#include get.cam
#include ret.cam

;--------------------------------------------------------------------
; Rewrite functions
;
; 0 + x = x                          <-->
; S(x) + y = S(x + y)                <-->
; 0 * x = 0                          <-->
; S(x) * y = x * y + y
;
;--------------------------------------------------------------------
;
; 0 + x -> x
;
FUNC RR1(x:X):X
RETURN if xMatch(x,O("+",<O("0",<>),'x>)) then RX(x) else x;

;
; S(x) + y -> S(x + y)
;
FUNC RR2(x:X):X
RETURN if xMatch(x,O("+",<O("S",<'x>),'y>))
       then O("S",<LX(LX(x)),RX(x)>) else x;

;
; 0 * x -> 0
;
FUNC RR3(x:X):X
RETURN if xMatch(x,O("*",<O("0",<>),'x>)) then O("0",<>) else x;

;
; S(x) * y -> x * y + y
;
FUNC RR4(x:X):X
RETURN if xMatch(x,O("*",<O("S",<'x>),'y>))
       then O("+",<O("*",<LX(LX(x)),RX(x)>),RX(x)>) else x;

FUNC rfPSTARTTRS(x:X,n:INT)
PRE is-X(x)
;STATE progn(gpSETTINGS(P(15,30,0,25,60,1,false,3,true,1,39)),
;STATE progn(gpSETTINGS(P(15,50,0,50,60,1,false,2,true,1,39)),
STATE progn(gpSETTINGS(P(5,50,3,50,60,0,false,2,true,2,39)),
            gpSHOWSETTINGS(),
            gpPSTART({1,2,3,4}),
            rfEVAL(x),
            princ("> Best(",0,"): ",rfBESTVAL(),"%\n> thinking..."),
            foreach(i,inseg(n),
                    gpSELECT(),gpCROSSOVER(),gpMUTATION(),rfEVAL(x),
                    princ(" best (",i,"): ",rfBESTVAL(),"%\n> thinking...")),
;                    rfSHOWBEST(x));
;                   rfSHOWREIF(x));
                   rfSHOWRESULT(x));

FUNC rfBEST():I->R
RETURN [ k -> G[k] | k <- dom(G) : gpSEL(k,2) == rfBESTVAL() ];

FUNC rfBESTVAL():INT
PRE not(gpEMPTY())
RETURN max-orio(0,{ gpSEL(x,2) | x <- dom(G) });

FUNC rfEVAL(x:X)
STATE G <- rcprob(_reify_(x,G));

_reify_(e,s) = if (s == []) then []
               else let (x = choice(dom(s)),
                         cx = gpSEL(x,1),
                         rx = if (GR(GV) == 2) then CONC(cx) else cx,
                         fx = rfEVALTRS(ApplyFirstMatch(e,rx)),
                         sx = gpSEL(x,3))
                    in [ x -> R(cx,fx,sx,0,0) ] + _reify_(e,s\{x});

FUNC rfEVALTRS(x:X):INT
RETURN pdiv(1,xComplex(x));

FUNC rfSHOWRESULT(x:X)
RETURN let (b = rfBEST(), k = choice(dom(b)), c = B1(b[k]))
;       in xString(erApplyFinalRule(ApplyFirstMatch(x,c)));
       in if (GR(GV) == 2)
          then xString(ApplyFirstMatch(x,CONC(c)))
          else xString(ApplyFirstMatch(x,c));

FUNC rfSHOWREIF(x:X)
RETURN let (b = rfBEST(), k = choice(dom(b)), c = B1(b[k]))
       in if (GR(GV) == 2)
          then _showreif_(x,CONC(c))
          else _showreif_(x,c);

_showreif_(x,c) =
    if (c == <>) then ""
    else let (h = head(c), t = tail(c), r = FirstMatch(x,h))
         in do(if (x != r)
               then princ("\n> applying ",h,"... ",xString(r)),
               _showreif_(r,t));

m<-O("+",<O("+",<O("0",<>),O("*",<O("0",<>),O("S",<O("0",<>)>)>)>),O("*",<O("0",<>),O("0",<>)>)>);