src/Provers/splitter.ML
author nipkow
Thu Sep 16 17:41:10 1993 +0200 (1993-09-16)
changeset 4 2695ba9b40f7
parent 0 a5a9c433f639
child 231 cb6a24451544
permissions -rw-r--r--
added header
     1 (*  Title:      Provers/splitter
     2     ID:         $Id$
     3     Author:     Tobias Nipkow
     4     Copyright   1993  TU Munich
     5 
     6 Generic case-splitter, suitable for most logics.
     7 
     8 Use:
     9 
    10 val split_tac = mk_case_split_tac iffD;
    11 
    12 by(case_split_tac splits i);
    13 
    14 where splits = [P(elim(...)) == rhs, ...]
    15       iffD  = [| P <-> Q; Q |] ==> P (* is called iffD2 in HOL *)
    16 
    17 *)
    18 
    19 fun mk_case_split_tac iffD =
    20 let
    21 
    22 val lift = prove_goal Pure.thy
    23   "[| !!x::'b::logic. Q(x) == R(x) |] ==> P(%x.Q(x)) == P(%x.R(x))::'a::logic"
    24   (fn [prem] => [rewtac prem, rtac reflexive_thm 1]);
    25 
    26 val trlift = lift RS transitive_thm;
    27 val _ $ (Var(P,PT)$_) $ _ = concl_of trlift;
    28 
    29 fun contains cmap =
    30   let fun isin i (Abs(_,_,b)) = isin 0 b
    31         | isin i (s$t) = isin (i+1) s orelse isin 0 t
    32         | isin i (Const(c,_)) = (case assoc(cmap,c) of
    33                                    Some(n,_) => n <= i
    34                                  | None => false)
    35         | isin _ _ = false
    36   in isin 0 end;
    37 
    38 fun mk_context cmap Ts maxi t =
    39   let fun var (t,i) = Var(("X",i),type_of1(Ts,t))
    40 
    41       fun mka((None,i,ts),t) = if contains cmap t
    42             then let val (u,T,j) = mk(t,i) in (Some(T),j,ts@[u]) end
    43             else (None,i+1,ts@[var(t,i)])
    44         | mka((some,i,ts),t) = (some,i+1,ts@[var(t,i)])
    45       and mk(t as Abs _, i) = (Bound 0,type_of1(Ts,t),i)
    46         | mk(t,i) =
    47             let val (f,ts) = strip_comb t
    48                 val (Some(T),j,us) = foldl mka ((None,i,[]),ts)
    49             in (list_comb(f,us),T,j) end
    50 
    51       val (u,T,_) = mk(t,maxi+1)
    52   in Abs("",T,u) end;
    53 
    54 fun nth_subgoal i thm = nth_elem(i-1,prems_of thm);
    55 
    56 fun goal_concl i thm = Logic.strip_assums_concl(nth_subgoal i thm);
    57 
    58 fun inst_lift cmap state lift i =
    59   let val sg = #sign(rep_thm state)
    60       val tsig = #tsig(Sign.rep_sg sg)
    61       val goali = nth_subgoal i state
    62       val Ts = map #2 (Logic.strip_params goali)
    63       val _ $ t $ _ = Logic.strip_assums_concl goali;
    64       val cntxt = mk_context cmap (rev Ts) (#maxidx(rep_thm lift)) t
    65       val cu = Sign.cterm_of sg cntxt
    66       val uT = #T(Sign.rep_cterm cu)
    67       val cP' = Sign.cterm_of sg (Var(P,uT))
    68       val ixnTs = Type.typ_match tsig ([],(PT,uT));
    69       val ixncTs = map (fn (x,y) => (x,Sign.ctyp_of sg y)) ixnTs;
    70   in instantiate (ixncTs, [(cP',cu)]) lift end;
    71 
    72 fun splittable al i thm =
    73   let val tm = goal_concl i thm
    74       fun nobound j k (Abs(_,_,t)) = nobound j (k+1) t
    75         | nobound j k (s$t) = nobound j k s andalso nobound j k t
    76         | nobound j k (Bound n) = n < k orelse k+j <= n
    77         | nobound _ _ _ = true;
    78       fun find j (None,t) = (case t of
    79             Abs(_,_,t) => find (j+1) (None,t)
    80           | _ => let val (h,args) = strip_comb t
    81                      fun no() = foldl (find j) (None,args)
    82                  in case h of
    83                       Const(c,_) =>
    84                         (case assoc(al,c) of
    85                            Some(n,thm) =>
    86                              if length args < n then no()
    87                              else if forall (nobound j 0) (take(n,args))
    88                                   then Some(thm)
    89                                   else no()
    90                          | None => no())
    91                     | _ => no()
    92                  end)
    93         | find _ (some,_) = some
    94   in find 0 (None,tm) end;
    95 
    96 fun split_tac [] i = no_tac
    97   | split_tac splits i =
    98   let fun const(thm) = let val _$(_$lhs)$_ = concl_of thm
    99                            val (Const(a,_),args) = strip_comb lhs
   100                        in (a,(length args,thm)) end
   101       val cmap = map const splits;
   102       fun lift thm = rtac (inst_lift cmap thm trlift i) i
   103       fun lift_split thm =
   104             case splittable cmap i thm of
   105               Some(split) => rtac split i
   106             | None => EVERY[STATE lift, rtac reflexive_thm (i+1),
   107                             STATE lift_split]
   108   in STATE(fn thm =>
   109        if (i <= nprems_of thm)  andalso  contains cmap (goal_concl i thm)
   110        then EVERY[rtac iffD i, STATE lift_split]
   111        else no_tac)
   112   end;
   113 
   114 in split_tac end;