Towards Machine-Verified Proofs for I/O

Abstract

In functional languages, the shape of the external world affects both our understanding of I/O and how we would wish to have I/O expressed. This paper takes the first tentative steps at examining the consequences of using an explicit model of the external world-state when reasoning (using tool-support) about the behaviour of lazy functional programs. We construct a file-system model and develop a monadic language which lets us structure I/O. Two proofs are then performed regarding the observable effect of real-world functional I/O, and it is shown how properties of the file-system lend themselves naturally to the modelling of concurrent behaviour on a single, global state. All proofs in this paper were machine-verified using the Sparkle proof-assistant.