = types_sorts th;
wenzelm@15669
   900
        val used = add_used th [];
wenzelm@16425
   901
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   902
wenzelm@16425
   903
fun read_instantiate_sg thy sinsts th =
wenzelm@16425
   904
  read_instantiate_sg' thy (map (apfst Syntax.indexname) sinsts) th;
paulson@8129
   905
paulson@8129
   906
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   907
fun read_instantiate sinsts th =
wenzelm@16425
   908
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   909
berghofe@15797
   910
fun read_instantiate' sinsts th =
wenzelm@16425
   911
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   912
paulson@8129
   913
paulson@8129
   914
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   915
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   916
local
wenzelm@16425
   917
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@16425
   918
    let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
wenzelm@16425
   919
        and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   920
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   921
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   922
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@10403
   923
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
wenzelm@16425
   924
    in  (thy', tye', maxi')  end;
paulson@8129
   925
in
paulson@8129
   926
fun cterm_instantiate ctpairs0 th =
wenzelm@16425
   927
  let val (thy,tye,_) = foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
paulson@14340
   928
      fun instT(ct,cu) = 
wenzelm@16425
   929
        let val inst = cterm_of thy o Envir.subst_TVars tye o term_of
paulson@14340
   930
        in (inst ct, inst cu) end
wenzelm@16425
   931
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy T)
berghofe@8406
   932
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   933
  handle TERM _ =>
wenzelm@16425
   934
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   935
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   936
end;
paulson@8129
   937
paulson@8129
   938
paulson@8129
   939
(** Derived rules mainly for METAHYPS **)
paulson@8129
   940
paulson@8129
   941
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   942
fun equal_abs_elim ca eqth =
wenzelm@16425
   943
  let val {thy=thya, t=a, ...} = rep_cterm ca
paulson@8129
   944
      and combth = combination eqth (reflexive ca)
wenzelm@16425
   945
      val {thy,prop,...} = rep_thm eqth
paulson@8129
   946
      val (abst,absu) = Logic.dest_equals prop
wenzelm@16425
   947
      val cterm = cterm_of (Theory.merge (thy,thya))
berghofe@10414
   948
  in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
berghofe@10414
   949
           (transitive combth (beta_conversion false (cterm (absu$a))))
paulson@8129
   950
  end
paulson@8129
   951
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   952
paulson@8129
   953
(*Calling equal_abs_elim with multiple terms*)
skalberg@15574
   954
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) th (rev cts);
paulson@8129
   955
paulson@8129
   956
wenzelm@18025
   957
(** protected propositions **)
wenzelm@4789
   958
wenzelm@4789
   959
local
wenzelm@16425
   960
  val cert = Thm.cterm_of ProtoPure.thy;
wenzelm@18025
   961
  val A = cert (Free ("A", propT));
wenzelm@18025
   962
  val prop_def = #1 (freeze_thaw ProtoPure.prop_def);
wenzelm@4789
   963
in
wenzelm@18025
   964
  val protect = Thm.capply (cert Logic.protectC);
wenzelm@18025
   965
  val protectI = store_thm "protectI" (kind_rule internalK (standard
wenzelm@18025
   966
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@18025
   967
  val protectD = store_thm "protectD" (kind_rule internalK (standard
wenzelm@18025
   968
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@4789
   969
end;
wenzelm@4789
   970
wenzelm@18025
   971
fun implies_intr_protected asms th =
wenzelm@18025
   972
  implies_elim_list (implies_intr_list asms th)
wenzelm@18025
   973
    (map (fn ct => Thm.assume (protect ct) RS protectD) asms)
wenzelm@18025
   974
  |> implies_intr_list (map protect asms);
wenzelm@11815
   975
wenzelm@4789
   976
wenzelm@5688
   977
(** variations on instantiate **)
wenzelm@4285
   978
paulson@8550
   979
(*shorthand for instantiating just one variable in the current theory*)
wenzelm@16425
   980
fun inst x t = read_instantiate_sg (the_context()) [(x,t)];
paulson@8550
   981
paulson@8550
   982
wenzelm@4285
   983
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   984
wenzelm@4285
   985
fun instantiate' cTs cts thm =
wenzelm@4285
   986
  let
wenzelm@4285
   987
    fun err msg =
wenzelm@4285
   988
      raise TYPE ("instantiate': " ^ msg,
skalberg@15570
   989
        List.mapPartial (Option.map Thm.typ_of) cTs,
skalberg@15570
   990
        List.mapPartial (Option.map Thm.term_of) cts);
wenzelm@4285
   991
wenzelm@4285
   992
    fun inst_of (v, ct) =
wenzelm@16425
   993
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   994
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   995
berghofe@15797
   996
    fun tyinst_of (v, cT) =
wenzelm@16425
   997
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   998
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   999
wenzelm@4285
  1000
    fun zip_vars _ [] = []
skalberg@15531
  1001
      | zip_vars (_ :: vs) (NONE :: opt_ts) = zip_vars vs opt_ts
skalberg@15531
  1002
      | zip_vars (v :: vs) (SOME t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
  1003
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
  1004
wenzelm@4285
  1005
    (*instantiate types first!*)
wenzelm@4285
  1006
    val thm' =
wenzelm@4285
  1007
      if forall is_none cTs then thm
berghofe@15797
  1008
      else Thm.instantiate (map tyinst_of (zip_vars (tvars_of thm) cTs), []) thm;
wenzelm@4285
  1009
    in
wenzelm@4285
  1010
      if forall is_none cts then thm'
wenzelm@4285
  1011
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
  1012
    end;
wenzelm@4285
  1013
wenzelm@4285
  1014
berghofe@14081
  1015
berghofe@14081
  1016
(** renaming of bound variables **)
berghofe@14081
  1017
berghofe@14081
  1018
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
  1019
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
  1020
berghofe@14081
  1021
fun rename_bvars [] thm = thm
berghofe@14081
  1022
  | rename_bvars vs thm =
berghofe@14081
  1023
    let
wenzelm@16425
  1024
      val {thy, prop, ...} = rep_thm thm;
haftmann@17325
  1025
      fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
berghofe@14081
  1026
        | ren (t $ u) = ren t $ ren u
berghofe@14081
  1027
        | ren t = t;
wenzelm@16425
  1028
    in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
berghofe@14081
  1029
berghofe@14081
  1030
berghofe@14081
  1031
(* renaming in left-to-right order *)
berghofe@14081
  1032
berghofe@14081
  1033
fun rename_bvars' xs thm =
berghofe@14081
  1034
  let
wenzelm@16425
  1035
    val {thy, prop, ...} = rep_thm thm;
berghofe@14081
  1036
    fun rename [] t = ([], t)
berghofe@14081
  1037
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
  1038
          let val (xs', t') = rename xs t
skalberg@15570
  1039
          in (xs', Abs (getOpt (x',x), T, t')) end
berghofe@14081
  1040
      | rename xs (t $ u) =
berghofe@14081
  1041
          let
berghofe@14081
  1042
            val (xs', t') = rename xs t;
berghofe@14081
  1043
            val (xs'', u') = rename xs' u
berghofe@14081
  1044
          in (xs'', t' $ u') end
berghofe@14081
  1045
      | rename xs t = (xs, t);
berghofe@14081
  1046
  in case rename xs prop of
wenzelm@16425
  1047
      ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
berghofe@14081
  1048
    | _ => error "More names than abstractions in theorem"
berghofe@14081
  1049
  end;
berghofe@14081
  1050
berghofe@14081
  1051
berghofe@14081
  1052
wenzelm@5688
  1053
(* unvarify(T) *)
wenzelm@5688
  1054
wenzelm@5688
  1055
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
  1056
wenzelm@5688
  1057
fun unvarifyT thm =
wenzelm@5688
  1058
  let
wenzelm@16425
  1059
    val cT = Thm.ctyp_of (Thm.theory_of_thm thm);
skalberg@15531
  1060
    val tfrees = map (fn ((x, _), S) => SOME (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
  1061
  in instantiate' tfrees [] thm end;
wenzelm@5688
  1062
wenzelm@5688
  1063
fun unvarify raw_thm =
wenzelm@5688
  1064
  let
wenzelm@5688
  1065
    val thm = unvarifyT raw_thm;
wenzelm@16425
  1066
    val ct = Thm.cterm_of (Thm.theory_of_thm thm);
skalberg@15531
  1067
    val frees = map (fn ((x, _), T) => SOME (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
  1068
  in instantiate' [] frees thm end;
wenzelm@5688
  1069
wenzelm@5688
  1070
wenzelm@8605
  1071
(* tvars_intr_list *)
wenzelm@8605
  1072
wenzelm@8605
  1073
fun tfrees_of thm =
wenzelm@8605
  1074
  let val {hyps, prop, ...} = Thm.rep_thm thm
berghofe@15797
  1075
  in foldr Term.add_term_tfrees [] (prop :: hyps) end;
wenzelm@8605
  1076
wenzelm@8605
  1077
fun tvars_intr_list tfrees thm =
berghofe@15797
  1078
  apsnd (map (fn ((s, S), ixn) => (s, (ixn, S)))) (Thm.varifyT'
berghofe@15797
  1079
    (gen_rems (op = o apfst fst) (tfrees_of thm, tfrees)) thm);
wenzelm@8605
  1080
wenzelm@8605
  1081
wenzelm@6435
  1082
(* increment var indexes *)
wenzelm@6435
  1083
wenzelm@18025
  1084
fun incr_indexes th = Thm.incr_indexes (#maxidx (Thm.rep_thm th) + 1);
wenzelm@18025
  1085
wenzelm@6435
  1086
fun incr_indexes_wrt is cTs cts thms =
wenzelm@6435
  1087
  let
wenzelm@6435
  1088
    val maxidx =
skalberg@15570
  1089
      Library.foldl Int.max (~1, is @
wenzelm@6435
  1090
        map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
wenzelm@6435
  1091
        map (#maxidx o Thm.rep_cterm) cts @
wenzelm@6435
  1092
        map (#maxidx o Thm.rep_thm) thms);
berghofe@10414
  1093
  in Thm.incr_indexes (maxidx + 1) end;
wenzelm@6435
  1094
wenzelm@6435
  1095
wenzelm@8328
  1096
(* freeze_all *)
wenzelm@8328
  1097
wenzelm@8328
  1098
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
  1099
wenzelm@8328
  1100
fun freeze_all_TVars thm =
wenzelm@8328
  1101
  (case tvars_of thm of
wenzelm@8328
  1102
    [] => thm
wenzelm@8328
  1103
  | tvars =>
wenzelm@16425
  1104
      let val cert = Thm.ctyp_of (Thm.theory_of_thm thm)
skalberg@15531
  1105
      in instantiate' (map (fn ((x, _), S) => SOME (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
  1106
wenzelm@8328
  1107
fun freeze_all_Vars thm =
wenzelm@8328
  1108
  (case vars_of thm of
wenzelm@8328
  1109
    [] => thm
wenzelm@8328
  1110
  | vars =>
wenzelm@16425
  1111
      let val cert = Thm.cterm_of (Thm.theory_of_thm thm)
skalberg@15531
  1112
      in instantiate' [] (map (fn ((x, _), T) => SOME (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
  1113
wenzelm@8328
  1114
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
  1115
wenzelm@8328
  1116
wenzelm@11975
  1117
wenzelm@11975
  1118
(** meta-level conjunction **)
wenzelm@11975
  1119
wenzelm@11975
  1120
local
wenzelm@11975
  1121
  val A = read_prop "PROP A";
wenzelm@11975
  1122
  val B = read_prop "PROP B";
wenzelm@11975
  1123
  val C = read_prop "PROP C";
wenzelm@11975
  1124
  val ABC = read_prop "PROP A ==> PROP B ==> PROP C";
wenzelm@11975
  1125
wenzelm@11975
  1126
  val proj1 =
wenzelm@11975
  1127
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume A))
wenzelm@11975
  1128
    |> forall_elim_vars 0;
wenzelm@11975
  1129
wenzelm@11975
  1130
  val proj2 =
wenzelm@11975
  1131
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume B))
wenzelm@11975
  1132
    |> forall_elim_vars 0;
wenzelm@11975
  1133
wenzelm@11975
  1134
  val conj_intr_rule =
wenzelm@11975
  1135
    forall_intr_list [A, B] (implies_intr_list [A, B]
wenzelm@11975
  1136
      (Thm.forall_intr C (Thm.implies_intr ABC
wenzelm@11975
  1137
        (implies_elim_list (Thm.assume ABC) [Thm.assume A, Thm.assume B]))))
wenzelm@11975
  1138
    |> forall_elim_vars 0;
wenzelm@11975
  1139
in
wenzelm@11975
  1140
wenzelm@18025
  1141
fun conj_intr tha thb = thb COMP (tha COMP incr_indexes_wrt [] [] [] [tha, thb] conj_intr_rule);
wenzelm@12756
  1142
wenzelm@12756
  1143
fun conj_intr_list [] = asm_rl
wenzelm@12756
  1144
  | conj_intr_list ths = foldr1 (uncurry conj_intr) ths;
wenzelm@11975
  1145
wenzelm@11975
  1146
fun conj_elim th =
wenzelm@11975
  1147
  let val th' = forall_elim_var (#maxidx (Thm.rep_thm th) + 1) th
wenzelm@18025
  1148
  in (incr_indexes th' proj1 COMP th', incr_indexes th' proj2 COMP th') end;
wenzelm@11975
  1149
wenzelm@11975
  1150
fun conj_elim_list th =
wenzelm@11975
  1151
  let val (th1, th2) = conj_elim th
wenzelm@11975
  1152
  in conj_elim_list th1 @ conj_elim_list th2 end handle THM _ => [th];
wenzelm@11975
  1153
wenzelm@12756
  1154
fun conj_elim_precise 0 _ = []
wenzelm@12756
  1155
  | conj_elim_precise 1 th = [th]
wenzelm@12135
  1156
  | conj_elim_precise n th =
wenzelm@12135
  1157
      let val (th1, th2) = conj_elim th
wenzelm@12135
  1158
      in th1 :: conj_elim_precise (n - 1) th2 end;
wenzelm@12135
  1159
wenzelm@12135
  1160
val conj_intr_thm = store_standard_thm_open "conjunctionI"
wenzelm@12135
  1161
  (implies_intr_list [A, B] (conj_intr (Thm.assume A) (Thm.assume B)));
wenzelm@12135
  1162
clasohm@0
  1163
end;
wenzelm@252
  1164
wenzelm@11975
  1165
end;
wenzelm@5903
  1166
wenzelm@5903
  1167
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1168
open BasicDrule;