IMPLEMENTATION Sequences

IMPORT Nat COMPLETELY
IMPORT Seq[nat] COMPLETELY
IMPORT Real COMPLETELY
IMPORT Seq[real] COMPLETELY

DEF scalar == \\s1,s2 . IF <>?(s1) THEN 0 ELSE IF <>?(s2) THEN 0 ELSE ft(s1)*ft(s2)+scalar(rt(s1),rt(s2)) FI FI

DEF genList == \\n . IF n=0 THEN <> ELSE n::genList(n-1) FI

DEF horner == \\k,x . LET k1 == ft(k)
                          k2 == ft(rt(k))
                          k3 == ft(rt(rt(k)))
                          k4 == ft(rt(rt(rt(k))))
                      IN (((k1)*x+k2)*x+k3)*x+k4