src/Pure/drule.ML
author wenzelm
Thu Jul 27 18:27:09 2000 +0200 (2000-07-27 ago)
changeset 9455 f23722b4fbe7
parent 9418 96973ec6fda4
child 9460 53d7ad5bec39
permissions -rw-r--r--
export has_internal;
tag some rules as internal;
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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 dest_implies      : 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 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 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 rewrite_rule_aux  : (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
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  val rewrite_thm       : bool * bool * bool
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                          -> (meta_simpset -> thm -> thm option)
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                          -> meta_simpset -> thm -> thm
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  val rewrite_cterm     : bool * bool * bool
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                          -> (meta_simpset -> thm -> thm option)
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                          -> meta_simpset -> cterm -> thm
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  val rewrite_goals_rule_aux: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
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  val rewrite_goal_rule : bool* bool * bool
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                          -> (meta_simpset -> thm -> thm option)
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                          -> meta_simpset -> int -> thm -> 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      : int -> 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 merge_rules	: thm list * thm list -> thm list
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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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(*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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(** 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 val {tsig,...} = Sign.rep_sg sign
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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 Type.typ_instance(tsig,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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(*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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          | varpairs((var as Var(v,T)) :: vars, b::bs) =
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                let val T' = typ_subst_TVars tye T
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                in (cterm_of sign (Var(v,T')),
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                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
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                end
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          | varpairs _ = raise TERM("varpairs", []);
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    in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
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(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
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    all generality expressed by Vars having index 0.*)
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fun standard th =
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  let val {maxidx,...} = rep_thm th
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  in
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    th |> implies_intr_hyps
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       |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
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       |> strip_shyps_warning
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       |> zero_var_indexes |> Thm.varifyT |> Thm.compress
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  end;
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clasohm@0
   313
wenzelm@8328
   314
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   315
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   316
  Similar code in type/freeze_thaw*)
paulson@4610
   317
fun freeze_thaw th =
paulson@7248
   318
 let val fth = freezeT th
paulson@7248
   319
     val {prop,sign,...} = rep_thm fth
paulson@7248
   320
 in
paulson@7248
   321
   case term_vars prop of
paulson@7248
   322
       [] => (fth, fn x => x)
paulson@7248
   323
     | vars =>
wenzelm@8328
   324
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   325
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   326
                   in  ((ix,v)::pairs, v::used)  end;
wenzelm@8328
   327
             val (alist, _) = foldr newName
wenzelm@8328
   328
                                (vars, ([], add_term_names (prop, [])))
wenzelm@8328
   329
             fun mk_inst (Var(v,T)) =
wenzelm@8328
   330
                 (cterm_of sign (Var(v,T)),
wenzelm@8328
   331
                  cterm_of sign (Free(the (assoc(alist,v)), T)))
wenzelm@8328
   332
             val insts = map mk_inst vars
wenzelm@8328
   333
             fun thaw th' =
wenzelm@8328
   334
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   335
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   336
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   337
 end;
paulson@4610
   338
paulson@4610
   339
paulson@7248
   340
(*Rotates a rule's premises to the left by k*)
paulson@7248
   341
val rotate_prems = permute_prems 0;
paulson@4610
   342
paulson@4610
   343
wenzelm@252
   344
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   345
  Generalizes over Free variables,
clasohm@0
   346
  creates the assumption, and then strips quantifiers.
clasohm@0
   347
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   348
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   349
fun assume_ax thy sP =
wenzelm@6390
   350
    let val sign = Theory.sign_of thy
paulson@4610
   351
        val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
lcp@229
   352
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   353
wenzelm@252
   354
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   355
fun tha RSN (i,thb) =
wenzelm@4270
   356
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   357
      ([th],_) => th
clasohm@0
   358
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   359
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   360
clasohm@0
   361
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   362
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   363
clasohm@0
   364
(*For joining lists of rules*)
wenzelm@252
   365
fun thas RLN (i,thbs) =
clasohm@0
   366
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   367
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   368
  in  List.concat (map resb thbs)  end;
clasohm@0
   369
clasohm@0
   370
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   371
lcp@11
   372
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   373
  makes proof trees*)
wenzelm@252
   374
fun rls MRS bottom_rl =
lcp@11
   375
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   376
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   377
  in  rs_aux 1 rls  end;
lcp@11
   378
lcp@11
   379
(*As above, but for rule lists*)
wenzelm@252
   380
fun rlss MRL bottom_rls =
lcp@11
   381
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   382
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   383
  in  rs_aux 1 rlss  end;
lcp@11
   384
wenzelm@9288
   385
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   386
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   387
wenzelm@252
   388
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   389
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   390
  ALWAYS deletes premise i *)
wenzelm@252
   391
fun compose(tha,i,thb) =
wenzelm@4270
   392
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   393
wenzelm@6946
   394
fun compose_single (tha,i,thb) =
wenzelm@6946
   395
  (case compose (tha,i,thb) of
wenzelm@6946
   396
    [th] => th
wenzelm@6946
   397
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   398
clasohm@0
   399
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   400
fun tha COMP thb =
clasohm@0
   401
    case compose(tha,1,thb) of
wenzelm@252
   402
        [th] => th
clasohm@0
   403
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   404
wenzelm@4016
   405
(** theorem equality **)
clasohm@0
   406
clasohm@0
   407
(*Do the two theorems have the same signature?*)
wenzelm@252
   408
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
wenzelm@9418
   409
fun merge_rules (ths1, ths2) = Library.generic_merge Thm.eq_thm I I ths1 ths2;
clasohm@0
   410
clasohm@0
   411
(*Useful "distance" function for BEST_FIRST*)
clasohm@0
   412
val size_of_thm = size_of_term o #prop o rep_thm;
clasohm@0
   413
clasohm@0
   414
lcp@1194
   415
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   416
    (some) type variable renaming **)
lcp@1194
   417
lcp@1194
   418
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   419
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   420
    in the term. *)
lcp@1194
   421
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   422
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   423
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   424
  | term_vars' _ = [];
lcp@1194
   425
lcp@1194
   426
fun forall_intr_vars th =
lcp@1194
   427
  let val {prop,sign,...} = rep_thm th;
lcp@1194
   428
      val vars = distinct (term_vars' prop);
lcp@1194
   429
  in forall_intr_list (map (cterm_of sign) vars) th end;
lcp@1194
   430
wenzelm@1237
   431
fun weak_eq_thm (tha,thb) =
lcp@1194
   432
    eq_thm(forall_intr_vars (freezeT tha), forall_intr_vars (freezeT thb));
lcp@1194
   433
lcp@1194
   434
lcp@1194
   435
clasohm@0
   436
(*** Meta-Rewriting Rules ***)
clasohm@0
   437
wenzelm@6390
   438
val proto_sign = Theory.sign_of ProtoPure.thy;
paulson@4610
   439
paulson@4610
   440
fun read_prop s = read_cterm proto_sign (s, propT);
paulson@4610
   441
wenzelm@9455
   442
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   443
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@4016
   444
clasohm@0
   445
val reflexive_thm =
paulson@4610
   446
  let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),logicS)))
wenzelm@9455
   447
  in store_standard_thm "reflexive" (Thm.reflexive cx) end;
clasohm@0
   448
clasohm@0
   449
val symmetric_thm =
paulson@4610
   450
  let val xy = read_prop "x::'a::logic == y"
wenzelm@9455
   451
  in store_standard_thm "symmetric" (Thm.implies_intr_hyps (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   452
clasohm@0
   453
val transitive_thm =
paulson@4610
   454
  let val xy = read_prop "x::'a::logic == y"
paulson@4610
   455
      val yz = read_prop "y::'a::logic == z"
clasohm@0
   456
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@9455
   457
  in store_standard_thm "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   458
nipkow@4679
   459
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   460
lcp@229
   461
(** Below, a "conversion" has type cterm -> thm **)
lcp@229
   462
paulson@4610
   463
val refl_implies = reflexive (cterm_of proto_sign implies);
clasohm@0
   464
clasohm@0
   465
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
nipkow@214
   466
(*Do not rewrite flex-flex pairs*)
wenzelm@252
   467
fun goals_conv pred cv =
lcp@229
   468
  let fun gconv i ct =
paulson@2004
   469
        let val (A,B) = dest_implies ct
lcp@229
   470
            val (thA,j) = case term_of A of
lcp@229
   471
                  Const("=?=",_)$_$_ => (reflexive A, i)
lcp@229
   472
                | _ => (if pred i then cv A else reflexive A, i+1)
paulson@2004
   473
        in  combination (combination refl_implies thA) (gconv j B) end
lcp@229
   474
        handle TERM _ => reflexive ct
clasohm@0
   475
  in gconv 1 end;
clasohm@0
   476
clasohm@0
   477
(*Use a conversion to transform a theorem*)
lcp@229
   478
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
clasohm@0
   479
clasohm@0
   480
(*rewriting conversion*)
lcp@229
   481
fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
clasohm@0
   482
clasohm@0
   483
(*Rewrite a theorem*)
wenzelm@3575
   484
fun rewrite_rule_aux _ []   th = th
wenzelm@3575
   485
  | rewrite_rule_aux prover thms th =
nipkow@4713
   486
      fconv_rule (rew_conv (true,false,false) prover (Thm.mss_of thms)) th;
clasohm@0
   487
wenzelm@3555
   488
fun rewrite_thm mode prover mss = fconv_rule (rew_conv mode prover mss);
wenzelm@5079
   489
fun rewrite_cterm mode prover mss = Thm.rewrite_cterm mode mss prover;
wenzelm@3555
   490
clasohm@0
   491
(*Rewrite the subgoals of a proof state (represented by a theorem) *)
wenzelm@3575
   492
fun rewrite_goals_rule_aux _ []   th = th
wenzelm@3575
   493
  | rewrite_goals_rule_aux prover thms th =
nipkow@4713
   494
      fconv_rule (goals_conv (K true) (rew_conv (true, true, false) prover
wenzelm@3575
   495
        (Thm.mss_of thms))) th;
clasohm@0
   496
clasohm@0
   497
(*Rewrite the subgoal of a proof state (represented by a theorem) *)
nipkow@214
   498
fun rewrite_goal_rule mode prover mss i thm =
nipkow@214
   499
  if 0 < i  andalso  i <= nprems_of thm
nipkow@214
   500
  then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
nipkow@214
   501
  else raise THM("rewrite_goal_rule",i,[thm]);
clasohm@0
   502
clasohm@0
   503
clasohm@0
   504
(*** Some useful meta-theorems ***)
clasohm@0
   505
clasohm@0
   506
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@9455
   507
val asm_rl = store_standard_thm "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   508
val _ = store_thm "_" asm_rl;
clasohm@0
   509
clasohm@0
   510
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   511
val cut_rl =
wenzelm@9455
   512
  store_standard_thm "cut_rl"
wenzelm@9455
   513
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   514
wenzelm@252
   515
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   516
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   517
val revcut_rl =
paulson@4610
   518
  let val V = read_prop "PROP V"
paulson@4610
   519
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   520
  in
wenzelm@9455
   521
    store_standard_thm "revcut_rl"
wenzelm@4016
   522
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   523
  end;
clasohm@0
   524
lcp@668
   525
(*for deleting an unwanted assumption*)
lcp@668
   526
val thin_rl =
paulson@4610
   527
  let val V = read_prop "PROP V"
paulson@4610
   528
      and W = read_prop "PROP W";
wenzelm@9455
   529
  in  store_standard_thm "thin_rl" (implies_intr V (implies_intr W (assume W)))
lcp@668
   530
  end;
lcp@668
   531
clasohm@0
   532
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   533
val triv_forall_equality =
paulson@4610
   534
  let val V  = read_prop "PROP V"
paulson@4610
   535
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@8086
   536
      and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
wenzelm@4016
   537
  in
wenzelm@9455
   538
    store_standard_thm "triv_forall_equality"
wenzelm@9455
   539
      (standard (equal_intr (implies_intr QV (forall_elim x (assume QV)))
wenzelm@9455
   540
        (implies_intr V  (forall_intr x (assume V)))))
clasohm@0
   541
  end;
clasohm@0
   542
nipkow@1756
   543
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   544
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   545
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   546
*)
nipkow@1756
   547
val swap_prems_rl =
paulson@4610
   548
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   549
      val major = assume cmajor;
paulson@4610
   550
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   551
      val minor1 = assume cminor1;
paulson@4610
   552
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   553
      val minor2 = assume cminor2;
wenzelm@9455
   554
  in store_standard_thm "swap_prems_rl"
nipkow@1756
   555
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   556
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   557
  end;
nipkow@1756
   558
nipkow@3653
   559
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   560
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   561
   Introduction rule for == as a meta-theorem.
nipkow@3653
   562
*)
nipkow@3653
   563
val equal_intr_rule =
paulson@4610
   564
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   565
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   566
  in
wenzelm@9455
   567
    store_standard_thm "equal_intr_rule"
wenzelm@4016
   568
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   569
  end;
nipkow@3653
   570
wenzelm@4285
   571
paulson@8129
   572
(*** Instantiate theorem th, reading instantiations under signature sg ****)
paulson@8129
   573
paulson@8129
   574
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   575
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   576
paulson@8129
   577
fun read_instantiate_sg sg sinsts th =
paulson@8129
   578
    let val ts = types_sorts th;
paulson@8129
   579
        val used = add_term_tvarnames(#prop(rep_thm th),[]);
paulson@8129
   580
    in  instantiate (read_insts sg ts ts used sinsts) th  end;
paulson@8129
   581
paulson@8129
   582
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   583
fun read_instantiate sinsts th =
paulson@8129
   584
    read_instantiate_sg (#sign (rep_thm th)) sinsts th;
paulson@8129
   585
paulson@8129
   586
paulson@8129
   587
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   588
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   589
local
paulson@8129
   590
  fun add_types ((ct,cu), (sign,tye,maxidx)) =
paulson@8129
   591
    let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
paulson@8129
   592
        and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   593
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
paulson@8129
   594
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
paulson@8129
   595
        val (tye',maxi') = Type.unify (#tsig(Sign.rep_sg sign')) maxi tye (T,U)
paulson@8129
   596
          handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
paulson@8129
   597
    in  (sign', tye', maxi')  end;
paulson@8129
   598
in
paulson@8129
   599
fun cterm_instantiate ctpairs0 th =
berghofe@8406
   600
  let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th), Vartab.empty, 0))
paulson@8129
   601
      val tsig = #tsig(Sign.rep_sg sign);
berghofe@8406
   602
      fun instT(ct,cu) = let val inst = subst_TVars_Vartab tye
paulson@8129
   603
                         in (cterm_fun inst ct, cterm_fun inst cu) end
paulson@8129
   604
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
berghofe@8406
   605
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   606
  handle TERM _ =>
paulson@8129
   607
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
paulson@8129
   608
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   609
end;
paulson@8129
   610
paulson@8129
   611
paulson@8129
   612
(** Derived rules mainly for METAHYPS **)
paulson@8129
   613
paulson@8129
   614
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   615
fun equal_abs_elim ca eqth =
paulson@8129
   616
  let val {sign=signa, t=a, ...} = rep_cterm ca
paulson@8129
   617
      and combth = combination eqth (reflexive ca)
paulson@8129
   618
      val {sign,prop,...} = rep_thm eqth
paulson@8129
   619
      val (abst,absu) = Logic.dest_equals prop
paulson@8129
   620
      val cterm = cterm_of (Sign.merge (sign,signa))
paulson@8129
   621
  in  transitive (symmetric (beta_conversion (cterm (abst$a))))
paulson@8129
   622
           (transitive combth (beta_conversion (cterm (absu$a))))
paulson@8129
   623
  end
paulson@8129
   624
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   625
paulson@8129
   626
(*Calling equal_abs_elim with multiple terms*)
paulson@8129
   627
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
paulson@8129
   628
paulson@8129
   629
local
paulson@8129
   630
  val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
paulson@8129
   631
  fun err th = raise THM("flexpair_inst: ", 0, [th])
paulson@8129
   632
  fun flexpair_inst def th =
paulson@8129
   633
    let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
paulson@8129
   634
        val cterm = cterm_of sign
paulson@8129
   635
        fun cvar a = cterm(Var((a,0),alpha))
paulson@8129
   636
        val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
paulson@8129
   637
                   def
paulson@8129
   638
    in  equal_elim def' th
paulson@8129
   639
    end
paulson@8129
   640
    handle THM _ => err th | Bind => err th
paulson@8129
   641
in
paulson@8129
   642
val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def)
paulson@8129
   643
and flexpair_elim = flexpair_inst ProtoPure.flexpair_def
paulson@8129
   644
end;
paulson@8129
   645
paulson@8129
   646
(*Version for flexflex pairs -- this supports lifting.*)
paulson@8129
   647
fun flexpair_abs_elim_list cts =
paulson@8129
   648
    flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
paulson@8129
   649
paulson@8129
   650
paulson@8129
   651
(*** GOAL (PROP A) <==> PROP A ***)
wenzelm@4789
   652
wenzelm@4789
   653
local
wenzelm@4789
   654
  val A = read_prop "PROP A";
wenzelm@4789
   655
  val G = read_prop "GOAL (PROP A)";
wenzelm@4789
   656
  val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
wenzelm@4789
   657
in
wenzelm@9455
   658
  val triv_goal = store_thm "triv_goal"
wenzelm@9455
   659
    (tag_rule internal_tag (standard (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume A))));
wenzelm@9455
   660
  val rev_triv_goal = store_thm "rev_triv_goal"
wenzelm@9455
   661
    (tag_rule internal_tag (standard (Thm.equal_elim G_def (Thm.assume G))));
wenzelm@4789
   662
end;
wenzelm@4789
   663
wenzelm@6995
   664
val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign (Const ("Goal", propT --> propT)));
wenzelm@6995
   665
fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
wenzelm@6995
   666
wenzelm@4789
   667
wenzelm@4285
   668
wenzelm@5688
   669
(** variations on instantiate **)
wenzelm@4285
   670
paulson@8550
   671
(*shorthand for instantiating just one variable in the current theory*)
paulson@8550
   672
fun inst x t = read_instantiate_sg (sign_of (the_context())) [(x,t)];
paulson@8550
   673
paulson@8550
   674
wenzelm@4285
   675
(* collect vars *)
wenzelm@4285
   676
wenzelm@4285
   677
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs);
wenzelm@4285
   678
val add_tvars = foldl_types add_tvarsT;
wenzelm@4285
   679
val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs);
wenzelm@4285
   680
wenzelm@5903
   681
fun tvars_of_terms ts = rev (foldl add_tvars ([], ts));
wenzelm@5903
   682
fun vars_of_terms ts = rev (foldl add_vars ([], ts));
wenzelm@5903
   683
wenzelm@5903
   684
fun tvars_of thm = tvars_of_terms [#prop (Thm.rep_thm thm)];
wenzelm@5903
   685
fun vars_of thm = vars_of_terms [#prop (Thm.rep_thm thm)];
wenzelm@4285
   686
wenzelm@4285
   687
wenzelm@4285
   688
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   689
wenzelm@4285
   690
fun instantiate' cTs cts thm =
wenzelm@4285
   691
  let
wenzelm@4285
   692
    fun err msg =
wenzelm@4285
   693
      raise TYPE ("instantiate': " ^ msg,
wenzelm@4285
   694
        mapfilter (apsome Thm.typ_of) cTs,
wenzelm@4285
   695
        mapfilter (apsome Thm.term_of) cts);
wenzelm@4285
   696
wenzelm@4285
   697
    fun inst_of (v, ct) =
wenzelm@4285
   698
      (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
wenzelm@4285
   699
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   700
wenzelm@4285
   701
    fun zip_vars _ [] = []
wenzelm@4285
   702
      | zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts
wenzelm@4285
   703
      | zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
   704
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
   705
wenzelm@4285
   706
    (*instantiate types first!*)
wenzelm@4285
   707
    val thm' =
wenzelm@4285
   708
      if forall is_none cTs then thm
wenzelm@4285
   709
      else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
wenzelm@4285
   710
    in
wenzelm@4285
   711
      if forall is_none cts then thm'
wenzelm@4285
   712
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
   713
    end;
wenzelm@4285
   714
wenzelm@4285
   715
wenzelm@5688
   716
(* unvarify(T) *)
wenzelm@5688
   717
wenzelm@5688
   718
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
   719
wenzelm@5688
   720
fun unvarifyT thm =
wenzelm@5688
   721
  let
wenzelm@5688
   722
    val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
wenzelm@5688
   723
    val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
   724
  in instantiate' tfrees [] thm end;
wenzelm@5688
   725
wenzelm@5688
   726
fun unvarify raw_thm =
wenzelm@5688
   727
  let
wenzelm@5688
   728
    val thm = unvarifyT raw_thm;
wenzelm@5688
   729
    val ct = Thm.cterm_of (Thm.sign_of_thm thm);
wenzelm@5688
   730
    val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
   731
  in instantiate' [] frees thm end;
wenzelm@5688
   732
wenzelm@5688
   733
wenzelm@8605
   734
(* tvars_intr_list *)
wenzelm@8605
   735
wenzelm@8605
   736
fun tfrees_of thm =
wenzelm@8605
   737
  let val {hyps, prop, ...} = Thm.rep_thm thm
wenzelm@8605
   738
  in foldr Term.add_term_tfree_names (prop :: hyps, []) end;
wenzelm@8605
   739
wenzelm@8605
   740
fun tvars_intr_list tfrees thm =
wenzelm@8605
   741
  Thm.varifyT' (tfrees_of thm \\ tfrees) thm;
wenzelm@8605
   742
wenzelm@8605
   743
wenzelm@6435
   744
(* increment var indexes *)
wenzelm@6435
   745
wenzelm@6435
   746
fun incr_indexes 0 thm = thm
wenzelm@6435
   747
  | incr_indexes inc thm =
wenzelm@6435
   748
      let
wenzelm@6435
   749
        val sign = Thm.sign_of_thm thm;
wenzelm@6435
   750
wenzelm@6435
   751
        fun inc_tvar ((x, i), S) = Some (Thm.ctyp_of sign (TVar ((x, i + inc), S)));
wenzelm@6435
   752
        fun inc_var ((x, i), T) = Some (Thm.cterm_of sign (Var ((x, i + inc), T)));
wenzelm@6930
   753
        val thm' = instantiate' (map inc_tvar (tvars_of thm)) [] thm;
wenzelm@6930
   754
        val thm'' = instantiate' [] (map inc_var (vars_of thm')) thm';
wenzelm@6930
   755
      in thm'' end;
wenzelm@6435
   756
wenzelm@6435
   757
fun incr_indexes_wrt is cTs cts thms =
wenzelm@6435
   758
  let
wenzelm@6435
   759
    val maxidx =
wenzelm@6435
   760
      foldl Int.max (~1, is @
wenzelm@6435
   761
        map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
wenzelm@6435
   762
        map (#maxidx o Thm.rep_cterm) cts @
wenzelm@6435
   763
        map (#maxidx o Thm.rep_thm) thms);
wenzelm@6435
   764
  in incr_indexes (maxidx + 1) end;
wenzelm@6435
   765
wenzelm@6435
   766
wenzelm@8328
   767
(* freeze_all *)
wenzelm@8328
   768
wenzelm@8328
   769
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
   770
wenzelm@8328
   771
fun freeze_all_TVars thm =
wenzelm@8328
   772
  (case tvars_of thm of
wenzelm@8328
   773
    [] => thm
wenzelm@8328
   774
  | tvars =>
wenzelm@8328
   775
      let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
wenzelm@8328
   776
      in instantiate' (map (fn ((x, _), S) => Some (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
   777
wenzelm@8328
   778
fun freeze_all_Vars thm =
wenzelm@8328
   779
  (case vars_of thm of
wenzelm@8328
   780
    [] => thm
wenzelm@8328
   781
  | vars =>
wenzelm@8328
   782
      let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
wenzelm@8328
   783
      in instantiate' [] (map (fn ((x, _), T) => Some (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
   784
wenzelm@8328
   785
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
   786
wenzelm@8328
   787
wenzelm@5688
   788
(* mk_triv_goal *)
wenzelm@5688
   789
wenzelm@5688
   790
(*make an initial proof state, "PROP A ==> (PROP A)" *)
paulson@5311
   791
fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal;
paulson@5311
   792
wenzelm@5688
   793
clasohm@0
   794
end;
wenzelm@252
   795
wenzelm@5903
   796
wenzelm@5903
   797
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
   798
open BasicDrule;