An Operational Semantics for I/O in a Lazy Functional Language

I/O mechanisms are needed if functional languages are to be suitable for general purpose programming and several implementations exist. But little is known about semantic methods for specifying and proving properties of lazy functional programs engaged in I/O. As a step towards formal methods of reasoning about realistic I/O we investigate three widely implemented mechanisms in the setting of teletype I/O: synchronised-stream (primitive in Haskell), continuation-passing (derived in Haskell) and Landin-stream I/O (where programs map an input stream to an output stream of characters). Using methods from Milner’s CCS we give a labelled transition semantics for the three mechanisms. We adopt bisimulation equivalence as equality on programs engaged in I/O and give functions to map between the three kinds of I/O. The main result is the first formal proof of semantic equivalence of the three mechanisms, generalising an informal argument of the Haskell committee.