A common attraction to functional programming is the ease with which proofs can be given of program properties. A common disappointment with functional programming is the difficulty of expressing input\/output (I\/O) while at the same time being able to verify programs. In this dissertation we show how a theory of functional programming can be smoothly extended to admit both an operational semantics for functional I\/O and verification of programs engaged in I\/O.<\/p>\n
The first half develops the operational theory of a semantic metalanguage used in the second half. The metalanguage M<\/b> is a simply-typed lambda-calculus with product, sum, function, lifted and recursive types. We study two definitions of operational equivalence: Morris-style contextual equivalence, and a typed form of Abramsky’s applicative bisimulation. We prove operational extensionality for M<\/b>—that these two definitions give rise to the same operational equivalence. We prove equational laws that are analogous to the axiomatic domain theory of LCF and derive a co-induction principle.<\/p>\n
The second half defines a small functional language, H<\/b>, and shows how the semantics of H<\/b> can be extended to accommodate I\/O. H<\/b> is essentially a fragment of Haskell. We give both operational and denotational semantics for H<\/b>. The denotational semantics uses M<\/b> in a case study of Moggi’s proposal to use monads to parameterise semantic descriptions. We define operational and denotational equivalences on H<\/b> and show that denotational implies operational equivalence. We develop a theory of H<\/b> based on equational laws and a co-induction principle.<\/p>\n
We study simplified forms of four widely-implemented I\/O mechanisms: side-effecting, Landin-stream, synchronised-stream and continuation-passing I\/O. We give reasons why side-effecting I\/O is unsuitable for lazy languages. We extend the semantics of H<\/b> to include the other three mechanisms and prove that the three are equivalent to each other in expressive power.<\/p>\n
We investigate monadic I\/O, a high-level model for functional I\/O based on Wadler’s suggestion that monads can express interaction with state in a functional language. We describe a simple monadic programming model, and give its semantics as a particular form of state transformer. Using the semantics we verify a simple programming example.<\/p>\n
Distinguished Dissertations in Computer Science (opens in new tab)<\/span><\/a>. Cambridge University Press, 1994. ISBN 0 521 47103 6 hardback. Publication dates 29 September 1994 (UK) and 27 January 1995 (USA).<\/p>\n A PDF<\/a> version is available online since August 14, 2007, as permitted<\/a> by Cambridge University Press, who own the copyright.<\/p>\n","protected":false},"excerpt":{"rendered":" A common attraction to functional programming is the ease with which proofs can be given of program properties. A common disappointment with functional programming is the difficulty of expressing input\/output (I\/O) while at the same time being able to verify programs. 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