src/Pure/drule.ML
author berghofe
Wed May 04 18:50:21 2005 +0200 (2005-05-04)
changeset 15925 f13f4694c36d
parent 15875 3e9a54e033b9
child 15949 fd02dd265b78
permissions -rw-r--r--
Added eta_long_conversion.
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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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          Sign.sg -> (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 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 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: Sign.sg -> (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_sg         : 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_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 strip_comb: cterm -> cterm * cterm list
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  val strip_type: ctyp -> ctyp list * ctyp
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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 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: Sign.sg -> term -> term
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  val triv_goal: thm
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  val rev_triv_goal: thm
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  val implies_intr_goals: cterm list -> thm -> thm
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  val freeze_all: thm -> thm
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  val mk_triv_goal: cterm -> 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': Sign.sg -> (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: much faster than calling cterm_of! **)
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(** SAME NAMES as in structure Logic: use compound identifiers! **)
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(*dest_implies for cterms. Note T=prop below*)
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fun dest_implies ct =
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    case 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 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, sign, ...} = Thm.rep_cterm ct
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  in Thm.cterm_of sign (f t) end;
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fun ctyp_fun f cT =
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  let val {T, sign, ...} = Thm.rep_ctyp cT
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  in Thm.ctyp_of sign (f T) end;
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val proto_sign = Theory.sign_of ProtoPure.thy;
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val implies = cterm_of proto_sign 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 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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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 sign (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 (sign,sorts) st;
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        in if Sign.typ_instance sign (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(sign,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 sign (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 sign (TVar (ixn, sort_of ixn)),
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      ctyp_of sign 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 = list_comb (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 assoc(frees,a) else assoc(vars,(a,i));
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        fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
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    in (typ,sort) end;
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fun add_used thm used =
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  let val {prop, hyps, tpairs, ...} = Thm.rep_thm thm in
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    add_term_tvarnames (prop, used)
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    |> fold (curry add_term_tvarnames) hyps
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    |> fold (curry add_term_tvarnames) (Thm.terms_of_tpairs tpairs)
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  end;
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wenzelm@7636
   306
wenzelm@9455
   307
wenzelm@9455
   308
(** basic attributes **)
wenzelm@9455
   309
wenzelm@9455
   310
(* dependent rules *)
wenzelm@9455
   311
wenzelm@9455
   312
fun rule_attribute f (x, thm) = (x, (f x thm));
wenzelm@9455
   313
wenzelm@9455
   314
wenzelm@9455
   315
(* add / delete tags *)
wenzelm@9455
   316
wenzelm@9455
   317
fun map_tags f thm =
wenzelm@9455
   318
  Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
wenzelm@9455
   319
wenzelm@9455
   320
fun tag_rule tg = map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]);
wenzelm@9455
   321
fun untag_rule s = map_tags (filter_out (equal s o #1));
wenzelm@9455
   322
wenzelm@9455
   323
fun tag tg x = rule_attribute (K (tag_rule tg)) x;
wenzelm@9455
   324
fun untag s x = rule_attribute (K (untag_rule s)) x;
wenzelm@9455
   325
wenzelm@9455
   326
fun simple_tag name x = tag (name, []) x;
wenzelm@9455
   327
wenzelm@11741
   328
wenzelm@11741
   329
(* theorem kinds *)
wenzelm@11741
   330
wenzelm@11741
   331
val theoremK = "theorem";
wenzelm@11741
   332
val lemmaK = "lemma";
wenzelm@11741
   333
val corollaryK = "corollary";
wenzelm@11741
   334
val internalK = "internal";
wenzelm@9455
   335
wenzelm@11741
   336
fun get_kind thm =
wenzelm@11741
   337
  (case Library.assoc (#2 (Thm.get_name_tags thm), "kind") of
skalberg@15531
   338
    SOME (k :: _) => k
wenzelm@11741
   339
  | _ => "unknown");
wenzelm@11741
   340
wenzelm@11741
   341
fun kind_rule k = tag_rule ("kind", [k]) o untag_rule "kind";
wenzelm@12710
   342
fun kind k x = if k = "" then x else rule_attribute (K (kind_rule k)) x;
wenzelm@11741
   343
fun kind_internal x = kind internalK x;
wenzelm@11741
   344
fun has_internal tags = exists (equal internalK o fst) tags;
wenzelm@9455
   345
wenzelm@9455
   346
wenzelm@9455
   347
clasohm@0
   348
(** Standardization of rules **)
clasohm@0
   349
wenzelm@7636
   350
(*Strip extraneous shyps as far as possible*)
wenzelm@7636
   351
fun strip_shyps_warning thm =
wenzelm@7636
   352
  let
wenzelm@14824
   353
    val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.sign_of_thm thm);
wenzelm@7636
   354
    val thm' = Thm.strip_shyps thm;
wenzelm@7636
   355
    val xshyps = Thm.extra_shyps thm';
wenzelm@7636
   356
  in
wenzelm@7636
   357
    if null xshyps then ()
wenzelm@7636
   358
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   359
    thm'
wenzelm@7636
   360
  end;
wenzelm@7636
   361
clasohm@0
   362
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   363
fun forall_intr_list [] th = th
clasohm@0
   364
  | forall_intr_list (y::ys) th =
wenzelm@252
   365
        let val gth = forall_intr_list ys th
wenzelm@252
   366
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   367
clasohm@0
   368
(*Generalization over all suitable Free variables*)
clasohm@0
   369
fun forall_intr_frees th =
clasohm@0
   370
    let val {prop,sign,...} = rep_thm th
clasohm@0
   371
    in  forall_intr_list
wenzelm@4440
   372
         (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
clasohm@0
   373
         th
clasohm@0
   374
    end;
clasohm@0
   375
wenzelm@7898
   376
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   377
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   378
wenzelm@12725
   379
fun gen_all thm =
wenzelm@12719
   380
  let
wenzelm@12719
   381
    val {sign, prop, maxidx, ...} = Thm.rep_thm thm;
wenzelm@12719
   382
    fun elim (th, (x, T)) = Thm.forall_elim (Thm.cterm_of sign (Var ((x, maxidx + 1), T))) th;
wenzelm@12719
   383
    val vs = Term.strip_all_vars prop;
skalberg@15570
   384
  in Library.foldl elim (thm, Term.variantlist (map #1 vs, []) ~~ map #2 vs) end;
wenzelm@9554
   385
clasohm@0
   386
(*Specialization over a list of cterms*)
skalberg@15574
   387
fun forall_elim_list cts th = foldr (uncurry forall_elim) th (rev cts);
clasohm@0
   388
wenzelm@11815
   389
(* maps A1,...,An |- B   to   [| A1;...;An |] ==> B  *)
skalberg@15574
   390
fun implies_intr_list cAs th = foldr (uncurry implies_intr) th cAs;
clasohm@0
   391
clasohm@0
   392
(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
skalberg@15570
   393
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   394
wenzelm@11960
   395
(* maps |- B to A1,...,An |- B *)
wenzelm@11960
   396
fun impose_hyps chyps th =
wenzelm@12092
   397
  let val chyps' = gen_rems (op aconv o apfst Thm.term_of) (chyps, #hyps (Thm.rep_thm th))
wenzelm@12092
   398
  in implies_elim_list (implies_intr_list chyps' th) (map Thm.assume chyps') end;
wenzelm@11960
   399
wenzelm@13389
   400
(* maps A1,...,An and A1,...,An |- B to |- B *)
wenzelm@13389
   401
fun satisfy_hyps ths th =
wenzelm@13389
   402
  implies_elim_list (implies_intr_list (map (#prop o Thm.crep_thm) ths) th) ths;
wenzelm@13389
   403
clasohm@0
   404
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   405
fun zero_var_indexes th =
dixon@15545
   406
    let val {prop,sign,tpairs,...} = rep_thm th;
dixon@15545
   407
        val (tpair_l, tpair_r) = Library.split_list tpairs;
skalberg@15574
   408
        val vars = foldr add_term_vars 
skalberg@15574
   409
                         (foldr add_term_vars (term_vars prop) tpair_l) tpair_r;
skalberg@15570
   410
        val bs = Library.foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
dixon@15545
   411
        val inrs = 
skalberg@15574
   412
            foldr add_term_tvars 
skalberg@15574
   413
                  (foldr add_term_tvars (term_tvars prop) tpair_l) tpair_r;
skalberg@15570
   414
        val nms' = rev(Library.foldl add_new_id ([], map (#1 o #1) inrs));
berghofe@15797
   415
        val tye = ListPair.map (fn ((v, rs), a) => (TVar (v, rs), TVar ((a, 0), rs)))
wenzelm@8328
   416
                     (inrs, nms')
berghofe@15797
   417
        val ctye = map (pairself (ctyp_of sign)) tye;
wenzelm@252
   418
        fun varpairs([],[]) = []
wenzelm@252
   419
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
berghofe@15797
   420
                let val T' = typ_subst_atomic tye T
wenzelm@252
   421
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   422
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   423
                end
wenzelm@252
   424
          | varpairs _ = raise TERM("varpairs", []);
paulson@8129
   425
    in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   426
clasohm@0
   427
paulson@14394
   428
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   429
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   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 =
paulson@14387
   434
    case Seq.chop (2, flexflex_rule th) of
paulson@14387
   435
      ([th],_) => th
paulson@14387
   436
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   437
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   438
wenzelm@10515
   439
fun close_derivation thm =
wenzelm@10515
   440
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   441
  else thm;
wenzelm@10515
   442
berghofe@11512
   443
fun standard' th =
wenzelm@10515
   444
  let val {maxidx,...} = rep_thm th in
wenzelm@10515
   445
    th
berghofe@14391
   446
    |> implies_intr_hyps
wenzelm@10515
   447
    |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
wenzelm@10515
   448
    |> strip_shyps_warning
berghofe@11512
   449
    |> zero_var_indexes |> Thm.varifyT |> Thm.compress
wenzelm@1218
   450
  end;
wenzelm@1218
   451
berghofe@14391
   452
val standard = close_derivation o standard' o flexflex_unique;
berghofe@11512
   453
wenzelm@12005
   454
fun local_standard th =
wenzelm@12221
   455
  th |> strip_shyps |> zero_var_indexes
wenzelm@12005
   456
  |> Thm.compress |> close_derivation;
wenzelm@12005
   457
clasohm@0
   458
wenzelm@8328
   459
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   460
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   461
  Similar code in type/freeze_thaw*)
paulson@15495
   462
paulson@15495
   463
fun freeze_thaw_robust th =
paulson@15495
   464
 let val fth = freezeT th
paulson@15495
   465
     val {prop, tpairs, sign, ...} = rep_thm fth
paulson@15495
   466
 in
skalberg@15574
   467
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   468
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   469
     | vars =>
paulson@15495
   470
         let fun newName (Var(ix,_), pairs) =
paulson@15495
   471
                   let val v = gensym (string_of_indexname ix)
paulson@15495
   472
                   in  ((ix,v)::pairs)  end;
skalberg@15574
   473
             val alist = foldr newName [] vars
paulson@15495
   474
             fun mk_inst (Var(v,T)) =
paulson@15495
   475
                 (cterm_of sign (Var(v,T)),
skalberg@15570
   476
                  cterm_of sign (Free(valOf (assoc(alist,v)), T)))
paulson@15495
   477
             val insts = map mk_inst vars
paulson@15495
   478
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   479
                 th' |> forall_intr_list (map #2 insts)
paulson@15495
   480
                     |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
paulson@15495
   481
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   482
 end;
paulson@15495
   483
paulson@15495
   484
(*Basic version of the function above. No option to rename Vars apart in thaw.
paulson@15495
   485
  The Frees created from Vars have nice names.*)
paulson@4610
   486
fun freeze_thaw th =
paulson@7248
   487
 let val fth = freezeT th
berghofe@13659
   488
     val {prop, tpairs, sign, ...} = rep_thm fth
paulson@7248
   489
 in
skalberg@15574
   490
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   491
       [] => (fth, fn x => x)
paulson@7248
   492
     | vars =>
wenzelm@8328
   493
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   494
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   495
                   in  ((ix,v)::pairs, v::used)  end;
skalberg@15574
   496
             val (alist, _) = foldr newName ([], Library.foldr add_term_names
skalberg@15574
   497
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   498
             fun mk_inst (Var(v,T)) =
wenzelm@8328
   499
                 (cterm_of sign (Var(v,T)),
skalberg@15570
   500
                  cterm_of sign (Free(valOf (assoc(alist,v)), T)))
wenzelm@8328
   501
             val insts = map mk_inst vars
wenzelm@8328
   502
             fun thaw th' =
wenzelm@8328
   503
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   504
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   505
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   506
 end;
paulson@4610
   507
paulson@7248
   508
(*Rotates a rule's premises to the left by k*)
paulson@7248
   509
val rotate_prems = permute_prems 0;
paulson@4610
   510
oheimb@11163
   511
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   512
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   513
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   514
val rearrange_prems = let
oheimb@11163
   515
  fun rearr new []      thm = thm
wenzelm@11815
   516
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   517
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   518
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   519
  in rearr 0 end;
paulson@4610
   520
wenzelm@252
   521
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   522
  Generalizes over Free variables,
clasohm@0
   523
  creates the assumption, and then strips quantifiers.
clasohm@0
   524
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   525
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   526
fun assume_ax thy sP =
wenzelm@6390
   527
    let val sign = Theory.sign_of thy
paulson@4610
   528
        val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
lcp@229
   529
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   530
wenzelm@252
   531
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   532
fun tha RSN (i,thb) =
wenzelm@4270
   533
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   534
      ([th],_) => th
clasohm@0
   535
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   536
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   537
clasohm@0
   538
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   539
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   540
clasohm@0
   541
(*For joining lists of rules*)
wenzelm@252
   542
fun thas RLN (i,thbs) =
clasohm@0
   543
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   544
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   545
  in  List.concat (map resb thbs)  end;
clasohm@0
   546
clasohm@0
   547
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   548
lcp@11
   549
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   550
  makes proof trees*)
wenzelm@252
   551
fun rls MRS bottom_rl =
lcp@11
   552
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   553
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   554
  in  rs_aux 1 rls  end;
lcp@11
   555
lcp@11
   556
(*As above, but for rule lists*)
wenzelm@252
   557
fun rlss MRL bottom_rls =
lcp@11
   558
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   559
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   560
  in  rs_aux 1 rlss  end;
lcp@11
   561
wenzelm@9288
   562
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   563
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   564
wenzelm@252
   565
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   566
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   567
  ALWAYS deletes premise i *)
wenzelm@252
   568
fun compose(tha,i,thb) =
wenzelm@4270
   569
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   570
wenzelm@6946
   571
fun compose_single (tha,i,thb) =
wenzelm@6946
   572
  (case compose (tha,i,thb) of
wenzelm@6946
   573
    [th] => th
wenzelm@6946
   574
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   575
clasohm@0
   576
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   577
fun tha COMP thb =
clasohm@0
   578
    case compose(tha,1,thb) of
wenzelm@252
   579
        [th] => th
clasohm@0
   580
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   581
wenzelm@13105
   582
wenzelm@4016
   583
(** theorem equality **)
clasohm@0
   584
paulson@13650
   585
(*True if the two theorems have the same signature.*)
wenzelm@13105
   586
val eq_thm_sg = Sign.eq_sg o pairself Thm.sign_of_thm;
paulson@13650
   587
paulson@13650
   588
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@13105
   589
val eq_thm_prop = op aconv o pairself Thm.prop_of;
clasohm@0
   590
clasohm@0
   591
(*Useful "distance" function for BEST_FIRST*)
wenzelm@12800
   592
val size_of_thm = size_of_term o prop_of;
clasohm@0
   593
wenzelm@9829
   594
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@13105
   595
fun del_rules rs rules = Library.gen_rems eq_thm_prop (rules, rs);
wenzelm@9862
   596
fun add_rules rs rules = rs @ del_rules rs rules;
wenzelm@12373
   597
val del_rule = del_rules o single;
wenzelm@12373
   598
val add_rule = add_rules o single;
wenzelm@13105
   599
fun merge_rules (rules1, rules2) = gen_merge_lists' eq_thm_prop rules1 rules2;
wenzelm@9829
   600
lcp@1194
   601
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   602
    (some) type variable renaming **)
lcp@1194
   603
lcp@1194
   604
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   605
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   606
    in the term. *)
lcp@1194
   607
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   608
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   609
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   610
  | term_vars' _ = [];
lcp@1194
   611
lcp@1194
   612
fun forall_intr_vars th =
lcp@1194
   613
  let val {prop,sign,...} = rep_thm th;
lcp@1194
   614
      val vars = distinct (term_vars' prop);
lcp@1194
   615
  in forall_intr_list (map (cterm_of sign) vars) th end;
lcp@1194
   616
wenzelm@13105
   617
val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
lcp@1194
   618
lcp@1194
   619
clasohm@0
   620
(*** Meta-Rewriting Rules ***)
clasohm@0
   621
paulson@4610
   622
fun read_prop s = read_cterm proto_sign (s, propT);
paulson@4610
   623
wenzelm@9455
   624
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   625
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   626
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   627
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   628
clasohm@0
   629
val reflexive_thm =
wenzelm@14854
   630
  let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   631
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   632
clasohm@0
   633
val symmetric_thm =
wenzelm@14854
   634
  let val xy = read_prop "x == y"
wenzelm@12135
   635
  in store_standard_thm_open "symmetric" (Thm.implies_intr_hyps (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   636
clasohm@0
   637
val transitive_thm =
wenzelm@14854
   638
  let val xy = read_prop "x == y"
wenzelm@14854
   639
      val yz = read_prop "y == z"
clasohm@0
   640
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   641
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   642
nipkow@4679
   643
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   644
berghofe@11512
   645
fun extensional eq =
berghofe@11512
   646
  let val eq' =
berghofe@11512
   647
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   648
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   649
berghofe@10414
   650
val imp_cong =
berghofe@10414
   651
  let
berghofe@10414
   652
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   653
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   654
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   655
    val A = read_prop "PROP A"
berghofe@10414
   656
  in
wenzelm@12135
   657
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   658
      (implies_intr AB (implies_intr A
berghofe@10414
   659
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   660
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   661
      (implies_intr AC (implies_intr A
berghofe@10414
   662
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   663
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   664
  end;
berghofe@10414
   665
berghofe@10414
   666
val swap_prems_eq =
berghofe@10414
   667
  let
berghofe@10414
   668
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   669
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   670
    val A = read_prop "PROP A"
berghofe@10414
   671
    val B = read_prop "PROP B"
berghofe@10414
   672
  in
wenzelm@12135
   673
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   674
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   675
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   676
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   677
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   678
  end;
lcp@229
   679
skalberg@15001
   680
val imp_cong' = combination o combination (reflexive implies)
clasohm@0
   681
berghofe@13325
   682
fun abs_def thm =
berghofe@13325
   683
  let
berghofe@13325
   684
    val (_, cvs) = strip_comb (fst (dest_equals (cprop_of thm)));
skalberg@15574
   685
    val thm' = foldr (fn (ct, thm) => Thm.abstract_rule
berghofe@13325
   686
      (case term_of ct of Var ((a, _), _) => a | Free (a, _) => a | _ => "x")
skalberg@15574
   687
        ct thm) thm cvs
berghofe@13325
   688
  in transitive
berghofe@13325
   689
    (symmetric (eta_conversion (fst (dest_equals (cprop_of thm'))))) thm'
berghofe@13325
   690
  end;
berghofe@13325
   691
clasohm@0
   692
skalberg@15001
   693
local
skalberg@15001
   694
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   695
  val rhs_of = snd o dest_eq
skalberg@15001
   696
in
skalberg@15001
   697
fun beta_eta_conversion t =
skalberg@15001
   698
  let val thm = beta_conversion true t
skalberg@15001
   699
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   700
end;
skalberg@15001
   701
berghofe@15925
   702
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   703
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   704
skalberg@15001
   705
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
skalberg@15001
   706
fun goals_conv pred cv =
skalberg@15001
   707
  let fun gconv i ct =
skalberg@15001
   708
        let val (A,B) = dest_implies ct
skalberg@15001
   709
        in imp_cong' (if pred i then cv A else reflexive A) (gconv (i+1) B) end
skalberg@15001
   710
        handle TERM _ => reflexive ct
skalberg@15001
   711
  in gconv 1 end
skalberg@15001
   712
skalberg@15001
   713
(* Rewrite A in !!x1,...,xn. A *)
skalberg@15001
   714
fun forall_conv cv ct =
skalberg@15001
   715
  let val p as (ct1, ct2) = Thm.dest_comb ct
skalberg@15001
   716
  in (case pairself term_of p of
skalberg@15001
   717
      (Const ("all", _), Abs (s, _, _)) =>
skalberg@15531
   718
         let val (v, ct') = Thm.dest_abs (SOME "@") ct2;
skalberg@15001
   719
         in Thm.combination (Thm.reflexive ct1)
skalberg@15001
   720
           (Thm.abstract_rule s v (forall_conv cv ct'))
skalberg@15001
   721
         end
skalberg@15001
   722
    | _ => cv ct)
skalberg@15001
   723
  end handle TERM _ => cv ct;
skalberg@15001
   724
skalberg@15001
   725
(*Use a conversion to transform a theorem*)
skalberg@15001
   726
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   727
wenzelm@15669
   728
(*** Some useful meta-theorems ***)
clasohm@0
   729
clasohm@0
   730
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   731
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   732
val _ = store_thm "_" asm_rl;
clasohm@0
   733
clasohm@0
   734
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   735
val cut_rl =
wenzelm@12135
   736
  store_standard_thm_open "cut_rl"
wenzelm@9455
   737
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   738
wenzelm@252
   739
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   740
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   741
val revcut_rl =
paulson@4610
   742
  let val V = read_prop "PROP V"
paulson@4610
   743
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   744
  in
wenzelm@12135
   745
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   746
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   747
  end;
clasohm@0
   748
lcp@668
   749
(*for deleting an unwanted assumption*)
lcp@668
   750
val thin_rl =
paulson@4610
   751
  let val V = read_prop "PROP V"
paulson@4610
   752
      and W = read_prop "PROP W";
wenzelm@12135
   753
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   754
clasohm@0
   755
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   756
val triv_forall_equality =
paulson@4610
   757
  let val V  = read_prop "PROP V"
paulson@4610
   758
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@8086
   759
      and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
wenzelm@4016
   760
  in
wenzelm@12135
   761
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   762
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   763
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   764
  end;
clasohm@0
   765
nipkow@1756
   766
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   767
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   768
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   769
*)
nipkow@1756
   770
val swap_prems_rl =
paulson@4610
   771
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   772
      val major = assume cmajor;
paulson@4610
   773
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   774
      val minor1 = assume cminor1;
paulson@4610
   775
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   776
      val minor2 = assume cminor2;
wenzelm@12135
   777
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   778
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   779
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   780
  end;
nipkow@1756
   781
nipkow@3653
   782
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   783
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   784
   Introduction rule for == as a meta-theorem.
nipkow@3653
   785
*)
nipkow@3653
   786
val equal_intr_rule =
paulson@4610
   787
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   788
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   789
  in
wenzelm@12135
   790
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   791
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   792
  end;
nipkow@3653
   793
wenzelm@13368
   794
(* [| PROP ?phi == PROP ?psi; PROP ?phi |] ==> PROP ?psi *)
wenzelm@13368
   795
val equal_elim_rule1 =
wenzelm@13368
   796
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   797
      and P = read_prop "PROP phi"
wenzelm@13368
   798
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   799
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   800
  end;
wenzelm@4285
   801
wenzelm@12297
   802
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   803
wenzelm@12297
   804
val remdups_rl =
wenzelm@12297
   805
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   806
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   807
wenzelm@12297
   808
wenzelm@9554
   809
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   810
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   811
wenzelm@9554
   812
val norm_hhf_eq =
wenzelm@9554
   813
  let
wenzelm@9554
   814
    val cert = Thm.cterm_of proto_sign;
wenzelm@14854
   815
    val aT = TFree ("'a", []);
wenzelm@9554
   816
    val all = Term.all aT;
wenzelm@9554
   817
    val x = Free ("x", aT);
wenzelm@9554
   818
    val phi = Free ("phi", propT);
wenzelm@9554
   819
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   820
wenzelm@9554
   821
    val cx = cert x;
wenzelm@9554
   822
    val cphi = cert phi;
wenzelm@9554
   823
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   824
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   825
  in
wenzelm@9554
   826
    Thm.equal_intr
wenzelm@9554
   827
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   828
        |> Thm.forall_elim cx
wenzelm@9554
   829
        |> Thm.implies_intr cphi
wenzelm@9554
   830
        |> Thm.forall_intr cx
wenzelm@9554
   831
        |> Thm.implies_intr lhs)
wenzelm@9554
   832
      (Thm.implies_elim
wenzelm@9554
   833
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   834
        |> Thm.forall_intr cx
wenzelm@9554
   835
        |> Thm.implies_intr cphi
wenzelm@9554
   836
        |> Thm.implies_intr rhs)
wenzelm@12135
   837
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   838
  end;
wenzelm@9554
   839
wenzelm@12800
   840
fun is_norm_hhf tm =
wenzelm@12800
   841
  let
wenzelm@12800
   842
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   843
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   844
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   845
      | is_norm _ = true;
wenzelm@12800
   846
  in is_norm (Pattern.beta_eta_contract tm) end;
wenzelm@12800
   847
wenzelm@12800
   848
fun norm_hhf sg t =
wenzelm@12800
   849
  if is_norm_hhf t then t
berghofe@13198
   850
  else Pattern.rewrite_term (Sign.tsig_of sg) [Logic.dest_equals (prop_of norm_hhf_eq)] [] t;
wenzelm@12800
   851
wenzelm@9554
   852
paulson@8129
   853
(*** Instantiate theorem th, reading instantiations under signature sg ****)
paulson@8129
   854
paulson@8129
   855
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   856
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   857
berghofe@15797
   858
fun read_instantiate_sg' sg sinsts th =
paulson@8129
   859
    let val ts = types_sorts th;
wenzelm@15669
   860
        val used = add_used th [];
berghofe@15797
   861
    in  instantiate (read_insts sg ts ts used sinsts) th  end;
berghofe@15797
   862
berghofe@15797
   863
fun read_instantiate_sg sg sinsts th =
berghofe@15797
   864
  read_instantiate_sg' sg (map (apfst Syntax.indexname) sinsts) th;
paulson@8129
   865
paulson@8129
   866
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   867
fun read_instantiate sinsts th =
wenzelm@14643
   868
    read_instantiate_sg (Thm.sign_of_thm th) sinsts th;
paulson@8129
   869
berghofe@15797
   870
fun read_instantiate' sinsts th =
berghofe@15797
   871
    read_instantiate_sg' (Thm.sign_of_thm th) sinsts th;
berghofe@15797
   872
paulson@8129
   873
paulson@8129
   874
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   875
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   876
local
paulson@8129
   877
  fun add_types ((ct,cu), (sign,tye,maxidx)) =
paulson@8129
   878
    let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
paulson@8129
   879
        and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   880
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
paulson@8129
   881
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
wenzelm@14643
   882
        val (tye',maxi') = Type.unify (Sign.tsig_of sign') (tye, maxi) (T, U)
wenzelm@10403
   883
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
paulson@8129
   884
    in  (sign', tye', maxi')  end;
paulson@8129
   885
in
paulson@8129
   886
fun cterm_instantiate ctpairs0 th =
skalberg@15574
   887
  let val (sign,tye,_) = foldr add_types (Thm.sign_of_thm th, Vartab.empty, 0) ctpairs0
paulson@14340
   888
      fun instT(ct,cu) = 
berghofe@15797
   889
        let val inst = cterm_of sign o Envir.subst_TVars tye o term_of
paulson@14340
   890
        in (inst ct, inst cu) end
berghofe@15797
   891
      fun ctyp2 (ixn, (S, T)) = (ctyp_of sign (TVar (ixn, S)), ctyp_of sign T)
berghofe@8406
   892
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   893
  handle TERM _ =>
paulson@8129
   894
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
paulson@8129
   895
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   896
end;
paulson@8129
   897
paulson@8129
   898
paulson@8129
   899
(** Derived rules mainly for METAHYPS **)
paulson@8129
   900
paulson@8129
   901
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   902
fun equal_abs_elim ca eqth =
paulson@8129
   903
  let val {sign=signa, t=a, ...} = rep_cterm ca
paulson@8129
   904
      and combth = combination eqth (reflexive ca)
paulson@8129
   905
      val {sign,prop,...} = rep_thm eqth
paulson@8129
   906
      val (abst,absu) = Logic.dest_equals prop
paulson@8129
   907
      val cterm = cterm_of (Sign.merge (sign,signa))
berghofe@10414
   908
  in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
berghofe@10414
   909
           (transitive combth (beta_conversion false (cterm (absu$a))))
paulson@8129
   910
  end
paulson@8129
   911
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   912
paulson@8129
   913
(*Calling equal_abs_elim with multiple terms*)
skalberg@15574
   914
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) th (rev cts);
paulson@8129
   915
paulson@8129
   916
wenzelm@10667
   917
(*** Goal (PROP A) <==> PROP A ***)
wenzelm@4789
   918
wenzelm@4789
   919
local
wenzelm@10667
   920
  val cert = Thm.cterm_of proto_sign;
wenzelm@10667
   921
  val A = Free ("A", propT);
wenzelm@10667
   922
  val G = Logic.mk_goal A;
wenzelm@4789
   923
  val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
wenzelm@4789
   924
in
wenzelm@11741
   925
  val triv_goal = store_thm "triv_goal" (kind_rule internalK (standard
wenzelm@10667
   926
      (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume (cert A)))));
wenzelm@11741
   927
  val rev_triv_goal = store_thm "rev_triv_goal" (kind_rule internalK (standard
wenzelm@10667
   928
      (Thm.equal_elim G_def (Thm.assume (cert G)))));
wenzelm@4789
   929
end;
wenzelm@4789
   930
wenzelm@9460
   931
val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign Logic.goal_const);
wenzelm@6995
   932
fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
wenzelm@6995
   933
wenzelm@11815
   934
fun implies_intr_goals cprops thm =
wenzelm@11815
   935
  implies_elim_list (implies_intr_list cprops thm) (map assume_goal cprops)
wenzelm@11815
   936
  |> implies_intr_list (map mk_cgoal cprops);
wenzelm@11815
   937
wenzelm@4789
   938
wenzelm@4285
   939
wenzelm@5688
   940
(** variations on instantiate **)
wenzelm@4285
   941
paulson@8550
   942
(*shorthand for instantiating just one variable in the current theory*)
paulson@8550
   943
fun inst x t = read_instantiate_sg (sign_of (the_context())) [(x,t)];
paulson@8550
   944
paulson@8550
   945
wenzelm@12495
   946
(* collect vars in left-to-right order *)
wenzelm@4285
   947
skalberg@15570
   948
fun tvars_of_terms ts = rev (Library.foldl Term.add_tvars ([], ts));
skalberg@15570
   949
fun vars_of_terms ts = rev (Library.foldl Term.add_vars ([], ts));
wenzelm@5903
   950
wenzelm@12800
   951
fun tvars_of thm = tvars_of_terms [prop_of thm];
wenzelm@12800
   952
fun vars_of thm = vars_of_terms [prop_of thm];
wenzelm@4285
   953
wenzelm@4285
   954
wenzelm@4285
   955
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   956
wenzelm@4285
   957
fun instantiate' cTs cts thm =
wenzelm@4285
   958
  let
wenzelm@4285
   959
    fun err msg =
wenzelm@4285
   960
      raise TYPE ("instantiate': " ^ msg,
skalberg@15570
   961
        List.mapPartial (Option.map Thm.typ_of) cTs,
skalberg@15570
   962
        List.mapPartial (Option.map Thm.term_of) cts);
wenzelm@4285
   963
wenzelm@4285
   964
    fun inst_of (v, ct) =
wenzelm@4285
   965
      (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
wenzelm@4285
   966
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   967
berghofe@15797
   968
    fun tyinst_of (v, cT) =
berghofe@15797
   969
      (Thm.ctyp_of (#sign (Thm.rep_ctyp cT)) (TVar v), cT)
berghofe@15797
   970
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   971
wenzelm@4285
   972
    fun zip_vars _ [] = []
skalberg@15531
   973
      | zip_vars (_ :: vs) (NONE :: opt_ts) = zip_vars vs opt_ts
skalberg@15531
   974
      | zip_vars (v :: vs) (SOME t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
   975
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
   976
wenzelm@4285
   977
    (*instantiate types first!*)
wenzelm@4285
   978
    val thm' =
wenzelm@4285
   979
      if forall is_none cTs then thm
berghofe@15797
   980
      else Thm.instantiate (map tyinst_of (zip_vars (tvars_of thm) cTs), []) thm;
wenzelm@4285
   981
    in
wenzelm@4285
   982
      if forall is_none cts then thm'
wenzelm@4285
   983
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
   984
    end;
wenzelm@4285
   985
wenzelm@4285
   986
berghofe@14081
   987
berghofe@14081
   988
(** renaming of bound variables **)
berghofe@14081
   989
berghofe@14081
   990
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   991
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   992
berghofe@14081
   993
fun rename_bvars [] thm = thm
berghofe@14081
   994
  | rename_bvars vs thm =
berghofe@14081
   995
    let
berghofe@14081
   996
      val {sign, prop, ...} = rep_thm thm;
skalberg@15570
   997
      fun ren (Abs (x, T, t)) = Abs (getOpt (assoc (vs, x), x), T, ren t)
berghofe@14081
   998
        | ren (t $ u) = ren t $ ren u
berghofe@14081
   999
        | ren t = t;
berghofe@14081
  1000
    in equal_elim (reflexive (cterm_of sign (ren prop))) thm end;
berghofe@14081
  1001
berghofe@14081
  1002
berghofe@14081
  1003
(* renaming in left-to-right order *)
berghofe@14081
  1004
berghofe@14081
  1005
fun rename_bvars' xs thm =
berghofe@14081
  1006
  let
berghofe@14081
  1007
    val {sign, prop, ...} = rep_thm thm;
berghofe@14081
  1008
    fun rename [] t = ([], t)
berghofe@14081
  1009
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
  1010
          let val (xs', t') = rename xs t
skalberg@15570
  1011
          in (xs', Abs (getOpt (x',x), T, t')) end
berghofe@14081
  1012
      | rename xs (t $ u) =
berghofe@14081
  1013
          let
berghofe@14081
  1014
            val (xs', t') = rename xs t;
berghofe@14081
  1015
            val (xs'', u') = rename xs' u
berghofe@14081
  1016
          in (xs'', t' $ u') end
berghofe@14081
  1017
      | rename xs t = (xs, t);
berghofe@14081
  1018
  in case rename xs prop of
berghofe@14081
  1019
      ([], prop') => equal_elim (reflexive (cterm_of sign prop')) thm
berghofe@14081
  1020
    | _ => error "More names than abstractions in theorem"
berghofe@14081
  1021
  end;
berghofe@14081
  1022
berghofe@14081
  1023
berghofe@14081
  1024
wenzelm@5688
  1025
(* unvarify(T) *)
wenzelm@5688
  1026
wenzelm@5688
  1027
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
  1028
wenzelm@5688
  1029
fun unvarifyT thm =
wenzelm@5688
  1030
  let
wenzelm@5688
  1031
    val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
skalberg@15531
  1032
    val tfrees = map (fn ((x, _), S) => SOME (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
  1033
  in instantiate' tfrees [] thm end;
wenzelm@5688
  1034
wenzelm@5688
  1035
fun unvarify raw_thm =
wenzelm@5688
  1036
  let
wenzelm@5688
  1037
    val thm = unvarifyT raw_thm;
wenzelm@5688
  1038
    val ct = Thm.cterm_of (Thm.sign_of_thm thm);
skalberg@15531
  1039
    val frees = map (fn ((x, _), T) => SOME (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
  1040
  in instantiate' [] frees thm end;
wenzelm@5688
  1041
wenzelm@5688
  1042
wenzelm@8605
  1043
(* tvars_intr_list *)
wenzelm@8605
  1044
wenzelm@8605
  1045
fun tfrees_of thm =
wenzelm@8605
  1046
  let val {hyps, prop, ...} = Thm.rep_thm thm
berghofe@15797
  1047
  in foldr Term.add_term_tfrees [] (prop :: hyps) end;
wenzelm@8605
  1048
wenzelm@8605
  1049
fun tvars_intr_list tfrees thm =
berghofe@15797
  1050
  apsnd (map (fn ((s, S), ixn) => (s, (ixn, S)))) (Thm.varifyT'
berghofe@15797
  1051
    (gen_rems (op = o apfst fst) (tfrees_of thm, tfrees)) thm);
wenzelm@8605
  1052
wenzelm@8605
  1053
wenzelm@6435
  1054
(* increment var indexes *)
wenzelm@6435
  1055
wenzelm@6435
  1056
fun incr_indexes_wrt is cTs cts thms =
wenzelm@6435
  1057
  let
wenzelm@6435
  1058
    val maxidx =
skalberg@15570
  1059
      Library.foldl Int.max (~1, is @
wenzelm@6435
  1060
        map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
wenzelm@6435
  1061
        map (#maxidx o Thm.rep_cterm) cts @
wenzelm@6435
  1062
        map (#maxidx o Thm.rep_thm) thms);
berghofe@10414
  1063
  in Thm.incr_indexes (maxidx + 1) end;
wenzelm@6435
  1064
wenzelm@6435
  1065
wenzelm@8328
  1066
(* freeze_all *)
wenzelm@8328
  1067
wenzelm@8328
  1068
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
  1069
wenzelm@8328
  1070
fun freeze_all_TVars thm =
wenzelm@8328
  1071
  (case tvars_of thm of
wenzelm@8328
  1072
    [] => thm
wenzelm@8328
  1073
  | tvars =>
wenzelm@8328
  1074
      let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
skalberg@15531
  1075
      in instantiate' (map (fn ((x, _), S) => SOME (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
  1076
wenzelm@8328
  1077
fun freeze_all_Vars thm =
wenzelm@8328
  1078
  (case vars_of thm of
wenzelm@8328
  1079
    [] => thm
wenzelm@8328
  1080
  | vars =>
wenzelm@8328
  1081
      let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
skalberg@15531
  1082
      in instantiate' [] (map (fn ((x, _), T) => SOME (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
  1083
wenzelm@8328
  1084
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
  1085
wenzelm@8328
  1086
wenzelm@5688
  1087
(* mk_triv_goal *)
wenzelm@5688
  1088
wenzelm@5688
  1089
(*make an initial proof state, "PROP A ==> (PROP A)" *)
skalberg@15531
  1090
fun mk_triv_goal ct = instantiate' [] [SOME ct] triv_goal;
paulson@5311
  1091
wenzelm@11975
  1092
wenzelm@11975
  1093
wenzelm@11975
  1094
(** meta-level conjunction **)
wenzelm@11975
  1095
wenzelm@11975
  1096
local
wenzelm@11975
  1097
  val A = read_prop "PROP A";
wenzelm@11975
  1098
  val B = read_prop "PROP B";
wenzelm@11975
  1099
  val C = read_prop "PROP C";
wenzelm@11975
  1100
  val ABC = read_prop "PROP A ==> PROP B ==> PROP C";
wenzelm@11975
  1101
wenzelm@11975
  1102
  val proj1 =
wenzelm@11975
  1103
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume A))
wenzelm@11975
  1104
    |> forall_elim_vars 0;
wenzelm@11975
  1105
wenzelm@11975
  1106
  val proj2 =
wenzelm@11975
  1107
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume B))
wenzelm@11975
  1108
    |> forall_elim_vars 0;
wenzelm@11975
  1109
wenzelm@11975
  1110
  val conj_intr_rule =
wenzelm@11975
  1111
    forall_intr_list [A, B] (implies_intr_list [A, B]
wenzelm@11975
  1112
      (Thm.forall_intr C (Thm.implies_intr ABC
wenzelm@11975
  1113
        (implies_elim_list (Thm.assume ABC) [Thm.assume A, Thm.assume B]))))
wenzelm@11975
  1114
    |> forall_elim_vars 0;
wenzelm@11975
  1115
wenzelm@11975
  1116
  val incr = incr_indexes_wrt [] [] [];
wenzelm@11975
  1117
in
wenzelm@11975
  1118
wenzelm@11975
  1119
fun conj_intr tha thb = thb COMP (tha COMP incr [tha, thb] conj_intr_rule);
wenzelm@12756
  1120
wenzelm@12756
  1121
fun conj_intr_list [] = asm_rl
wenzelm@12756
  1122
  | conj_intr_list ths = foldr1 (uncurry conj_intr) ths;
wenzelm@11975
  1123
wenzelm@11975
  1124
fun conj_elim th =
wenzelm@11975
  1125
  let val th' = forall_elim_var (#maxidx (Thm.rep_thm th) + 1) th
wenzelm@11975
  1126
  in (incr [th'] proj1 COMP th', incr [th'] proj2 COMP th') end;
wenzelm@11975
  1127
wenzelm@11975
  1128
fun conj_elim_list th =
wenzelm@11975
  1129
  let val (th1, th2) = conj_elim th
wenzelm@11975
  1130
  in conj_elim_list th1 @ conj_elim_list th2 end handle THM _ => [th];
wenzelm@11975
  1131
wenzelm@12756
  1132
fun conj_elim_precise 0 _ = []
wenzelm@12756
  1133
  | conj_elim_precise 1 th = [th]
wenzelm@12135
  1134
  | conj_elim_precise n th =
wenzelm@12135
  1135
      let val (th1, th2) = conj_elim th
wenzelm@12135
  1136
      in th1 :: conj_elim_precise (n - 1) th2 end;
wenzelm@12135
  1137
wenzelm@12135
  1138
val conj_intr_thm = store_standard_thm_open "conjunctionI"
wenzelm@12135
  1139
  (implies_intr_list [A, B] (conj_intr (Thm.assume A) (Thm.assume B)));
wenzelm@12135
  1140
clasohm@0
  1141
end;
wenzelm@252
  1142
wenzelm@11975
  1143
end;
wenzelm@5903
  1144
wenzelm@5903
  1145
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1146
open BasicDrule;