src/Pure/drule.ML
author wenzelm
Fri Nov 10 19:09:40 2000 +0100 (2000-11-10)
changeset 10441 d727c39c4a4b
parent 10414 f7aeff3e9e1e
child 10515 8430c8fa8a9f
permissions -rw-r--r--
store_standard_thm "norm_hhf_eq";
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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 skip_flexpairs    : 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 -> (string*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 forall_elim_vars_safe  : 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 rotate_prems      : int -> 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 weak_eq_thm       : thm * thm -> bool
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  val eq_thm_sg         : 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 refl_implies      : thm
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  val symmetric_fun     : 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 flexpair_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 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 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 tag_lemma         : 'a attribute
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  val tag_assumption    : 'a attribute
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  val tag_internal      : 'a attribute
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  val has_internal	: tag list -> bool
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  val compose_single    : thm * int * thm -> thm
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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 norm_hhf_eq	: thm
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  val triv_goal         : thm
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  val rev_triv_goal     : 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 mk_cgoal          : cterm -> cterm
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  val assume_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 unvarifyT         : thm -> thm
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  val unvarify          : thm -> thm
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  val tvars_intr_list	: string list -> thm -> thm
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end;
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structure Drule: DRULE =
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struct
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(** some cterm->cterm operations: much faster than calling cterm_of! **)
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(** SAME NAMES as in structure Logic: use compound identifiers! **)
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(*dest_implies for cterms. Note T=prop below*)
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fun dest_implies ct =
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    case term_of ct of
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        (Const("==>", _) $ _ $ _) =>
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            let val (ct1,ct2) = dest_comb ct
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            in  (#2 (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) = dest_comb ct
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            in  (#2 (dest_comb ct1), ct2)  end
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      | _ => raise TERM ("dest_equals", [term_of ct]) ;
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(*Discard flexflex pairs; return a cterm*)
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fun skip_flexpairs ct =
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    case term_of ct of
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        (Const("==>", _) $ (Const("=?=",_)$_$_) $ _) =>
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            skip_flexpairs (#2 (dest_implies ct))
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      | _ => 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 (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 skip_flexpairs 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) = capply (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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(** 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 split([],tvs,vs) = (tvs,vs)
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      | split((sv,st)::l,tvs,vs) = (case Symbol.explode sv of
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                  "'"::cs => split(l,(Syntax.indexname cs,st)::tvs,vs)
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                | cs => split(l,tvs,(Syntax.indexname cs,st)::vs));
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    val (tvs,vs) = split(insts,[],[]);
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    fun readT((a,i),st) =
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        let val ixn = ("'" ^ a,i);
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            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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fun tag_lemma x = simple_tag "lemma" x;
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fun tag_assumption x = simple_tag "assumption" x;
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val internal_tag = ("internal", []);
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fun tag_internal x = tag internal_tag x;
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fun has_internal tags = exists (equal internal_tag) 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 = Sign.str_of_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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  in
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    if null xshyps then ()
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    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
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    thm'
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  end;
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(*Generalization over a list of variables, IGNORING bad ones*)
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fun forall_intr_list [] th = th
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  | forall_intr_list (y::ys) th =
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        let val gth = forall_intr_list ys th
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        in  forall_intr y gth   handle THM _ =>  gth  end;
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(*Generalization over all suitable Free variables*)
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fun forall_intr_frees th =
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    let val {prop,sign,...} = rep_thm th
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    in  forall_intr_list
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         (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
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         th
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    end;
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val forall_elim_var = PureThy.forall_elim_var;
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val forall_elim_vars = PureThy.forall_elim_vars;
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fun forall_elim_vars_safe th =
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  forall_elim_vars_safe (forall_elim_var (#maxidx (Thm.rep_thm th) + 1) th)
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    handle THM _ => th;
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(*Specialization over a list of cterms*)
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fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
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(* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
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fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
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(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
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fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
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(*Reset Var indexes to zero, renaming to preserve distinctness*)
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fun zero_var_indexes th =
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    let val {prop,sign,...} = rep_thm th;
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        val vars = term_vars prop
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        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
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        val inrs = add_term_tvars(prop,[]);
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        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
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        val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs)))
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                     (inrs, nms')
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        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
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        fun varpairs([],[]) = []
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   314
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
wenzelm@252
   315
                let val T' = typ_subst_TVars tye T
wenzelm@252
   316
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   317
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   318
                end
wenzelm@252
   319
          | varpairs _ = raise TERM("varpairs", []);
paulson@8129
   320
    in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   321
clasohm@0
   322
clasohm@0
   323
(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
clasohm@0
   324
    all generality expressed by Vars having index 0.*)
clasohm@0
   325
fun standard th =
wenzelm@1218
   326
  let val {maxidx,...} = rep_thm th
wenzelm@1237
   327
  in
wenzelm@1218
   328
    th |> implies_intr_hyps
paulson@1412
   329
       |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
wenzelm@7636
   330
       |> strip_shyps_warning
paulson@1412
   331
       |> zero_var_indexes |> Thm.varifyT |> Thm.compress
wenzelm@1218
   332
  end;
wenzelm@1218
   333
clasohm@0
   334
wenzelm@8328
   335
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   336
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   337
  Similar code in type/freeze_thaw*)
paulson@4610
   338
fun freeze_thaw th =
paulson@7248
   339
 let val fth = freezeT th
paulson@7248
   340
     val {prop,sign,...} = rep_thm fth
paulson@7248
   341
 in
paulson@7248
   342
   case term_vars prop of
paulson@7248
   343
       [] => (fth, fn x => x)
paulson@7248
   344
     | vars =>
wenzelm@8328
   345
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   346
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   347
                   in  ((ix,v)::pairs, v::used)  end;
wenzelm@8328
   348
             val (alist, _) = foldr newName
wenzelm@8328
   349
                                (vars, ([], add_term_names (prop, [])))
wenzelm@8328
   350
             fun mk_inst (Var(v,T)) =
wenzelm@8328
   351
                 (cterm_of sign (Var(v,T)),
wenzelm@8328
   352
                  cterm_of sign (Free(the (assoc(alist,v)), T)))
wenzelm@8328
   353
             val insts = map mk_inst vars
wenzelm@8328
   354
             fun thaw th' =
wenzelm@8328
   355
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   356
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   357
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   358
 end;
paulson@4610
   359
paulson@4610
   360
paulson@7248
   361
(*Rotates a rule's premises to the left by k*)
paulson@7248
   362
val rotate_prems = permute_prems 0;
paulson@4610
   363
paulson@4610
   364
wenzelm@252
   365
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   366
  Generalizes over Free variables,
clasohm@0
   367
  creates the assumption, and then strips quantifiers.
clasohm@0
   368
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   369
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   370
fun assume_ax thy sP =
wenzelm@6390
   371
    let val sign = Theory.sign_of thy
paulson@4610
   372
        val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
lcp@229
   373
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   374
wenzelm@252
   375
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   376
fun tha RSN (i,thb) =
wenzelm@4270
   377
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   378
      ([th],_) => th
clasohm@0
   379
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   380
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   381
clasohm@0
   382
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   383
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   384
clasohm@0
   385
(*For joining lists of rules*)
wenzelm@252
   386
fun thas RLN (i,thbs) =
clasohm@0
   387
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   388
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   389
  in  List.concat (map resb thbs)  end;
clasohm@0
   390
clasohm@0
   391
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   392
lcp@11
   393
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   394
  makes proof trees*)
wenzelm@252
   395
fun rls MRS bottom_rl =
lcp@11
   396
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   397
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   398
  in  rs_aux 1 rls  end;
lcp@11
   399
lcp@11
   400
(*As above, but for rule lists*)
wenzelm@252
   401
fun rlss MRL bottom_rls =
lcp@11
   402
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   403
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   404
  in  rs_aux 1 rlss  end;
lcp@11
   405
wenzelm@9288
   406
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   407
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   408
wenzelm@252
   409
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   410
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   411
  ALWAYS deletes premise i *)
wenzelm@252
   412
fun compose(tha,i,thb) =
wenzelm@4270
   413
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   414
wenzelm@6946
   415
fun compose_single (tha,i,thb) =
wenzelm@6946
   416
  (case compose (tha,i,thb) of
wenzelm@6946
   417
    [th] => th
wenzelm@6946
   418
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   419
clasohm@0
   420
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   421
fun tha COMP thb =
clasohm@0
   422
    case compose(tha,1,thb) of
wenzelm@252
   423
        [th] => th
clasohm@0
   424
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   425
wenzelm@4016
   426
(** theorem equality **)
clasohm@0
   427
clasohm@0
   428
(*Do the two theorems have the same signature?*)
wenzelm@252
   429
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
clasohm@0
   430
clasohm@0
   431
(*Useful "distance" function for BEST_FIRST*)
clasohm@0
   432
val size_of_thm = size_of_term o #prop o rep_thm;
clasohm@0
   433
wenzelm@9829
   434
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@9829
   435
fun del_rules rs rules = Library.gen_rems Thm.eq_thm (rules, rs);
wenzelm@9862
   436
fun add_rules rs rules = rs @ del_rules rs rules;
wenzelm@9829
   437
fun merge_rules (rules1, rules2) = Library.generic_merge Thm.eq_thm I I rules1 rules2;
wenzelm@9829
   438
clasohm@0
   439
lcp@1194
   440
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   441
    (some) type variable renaming **)
lcp@1194
   442
lcp@1194
   443
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   444
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   445
    in the term. *)
lcp@1194
   446
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   447
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   448
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   449
  | term_vars' _ = [];
lcp@1194
   450
lcp@1194
   451
fun forall_intr_vars th =
lcp@1194
   452
  let val {prop,sign,...} = rep_thm th;
lcp@1194
   453
      val vars = distinct (term_vars' prop);
lcp@1194
   454
  in forall_intr_list (map (cterm_of sign) vars) th end;
lcp@1194
   455
wenzelm@1237
   456
fun weak_eq_thm (tha,thb) =
lcp@1194
   457
    eq_thm(forall_intr_vars (freezeT tha), forall_intr_vars (freezeT thb));
lcp@1194
   458
lcp@1194
   459
lcp@1194
   460
clasohm@0
   461
(*** Meta-Rewriting Rules ***)
clasohm@0
   462
paulson@4610
   463
fun read_prop s = read_cterm proto_sign (s, propT);
paulson@4610
   464
wenzelm@9455
   465
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   466
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@4016
   467
clasohm@0
   468
val reflexive_thm =
paulson@4610
   469
  let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),logicS)))
wenzelm@9455
   470
  in store_standard_thm "reflexive" (Thm.reflexive cx) end;
clasohm@0
   471
clasohm@0
   472
val symmetric_thm =
paulson@4610
   473
  let val xy = read_prop "x::'a::logic == y"
wenzelm@9455
   474
  in store_standard_thm "symmetric" (Thm.implies_intr_hyps (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   475
clasohm@0
   476
val transitive_thm =
paulson@4610
   477
  let val xy = read_prop "x::'a::logic == y"
paulson@4610
   478
      val yz = read_prop "y::'a::logic == z"
clasohm@0
   479
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@9455
   480
  in store_standard_thm "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   481
nipkow@4679
   482
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   483
berghofe@10414
   484
val imp_cong =
berghofe@10414
   485
  let
berghofe@10414
   486
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   487
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   488
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   489
    val A = read_prop "PROP A"
berghofe@10414
   490
  in
berghofe@10414
   491
    store_standard_thm "imp_cong2" (implies_intr ABC (equal_intr
berghofe@10414
   492
      (implies_intr AB (implies_intr A
berghofe@10414
   493
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   494
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   495
      (implies_intr AC (implies_intr A
berghofe@10414
   496
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   497
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   498
  end;
berghofe@10414
   499
berghofe@10414
   500
val swap_prems_eq =
berghofe@10414
   501
  let
berghofe@10414
   502
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   503
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   504
    val A = read_prop "PROP A"
berghofe@10414
   505
    val B = read_prop "PROP B"
berghofe@10414
   506
  in
berghofe@10414
   507
    store_standard_thm "swap_prems_eq" (equal_intr
berghofe@10414
   508
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   509
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   510
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   511
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   512
  end;
lcp@229
   513
paulson@9547
   514
val refl_implies = reflexive implies;
clasohm@0
   515
clasohm@0
   516
clasohm@0
   517
(*** Some useful meta-theorems ***)
clasohm@0
   518
clasohm@0
   519
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@9455
   520
val asm_rl = store_standard_thm "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   521
val _ = store_thm "_" asm_rl;
clasohm@0
   522
clasohm@0
   523
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   524
val cut_rl =
wenzelm@9455
   525
  store_standard_thm "cut_rl"
wenzelm@9455
   526
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   527
wenzelm@252
   528
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   529
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   530
val revcut_rl =
paulson@4610
   531
  let val V = read_prop "PROP V"
paulson@4610
   532
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   533
  in
wenzelm@9455
   534
    store_standard_thm "revcut_rl"
wenzelm@4016
   535
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   536
  end;
clasohm@0
   537
lcp@668
   538
(*for deleting an unwanted assumption*)
lcp@668
   539
val thin_rl =
paulson@4610
   540
  let val V = read_prop "PROP V"
paulson@4610
   541
      and W = read_prop "PROP W";
wenzelm@9455
   542
  in  store_standard_thm "thin_rl" (implies_intr V (implies_intr W (assume W)))
lcp@668
   543
  end;
lcp@668
   544
clasohm@0
   545
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   546
val triv_forall_equality =
paulson@4610
   547
  let val V  = read_prop "PROP V"
paulson@4610
   548
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@8086
   549
      and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
wenzelm@4016
   550
  in
wenzelm@9455
   551
    store_standard_thm "triv_forall_equality"
wenzelm@9455
   552
      (standard (equal_intr (implies_intr QV (forall_elim x (assume QV)))
wenzelm@9455
   553
        (implies_intr V  (forall_intr x (assume V)))))
clasohm@0
   554
  end;
clasohm@0
   555
nipkow@1756
   556
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   557
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   558
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   559
*)
nipkow@1756
   560
val swap_prems_rl =
paulson@4610
   561
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   562
      val major = assume cmajor;
paulson@4610
   563
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   564
      val minor1 = assume cminor1;
paulson@4610
   565
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   566
      val minor2 = assume cminor2;
wenzelm@9455
   567
  in store_standard_thm "swap_prems_rl"
nipkow@1756
   568
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   569
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   570
  end;
nipkow@1756
   571
nipkow@3653
   572
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   573
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   574
   Introduction rule for == as a meta-theorem.
nipkow@3653
   575
*)
nipkow@3653
   576
val equal_intr_rule =
paulson@4610
   577
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   578
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   579
  in
wenzelm@9455
   580
    store_standard_thm "equal_intr_rule"
wenzelm@4016
   581
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   582
  end;
nipkow@3653
   583
wenzelm@4285
   584
wenzelm@9554
   585
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@9554
   586
  Rewrite rule for HHF normalization.
wenzelm@9554
   587
wenzelm@9554
   588
  Note: the syntax of ProtoPure is insufficient to handle this
wenzelm@9554
   589
  statement; storing it would be asking for trouble, e.g. when someone
wenzelm@9554
   590
  tries to print the theory later.
wenzelm@9554
   591
*)
wenzelm@9554
   592
wenzelm@9554
   593
val norm_hhf_eq =
wenzelm@9554
   594
  let
wenzelm@9554
   595
    val cert = Thm.cterm_of proto_sign;
wenzelm@9554
   596
    val aT = TFree ("'a", Term.logicS);
wenzelm@9554
   597
    val all = Term.all aT;
wenzelm@9554
   598
    val x = Free ("x", aT);
wenzelm@9554
   599
    val phi = Free ("phi", propT);
wenzelm@9554
   600
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   601
wenzelm@9554
   602
    val cx = cert x;
wenzelm@9554
   603
    val cphi = cert phi;
wenzelm@9554
   604
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   605
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   606
  in
wenzelm@9554
   607
    Thm.equal_intr
wenzelm@9554
   608
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   609
        |> Thm.forall_elim cx
wenzelm@9554
   610
        |> Thm.implies_intr cphi
wenzelm@9554
   611
        |> Thm.forall_intr cx
wenzelm@9554
   612
        |> Thm.implies_intr lhs)
wenzelm@9554
   613
      (Thm.implies_elim
wenzelm@9554
   614
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   615
        |> Thm.forall_intr cx
wenzelm@9554
   616
        |> Thm.implies_intr cphi
wenzelm@9554
   617
        |> Thm.implies_intr rhs)
wenzelm@10441
   618
    |> store_standard_thm "norm_hhf_eq"
wenzelm@9554
   619
  end;
wenzelm@9554
   620
wenzelm@9554
   621
paulson@8129
   622
(*** Instantiate theorem th, reading instantiations under signature sg ****)
paulson@8129
   623
paulson@8129
   624
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   625
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   626
paulson@8129
   627
fun read_instantiate_sg sg sinsts th =
paulson@8129
   628
    let val ts = types_sorts th;
paulson@8129
   629
        val used = add_term_tvarnames(#prop(rep_thm th),[]);
paulson@8129
   630
    in  instantiate (read_insts sg ts ts used sinsts) th  end;
paulson@8129
   631
paulson@8129
   632
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   633
fun read_instantiate sinsts th =
paulson@8129
   634
    read_instantiate_sg (#sign (rep_thm th)) sinsts th;
paulson@8129
   635
paulson@8129
   636
paulson@8129
   637
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   638
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   639
local
paulson@8129
   640
  fun add_types ((ct,cu), (sign,tye,maxidx)) =
paulson@8129
   641
    let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
paulson@8129
   642
        and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   643
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
paulson@8129
   644
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
paulson@8129
   645
        val (tye',maxi') = Type.unify (#tsig(Sign.rep_sg sign')) maxi tye (T,U)
wenzelm@10403
   646
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
paulson@8129
   647
    in  (sign', tye', maxi')  end;
paulson@8129
   648
in
paulson@8129
   649
fun cterm_instantiate ctpairs0 th =
berghofe@8406
   650
  let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th), Vartab.empty, 0))
berghofe@8406
   651
      fun instT(ct,cu) = let val inst = subst_TVars_Vartab tye
paulson@8129
   652
                         in (cterm_fun inst ct, cterm_fun inst cu) end
paulson@8129
   653
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
berghofe@8406
   654
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   655
  handle TERM _ =>
paulson@8129
   656
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
paulson@8129
   657
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   658
end;
paulson@8129
   659
paulson@8129
   660
paulson@8129
   661
(** Derived rules mainly for METAHYPS **)
paulson@8129
   662
paulson@8129
   663
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   664
fun equal_abs_elim ca eqth =
paulson@8129
   665
  let val {sign=signa, t=a, ...} = rep_cterm ca
paulson@8129
   666
      and combth = combination eqth (reflexive ca)
paulson@8129
   667
      val {sign,prop,...} = rep_thm eqth
paulson@8129
   668
      val (abst,absu) = Logic.dest_equals prop
paulson@8129
   669
      val cterm = cterm_of (Sign.merge (sign,signa))
berghofe@10414
   670
  in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
berghofe@10414
   671
           (transitive combth (beta_conversion false (cterm (absu$a))))
paulson@8129
   672
  end
paulson@8129
   673
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   674
paulson@8129
   675
(*Calling equal_abs_elim with multiple terms*)
paulson@8129
   676
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
paulson@8129
   677
paulson@8129
   678
local
paulson@8129
   679
  val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
paulson@8129
   680
  fun err th = raise THM("flexpair_inst: ", 0, [th])
paulson@8129
   681
  fun flexpair_inst def th =
paulson@8129
   682
    let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
paulson@8129
   683
        val cterm = cterm_of sign
paulson@8129
   684
        fun cvar a = cterm(Var((a,0),alpha))
paulson@8129
   685
        val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
paulson@8129
   686
                   def
paulson@8129
   687
    in  equal_elim def' th
paulson@8129
   688
    end
paulson@8129
   689
    handle THM _ => err th | Bind => err th
paulson@8129
   690
in
paulson@8129
   691
val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def)
paulson@8129
   692
and flexpair_elim = flexpair_inst ProtoPure.flexpair_def
paulson@8129
   693
end;
paulson@8129
   694
paulson@8129
   695
(*Version for flexflex pairs -- this supports lifting.*)
paulson@8129
   696
fun flexpair_abs_elim_list cts =
paulson@8129
   697
    flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
paulson@8129
   698
paulson@8129
   699
paulson@8129
   700
(*** GOAL (PROP A) <==> PROP A ***)
wenzelm@4789
   701
wenzelm@4789
   702
local
wenzelm@4789
   703
  val A = read_prop "PROP A";
wenzelm@4789
   704
  val G = read_prop "GOAL (PROP A)";
wenzelm@4789
   705
  val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
wenzelm@4789
   706
in
wenzelm@9455
   707
  val triv_goal = store_thm "triv_goal"
wenzelm@9455
   708
    (tag_rule internal_tag (standard (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume A))));
wenzelm@9455
   709
  val rev_triv_goal = store_thm "rev_triv_goal"
wenzelm@9455
   710
    (tag_rule internal_tag (standard (Thm.equal_elim G_def (Thm.assume G))));
wenzelm@4789
   711
end;
wenzelm@4789
   712
wenzelm@9460
   713
val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign Logic.goal_const);
wenzelm@6995
   714
fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
wenzelm@6995
   715
wenzelm@4789
   716
wenzelm@4285
   717
wenzelm@5688
   718
(** variations on instantiate **)
wenzelm@4285
   719
paulson@8550
   720
(*shorthand for instantiating just one variable in the current theory*)
paulson@8550
   721
fun inst x t = read_instantiate_sg (sign_of (the_context())) [(x,t)];
paulson@8550
   722
paulson@8550
   723
wenzelm@4285
   724
(* collect vars *)
wenzelm@4285
   725
wenzelm@4285
   726
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs);
wenzelm@4285
   727
val add_tvars = foldl_types add_tvarsT;
wenzelm@4285
   728
val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs);
wenzelm@4285
   729
wenzelm@5903
   730
fun tvars_of_terms ts = rev (foldl add_tvars ([], ts));
wenzelm@5903
   731
fun vars_of_terms ts = rev (foldl add_vars ([], ts));
wenzelm@5903
   732
wenzelm@5903
   733
fun tvars_of thm = tvars_of_terms [#prop (Thm.rep_thm thm)];
wenzelm@5903
   734
fun vars_of thm = vars_of_terms [#prop (Thm.rep_thm thm)];
wenzelm@4285
   735
wenzelm@4285
   736
wenzelm@4285
   737
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   738
wenzelm@4285
   739
fun instantiate' cTs cts thm =
wenzelm@4285
   740
  let
wenzelm@4285
   741
    fun err msg =
wenzelm@4285
   742
      raise TYPE ("instantiate': " ^ msg,
wenzelm@4285
   743
        mapfilter (apsome Thm.typ_of) cTs,
wenzelm@4285
   744
        mapfilter (apsome Thm.term_of) cts);
wenzelm@4285
   745
wenzelm@4285
   746
    fun inst_of (v, ct) =
wenzelm@4285
   747
      (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
wenzelm@4285
   748
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   749
wenzelm@4285
   750
    fun zip_vars _ [] = []
wenzelm@4285
   751
      | zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts
wenzelm@4285
   752
      | zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
   753
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
   754
wenzelm@4285
   755
    (*instantiate types first!*)
wenzelm@4285
   756
    val thm' =
wenzelm@4285
   757
      if forall is_none cTs then thm
wenzelm@4285
   758
      else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
wenzelm@4285
   759
    in
wenzelm@4285
   760
      if forall is_none cts then thm'
wenzelm@4285
   761
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
   762
    end;
wenzelm@4285
   763
wenzelm@4285
   764
wenzelm@5688
   765
(* unvarify(T) *)
wenzelm@5688
   766
wenzelm@5688
   767
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
   768
wenzelm@5688
   769
fun unvarifyT thm =
wenzelm@5688
   770
  let
wenzelm@5688
   771
    val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
wenzelm@5688
   772
    val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
   773
  in instantiate' tfrees [] thm end;
wenzelm@5688
   774
wenzelm@5688
   775
fun unvarify raw_thm =
wenzelm@5688
   776
  let
wenzelm@5688
   777
    val thm = unvarifyT raw_thm;
wenzelm@5688
   778
    val ct = Thm.cterm_of (Thm.sign_of_thm thm);
wenzelm@5688
   779
    val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
   780
  in instantiate' [] frees thm end;
wenzelm@5688
   781
wenzelm@5688
   782
wenzelm@8605
   783
(* tvars_intr_list *)
wenzelm@8605
   784
wenzelm@8605
   785
fun tfrees_of thm =
wenzelm@8605
   786
  let val {hyps, prop, ...} = Thm.rep_thm thm
wenzelm@8605
   787
  in foldr Term.add_term_tfree_names (prop :: hyps, []) end;
wenzelm@8605
   788
wenzelm@8605
   789
fun tvars_intr_list tfrees thm =
wenzelm@8605
   790
  Thm.varifyT' (tfrees_of thm \\ tfrees) thm;
wenzelm@8605
   791
wenzelm@8605
   792
wenzelm@6435
   793
(* increment var indexes *)
wenzelm@6435
   794
wenzelm@6435
   795
fun incr_indexes_wrt is cTs cts thms =
wenzelm@6435
   796
  let
wenzelm@6435
   797
    val maxidx =
wenzelm@6435
   798
      foldl Int.max (~1, is @
wenzelm@6435
   799
        map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
wenzelm@6435
   800
        map (#maxidx o Thm.rep_cterm) cts @
wenzelm@6435
   801
        map (#maxidx o Thm.rep_thm) thms);
berghofe@10414
   802
  in Thm.incr_indexes (maxidx + 1) end;
wenzelm@6435
   803
wenzelm@6435
   804
wenzelm@8328
   805
(* freeze_all *)
wenzelm@8328
   806
wenzelm@8328
   807
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
   808
wenzelm@8328
   809
fun freeze_all_TVars thm =
wenzelm@8328
   810
  (case tvars_of thm of
wenzelm@8328
   811
    [] => thm
wenzelm@8328
   812
  | tvars =>
wenzelm@8328
   813
      let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
wenzelm@8328
   814
      in instantiate' (map (fn ((x, _), S) => Some (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
   815
wenzelm@8328
   816
fun freeze_all_Vars thm =
wenzelm@8328
   817
  (case vars_of thm of
wenzelm@8328
   818
    [] => thm
wenzelm@8328
   819
  | vars =>
wenzelm@8328
   820
      let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
wenzelm@8328
   821
      in instantiate' [] (map (fn ((x, _), T) => Some (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
   822
wenzelm@8328
   823
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
   824
wenzelm@8328
   825
wenzelm@5688
   826
(* mk_triv_goal *)
wenzelm@5688
   827
wenzelm@5688
   828
(*make an initial proof state, "PROP A ==> (PROP A)" *)
paulson@5311
   829
fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal;
paulson@5311
   830
clasohm@0
   831
end;
wenzelm@252
   832
wenzelm@5903
   833
wenzelm@5903
   834
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
   835
open BasicDrule;