Functional Elimination of Φ-instructions

We present a functional analogue of the elimination of Φ-instructions from Static Single Assignment (SSA) code. Extending earlier work on the relationship between SSA and functional languages we show that transformations from A-normal form (ANF) into a more restrictive form called GNF require the same compensating instructions to be inserted as are commonly inserted during the translation from SSA to machine code. Lifting the translation from the syntactic level to the type level, we introduce type systems that mediate the transition from ANF code into correctly register-allocated machine code and allow code optimisations and transformations to be performed in a typed functional setting.