src/Pure/drule.ML
author skalberg
Sun Feb 13 17:15:14 2005 +0100 (2005-02-13)
changeset 15531 08c8dad8e399
parent 15495 50fde6f04e4c
child 15545 0efa7126003f
permissions -rw-r--r--
Deleted Library.option type.
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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 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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                  -> (indexname*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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    (indexname * 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 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 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) 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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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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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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(** 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) = partition is_tv insts;
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    fun readT (ixn, st) =
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        let val S = case rsorts ixn of SOME S => S | NONE => absent 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) => (ixn,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,...} = rep_thm thm;
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        val big = list_comb(prop,hyps); (* bogus term! *)
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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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(** basic attributes **)
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(* dependent rules *)
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fun rule_attribute f (x, thm) = (x, (f x thm));
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(* add / delete tags *)
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fun map_tags f thm =
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  Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
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fun tag_rule tg = map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]);
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fun untag_rule s = map_tags (filter_out (equal s o #1));
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fun tag tg x = rule_attribute (K (tag_rule tg)) x;
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fun untag s x = rule_attribute (K (untag_rule s)) x;
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fun simple_tag name x = tag (name, []) x;
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(* theorem kinds *)
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val theoremK = "theorem";
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val lemmaK = "lemma";
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val corollaryK = "corollary";
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val internalK = "internal";
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fun get_kind thm =
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  (case Library.assoc (#2 (Thm.get_name_tags thm), "kind") of
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    SOME (k :: _) => k
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  | _ => "unknown");
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fun kind_rule k = tag_rule ("kind", [k]) o untag_rule "kind";
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fun kind k x = if k = "" then x else rule_attribute (K (kind_rule k)) x;
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fun kind_internal x = kind internalK x;
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fun has_internal tags = exists (equal internalK o fst) tags;
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(** Standardization of rules **)
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(*Strip extraneous shyps as far as possible*)
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fun strip_shyps_warning thm =
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  let
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    val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.sign_of_thm thm);
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    val thm' = Thm.strip_shyps thm;
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   314
    val xshyps = Thm.extra_shyps thm';
wenzelm@7636
   315
  in
wenzelm@7636
   316
    if null xshyps then ()
wenzelm@7636
   317
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   318
    thm'
wenzelm@7636
   319
  end;
wenzelm@7636
   320
clasohm@0
   321
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   322
fun forall_intr_list [] th = th
clasohm@0
   323
  | forall_intr_list (y::ys) th =
wenzelm@252
   324
        let val gth = forall_intr_list ys th
wenzelm@252
   325
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   326
clasohm@0
   327
(*Generalization over all suitable Free variables*)
clasohm@0
   328
fun forall_intr_frees th =
clasohm@0
   329
    let val {prop,sign,...} = rep_thm th
clasohm@0
   330
    in  forall_intr_list
wenzelm@4440
   331
         (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
clasohm@0
   332
         th
clasohm@0
   333
    end;
clasohm@0
   334
wenzelm@7898
   335
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   336
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   337
wenzelm@12725
   338
fun gen_all thm =
wenzelm@12719
   339
  let
wenzelm@12719
   340
    val {sign, prop, maxidx, ...} = Thm.rep_thm thm;
wenzelm@12719
   341
    fun elim (th, (x, T)) = Thm.forall_elim (Thm.cterm_of sign (Var ((x, maxidx + 1), T))) th;
wenzelm@12719
   342
    val vs = Term.strip_all_vars prop;
wenzelm@12719
   343
  in foldl elim (thm, Term.variantlist (map #1 vs, []) ~~ map #2 vs) end;
wenzelm@9554
   344
clasohm@0
   345
(*Specialization over a list of cterms*)
clasohm@0
   346
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
clasohm@0
   347
wenzelm@11815
   348
(* maps A1,...,An |- B   to   [| A1;...;An |] ==> B  *)
clasohm@0
   349
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
clasohm@0
   350
clasohm@0
   351
(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
clasohm@0
   352
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   353
wenzelm@11960
   354
(* maps |- B to A1,...,An |- B *)
wenzelm@11960
   355
fun impose_hyps chyps th =
wenzelm@12092
   356
  let val chyps' = gen_rems (op aconv o apfst Thm.term_of) (chyps, #hyps (Thm.rep_thm th))
wenzelm@12092
   357
  in implies_elim_list (implies_intr_list chyps' th) (map Thm.assume chyps') end;
wenzelm@11960
   358
wenzelm@13389
   359
(* maps A1,...,An and A1,...,An |- B to |- B *)
wenzelm@13389
   360
fun satisfy_hyps ths th =
wenzelm@13389
   361
  implies_elim_list (implies_intr_list (map (#prop o Thm.crep_thm) ths) th) ths;
wenzelm@13389
   362
clasohm@0
   363
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   364
fun zero_var_indexes th =
clasohm@0
   365
    let val {prop,sign,...} = rep_thm th;
clasohm@0
   366
        val vars = term_vars prop
clasohm@0
   367
        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
wenzelm@252
   368
        val inrs = add_term_tvars(prop,[]);
wenzelm@252
   369
        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
paulson@2266
   370
        val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs)))
wenzelm@8328
   371
                     (inrs, nms')
wenzelm@252
   372
        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
wenzelm@252
   373
        fun varpairs([],[]) = []
wenzelm@252
   374
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
wenzelm@252
   375
                let val T' = typ_subst_TVars tye T
wenzelm@252
   376
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   377
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   378
                end
wenzelm@252
   379
          | varpairs _ = raise TERM("varpairs", []);
paulson@8129
   380
    in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   381
clasohm@0
   382
paulson@14394
   383
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   384
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   385
paulson@14394
   386
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   387
  This step can lose information.*)
paulson@14387
   388
fun flexflex_unique th =
paulson@14387
   389
    case Seq.chop (2, flexflex_rule th) of
paulson@14387
   390
      ([th],_) => th
paulson@14387
   391
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   392
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   393
wenzelm@10515
   394
fun close_derivation thm =
wenzelm@10515
   395
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   396
  else thm;
wenzelm@10515
   397
berghofe@11512
   398
fun standard' th =
wenzelm@10515
   399
  let val {maxidx,...} = rep_thm th in
wenzelm@10515
   400
    th
berghofe@14391
   401
    |> implies_intr_hyps
wenzelm@10515
   402
    |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
wenzelm@10515
   403
    |> strip_shyps_warning
berghofe@11512
   404
    |> zero_var_indexes |> Thm.varifyT |> Thm.compress
wenzelm@1218
   405
  end;
wenzelm@1218
   406
berghofe@14391
   407
val standard = close_derivation o standard' o flexflex_unique;
berghofe@11512
   408
wenzelm@12005
   409
fun local_standard th =
wenzelm@12221
   410
  th |> strip_shyps |> zero_var_indexes
wenzelm@12005
   411
  |> Thm.compress |> close_derivation;
wenzelm@12005
   412
clasohm@0
   413
wenzelm@8328
   414
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   415
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   416
  Similar code in type/freeze_thaw*)
paulson@15495
   417
paulson@15495
   418
fun freeze_thaw_robust th =
paulson@15495
   419
 let val fth = freezeT th
paulson@15495
   420
     val {prop, tpairs, sign, ...} = rep_thm fth
paulson@15495
   421
 in
paulson@15495
   422
   case foldr add_term_vars (prop :: Thm.terms_of_tpairs tpairs, []) of
paulson@15495
   423
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   424
     | vars =>
paulson@15495
   425
         let fun newName (Var(ix,_), pairs) =
paulson@15495
   426
                   let val v = gensym (string_of_indexname ix)
paulson@15495
   427
                   in  ((ix,v)::pairs)  end;
paulson@15495
   428
             val alist = foldr newName (vars,[])
paulson@15495
   429
             fun mk_inst (Var(v,T)) =
paulson@15495
   430
                 (cterm_of sign (Var(v,T)),
paulson@15495
   431
                  cterm_of sign (Free(the (assoc(alist,v)), T)))
paulson@15495
   432
             val insts = map mk_inst vars
paulson@15495
   433
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   434
                 th' |> forall_intr_list (map #2 insts)
paulson@15495
   435
                     |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
paulson@15495
   436
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   437
 end;
paulson@15495
   438
paulson@15495
   439
(*Basic version of the function above. No option to rename Vars apart in thaw.
paulson@15495
   440
  The Frees created from Vars have nice names.*)
paulson@4610
   441
fun freeze_thaw th =
paulson@7248
   442
 let val fth = freezeT th
berghofe@13659
   443
     val {prop, tpairs, sign, ...} = rep_thm fth
paulson@7248
   444
 in
berghofe@13659
   445
   case foldr add_term_vars (prop :: Thm.terms_of_tpairs tpairs, []) of
paulson@7248
   446
       [] => (fth, fn x => x)
paulson@7248
   447
     | vars =>
wenzelm@8328
   448
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   449
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   450
                   in  ((ix,v)::pairs, v::used)  end;
berghofe@13659
   451
             val (alist, _) = foldr newName (vars, ([], foldr add_term_names
berghofe@13659
   452
               (prop :: Thm.terms_of_tpairs tpairs, [])))
wenzelm@8328
   453
             fun mk_inst (Var(v,T)) =
wenzelm@8328
   454
                 (cterm_of sign (Var(v,T)),
wenzelm@8328
   455
                  cterm_of sign (Free(the (assoc(alist,v)), T)))
wenzelm@8328
   456
             val insts = map mk_inst vars
wenzelm@8328
   457
             fun thaw th' =
wenzelm@8328
   458
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   459
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   460
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   461
 end;
paulson@4610
   462
paulson@7248
   463
(*Rotates a rule's premises to the left by k*)
paulson@7248
   464
val rotate_prems = permute_prems 0;
paulson@4610
   465
oheimb@11163
   466
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   467
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   468
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   469
val rearrange_prems = let
oheimb@11163
   470
  fun rearr new []      thm = thm
wenzelm@11815
   471
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   472
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   473
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   474
  in rearr 0 end;
paulson@4610
   475
wenzelm@252
   476
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   477
  Generalizes over Free variables,
clasohm@0
   478
  creates the assumption, and then strips quantifiers.
clasohm@0
   479
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   480
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   481
fun assume_ax thy sP =
wenzelm@6390
   482
    let val sign = Theory.sign_of thy
paulson@4610
   483
        val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
lcp@229
   484
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   485
wenzelm@252
   486
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   487
fun tha RSN (i,thb) =
wenzelm@4270
   488
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   489
      ([th],_) => th
clasohm@0
   490
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   491
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   492
clasohm@0
   493
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   494
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   495
clasohm@0
   496
(*For joining lists of rules*)
wenzelm@252
   497
fun thas RLN (i,thbs) =
clasohm@0
   498
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   499
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   500
  in  List.concat (map resb thbs)  end;
clasohm@0
   501
clasohm@0
   502
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   503
lcp@11
   504
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   505
  makes proof trees*)
wenzelm@252
   506
fun rls MRS bottom_rl =
lcp@11
   507
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   508
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   509
  in  rs_aux 1 rls  end;
lcp@11
   510
lcp@11
   511
(*As above, but for rule lists*)
wenzelm@252
   512
fun rlss MRL bottom_rls =
lcp@11
   513
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   514
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   515
  in  rs_aux 1 rlss  end;
lcp@11
   516
wenzelm@9288
   517
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   518
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   519
wenzelm@252
   520
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   521
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   522
  ALWAYS deletes premise i *)
wenzelm@252
   523
fun compose(tha,i,thb) =
wenzelm@4270
   524
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   525
wenzelm@6946
   526
fun compose_single (tha,i,thb) =
wenzelm@6946
   527
  (case compose (tha,i,thb) of
wenzelm@6946
   528
    [th] => th
wenzelm@6946
   529
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   530
clasohm@0
   531
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   532
fun tha COMP thb =
clasohm@0
   533
    case compose(tha,1,thb) of
wenzelm@252
   534
        [th] => th
clasohm@0
   535
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   536
wenzelm@13105
   537
wenzelm@4016
   538
(** theorem equality **)
clasohm@0
   539
paulson@13650
   540
(*True if the two theorems have the same signature.*)
wenzelm@13105
   541
val eq_thm_sg = Sign.eq_sg o pairself Thm.sign_of_thm;
paulson@13650
   542
paulson@13650
   543
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@13105
   544
val eq_thm_prop = op aconv o pairself Thm.prop_of;
clasohm@0
   545
clasohm@0
   546
(*Useful "distance" function for BEST_FIRST*)
wenzelm@12800
   547
val size_of_thm = size_of_term o prop_of;
clasohm@0
   548
wenzelm@9829
   549
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@13105
   550
fun del_rules rs rules = Library.gen_rems eq_thm_prop (rules, rs);
wenzelm@9862
   551
fun add_rules rs rules = rs @ del_rules rs rules;
wenzelm@12373
   552
val del_rule = del_rules o single;
wenzelm@12373
   553
val add_rule = add_rules o single;
wenzelm@13105
   554
fun merge_rules (rules1, rules2) = gen_merge_lists' eq_thm_prop rules1 rules2;
wenzelm@9829
   555
lcp@1194
   556
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   557
    (some) type variable renaming **)
lcp@1194
   558
lcp@1194
   559
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   560
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   561
    in the term. *)
lcp@1194
   562
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   563
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   564
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   565
  | term_vars' _ = [];
lcp@1194
   566
lcp@1194
   567
fun forall_intr_vars th =
lcp@1194
   568
  let val {prop,sign,...} = rep_thm th;
lcp@1194
   569
      val vars = distinct (term_vars' prop);
lcp@1194
   570
  in forall_intr_list (map (cterm_of sign) vars) th end;
lcp@1194
   571
wenzelm@13105
   572
val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
lcp@1194
   573
lcp@1194
   574
clasohm@0
   575
(*** Meta-Rewriting Rules ***)
clasohm@0
   576
paulson@4610
   577
fun read_prop s = read_cterm proto_sign (s, propT);
paulson@4610
   578
wenzelm@9455
   579
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   580
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   581
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   582
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   583
clasohm@0
   584
val reflexive_thm =
wenzelm@14854
   585
  let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   586
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   587
clasohm@0
   588
val symmetric_thm =
wenzelm@14854
   589
  let val xy = read_prop "x == y"
wenzelm@12135
   590
  in store_standard_thm_open "symmetric" (Thm.implies_intr_hyps (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   591
clasohm@0
   592
val transitive_thm =
wenzelm@14854
   593
  let val xy = read_prop "x == y"
wenzelm@14854
   594
      val yz = read_prop "y == z"
clasohm@0
   595
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   596
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   597
nipkow@4679
   598
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   599
berghofe@11512
   600
fun extensional eq =
berghofe@11512
   601
  let val eq' =
berghofe@11512
   602
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   603
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   604
berghofe@10414
   605
val imp_cong =
berghofe@10414
   606
  let
berghofe@10414
   607
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   608
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   609
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   610
    val A = read_prop "PROP A"
berghofe@10414
   611
  in
wenzelm@12135
   612
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   613
      (implies_intr AB (implies_intr A
berghofe@10414
   614
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   615
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   616
      (implies_intr AC (implies_intr A
berghofe@10414
   617
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   618
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   619
  end;
berghofe@10414
   620
berghofe@10414
   621
val swap_prems_eq =
berghofe@10414
   622
  let
berghofe@10414
   623
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   624
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   625
    val A = read_prop "PROP A"
berghofe@10414
   626
    val B = read_prop "PROP B"
berghofe@10414
   627
  in
wenzelm@12135
   628
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   629
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   630
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   631
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   632
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   633
  end;
lcp@229
   634
skalberg@15001
   635
val imp_cong' = combination o combination (reflexive implies)
clasohm@0
   636
berghofe@13325
   637
fun abs_def thm =
berghofe@13325
   638
  let
berghofe@13325
   639
    val (_, cvs) = strip_comb (fst (dest_equals (cprop_of thm)));
berghofe@13325
   640
    val thm' = foldr (fn (ct, thm) => Thm.abstract_rule
berghofe@13325
   641
      (case term_of ct of Var ((a, _), _) => a | Free (a, _) => a | _ => "x")
berghofe@13325
   642
        ct thm) (cvs, thm)
berghofe@13325
   643
  in transitive
berghofe@13325
   644
    (symmetric (eta_conversion (fst (dest_equals (cprop_of thm'))))) thm'
berghofe@13325
   645
  end;
berghofe@13325
   646
clasohm@0
   647
skalberg@15001
   648
local
skalberg@15001
   649
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   650
  val rhs_of = snd o dest_eq
skalberg@15001
   651
in
skalberg@15001
   652
fun beta_eta_conversion t =
skalberg@15001
   653
  let val thm = beta_conversion true t
skalberg@15001
   654
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   655
end;
skalberg@15001
   656
skalberg@15001
   657
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
skalberg@15001
   658
fun goals_conv pred cv =
skalberg@15001
   659
  let fun gconv i ct =
skalberg@15001
   660
        let val (A,B) = dest_implies ct
skalberg@15001
   661
        in imp_cong' (if pred i then cv A else reflexive A) (gconv (i+1) B) end
skalberg@15001
   662
        handle TERM _ => reflexive ct
skalberg@15001
   663
  in gconv 1 end
skalberg@15001
   664
skalberg@15001
   665
(* Rewrite A in !!x1,...,xn. A *)
skalberg@15001
   666
fun forall_conv cv ct =
skalberg@15001
   667
  let val p as (ct1, ct2) = Thm.dest_comb ct
skalberg@15001
   668
  in (case pairself term_of p of
skalberg@15001
   669
      (Const ("all", _), Abs (s, _, _)) =>
skalberg@15531
   670
         let val (v, ct') = Thm.dest_abs (SOME "@") ct2;
skalberg@15001
   671
         in Thm.combination (Thm.reflexive ct1)
skalberg@15001
   672
           (Thm.abstract_rule s v (forall_conv cv ct'))
skalberg@15001
   673
         end
skalberg@15001
   674
    | _ => cv ct)
skalberg@15001
   675
  end handle TERM _ => cv ct;
skalberg@15001
   676
skalberg@15001
   677
(*Use a conversion to transform a theorem*)
skalberg@15001
   678
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   679
skalberg@15531
   680
(*** SOME useful meta-theorems ***)
clasohm@0
   681
clasohm@0
   682
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   683
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   684
val _ = store_thm "_" asm_rl;
clasohm@0
   685
clasohm@0
   686
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   687
val cut_rl =
wenzelm@12135
   688
  store_standard_thm_open "cut_rl"
wenzelm@9455
   689
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   690
wenzelm@252
   691
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   692
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   693
val revcut_rl =
paulson@4610
   694
  let val V = read_prop "PROP V"
paulson@4610
   695
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   696
  in
wenzelm@12135
   697
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   698
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   699
  end;
clasohm@0
   700
lcp@668
   701
(*for deleting an unwanted assumption*)
lcp@668
   702
val thin_rl =
paulson@4610
   703
  let val V = read_prop "PROP V"
paulson@4610
   704
      and W = read_prop "PROP W";
wenzelm@12135
   705
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   706
clasohm@0
   707
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   708
val triv_forall_equality =
paulson@4610
   709
  let val V  = read_prop "PROP V"
paulson@4610
   710
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@8086
   711
      and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
wenzelm@4016
   712
  in
wenzelm@12135
   713
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   714
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   715
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   716
  end;
clasohm@0
   717
nipkow@1756
   718
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   719
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   720
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   721
*)
nipkow@1756
   722
val swap_prems_rl =
paulson@4610
   723
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   724
      val major = assume cmajor;
paulson@4610
   725
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   726
      val minor1 = assume cminor1;
paulson@4610
   727
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   728
      val minor2 = assume cminor2;
wenzelm@12135
   729
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   730
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   731
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   732
  end;
nipkow@1756
   733
nipkow@3653
   734
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   735
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   736
   Introduction rule for == as a meta-theorem.
nipkow@3653
   737
*)
nipkow@3653
   738
val equal_intr_rule =
paulson@4610
   739
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   740
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   741
  in
wenzelm@12135
   742
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   743
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   744
  end;
nipkow@3653
   745
wenzelm@13368
   746
(* [| PROP ?phi == PROP ?psi; PROP ?phi |] ==> PROP ?psi *)
wenzelm@13368
   747
val equal_elim_rule1 =
wenzelm@13368
   748
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   749
      and P = read_prop "PROP phi"
wenzelm@13368
   750
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   751
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   752
  end;
wenzelm@4285
   753
wenzelm@12297
   754
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   755
wenzelm@12297
   756
val remdups_rl =
wenzelm@12297
   757
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   758
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   759
wenzelm@12297
   760
wenzelm@9554
   761
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   762
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   763
wenzelm@9554
   764
val norm_hhf_eq =
wenzelm@9554
   765
  let
wenzelm@9554
   766
    val cert = Thm.cterm_of proto_sign;
wenzelm@14854
   767
    val aT = TFree ("'a", []);
wenzelm@9554
   768
    val all = Term.all aT;
wenzelm@9554
   769
    val x = Free ("x", aT);
wenzelm@9554
   770
    val phi = Free ("phi", propT);
wenzelm@9554
   771
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   772
wenzelm@9554
   773
    val cx = cert x;
wenzelm@9554
   774
    val cphi = cert phi;
wenzelm@9554
   775
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   776
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   777
  in
wenzelm@9554
   778
    Thm.equal_intr
wenzelm@9554
   779
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   780
        |> Thm.forall_elim cx
wenzelm@9554
   781
        |> Thm.implies_intr cphi
wenzelm@9554
   782
        |> Thm.forall_intr cx
wenzelm@9554
   783
        |> Thm.implies_intr lhs)
wenzelm@9554
   784
      (Thm.implies_elim
wenzelm@9554
   785
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   786
        |> Thm.forall_intr cx
wenzelm@9554
   787
        |> Thm.implies_intr cphi
wenzelm@9554
   788
        |> Thm.implies_intr rhs)
wenzelm@12135
   789
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   790
  end;
wenzelm@9554
   791
wenzelm@12800
   792
fun is_norm_hhf tm =
wenzelm@12800
   793
  let
wenzelm@12800
   794
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   795
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   796
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   797
      | is_norm _ = true;
wenzelm@12800
   798
  in is_norm (Pattern.beta_eta_contract tm) end;
wenzelm@12800
   799
wenzelm@12800
   800
fun norm_hhf sg t =
wenzelm@12800
   801
  if is_norm_hhf t then t
berghofe@13198
   802
  else Pattern.rewrite_term (Sign.tsig_of sg) [Logic.dest_equals (prop_of norm_hhf_eq)] [] t;
wenzelm@12800
   803
wenzelm@9554
   804
paulson@8129
   805
(*** Instantiate theorem th, reading instantiations under signature sg ****)
paulson@8129
   806
paulson@8129
   807
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   808
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   809
paulson@8129
   810
fun read_instantiate_sg sg sinsts th =
paulson@8129
   811
    let val ts = types_sorts th;
wenzelm@12800
   812
        val used = add_term_tvarnames (prop_of th, []);
berghofe@15442
   813
        val sinsts' = map (apfst Syntax.indexname) sinsts
berghofe@15442
   814
    in  instantiate (read_insts sg ts ts used sinsts') th  end;
paulson@8129
   815
paulson@8129
   816
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   817
fun read_instantiate sinsts th =
wenzelm@14643
   818
    read_instantiate_sg (Thm.sign_of_thm th) sinsts th;
paulson@8129
   819
paulson@8129
   820
paulson@8129
   821
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   822
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   823
local
paulson@8129
   824
  fun add_types ((ct,cu), (sign,tye,maxidx)) =
paulson@8129
   825
    let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
paulson@8129
   826
        and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   827
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
paulson@8129
   828
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
wenzelm@14643
   829
        val (tye',maxi') = Type.unify (Sign.tsig_of sign') (tye, maxi) (T, U)
wenzelm@10403
   830
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
paulson@8129
   831
    in  (sign', tye', maxi')  end;
paulson@8129
   832
in
paulson@8129
   833
fun cterm_instantiate ctpairs0 th =
wenzelm@14643
   834
  let val (sign,tye,_) = foldr add_types (ctpairs0, (Thm.sign_of_thm th, Vartab.empty, 0))
paulson@14340
   835
      fun instT(ct,cu) = 
paulson@14340
   836
        let val inst = cterm_of sign o subst_TVars_Vartab tye o term_of
paulson@14340
   837
        in (inst ct, inst cu) end
paulson@8129
   838
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
berghofe@8406
   839
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   840
  handle TERM _ =>
paulson@8129
   841
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
paulson@8129
   842
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   843
end;
paulson@8129
   844
paulson@8129
   845
paulson@8129
   846
(** Derived rules mainly for METAHYPS **)
paulson@8129
   847
paulson@8129
   848
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   849
fun equal_abs_elim ca eqth =
paulson@8129
   850
  let val {sign=signa, t=a, ...} = rep_cterm ca
paulson@8129
   851
      and combth = combination eqth (reflexive ca)
paulson@8129
   852
      val {sign,prop,...} = rep_thm eqth
paulson@8129
   853
      val (abst,absu) = Logic.dest_equals prop
paulson@8129
   854
      val cterm = cterm_of (Sign.merge (sign,signa))
berghofe@10414
   855
  in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
berghofe@10414
   856
           (transitive combth (beta_conversion false (cterm (absu$a))))
paulson@8129
   857
  end
paulson@8129
   858
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   859
paulson@8129
   860
(*Calling equal_abs_elim with multiple terms*)
paulson@8129
   861
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
paulson@8129
   862
paulson@8129
   863
wenzelm@10667
   864
(*** Goal (PROP A) <==> PROP A ***)
wenzelm@4789
   865
wenzelm@4789
   866
local
wenzelm@10667
   867
  val cert = Thm.cterm_of proto_sign;
wenzelm@10667
   868
  val A = Free ("A", propT);
wenzelm@10667
   869
  val G = Logic.mk_goal A;
wenzelm@4789
   870
  val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
wenzelm@4789
   871
in
wenzelm@11741
   872
  val triv_goal = store_thm "triv_goal" (kind_rule internalK (standard
wenzelm@10667
   873
      (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume (cert A)))));
wenzelm@11741
   874
  val rev_triv_goal = store_thm "rev_triv_goal" (kind_rule internalK (standard
wenzelm@10667
   875
      (Thm.equal_elim G_def (Thm.assume (cert G)))));
wenzelm@4789
   876
end;
wenzelm@4789
   877
wenzelm@9460
   878
val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign Logic.goal_const);
wenzelm@6995
   879
fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
wenzelm@6995
   880
wenzelm@11815
   881
fun implies_intr_goals cprops thm =
wenzelm@11815
   882
  implies_elim_list (implies_intr_list cprops thm) (map assume_goal cprops)
wenzelm@11815
   883
  |> implies_intr_list (map mk_cgoal cprops);
wenzelm@11815
   884
wenzelm@4789
   885
wenzelm@4285
   886
wenzelm@5688
   887
(** variations on instantiate **)
wenzelm@4285
   888
paulson@8550
   889
(*shorthand for instantiating just one variable in the current theory*)
paulson@8550
   890
fun inst x t = read_instantiate_sg (sign_of (the_context())) [(x,t)];
paulson@8550
   891
paulson@8550
   892
wenzelm@12495
   893
(* collect vars in left-to-right order *)
wenzelm@4285
   894
wenzelm@12495
   895
fun tvars_of_terms ts = rev (foldl Term.add_tvars ([], ts));
wenzelm@12495
   896
fun vars_of_terms ts = rev (foldl Term.add_vars ([], ts));
wenzelm@5903
   897
wenzelm@12800
   898
fun tvars_of thm = tvars_of_terms [prop_of thm];
wenzelm@12800
   899
fun vars_of thm = vars_of_terms [prop_of thm];
wenzelm@4285
   900
wenzelm@4285
   901
wenzelm@4285
   902
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   903
wenzelm@4285
   904
fun instantiate' cTs cts thm =
wenzelm@4285
   905
  let
wenzelm@4285
   906
    fun err msg =
wenzelm@4285
   907
      raise TYPE ("instantiate': " ^ msg,
wenzelm@4285
   908
        mapfilter (apsome Thm.typ_of) cTs,
wenzelm@4285
   909
        mapfilter (apsome Thm.term_of) cts);
wenzelm@4285
   910
wenzelm@4285
   911
    fun inst_of (v, ct) =
wenzelm@4285
   912
      (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
wenzelm@4285
   913
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   914
wenzelm@4285
   915
    fun zip_vars _ [] = []
skalberg@15531
   916
      | zip_vars (_ :: vs) (NONE :: opt_ts) = zip_vars vs opt_ts
skalberg@15531
   917
      | zip_vars (v :: vs) (SOME t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
   918
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
   919
wenzelm@4285
   920
    (*instantiate types first!*)
wenzelm@4285
   921
    val thm' =
wenzelm@4285
   922
      if forall is_none cTs then thm
wenzelm@4285
   923
      else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
wenzelm@4285
   924
    in
wenzelm@4285
   925
      if forall is_none cts then thm'
wenzelm@4285
   926
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
   927
    end;
wenzelm@4285
   928
wenzelm@4285
   929
berghofe@14081
   930
berghofe@14081
   931
(** renaming of bound variables **)
berghofe@14081
   932
berghofe@14081
   933
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   934
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   935
berghofe@14081
   936
fun rename_bvars [] thm = thm
berghofe@14081
   937
  | rename_bvars vs thm =
berghofe@14081
   938
    let
berghofe@14081
   939
      val {sign, prop, ...} = rep_thm thm;
berghofe@14081
   940
      fun ren (Abs (x, T, t)) = Abs (if_none (assoc (vs, x)) x, T, ren t)
berghofe@14081
   941
        | ren (t $ u) = ren t $ ren u
berghofe@14081
   942
        | ren t = t;
berghofe@14081
   943
    in equal_elim (reflexive (cterm_of sign (ren prop))) thm end;
berghofe@14081
   944
berghofe@14081
   945
berghofe@14081
   946
(* renaming in left-to-right order *)
berghofe@14081
   947
berghofe@14081
   948
fun rename_bvars' xs thm =
berghofe@14081
   949
  let
berghofe@14081
   950
    val {sign, prop, ...} = rep_thm thm;
berghofe@14081
   951
    fun rename [] t = ([], t)
berghofe@14081
   952
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   953
          let val (xs', t') = rename xs t
berghofe@14081
   954
          in (xs', Abs (if_none x' x, T, t')) end
berghofe@14081
   955
      | rename xs (t $ u) =
berghofe@14081
   956
          let
berghofe@14081
   957
            val (xs', t') = rename xs t;
berghofe@14081
   958
            val (xs'', u') = rename xs' u
berghofe@14081
   959
          in (xs'', t' $ u') end
berghofe@14081
   960
      | rename xs t = (xs, t);
berghofe@14081
   961
  in case rename xs prop of
berghofe@14081
   962
      ([], prop') => equal_elim (reflexive (cterm_of sign prop')) thm
berghofe@14081
   963
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   964
  end;
berghofe@14081
   965
berghofe@14081
   966
berghofe@14081
   967
wenzelm@5688
   968
(* unvarify(T) *)
wenzelm@5688
   969
wenzelm@5688
   970
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
   971
wenzelm@5688
   972
fun unvarifyT thm =
wenzelm@5688
   973
  let
wenzelm@5688
   974
    val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
skalberg@15531
   975
    val tfrees = map (fn ((x, _), S) => SOME (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
   976
  in instantiate' tfrees [] thm end;
wenzelm@5688
   977
wenzelm@5688
   978
fun unvarify raw_thm =
wenzelm@5688
   979
  let
wenzelm@5688
   980
    val thm = unvarifyT raw_thm;
wenzelm@5688
   981
    val ct = Thm.cterm_of (Thm.sign_of_thm thm);
skalberg@15531
   982
    val frees = map (fn ((x, _), T) => SOME (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
   983
  in instantiate' [] frees thm end;
wenzelm@5688
   984
wenzelm@5688
   985
wenzelm@8605
   986
(* tvars_intr_list *)
wenzelm@8605
   987
wenzelm@8605
   988
fun tfrees_of thm =
wenzelm@8605
   989
  let val {hyps, prop, ...} = Thm.rep_thm thm
wenzelm@8605
   990
  in foldr Term.add_term_tfree_names (prop :: hyps, []) end;
wenzelm@8605
   991
wenzelm@8605
   992
fun tvars_intr_list tfrees thm =
wenzelm@8605
   993
  Thm.varifyT' (tfrees_of thm \\ tfrees) thm;
wenzelm@8605
   994
wenzelm@8605
   995
wenzelm@6435
   996
(* increment var indexes *)
wenzelm@6435
   997
wenzelm@6435
   998
fun incr_indexes_wrt is cTs cts thms =
wenzelm@6435
   999
  let
wenzelm@6435
  1000
    val maxidx =
wenzelm@6435
  1001
      foldl Int.max (~1, is @
wenzelm@6435
  1002
        map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
wenzelm@6435
  1003
        map (#maxidx o Thm.rep_cterm) cts @
wenzelm@6435
  1004
        map (#maxidx o Thm.rep_thm) thms);
berghofe@10414
  1005
  in Thm.incr_indexes (maxidx + 1) end;
wenzelm@6435
  1006
wenzelm@6435
  1007
wenzelm@8328
  1008
(* freeze_all *)
wenzelm@8328
  1009
wenzelm@8328
  1010
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
  1011
wenzelm@8328
  1012
fun freeze_all_TVars thm =
wenzelm@8328
  1013
  (case tvars_of thm of
wenzelm@8328
  1014
    [] => thm
wenzelm@8328
  1015
  | tvars =>
wenzelm@8328
  1016
      let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
skalberg@15531
  1017
      in instantiate' (map (fn ((x, _), S) => SOME (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
  1018
wenzelm@8328
  1019
fun freeze_all_Vars thm =
wenzelm@8328
  1020
  (case vars_of thm of
wenzelm@8328
  1021
    [] => thm
wenzelm@8328
  1022
  | vars =>
wenzelm@8328
  1023
      let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
skalberg@15531
  1024
      in instantiate' [] (map (fn ((x, _), T) => SOME (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
  1025
wenzelm@8328
  1026
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
  1027
wenzelm@8328
  1028
wenzelm@5688
  1029
(* mk_triv_goal *)
wenzelm@5688
  1030
wenzelm@5688
  1031
(*make an initial proof state, "PROP A ==> (PROP A)" *)
skalberg@15531
  1032
fun mk_triv_goal ct = instantiate' [] [SOME ct] triv_goal;
paulson@5311
  1033
wenzelm@11975
  1034
wenzelm@11975
  1035
wenzelm@11975
  1036
(** meta-level conjunction **)
wenzelm@11975
  1037
wenzelm@11975
  1038
local
wenzelm@11975
  1039
  val A = read_prop "PROP A";
wenzelm@11975
  1040
  val B = read_prop "PROP B";
wenzelm@11975
  1041
  val C = read_prop "PROP C";
wenzelm@11975
  1042
  val ABC = read_prop "PROP A ==> PROP B ==> PROP C";
wenzelm@11975
  1043
wenzelm@11975
  1044
  val proj1 =
wenzelm@11975
  1045
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume A))
wenzelm@11975
  1046
    |> forall_elim_vars 0;
wenzelm@11975
  1047
wenzelm@11975
  1048
  val proj2 =
wenzelm@11975
  1049
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume B))
wenzelm@11975
  1050
    |> forall_elim_vars 0;
wenzelm@11975
  1051
wenzelm@11975
  1052
  val conj_intr_rule =
wenzelm@11975
  1053
    forall_intr_list [A, B] (implies_intr_list [A, B]
wenzelm@11975
  1054
      (Thm.forall_intr C (Thm.implies_intr ABC
wenzelm@11975
  1055
        (implies_elim_list (Thm.assume ABC) [Thm.assume A, Thm.assume B]))))
wenzelm@11975
  1056
    |> forall_elim_vars 0;
wenzelm@11975
  1057
wenzelm@11975
  1058
  val incr = incr_indexes_wrt [] [] [];
wenzelm@11975
  1059
in
wenzelm@11975
  1060
wenzelm@11975
  1061
fun conj_intr tha thb = thb COMP (tha COMP incr [tha, thb] conj_intr_rule);
wenzelm@12756
  1062
wenzelm@12756
  1063
fun conj_intr_list [] = asm_rl
wenzelm@12756
  1064
  | conj_intr_list ths = foldr1 (uncurry conj_intr) ths;
wenzelm@11975
  1065
wenzelm@11975
  1066
fun conj_elim th =
wenzelm@11975
  1067
  let val th' = forall_elim_var (#maxidx (Thm.rep_thm th) + 1) th
wenzelm@11975
  1068
  in (incr [th'] proj1 COMP th', incr [th'] proj2 COMP th') end;
wenzelm@11975
  1069
wenzelm@11975
  1070
fun conj_elim_list th =
wenzelm@11975
  1071
  let val (th1, th2) = conj_elim th
wenzelm@11975
  1072
  in conj_elim_list th1 @ conj_elim_list th2 end handle THM _ => [th];
wenzelm@11975
  1073
wenzelm@12756
  1074
fun conj_elim_precise 0 _ = []
wenzelm@12756
  1075
  | conj_elim_precise 1 th = [th]
wenzelm@12135
  1076
  | conj_elim_precise n th =
wenzelm@12135
  1077
      let val (th1, th2) = conj_elim th
wenzelm@12135
  1078
      in th1 :: conj_elim_precise (n - 1) th2 end;
wenzelm@12135
  1079
wenzelm@12135
  1080
val conj_intr_thm = store_standard_thm_open "conjunctionI"
wenzelm@12135
  1081
  (implies_intr_list [A, B] (conj_intr (Thm.assume A) (Thm.assume B)));
wenzelm@12135
  1082
clasohm@0
  1083
end;
wenzelm@252
  1084
wenzelm@11975
  1085
end;
wenzelm@5903
  1086
wenzelm@5903
  1087
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1088
open BasicDrule;