Supercompilation is a method of transforming programs to obtain
equivalent programs that perform fewer computation steps and
allocates less memory. A transformed program defines new functions
that are combinations of functions from the original program, but
the datatypes in the transformed program is a subset of the
datatypes defined in the original program. We will change this by
extending supercompilation to create new datatypes.

We do this by creating new constructors that combine several
constructors from the original program in a way reminiscent of how
supercompilation combines several functions to create new functions.