src/Provers/splitter.ML
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(*  Title:      Provers/splitter.ML
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    Author:     Tobias Nipkow
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    Copyright   1995  TU Munich
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Generic case-splitter, suitable for most logics.
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Deals with equalities of the form ?P(f args) = ...
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where "f args" must be a first-order term without duplicate variables.
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*)
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signature SPLITTER_DATA =
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sig
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  val context       : Proof.context
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  val mk_eq         : thm -> thm
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  val meta_eq_to_iff: thm (* "x == y ==> x = y"                      *)
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  val iffD          : thm (* "[| P = Q; Q |] ==> P"                  *)
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  val disjE         : thm (* "[| P | Q; P ==> R; Q ==> R |] ==> R"   *)
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  val conjE         : thm (* "[| P & Q; [| P; Q |] ==> R |] ==> R"   *)
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  val exE           : thm (* "[| EX x. P x; !!x. P x ==> Q |] ==> Q" *)
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  val contrapos     : thm (* "[| ~ Q; P ==> Q |] ==> ~ P"            *)
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  val contrapos2    : thm (* "[| Q; ~ P ==> ~ Q |] ==> P"            *)
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  val notnotD       : thm (* "~ ~ P ==> P"                           *)
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  val safe_tac      : Proof.context -> tactic
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end
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signature SPLITTER =
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sig
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  (* somewhat more internal functions *)
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  val cmap_of_split_thms: thm list -> (string * (typ * term * thm * typ * int) list) list
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  val split_posns: (string * (typ * term * thm * typ * int) list) list ->
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    theory -> typ list -> term -> (thm * (typ * typ * int list) list * int list * typ * term) list
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    (* first argument is a "cmap", returns a list of "split packs" *)
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  (* the "real" interface, providing a number of tactics *)
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  val split_tac       : Proof.context -> thm list -> int -> tactic
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  val split_inside_tac: Proof.context -> thm list -> int -> tactic
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  val split_asm_tac   : Proof.context -> thm list -> int -> tactic
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  val add_split: thm -> Proof.context -> Proof.context
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  val add_split_bang: thm -> Proof.context -> Proof.context
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  val del_split: thm -> Proof.context -> Proof.context
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  val split_modifiers : Method.modifier parser list
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end;
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functor Splitter(Data: SPLITTER_DATA): SPLITTER =
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struct
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val Const (const_not, _) $ _ =
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  Object_Logic.drop_judgment Data.context
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    (#1 (Logic.dest_implies (Thm.prop_of Data.notnotD)));
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val Const (const_or , _) $ _ $ _ =
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  Object_Logic.drop_judgment Data.context
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    (#1 (Logic.dest_implies (Thm.prop_of Data.disjE)));
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val const_Trueprop = Object_Logic.judgment_name Data.context;
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fun split_format_err () = error "Wrong format for split rule";
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fun split_thm_info thm =
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  (case Thm.concl_of (Data.mk_eq thm) of
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    Const(\<^const_name>\<open>Pure.eq\<close>, _) $ (Var _ $ t) $ c =>
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      (case strip_comb t of
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        (Const p, _) => (p, case c of (Const (s, _) $ _) => s = const_not | _ => false)
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      | _ => split_format_err ())
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  | _ => split_format_err ());
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fun cmap_of_split_thms thms =
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let
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  val splits = map Data.mk_eq thms
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  fun add_thm thm cmap =
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    (case Thm.concl_of thm of _ $ (t as _ $ lhs) $ _ =>
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       (case strip_comb lhs of (Const(a,aT),args) =>
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          let val info = (aT,lhs,thm,fastype_of t,length args)
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          in case AList.lookup (op =) cmap a of
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               SOME infos => AList.update (op =) (a, info::infos) cmap
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             | NONE => (a,[info])::cmap
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          end
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        | _ => split_format_err())
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     | _ => split_format_err())
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in
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  fold add_thm splits []
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end;
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val abss = fold (Term.abs o pair "");
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(* ------------------------------------------------------------------------- *)
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(* mk_case_split_tac                                                         *)
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(* ------------------------------------------------------------------------- *)
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fun mk_case_split_tac order =
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let
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(************************************************************
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   Create lift-theorem "trlift" :
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   [| !!x. Q x == R x; P(%x. R x) == C |] ==> P (%x. Q x) == C
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*************************************************************)
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val meta_iffD = Data.meta_eq_to_iff RS Data.iffD;  (* (P == Q) ==> Q ==> P *)
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val lift = Goal.prove_global \<^theory> ["P", "Q", "R"]
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  [Syntax.read_prop_global \<^theory>\<open>Pure\<close> "!!x :: 'b. Q(x) == R(x) :: 'c"]
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  (Syntax.read_prop_global \<^theory>\<open>Pure\<close> "P(%x. Q(x)) == P(%x. R(x))")
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  (fn {context = ctxt, prems} =>
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    rewrite_goals_tac ctxt prems THEN resolve_tac ctxt [reflexive_thm] 1)
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val _ $ _ $ (_ $ (_ $ abs_lift) $ _) = Thm.prop_of lift;
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val trlift = lift RS transitive_thm;
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(************************************************************************
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   Set up term for instantiation of P in the lift-theorem
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   t     : lefthand side of meta-equality in subgoal
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           the lift theorem is applied to (see select)
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   pos   : "path" leading to abstraction, coded as a list
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   T     : type of body of P(...)
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*************************************************************************)
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fun mk_cntxt t pos T =
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  let
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    fun down [] t = (Bound 0, t)
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      | down (p :: ps) t =
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          let
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            val (h, ts) = strip_comb t
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            val (ts1, u :: ts2) = chop p ts
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            val (u1, u2) = down ps u
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          in
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            (list_comb (incr_boundvars 1 h,
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               map (incr_boundvars 1) ts1 @ u1 ::
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               map (incr_boundvars 1) ts2),
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             u2)
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          end;
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    val (u1, u2) = down (rev pos) t
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  in (Abs ("", T, u1), u2) end;
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(************************************************************************
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   Set up term for instantiation of P in the split-theorem
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   P(...) == rhs
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   t     : lefthand side of meta-equality in subgoal
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           the split theorem is applied to (see select)
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   T     : type of body of P(...)
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   tt    : the term  Const(key,..) $ ...
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*************************************************************************)
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fun mk_cntxt_splitthm t tt T =
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  let fun repl lev t =
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    if Envir.aeconv(incr_boundvars lev tt, t) then Bound lev
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    else case t of
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        (Abs (v, T2, t)) => Abs (v, T2, repl (lev+1) t)
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      | (Bound i) => Bound (if i>=lev then i+1 else i)
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      | (t1 $ t2) => (repl lev t1) $ (repl lev t2)
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      | t => t
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  in Abs("", T, repl 0 t) end;
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(* add all loose bound variables in t to list is *)
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fun add_lbnos t is = add_loose_bnos (t, 0, is);
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(* check if the innermost abstraction that needs to be removed
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   has a body of type T; otherwise the expansion thm will fail later on
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*)
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fun type_test (T, lbnos, apsns) =
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  let val (_, U: typ, _) = nth apsns (foldl1 Int.min lbnos)
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  in T = U end;
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(*************************************************************************
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   Create a "split_pack".
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   thm   : the relevant split-theorem, i.e. P(...) == rhs , where P(...)
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           is of the form
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           P( Const(key,...) $ t_1 $ ... $ t_n )      (e.g. key = "if")
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   T     : type of P(...)
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   T'    : type of term to be scanned
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   n     : number of arguments expected by Const(key,...)
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   ts    : list of arguments actually found
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   apsns : list of tuples of the form (T,U,pos), one tuple for each
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           abstraction that is encountered on the way to the position where
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           Const(key, ...) $ ...  occurs, where
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           T   : type of the variable bound by the abstraction
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           U   : type of the abstraction's body
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           pos : "path" leading to the body of the abstraction
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   pos   : "path" leading to the position where Const(key, ...) $ ...  occurs.
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   TB    : type of  Const(key,...) $ t_1 $ ... $ t_n
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   t     : the term Const(key,...) $ t_1 $ ... $ t_n
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   A split pack is a tuple of the form
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   (thm, apsns, pos, TB, tt)
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   Note : apsns is reversed, so that the outermost quantifier's position
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          comes first ! If the terms in ts don't contain variables bound
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          by other than meta-quantifiers, apsns is empty, because no further
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          lifting is required before applying the split-theorem.
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******************************************************************************)
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fun mk_split_pack (thm, T: typ, T', n, ts, apsns, pos, TB, t) =
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  if n > length ts then []
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  else let val lev = length apsns
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           val lbnos = fold add_lbnos (take n ts) []
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           val flbnos = filter (fn i => i < lev) lbnos
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           val tt = incr_boundvars (~lev) t
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       in if null flbnos then
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            if T = T' then [(thm,[],pos,TB,tt)] else []
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          else if type_test(T,flbnos,apsns) then [(thm, rev apsns,pos,TB,tt)]
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               else []
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       end;
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(****************************************************************************
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   Recursively scans term for occurrences of Const(key,...) $ ...
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   Returns a list of "split-packs" (one for each occurrence of Const(key,...) )
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   cmap : association list of split-theorems that should be tried.
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          The elements have the format (key,(thm,T,n)) , where
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          key : the theorem's key constant ( Const(key,...) $ ... )
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          thm : the theorem itself
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          T   : type of P( Const(key,...) $ ... )
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          n   : number of arguments expected by Const(key,...)
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   Ts   : types of parameters
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   t    : the term to be scanned
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******************************************************************************)
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(* Simplified first-order matching;
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   assumes that all Vars in the pattern are distinct;
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   see Pure/pattern.ML for the full version;
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*)
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local
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  exception MATCH
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in
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  fun typ_match thy (tyenv, TU) = Sign.typ_match thy TU tyenv
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    handle Type.TYPE_MATCH => raise MATCH;
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  fun fomatch thy args =
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    let
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      fun mtch tyinsts = fn
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          (Ts, Var(_,T), t) =>
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            typ_match thy (tyinsts, (T, fastype_of1(Ts,t)))
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        | (_, Free (a,T), Free (b,U)) =>
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            if a=b then typ_match thy (tyinsts,(T,U)) else raise MATCH
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        | (_, Const (a,T), Const (b,U)) =>
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            if a=b then typ_match thy (tyinsts,(T,U)) else raise MATCH
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        | (_, Bound i, Bound j) =>
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            if i=j then tyinsts else raise MATCH
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        | (Ts, Abs(_,T,t), Abs(_,U,u)) =>
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            mtch (typ_match thy (tyinsts,(T,U))) (U::Ts,t,u)
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        | (Ts, f$t, g$u) =>
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            mtch (mtch tyinsts (Ts,f,g)) (Ts, t, u)
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        | _ => raise MATCH
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    in (mtch Vartab.empty args; true) handle MATCH => false end;
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end;
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fun split_posns (cmap : (string * (typ * term * thm * typ * int) list) list) thy Ts t =
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  let
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    val T' = fastype_of1 (Ts, t);
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    fun posns Ts pos apsns (Abs (_, T, t)) =
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          let val U = fastype_of1 (T::Ts,t)
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          in posns (T::Ts) (0::pos) ((T, U, pos)::apsns) t end
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      | posns Ts pos apsns t =
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          let
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            val (h, ts) = strip_comb t
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            fun iter t (i, a) = (i+1, (posns Ts (i::pos) apsns t) @ a);
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            val a =
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              case h of
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                Const(c, cT) =>
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                  let fun find [] = []
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                        | find ((gcT, pat, thm, T, n)::tups) =
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                            let val t2 = list_comb (h, take n ts) in
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                              if Sign.typ_instance thy (cT, gcT) andalso fomatch thy (Ts, pat, t2)
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                              then mk_split_pack(thm,T,T',n,ts,apsns,pos,type_of1(Ts,t2),t2)
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                              else find tups
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                            end
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                  in find (these (AList.lookup (op =) cmap c)) end
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              | _ => []
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          in snd (fold iter ts (0, a)) end
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  in posns Ts [] [] t end;
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fun shorter ((_,ps,pos,_,_), (_,qs,qos,_,_)) =
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  prod_ord (int_ord o apply2 length) (order o apply2 length)
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    ((ps, pos), (qs, qos));
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(************************************************************
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   call split_posns with appropriate parameters
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*************************************************************)
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fun select thy cmap state i =
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  let
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    val goal = Thm.term_of (Thm.cprem_of state i);
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    val Ts = rev (map #2 (Logic.strip_params goal));
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    val _ $ t $ _ = Logic.strip_assums_concl goal;
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  in (Ts, t, sort shorter (split_posns cmap thy Ts t)) end;
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fun exported_split_posns cmap thy Ts t =
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  sort shorter (split_posns cmap thy Ts t);
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c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
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   298
(*************************************************************
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
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   instantiate lift theorem
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
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c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
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   if t is of the form
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   ... ( Const(...,...) $ Abs( .... ) ) ...
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   303
   then
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   304
   P = %a.  ... ( Const(...,...) $ a ) ...
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   where a has type T --> U
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c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
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   Ts      : types of parameters
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   t       : lefthand side of meta-equality in subgoal
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             the split theorem is applied to (see cmap)
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   310
   T,U,pos : see mk_split_pack
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   state   : current proof state
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   i       : no. of subgoal
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**************************************************************)
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
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   314
60362
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fun inst_lift ctxt Ts t (T, U, pos) state i =
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   316
  let
54216
c0c453ce70a7 inst_lift now fully instantiates context to avoid problems with loose bound variables
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   317
    val (cntxt, u) = mk_cntxt t pos (T --> U);
c0c453ce70a7 inst_lift now fully instantiates context to avoid problems with loose bound variables
berghofe
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   318
    val trlift' = Thm.lift_rule (Thm.cprem_of state i)
c0c453ce70a7 inst_lift now fully instantiates context to avoid problems with loose bound variables
berghofe
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   319
      (Thm.rename_boundvars abs_lift u trlift);
60781
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wenzelm
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   320
    val (Var (P, _), _) =
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wenzelm
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   321
      strip_comb (fst (Logic.dest_equals
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wenzelm
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   322
        (Logic.strip_assums_concl (Thm.prop_of trlift'))));
2da59cdf531c updated to infer_instantiate;
wenzelm
parents: 60362
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   323
  in infer_instantiate ctxt [(P, Thm.cterm_of ctxt (abss Ts cntxt))] trlift' end;
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clasohm
parents:
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   324
a5a9c433f639 Initial revision
clasohm
parents:
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   325
1686
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents: 1064
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   326
(*************************************************************
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents: 1064
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   327
   instantiate split theorem
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents: 1064
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   328
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents: 1064
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   329
   Ts    : types of parameters
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berghofe
parents: 1064
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   330
   t     : lefthand side of meta-equality in subgoal
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
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   331
           the split theorem is applied to (see cmap)
4232
29f3875596ad Tuned function mk_cntxt_splitthm.
berghofe
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   332
   tt    : the term  Const(key,..) $ ...
1686
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   333
   thm   : the split theorem
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berghofe
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   334
   TB    : type of body of P(...)
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
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   335
   state : current proof state
4232
29f3875596ad Tuned function mk_cntxt_splitthm.
berghofe
parents: 4202
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   336
   i     : number of subgoal
1686
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   337
**************************************************************)
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents: 1064
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   338
60362
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wenzelm
parents: 59970
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   339
fun inst_split ctxt Ts t tt thm TB state i =
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wenzelm
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   340
  let
18145
6757627acf59 renamed Thm.cgoal_of to Thm.cprem_of;
wenzelm
parents: 18023
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   341
    val thm' = Thm.lift_rule (Thm.cprem_of state i) thm;
60781
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wenzelm
parents: 60362
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   342
    val (Var (P, _), _) =
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wenzelm
parents: 60362
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   343
      strip_comb (fst (Logic.dest_equals
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wenzelm
parents: 60362
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   344
        (Logic.strip_assums_concl (Thm.prop_of thm'))));
7672
c092e67d12f8 - Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents: 6130
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   345
    val cntxt = mk_cntxt_splitthm t tt TB;
60781
2da59cdf531c updated to infer_instantiate;
wenzelm
parents: 60362
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   346
  in infer_instantiate ctxt [(P, Thm.cterm_of ctxt (abss Ts cntxt))] thm' end;
1686
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berghofe
parents: 1064
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   347
7672
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berghofe
parents: 6130
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   348
1686
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents: 1064
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   349
(*****************************************************************************
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents: 1064
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   350
   The split-tactic
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
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   351
1686
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berghofe
parents: 1064
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   352
   splits : list of split-theorems to be tried
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berghofe
parents: 1064
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   353
   i      : number of subgoal the tactic should be applied to
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents: 1064
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   354
*****************************************************************************)
c67d543bc395 Added functions mk_cntxt_splitthm and inst_split which instantiate
berghofe
parents: 1064
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   355
58956
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
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   356
fun split_tac _ [] i = no_tac
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
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   357
  | split_tac ctxt splits i =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 18988
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   358
  let val cmap = cmap_of_split_thms splits
60362
befdc10ebb42 clarified context;
wenzelm
parents: 59970
diff changeset
   359
      fun lift_tac Ts t p st = compose_tac ctxt (false, inst_lift ctxt Ts t p st i, 2) i st
7672
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berghofe
parents: 6130
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   360
      fun lift_split_tac state =
60362
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wenzelm
parents: 59970
diff changeset
   361
            let val (Ts, t, splits) = select (Proof_Context.theory_of ctxt) cmap state i
1030
1d8fa2fc4b9c Completely rewrote split_tac. The old one failed in strange circumstances.
nipkow
parents: 943
diff changeset
   362
            in case splits of
7672
c092e67d12f8 - Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents: 6130
diff changeset
   363
                 [] => no_tac state
c092e67d12f8 - Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents: 6130
diff changeset
   364
               | (thm, apsns, pos, TB, tt)::_ =>
1030
1d8fa2fc4b9c Completely rewrote split_tac. The old one failed in strange circumstances.
nipkow
parents: 943
diff changeset
   365
                   (case apsns of
60362
befdc10ebb42 clarified context;
wenzelm
parents: 59970
diff changeset
   366
                      [] =>
befdc10ebb42 clarified context;
wenzelm
parents: 59970
diff changeset
   367
                        compose_tac ctxt (false, inst_split ctxt Ts t tt thm TB state i, 0) i state
7672
c092e67d12f8 - Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents: 6130
diff changeset
   368
                    | p::_ => EVERY [lift_tac Ts t p,
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 59058
diff changeset
   369
                                     resolve_tac ctxt [reflexive_thm] (i+1),
7672
c092e67d12f8 - Fixed bug in mk_split_pack which caused application of expansion theorem
berghofe
parents: 6130
diff changeset
   370
                                     lift_split_tac] state)
1030
1d8fa2fc4b9c Completely rewrote split_tac. The old one failed in strange circumstances.
nipkow
parents: 943
diff changeset
   371
            end
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   372
  in COND (has_fewer_prems i) no_tac
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 59058
diff changeset
   373
          (resolve_tac ctxt [meta_iffD] i THEN lift_split_tac)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   374
  end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   375
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 18988
diff changeset
   376
in (split_tac, exported_split_posns) end;  (* mk_case_split_tac *)
1721
445654b6cb95 Rewrote mk_cntxt_splitthm. Added function mk_case_split_inside_tac.
berghofe
parents: 1686
diff changeset
   377
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 4930
diff changeset
   378
33242
99577c7085c8 misc tuning and simplification;
wenzelm
parents: 33029
diff changeset
   379
val (split_tac, split_posns) = mk_case_split_tac int_ord;
4189
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   380
33242
99577c7085c8 misc tuning and simplification;
wenzelm
parents: 33029
diff changeset
   381
val (split_inside_tac, _) = mk_case_split_tac (rev_order o int_ord);
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 4930
diff changeset
   382
4189
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   383
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   384
(*****************************************************************************
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   385
   The split-tactic for premises
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   386
4189
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   387
   splits : list of split-theorems to be tried
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 4930
diff changeset
   388
****************************************************************************)
58956
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
diff changeset
   389
fun split_asm_tac _ [] = K no_tac
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
diff changeset
   390
  | split_asm_tac ctxt splits =
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 4930
diff changeset
   391
13855
644692eca537 addsplits / delsplits no longer ignore type of constant.
berghofe
parents: 13157
diff changeset
   392
  let val cname_list = map (fst o fst o split_thm_info) splits;
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   393
      fun tac (t,i) =
20664
ffbc5a57191a member (op =);
wenzelm
parents: 20237
diff changeset
   394
          let val n = find_index (exists_Const (member (op =) cname_list o #1))
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   395
                                 (Logic.strip_assums_hyp t);
69593
3dda49e08b9d isabelle update -u control_cartouches;
wenzelm
parents: 67649
diff changeset
   396
              fun first_prem_is_disj (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ (Const (c, _)
18545
e2b09fda748c avoid hardwired Trueprop;
wenzelm
parents: 18145
diff changeset
   397
                    $ (Const (s, _) $ _ $ _ )) $ _ ) = c = const_Trueprop andalso s = const_or
69593
3dda49e08b9d isabelle update -u control_cartouches;
wenzelm
parents: 67649
diff changeset
   398
              |   first_prem_is_disj (Const(\<^const_name>\<open>Pure.all\<close>,_)$Abs(_,_,t)) =
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   399
                                        first_prem_is_disj t
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   400
              |   first_prem_is_disj _ = false;
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 18988
diff changeset
   401
      (* does not work properly if the split variable is bound by a quantifier *)
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   402
              fun flat_prems_tac i = SUBGOAL (fn (t,i) =>
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   403
                           (if first_prem_is_disj t
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 59058
diff changeset
   404
                            then EVERY[eresolve_tac ctxt [Data.disjE] i, rotate_tac ~1 i,
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   405
                                       rotate_tac ~1  (i+1),
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   406
                                       flat_prems_tac (i+1)]
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   407
                            else all_tac)
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 59058
diff changeset
   408
                           THEN REPEAT (eresolve_tac ctxt [Data.conjE,Data.exE] i)
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 59058
diff changeset
   409
                           THEN REPEAT (dresolve_tac ctxt [Data.notnotD]   i)) i;
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 18988
diff changeset
   410
          in if n<0 then  no_tac  else (DETERM (EVERY'
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 59058
diff changeset
   411
                [rotate_tac n, eresolve_tac ctxt [Data.contrapos2],
58956
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
diff changeset
   412
                 split_tac ctxt splits,
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 59058
diff changeset
   413
                 rotate_tac ~1, eresolve_tac ctxt [Data.contrapos], rotate_tac ~1,
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 18988
diff changeset
   414
                 flat_prems_tac] i))
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   415
          end;
4189
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   416
  in SUBGOAL tac
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   417
  end;
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   418
58956
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
diff changeset
   419
fun gen_split_tac _ [] = K no_tac
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
diff changeset
   420
  | gen_split_tac ctxt (split::splits) =
10652
e6a4bb832b46 sar split method uses new gen_split_tac.
nipkow
parents: 10411
diff changeset
   421
      let val (_,asm) = split_thm_info split
58956
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
diff changeset
   422
      in (if asm then split_asm_tac else split_tac) ctxt [split] ORELSE'
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
diff changeset
   423
         gen_split_tac ctxt splits
10652
e6a4bb832b46 sar split method uses new gen_split_tac.
nipkow
parents: 10411
diff changeset
   424
      end;
8468
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   425
18688
abf0f018b5ec generic attributes;
wenzelm
parents: 18545
diff changeset
   426
8468
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   427
(** declare split rules **)
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   428
45620
f2a587696afb modernized some old-style infix operations, which were left over from the time of ML proof scripts;
wenzelm
parents: 42367
diff changeset
   429
(* add_split / del_split *)
8468
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   430
33242
99577c7085c8 misc tuning and simplification;
wenzelm
parents: 33029
diff changeset
   431
fun string_of_typ (Type (s, Ts)) =
99577c7085c8 misc tuning and simplification;
wenzelm
parents: 33029
diff changeset
   432
      (if null Ts then "" else enclose "(" ")" (commas (map string_of_typ Ts))) ^ s
13859
adf68d9e5dec split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents: 13855
diff changeset
   433
  | string_of_typ _ = "_";
adf68d9e5dec split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents: 13855
diff changeset
   434
17881
2b3709f5e477 functor: no Simplifier argument;
wenzelm
parents: 17325
diff changeset
   435
fun split_name (name, T) asm = "split " ^
13859
adf68d9e5dec split_name no longer uses Sign.string_of_typ to encode types, since
berghofe
parents: 13855
diff changeset
   436
  (if asm then "asm " else "") ^ name ^ " :: " ^ string_of_typ T;
4189
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   437
63636
6f38b7abb648 introduced aggressive splitter "split!"
nipkow
parents: 62870
diff changeset
   438
fun gen_add_split bang split ctxt =
33242
99577c7085c8 misc tuning and simplification;
wenzelm
parents: 33029
diff changeset
   439
  let
45620
f2a587696afb modernized some old-style infix operations, which were left over from the time of ML proof scripts;
wenzelm
parents: 42367
diff changeset
   440
    val (name, asm) = split_thm_info split
67644
15c6256709d6 trim context of persistent data;
wenzelm
parents: 64556
diff changeset
   441
    val split0 = Thm.trim_context split
63636
6f38b7abb648 introduced aggressive splitter "split!"
nipkow
parents: 62870
diff changeset
   442
    fun tac ctxt' =
67649
1e1782c1aedf tuned signature;
wenzelm
parents: 67644
diff changeset
   443
      let val split' = Thm.transfer' ctxt' split0 in
67644
15c6256709d6 trim context of persistent data;
wenzelm
parents: 64556
diff changeset
   444
        (if asm then split_asm_tac ctxt' [split']
15c6256709d6 trim context of persistent data;
wenzelm
parents: 64556
diff changeset
   445
         else if bang
15c6256709d6 trim context of persistent data;
wenzelm
parents: 64556
diff changeset
   446
              then split_tac ctxt' [split'] THEN_ALL_NEW
15c6256709d6 trim context of persistent data;
wenzelm
parents: 64556
diff changeset
   447
                   TRY o (SELECT_GOAL (Data.safe_tac ctxt'))
15c6256709d6 trim context of persistent data;
wenzelm
parents: 64556
diff changeset
   448
              else split_tac ctxt' [split'])
15c6256709d6 trim context of persistent data;
wenzelm
parents: 64556
diff changeset
   449
      end
58956
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
diff changeset
   450
  in Simplifier.addloop (ctxt, (split_name name asm, tac)) end;
1721
445654b6cb95 Rewrote mk_cntxt_splitthm. Added function mk_case_split_inside_tac.
berghofe
parents: 1686
diff changeset
   451
63636
6f38b7abb648 introduced aggressive splitter "split!"
nipkow
parents: 62870
diff changeset
   452
val add_split = gen_add_split false;
6f38b7abb648 introduced aggressive splitter "split!"
nipkow
parents: 62870
diff changeset
   453
val add_split_bang = gen_add_split true;
6f38b7abb648 introduced aggressive splitter "split!"
nipkow
parents: 62870
diff changeset
   454
51717
9e7d1c139569 simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents: 45620
diff changeset
   455
fun del_split split ctxt =
45620
f2a587696afb modernized some old-style infix operations, which were left over from the time of ML proof scripts;
wenzelm
parents: 42367
diff changeset
   456
  let val (name, asm) = split_thm_info split
51717
9e7d1c139569 simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents: 45620
diff changeset
   457
  in Simplifier.delloop (ctxt, split_name name asm) end;
1721
445654b6cb95 Rewrote mk_cntxt_splitthm. Added function mk_case_split_inside_tac.
berghofe
parents: 1686
diff changeset
   458
8468
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   459
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   460
(* attributes *)
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   461
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   462
val splitN = "split";
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   463
63636
6f38b7abb648 introduced aggressive splitter "split!"
nipkow
parents: 62870
diff changeset
   464
fun split_add bang = Simplifier.attrib (gen_add_split bang);
45620
f2a587696afb modernized some old-style infix operations, which were left over from the time of ML proof scripts;
wenzelm
parents: 42367
diff changeset
   465
val split_del = Simplifier.attrib del_split;
8634
3f34637cb9c0 use Attrib.add_del_args;
wenzelm
parents: 8476
diff changeset
   466
63650
50cadecbe5bc "split add" -> "split".
nipkow
parents: 63636
diff changeset
   467
val add_del = Scan.lift
50cadecbe5bc "split add" -> "split".
nipkow
parents: 63636
diff changeset
   468
  (Args.bang >> K (split_add true)
50cadecbe5bc "split add" -> "split".
nipkow
parents: 63636
diff changeset
   469
   || Args.del >> K split_del
50cadecbe5bc "split add" -> "split".
nipkow
parents: 63636
diff changeset
   470
   || Scan.succeed (split_add false));
63636
6f38b7abb648 introduced aggressive splitter "split!"
nipkow
parents: 62870
diff changeset
   471
6f38b7abb648 introduced aggressive splitter "split!"
nipkow
parents: 62870
diff changeset
   472
val _ = Theory.setup
69593
3dda49e08b9d isabelle update -u control_cartouches;
wenzelm
parents: 67649
diff changeset
   473
  (Attrib.setup \<^binding>\<open>split\<close> add_del "declare case split rule");
58826
2ed2eaabe3df modernized setup;
wenzelm
parents: 58318
diff changeset
   474
8634
3f34637cb9c0 use Attrib.add_del_args;
wenzelm
parents: 8476
diff changeset
   475
9703
bf65780eed02 added 'split' method;
wenzelm
parents: 9267
diff changeset
   476
(* methods *)
8468
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   477
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   478
val split_modifiers =
64556
851ae0e7b09c more symbols;
wenzelm
parents: 63650
diff changeset
   479
 [Args.$$$ splitN -- Args.colon >> K (Method.modifier (split_add false) \<^here>),
851ae0e7b09c more symbols;
wenzelm
parents: 63650
diff changeset
   480
  Args.$$$ splitN -- Args.bang_colon >> K (Method.modifier (split_add true) \<^here>),
851ae0e7b09c more symbols;
wenzelm
parents: 63650
diff changeset
   481
  Args.$$$ splitN -- Args.del -- Args.colon >> K (Method.modifier split_del \<^here>)];
8468
d99902232df8 added attributes, method modifiers, theory setup;
wenzelm
parents: 7672
diff changeset
   482
58826
2ed2eaabe3df modernized setup;
wenzelm
parents: 58318
diff changeset
   483
val _ =
2ed2eaabe3df modernized setup;
wenzelm
parents: 58318
diff changeset
   484
  Theory.setup
69593
3dda49e08b9d isabelle update -u control_cartouches;
wenzelm
parents: 67649
diff changeset
   485
    (Method.setup \<^binding>\<open>split\<close>
58956
a816aa3ff391 proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents: 58838
diff changeset
   486
      (Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD' (CHANGED_PROP o gen_split_tac ctxt ths)))
58826
2ed2eaabe3df modernized setup;
wenzelm
parents: 58318
diff changeset
   487
      "apply case split rule");
4189
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 3918
diff changeset
   488
1721
445654b6cb95 Rewrote mk_cntxt_splitthm. Added function mk_case_split_inside_tac.
berghofe
parents: 1686
diff changeset
   489
end;