A higher-order removal method

A major attraction of functional languages is their support for higher-order functions. This facility increases the expressive power of functional languages by allowing concise and reusable programs to be written. However, higher-order functions are more expensive to execute and to analyse for optimisations.To reduce the performance penalties of using higher-order functions, this paper proposes two transformation algorithms which could automatically removemost higher-order functions from functional programs. The first algorithm uses aneta-expansion technique to eliminate expressions which return function-type results. The second algorithm uses afunction specialisation technique to eliminate expressions with function-type arguments. Together, they remove higher-order functions by transforming each higher-order program to an equivalent first-order (or lower-order) program. We shall prove that the two algorithms areterminating (when applied to well-typed programs) and alsototally-correct (preserving non-strict semantics).