Make a long type signature
Haskell, ~2^(2^18)
f x=(x,x)
g=f.f.f.f
h=g.g.g.g
i=h.h.h.h
j=i.i.i.i
k=j.j.j.j
l=k.k.k.k
m=l.l.l.l
n=m.m.m.m
n.n.n.n$0

Each application of f roughly double the type signature by transforming the type signature T to (T,T). For example, the fourfold composition f.f.f.f$0 has type
Num a =&gt; ((((a, a), (a, a)), ((a, a), (a, a))), (((a, a), (a, a)), ((a, a), (a, a))))

Each line quadraples the number of applications of f, giving 4^9 = 2^18 at the end. So, the type signature has size of the order of 2^(2^18).