src/Pure/drule.ML
author berghofe
Tue Jan 18 14:34:24 2005 +0100 (2005-01-18 ago)
changeset 15442 3b75e1b22ff1
parent 15262 49f70168f4c0
child 15495 50fde6f04e4c
permissions -rw-r--r--
Added variants of instantiation functions that operate on pairs of type
(indexname * string) instead of (string * string).
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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 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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    val xshyps = Thm.extra_shyps thm';
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   314
  in
wenzelm@7636
   315
    if null xshyps then ()
wenzelm@7636
   316
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   317
    thm'
wenzelm@7636
   318
  end;
wenzelm@7636
   319
clasohm@0
   320
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   321
fun forall_intr_list [] th = th
clasohm@0
   322
  | forall_intr_list (y::ys) th =
wenzelm@252
   323
        let val gth = forall_intr_list ys th
wenzelm@252
   324
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   325
clasohm@0
   326
(*Generalization over all suitable Free variables*)
clasohm@0
   327
fun forall_intr_frees th =
clasohm@0
   328
    let val {prop,sign,...} = rep_thm th
clasohm@0
   329
    in  forall_intr_list
wenzelm@4440
   330
         (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
clasohm@0
   331
         th
clasohm@0
   332
    end;
clasohm@0
   333
wenzelm@7898
   334
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   335
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   336
wenzelm@12725
   337
fun gen_all thm =
wenzelm@12719
   338
  let
wenzelm@12719
   339
    val {sign, prop, maxidx, ...} = Thm.rep_thm thm;
wenzelm@12719
   340
    fun elim (th, (x, T)) = Thm.forall_elim (Thm.cterm_of sign (Var ((x, maxidx + 1), T))) th;
wenzelm@12719
   341
    val vs = Term.strip_all_vars prop;
wenzelm@12719
   342
  in foldl elim (thm, Term.variantlist (map #1 vs, []) ~~ map #2 vs) end;
wenzelm@9554
   343
clasohm@0
   344
(*Specialization over a list of cterms*)
clasohm@0
   345
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
clasohm@0
   346
wenzelm@11815
   347
(* maps A1,...,An |- B   to   [| A1;...;An |] ==> B  *)
clasohm@0
   348
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
clasohm@0
   349
clasohm@0
   350
(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
clasohm@0
   351
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   352
wenzelm@11960
   353
(* maps |- B to A1,...,An |- B *)
wenzelm@11960
   354
fun impose_hyps chyps th =
wenzelm@12092
   355
  let val chyps' = gen_rems (op aconv o apfst Thm.term_of) (chyps, #hyps (Thm.rep_thm th))
wenzelm@12092
   356
  in implies_elim_list (implies_intr_list chyps' th) (map Thm.assume chyps') end;
wenzelm@11960
   357
wenzelm@13389
   358
(* maps A1,...,An and A1,...,An |- B to |- B *)
wenzelm@13389
   359
fun satisfy_hyps ths th =
wenzelm@13389
   360
  implies_elim_list (implies_intr_list (map (#prop o Thm.crep_thm) ths) th) ths;
wenzelm@13389
   361
clasohm@0
   362
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   363
fun zero_var_indexes th =
clasohm@0
   364
    let val {prop,sign,...} = rep_thm th;
clasohm@0
   365
        val vars = term_vars prop
clasohm@0
   366
        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
wenzelm@252
   367
        val inrs = add_term_tvars(prop,[]);
wenzelm@252
   368
        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
paulson@2266
   369
        val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs)))
wenzelm@8328
   370
                     (inrs, nms')
wenzelm@252
   371
        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
wenzelm@252
   372
        fun varpairs([],[]) = []
wenzelm@252
   373
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
wenzelm@252
   374
                let val T' = typ_subst_TVars tye T
wenzelm@252
   375
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   376
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   377
                end
wenzelm@252
   378
          | varpairs _ = raise TERM("varpairs", []);
paulson@8129
   379
    in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   380
clasohm@0
   381
paulson@14394
   382
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   383
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   384
paulson@14394
   385
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   386
  This step can lose information.*)
paulson@14387
   387
fun flexflex_unique th =
paulson@14387
   388
    case Seq.chop (2, flexflex_rule th) of
paulson@14387
   389
      ([th],_) => th
paulson@14387
   390
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   391
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   392
wenzelm@10515
   393
fun close_derivation thm =
wenzelm@10515
   394
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   395
  else thm;
wenzelm@10515
   396
berghofe@11512
   397
fun standard' th =
wenzelm@10515
   398
  let val {maxidx,...} = rep_thm th in
wenzelm@10515
   399
    th
berghofe@14391
   400
    |> implies_intr_hyps
wenzelm@10515
   401
    |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
wenzelm@10515
   402
    |> strip_shyps_warning
berghofe@11512
   403
    |> zero_var_indexes |> Thm.varifyT |> Thm.compress
wenzelm@1218
   404
  end;
wenzelm@1218
   405
berghofe@14391
   406
val standard = close_derivation o standard' o flexflex_unique;
berghofe@11512
   407
wenzelm@12005
   408
fun local_standard th =
wenzelm@12221
   409
  th |> strip_shyps |> zero_var_indexes
wenzelm@12005
   410
  |> Thm.compress |> close_derivation;
wenzelm@12005
   411
clasohm@0
   412
wenzelm@8328
   413
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   414
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   415
  Similar code in type/freeze_thaw*)
paulson@4610
   416
fun freeze_thaw th =
paulson@7248
   417
 let val fth = freezeT th
berghofe@13659
   418
     val {prop, tpairs, sign, ...} = rep_thm fth
paulson@7248
   419
 in
berghofe@13659
   420
   case foldr add_term_vars (prop :: Thm.terms_of_tpairs tpairs, []) of
paulson@7248
   421
       [] => (fth, fn x => x)
paulson@7248
   422
     | vars =>
wenzelm@8328
   423
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   424
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   425
                   in  ((ix,v)::pairs, v::used)  end;
berghofe@13659
   426
             val (alist, _) = foldr newName (vars, ([], foldr add_term_names
berghofe@13659
   427
               (prop :: Thm.terms_of_tpairs tpairs, [])))
wenzelm@8328
   428
             fun mk_inst (Var(v,T)) =
wenzelm@8328
   429
                 (cterm_of sign (Var(v,T)),
wenzelm@8328
   430
                  cterm_of sign (Free(the (assoc(alist,v)), T)))
wenzelm@8328
   431
             val insts = map mk_inst vars
wenzelm@8328
   432
             fun thaw th' =
wenzelm@8328
   433
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   434
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   435
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   436
 end;
paulson@4610
   437
paulson@4610
   438
paulson@7248
   439
(*Rotates a rule's premises to the left by k*)
paulson@7248
   440
val rotate_prems = permute_prems 0;
paulson@4610
   441
oheimb@11163
   442
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   443
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   444
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   445
val rearrange_prems = let
oheimb@11163
   446
  fun rearr new []      thm = thm
wenzelm@11815
   447
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   448
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   449
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   450
  in rearr 0 end;
paulson@4610
   451
wenzelm@252
   452
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   453
  Generalizes over Free variables,
clasohm@0
   454
  creates the assumption, and then strips quantifiers.
clasohm@0
   455
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   456
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   457
fun assume_ax thy sP =
wenzelm@6390
   458
    let val sign = Theory.sign_of thy
paulson@4610
   459
        val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
lcp@229
   460
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   461
wenzelm@252
   462
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   463
fun tha RSN (i,thb) =
wenzelm@4270
   464
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   465
      ([th],_) => th
clasohm@0
   466
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   467
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   468
clasohm@0
   469
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   470
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   471
clasohm@0
   472
(*For joining lists of rules*)
wenzelm@252
   473
fun thas RLN (i,thbs) =
clasohm@0
   474
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   475
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   476
  in  List.concat (map resb thbs)  end;
clasohm@0
   477
clasohm@0
   478
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   479
lcp@11
   480
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   481
  makes proof trees*)
wenzelm@252
   482
fun rls MRS bottom_rl =
lcp@11
   483
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   484
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   485
  in  rs_aux 1 rls  end;
lcp@11
   486
lcp@11
   487
(*As above, but for rule lists*)
wenzelm@252
   488
fun rlss MRL bottom_rls =
lcp@11
   489
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   490
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   491
  in  rs_aux 1 rlss  end;
lcp@11
   492
wenzelm@9288
   493
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   494
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   495
wenzelm@252
   496
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   497
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   498
  ALWAYS deletes premise i *)
wenzelm@252
   499
fun compose(tha,i,thb) =
wenzelm@4270
   500
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   501
wenzelm@6946
   502
fun compose_single (tha,i,thb) =
wenzelm@6946
   503
  (case compose (tha,i,thb) of
wenzelm@6946
   504
    [th] => th
wenzelm@6946
   505
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   506
clasohm@0
   507
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   508
fun tha COMP thb =
clasohm@0
   509
    case compose(tha,1,thb) of
wenzelm@252
   510
        [th] => th
clasohm@0
   511
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   512
wenzelm@13105
   513
wenzelm@4016
   514
(** theorem equality **)
clasohm@0
   515
paulson@13650
   516
(*True if the two theorems have the same signature.*)
wenzelm@13105
   517
val eq_thm_sg = Sign.eq_sg o pairself Thm.sign_of_thm;
paulson@13650
   518
paulson@13650
   519
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@13105
   520
val eq_thm_prop = op aconv o pairself Thm.prop_of;
clasohm@0
   521
clasohm@0
   522
(*Useful "distance" function for BEST_FIRST*)
wenzelm@12800
   523
val size_of_thm = size_of_term o prop_of;
clasohm@0
   524
wenzelm@9829
   525
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@13105
   526
fun del_rules rs rules = Library.gen_rems eq_thm_prop (rules, rs);
wenzelm@9862
   527
fun add_rules rs rules = rs @ del_rules rs rules;
wenzelm@12373
   528
val del_rule = del_rules o single;
wenzelm@12373
   529
val add_rule = add_rules o single;
wenzelm@13105
   530
fun merge_rules (rules1, rules2) = gen_merge_lists' eq_thm_prop rules1 rules2;
wenzelm@9829
   531
lcp@1194
   532
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   533
    (some) type variable renaming **)
lcp@1194
   534
lcp@1194
   535
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   536
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   537
    in the term. *)
lcp@1194
   538
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   539
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   540
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   541
  | term_vars' _ = [];
lcp@1194
   542
lcp@1194
   543
fun forall_intr_vars th =
lcp@1194
   544
  let val {prop,sign,...} = rep_thm th;
lcp@1194
   545
      val vars = distinct (term_vars' prop);
lcp@1194
   546
  in forall_intr_list (map (cterm_of sign) vars) th end;
lcp@1194
   547
wenzelm@13105
   548
val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
lcp@1194
   549
lcp@1194
   550
clasohm@0
   551
(*** Meta-Rewriting Rules ***)
clasohm@0
   552
paulson@4610
   553
fun read_prop s = read_cterm proto_sign (s, propT);
paulson@4610
   554
wenzelm@9455
   555
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   556
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   557
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   558
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   559
clasohm@0
   560
val reflexive_thm =
wenzelm@14854
   561
  let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   562
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   563
clasohm@0
   564
val symmetric_thm =
wenzelm@14854
   565
  let val xy = read_prop "x == y"
wenzelm@12135
   566
  in store_standard_thm_open "symmetric" (Thm.implies_intr_hyps (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   567
clasohm@0
   568
val transitive_thm =
wenzelm@14854
   569
  let val xy = read_prop "x == y"
wenzelm@14854
   570
      val yz = read_prop "y == z"
clasohm@0
   571
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   572
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   573
nipkow@4679
   574
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   575
berghofe@11512
   576
fun extensional eq =
berghofe@11512
   577
  let val eq' =
berghofe@11512
   578
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   579
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   580
berghofe@10414
   581
val imp_cong =
berghofe@10414
   582
  let
berghofe@10414
   583
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   584
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   585
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   586
    val A = read_prop "PROP A"
berghofe@10414
   587
  in
wenzelm@12135
   588
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   589
      (implies_intr AB (implies_intr A
berghofe@10414
   590
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   591
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   592
      (implies_intr AC (implies_intr A
berghofe@10414
   593
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   594
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   595
  end;
berghofe@10414
   596
berghofe@10414
   597
val swap_prems_eq =
berghofe@10414
   598
  let
berghofe@10414
   599
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   600
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   601
    val A = read_prop "PROP A"
berghofe@10414
   602
    val B = read_prop "PROP B"
berghofe@10414
   603
  in
wenzelm@12135
   604
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   605
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   606
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   607
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   608
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   609
  end;
lcp@229
   610
skalberg@15001
   611
val imp_cong' = combination o combination (reflexive implies)
clasohm@0
   612
berghofe@13325
   613
fun abs_def thm =
berghofe@13325
   614
  let
berghofe@13325
   615
    val (_, cvs) = strip_comb (fst (dest_equals (cprop_of thm)));
berghofe@13325
   616
    val thm' = foldr (fn (ct, thm) => Thm.abstract_rule
berghofe@13325
   617
      (case term_of ct of Var ((a, _), _) => a | Free (a, _) => a | _ => "x")
berghofe@13325
   618
        ct thm) (cvs, thm)
berghofe@13325
   619
  in transitive
berghofe@13325
   620
    (symmetric (eta_conversion (fst (dest_equals (cprop_of thm'))))) thm'
berghofe@13325
   621
  end;
berghofe@13325
   622
clasohm@0
   623
skalberg@15001
   624
local
skalberg@15001
   625
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   626
  val rhs_of = snd o dest_eq
skalberg@15001
   627
in
skalberg@15001
   628
fun beta_eta_conversion t =
skalberg@15001
   629
  let val thm = beta_conversion true t
skalberg@15001
   630
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   631
end;
skalberg@15001
   632
skalberg@15001
   633
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
skalberg@15001
   634
fun goals_conv pred cv =
skalberg@15001
   635
  let fun gconv i ct =
skalberg@15001
   636
        let val (A,B) = dest_implies ct
skalberg@15001
   637
        in imp_cong' (if pred i then cv A else reflexive A) (gconv (i+1) B) end
skalberg@15001
   638
        handle TERM _ => reflexive ct
skalberg@15001
   639
  in gconv 1 end
skalberg@15001
   640
skalberg@15001
   641
(* Rewrite A in !!x1,...,xn. A *)
skalberg@15001
   642
fun forall_conv cv ct =
skalberg@15001
   643
  let val p as (ct1, ct2) = Thm.dest_comb ct
skalberg@15001
   644
  in (case pairself term_of p of
skalberg@15001
   645
      (Const ("all", _), Abs (s, _, _)) =>
skalberg@15001
   646
         let val (v, ct') = Thm.dest_abs (Some "@") ct2;
skalberg@15001
   647
         in Thm.combination (Thm.reflexive ct1)
skalberg@15001
   648
           (Thm.abstract_rule s v (forall_conv cv ct'))
skalberg@15001
   649
         end
skalberg@15001
   650
    | _ => cv ct)
skalberg@15001
   651
  end handle TERM _ => cv ct;
skalberg@15001
   652
skalberg@15001
   653
(*Use a conversion to transform a theorem*)
skalberg@15001
   654
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   655
clasohm@0
   656
(*** Some useful meta-theorems ***)
clasohm@0
   657
clasohm@0
   658
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   659
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   660
val _ = store_thm "_" asm_rl;
clasohm@0
   661
clasohm@0
   662
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   663
val cut_rl =
wenzelm@12135
   664
  store_standard_thm_open "cut_rl"
wenzelm@9455
   665
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   666
wenzelm@252
   667
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   668
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   669
val revcut_rl =
paulson@4610
   670
  let val V = read_prop "PROP V"
paulson@4610
   671
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   672
  in
wenzelm@12135
   673
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   674
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   675
  end;
clasohm@0
   676
lcp@668
   677
(*for deleting an unwanted assumption*)
lcp@668
   678
val thin_rl =
paulson@4610
   679
  let val V = read_prop "PROP V"
paulson@4610
   680
      and W = read_prop "PROP W";
wenzelm@12135
   681
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   682
clasohm@0
   683
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   684
val triv_forall_equality =
paulson@4610
   685
  let val V  = read_prop "PROP V"
paulson@4610
   686
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@8086
   687
      and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
wenzelm@4016
   688
  in
wenzelm@12135
   689
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   690
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   691
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   692
  end;
clasohm@0
   693
nipkow@1756
   694
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   695
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   696
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   697
*)
nipkow@1756
   698
val swap_prems_rl =
paulson@4610
   699
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   700
      val major = assume cmajor;
paulson@4610
   701
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   702
      val minor1 = assume cminor1;
paulson@4610
   703
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   704
      val minor2 = assume cminor2;
wenzelm@12135
   705
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   706
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   707
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   708
  end;
nipkow@1756
   709
nipkow@3653
   710
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   711
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   712
   Introduction rule for == as a meta-theorem.
nipkow@3653
   713
*)
nipkow@3653
   714
val equal_intr_rule =
paulson@4610
   715
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   716
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   717
  in
wenzelm@12135
   718
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   719
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   720
  end;
nipkow@3653
   721
wenzelm@13368
   722
(* [| PROP ?phi == PROP ?psi; PROP ?phi |] ==> PROP ?psi *)
wenzelm@13368
   723
val equal_elim_rule1 =
wenzelm@13368
   724
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   725
      and P = read_prop "PROP phi"
wenzelm@13368
   726
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   727
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   728
  end;
wenzelm@4285
   729
wenzelm@12297
   730
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   731
wenzelm@12297
   732
val remdups_rl =
wenzelm@12297
   733
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   734
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   735
wenzelm@12297
   736
wenzelm@9554
   737
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   738
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   739
wenzelm@9554
   740
val norm_hhf_eq =
wenzelm@9554
   741
  let
wenzelm@9554
   742
    val cert = Thm.cterm_of proto_sign;
wenzelm@14854
   743
    val aT = TFree ("'a", []);
wenzelm@9554
   744
    val all = Term.all aT;
wenzelm@9554
   745
    val x = Free ("x", aT);
wenzelm@9554
   746
    val phi = Free ("phi", propT);
wenzelm@9554
   747
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   748
wenzelm@9554
   749
    val cx = cert x;
wenzelm@9554
   750
    val cphi = cert phi;
wenzelm@9554
   751
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   752
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   753
  in
wenzelm@9554
   754
    Thm.equal_intr
wenzelm@9554
   755
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   756
        |> Thm.forall_elim cx
wenzelm@9554
   757
        |> Thm.implies_intr cphi
wenzelm@9554
   758
        |> Thm.forall_intr cx
wenzelm@9554
   759
        |> Thm.implies_intr lhs)
wenzelm@9554
   760
      (Thm.implies_elim
wenzelm@9554
   761
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   762
        |> Thm.forall_intr cx
wenzelm@9554
   763
        |> Thm.implies_intr cphi
wenzelm@9554
   764
        |> Thm.implies_intr rhs)
wenzelm@12135
   765
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   766
  end;
wenzelm@9554
   767
wenzelm@12800
   768
fun is_norm_hhf tm =
wenzelm@12800
   769
  let
wenzelm@12800
   770
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   771
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   772
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   773
      | is_norm _ = true;
wenzelm@12800
   774
  in is_norm (Pattern.beta_eta_contract tm) end;
wenzelm@12800
   775
wenzelm@12800
   776
fun norm_hhf sg t =
wenzelm@12800
   777
  if is_norm_hhf t then t
berghofe@13198
   778
  else Pattern.rewrite_term (Sign.tsig_of sg) [Logic.dest_equals (prop_of norm_hhf_eq)] [] t;
wenzelm@12800
   779
wenzelm@9554
   780
paulson@8129
   781
(*** Instantiate theorem th, reading instantiations under signature sg ****)
paulson@8129
   782
paulson@8129
   783
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   784
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   785
paulson@8129
   786
fun read_instantiate_sg sg sinsts th =
paulson@8129
   787
    let val ts = types_sorts th;
wenzelm@12800
   788
        val used = add_term_tvarnames (prop_of th, []);
berghofe@15442
   789
        val sinsts' = map (apfst Syntax.indexname) sinsts
berghofe@15442
   790
    in  instantiate (read_insts sg ts ts used sinsts') th  end;
paulson@8129
   791
paulson@8129
   792
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   793
fun read_instantiate sinsts th =
wenzelm@14643
   794
    read_instantiate_sg (Thm.sign_of_thm th) sinsts th;
paulson@8129
   795
paulson@8129
   796
paulson@8129
   797
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   798
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   799
local
paulson@8129
   800
  fun add_types ((ct,cu), (sign,tye,maxidx)) =
paulson@8129
   801
    let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
paulson@8129
   802
        and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   803
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
paulson@8129
   804
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
wenzelm@14643
   805
        val (tye',maxi') = Type.unify (Sign.tsig_of sign') (tye, maxi) (T, U)
wenzelm@10403
   806
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
paulson@8129
   807
    in  (sign', tye', maxi')  end;
paulson@8129
   808
in
paulson@8129
   809
fun cterm_instantiate ctpairs0 th =
wenzelm@14643
   810
  let val (sign,tye,_) = foldr add_types (ctpairs0, (Thm.sign_of_thm th, Vartab.empty, 0))
paulson@14340
   811
      fun instT(ct,cu) = 
paulson@14340
   812
        let val inst = cterm_of sign o subst_TVars_Vartab tye o term_of
paulson@14340
   813
        in (inst ct, inst cu) end
paulson@8129
   814
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
berghofe@8406
   815
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   816
  handle TERM _ =>
paulson@8129
   817
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
paulson@8129
   818
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   819
end;
paulson@8129
   820
paulson@8129
   821
paulson@8129
   822
(** Derived rules mainly for METAHYPS **)
paulson@8129
   823
paulson@8129
   824
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   825
fun equal_abs_elim ca eqth =
paulson@8129
   826
  let val {sign=signa, t=a, ...} = rep_cterm ca
paulson@8129
   827
      and combth = combination eqth (reflexive ca)
paulson@8129
   828
      val {sign,prop,...} = rep_thm eqth
paulson@8129
   829
      val (abst,absu) = Logic.dest_equals prop
paulson@8129
   830
      val cterm = cterm_of (Sign.merge (sign,signa))
berghofe@10414
   831
  in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
berghofe@10414
   832
           (transitive combth (beta_conversion false (cterm (absu$a))))
paulson@8129
   833
  end
paulson@8129
   834
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   835
paulson@8129
   836
(*Calling equal_abs_elim with multiple terms*)
paulson@8129
   837
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
paulson@8129
   838
paulson@8129
   839
wenzelm@10667
   840
(*** Goal (PROP A) <==> PROP A ***)
wenzelm@4789
   841
wenzelm@4789
   842
local
wenzelm@10667
   843
  val cert = Thm.cterm_of proto_sign;
wenzelm@10667
   844
  val A = Free ("A", propT);
wenzelm@10667
   845
  val G = Logic.mk_goal A;
wenzelm@4789
   846
  val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
wenzelm@4789
   847
in
wenzelm@11741
   848
  val triv_goal = store_thm "triv_goal" (kind_rule internalK (standard
wenzelm@10667
   849
      (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume (cert A)))));
wenzelm@11741
   850
  val rev_triv_goal = store_thm "rev_triv_goal" (kind_rule internalK (standard
wenzelm@10667
   851
      (Thm.equal_elim G_def (Thm.assume (cert G)))));
wenzelm@4789
   852
end;
wenzelm@4789
   853
wenzelm@9460
   854
val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign Logic.goal_const);
wenzelm@6995
   855
fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
wenzelm@6995
   856
wenzelm@11815
   857
fun implies_intr_goals cprops thm =
wenzelm@11815
   858
  implies_elim_list (implies_intr_list cprops thm) (map assume_goal cprops)
wenzelm@11815
   859
  |> implies_intr_list (map mk_cgoal cprops);
wenzelm@11815
   860
wenzelm@4789
   861
wenzelm@4285
   862
wenzelm@5688
   863
(** variations on instantiate **)
wenzelm@4285
   864
paulson@8550
   865
(*shorthand for instantiating just one variable in the current theory*)
paulson@8550
   866
fun inst x t = read_instantiate_sg (sign_of (the_context())) [(x,t)];
paulson@8550
   867
paulson@8550
   868
wenzelm@12495
   869
(* collect vars in left-to-right order *)
wenzelm@4285
   870
wenzelm@12495
   871
fun tvars_of_terms ts = rev (foldl Term.add_tvars ([], ts));
wenzelm@12495
   872
fun vars_of_terms ts = rev (foldl Term.add_vars ([], ts));
wenzelm@5903
   873
wenzelm@12800
   874
fun tvars_of thm = tvars_of_terms [prop_of thm];
wenzelm@12800
   875
fun vars_of thm = vars_of_terms [prop_of thm];
wenzelm@4285
   876
wenzelm@4285
   877
wenzelm@4285
   878
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   879
wenzelm@4285
   880
fun instantiate' cTs cts thm =
wenzelm@4285
   881
  let
wenzelm@4285
   882
    fun err msg =
wenzelm@4285
   883
      raise TYPE ("instantiate': " ^ msg,
wenzelm@4285
   884
        mapfilter (apsome Thm.typ_of) cTs,
wenzelm@4285
   885
        mapfilter (apsome Thm.term_of) cts);
wenzelm@4285
   886
wenzelm@4285
   887
    fun inst_of (v, ct) =
wenzelm@4285
   888
      (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
wenzelm@4285
   889
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   890
wenzelm@4285
   891
    fun zip_vars _ [] = []
wenzelm@4285
   892
      | zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts
wenzelm@4285
   893
      | zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
   894
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
   895
wenzelm@4285
   896
    (*instantiate types first!*)
wenzelm@4285
   897
    val thm' =
wenzelm@4285
   898
      if forall is_none cTs then thm
wenzelm@4285
   899
      else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
wenzelm@4285
   900
    in
wenzelm@4285
   901
      if forall is_none cts then thm'
wenzelm@4285
   902
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
   903
    end;
wenzelm@4285
   904
wenzelm@4285
   905
berghofe@14081
   906
berghofe@14081
   907
(** renaming of bound variables **)
berghofe@14081
   908
berghofe@14081
   909
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   910
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   911
berghofe@14081
   912
fun rename_bvars [] thm = thm
berghofe@14081
   913
  | rename_bvars vs thm =
berghofe@14081
   914
    let
berghofe@14081
   915
      val {sign, prop, ...} = rep_thm thm;
berghofe@14081
   916
      fun ren (Abs (x, T, t)) = Abs (if_none (assoc (vs, x)) x, T, ren t)
berghofe@14081
   917
        | ren (t $ u) = ren t $ ren u
berghofe@14081
   918
        | ren t = t;
berghofe@14081
   919
    in equal_elim (reflexive (cterm_of sign (ren prop))) thm end;
berghofe@14081
   920
berghofe@14081
   921
berghofe@14081
   922
(* renaming in left-to-right order *)
berghofe@14081
   923
berghofe@14081
   924
fun rename_bvars' xs thm =
berghofe@14081
   925
  let
berghofe@14081
   926
    val {sign, prop, ...} = rep_thm thm;
berghofe@14081
   927
    fun rename [] t = ([], t)
berghofe@14081
   928
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   929
          let val (xs', t') = rename xs t
berghofe@14081
   930
          in (xs', Abs (if_none x' x, T, t')) end
berghofe@14081
   931
      | rename xs (t $ u) =
berghofe@14081
   932
          let
berghofe@14081
   933
            val (xs', t') = rename xs t;
berghofe@14081
   934
            val (xs'', u') = rename xs' u
berghofe@14081
   935
          in (xs'', t' $ u') end
berghofe@14081
   936
      | rename xs t = (xs, t);
berghofe@14081
   937
  in case rename xs prop of
berghofe@14081
   938
      ([], prop') => equal_elim (reflexive (cterm_of sign prop')) thm
berghofe@14081
   939
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   940
  end;
berghofe@14081
   941
berghofe@14081
   942
berghofe@14081
   943
wenzelm@5688
   944
(* unvarify(T) *)
wenzelm@5688
   945
wenzelm@5688
   946
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
   947
wenzelm@5688
   948
fun unvarifyT thm =
wenzelm@5688
   949
  let
wenzelm@5688
   950
    val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
wenzelm@5688
   951
    val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
   952
  in instantiate' tfrees [] thm end;
wenzelm@5688
   953
wenzelm@5688
   954
fun unvarify raw_thm =
wenzelm@5688
   955
  let
wenzelm@5688
   956
    val thm = unvarifyT raw_thm;
wenzelm@5688
   957
    val ct = Thm.cterm_of (Thm.sign_of_thm thm);
wenzelm@5688
   958
    val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
   959
  in instantiate' [] frees thm end;
wenzelm@5688
   960
wenzelm@5688
   961
wenzelm@8605
   962
(* tvars_intr_list *)
wenzelm@8605
   963
wenzelm@8605
   964
fun tfrees_of thm =
wenzelm@8605
   965
  let val {hyps, prop, ...} = Thm.rep_thm thm
wenzelm@8605
   966
  in foldr Term.add_term_tfree_names (prop :: hyps, []) end;
wenzelm@8605
   967
wenzelm@8605
   968
fun tvars_intr_list tfrees thm =
wenzelm@8605
   969
  Thm.varifyT' (tfrees_of thm \\ tfrees) thm;
wenzelm@8605
   970
wenzelm@8605
   971
wenzelm@6435
   972
(* increment var indexes *)
wenzelm@6435
   973
wenzelm@6435
   974
fun incr_indexes_wrt is cTs cts thms =
wenzelm@6435
   975
  let
wenzelm@6435
   976
    val maxidx =
wenzelm@6435
   977
      foldl Int.max (~1, is @
wenzelm@6435
   978
        map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
wenzelm@6435
   979
        map (#maxidx o Thm.rep_cterm) cts @
wenzelm@6435
   980
        map (#maxidx o Thm.rep_thm) thms);
berghofe@10414
   981
  in Thm.incr_indexes (maxidx + 1) end;
wenzelm@6435
   982
wenzelm@6435
   983
wenzelm@8328
   984
(* freeze_all *)
wenzelm@8328
   985
wenzelm@8328
   986
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
   987
wenzelm@8328
   988
fun freeze_all_TVars thm =
wenzelm@8328
   989
  (case tvars_of thm of
wenzelm@8328
   990
    [] => thm
wenzelm@8328
   991
  | tvars =>
wenzelm@8328
   992
      let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
wenzelm@8328
   993
      in instantiate' (map (fn ((x, _), S) => Some (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
   994
wenzelm@8328
   995
fun freeze_all_Vars thm =
wenzelm@8328
   996
  (case vars_of thm of
wenzelm@8328
   997
    [] => thm
wenzelm@8328
   998
  | vars =>
wenzelm@8328
   999
      let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
wenzelm@8328
  1000
      in instantiate' [] (map (fn ((x, _), T) => Some (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
  1001
wenzelm@8328
  1002
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
  1003
wenzelm@8328
  1004
wenzelm@5688
  1005
(* mk_triv_goal *)
wenzelm@5688
  1006
wenzelm@5688
  1007
(*make an initial proof state, "PROP A ==> (PROP A)" *)
paulson@5311
  1008
fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal;
paulson@5311
  1009
wenzelm@11975
  1010
wenzelm@11975
  1011
wenzelm@11975
  1012
(** meta-level conjunction **)
wenzelm@11975
  1013
wenzelm@11975
  1014
local
wenzelm@11975
  1015
  val A = read_prop "PROP A";
wenzelm@11975
  1016
  val B = read_prop "PROP B";
wenzelm@11975
  1017
  val C = read_prop "PROP C";
wenzelm@11975
  1018
  val ABC = read_prop "PROP A ==> PROP B ==> PROP C";
wenzelm@11975
  1019
wenzelm@11975
  1020
  val proj1 =
wenzelm@11975
  1021
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume A))
wenzelm@11975
  1022
    |> forall_elim_vars 0;
wenzelm@11975
  1023
wenzelm@11975
  1024
  val proj2 =
wenzelm@11975
  1025
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume B))
wenzelm@11975
  1026
    |> forall_elim_vars 0;
wenzelm@11975
  1027
wenzelm@11975
  1028
  val conj_intr_rule =
wenzelm@11975
  1029
    forall_intr_list [A, B] (implies_intr_list [A, B]
wenzelm@11975
  1030
      (Thm.forall_intr C (Thm.implies_intr ABC
wenzelm@11975
  1031
        (implies_elim_list (Thm.assume ABC) [Thm.assume A, Thm.assume B]))))
wenzelm@11975
  1032
    |> forall_elim_vars 0;
wenzelm@11975
  1033
wenzelm@11975
  1034
  val incr = incr_indexes_wrt [] [] [];
wenzelm@11975
  1035
in
wenzelm@11975
  1036
wenzelm@11975
  1037
fun conj_intr tha thb = thb COMP (tha COMP incr [tha, thb] conj_intr_rule);
wenzelm@12756
  1038
wenzelm@12756
  1039
fun conj_intr_list [] = asm_rl
wenzelm@12756
  1040
  | conj_intr_list ths = foldr1 (uncurry conj_intr) ths;
wenzelm@11975
  1041
wenzelm@11975
  1042
fun conj_elim th =
wenzelm@11975
  1043
  let val th' = forall_elim_var (#maxidx (Thm.rep_thm th) + 1) th
wenzelm@11975
  1044
  in (incr [th'] proj1 COMP th', incr [th'] proj2 COMP th') end;
wenzelm@11975
  1045
wenzelm@11975
  1046
fun conj_elim_list th =
wenzelm@11975
  1047
  let val (th1, th2) = conj_elim th
wenzelm@11975
  1048
  in conj_elim_list th1 @ conj_elim_list th2 end handle THM _ => [th];
wenzelm@11975
  1049
wenzelm@12756
  1050
fun conj_elim_precise 0 _ = []
wenzelm@12756
  1051
  | conj_elim_precise 1 th = [th]
wenzelm@12135
  1052
  | conj_elim_precise n th =
wenzelm@12135
  1053
      let val (th1, th2) = conj_elim th
wenzelm@12135
  1054
      in th1 :: conj_elim_precise (n - 1) th2 end;
wenzelm@12135
  1055
wenzelm@12135
  1056
val conj_intr_thm = store_standard_thm_open "conjunctionI"
wenzelm@12135
  1057
  (implies_intr_list [A, B] (conj_intr (Thm.assume A) (Thm.assume B)));
wenzelm@12135
  1058
clasohm@0
  1059
end;
wenzelm@252
  1060
wenzelm@11975
  1061
end;
wenzelm@5903
  1062
wenzelm@5903
  1063
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1064
open BasicDrule;