The Curry-Howard correspondence is a mapping between logic and type systems. On the one hand you have logic systems with propositions and proofs. On the other hand you have type systems with types and programs (or functions). As it turns out these two very different things have very similar rules. This article will explore the Curry-Howard correspondence by constructing a proof system using the Haskell type system (how appropriate since Haskell is named after Haskell Curry, the "Curry" in "Curry-Howard"). We'll set up the rules of logic using Haskell types and programs. Then we'll use these rules as an abstract interface to perform some logic profs.
Epigram is a dependently typed programming language and an interactive programming environment. Epigram has got a type system which is strong enough to express the behaviour of programs, the type checker then guarantees that the program is well behaved. However, you don't have to go as far, you can write ordinary programs and refactor them into more trustworthy, formally checked deliverables -- Epigram supports a pay as you go approach to formal methods. Epigram is freely available this page provides access to downloads of version 1 as source or binaries for the major platforms along with relevant documentation. Development on version 2 is under way we hope this will considerably improve on the first, and details of its current state are available, in the form of a developers' 'blog.
Metamorphic programming is an approach to extend the structured recursive programming discipline, which favors the use of fold operations over general recursion, to abstract data types. The key idea is to represent an ADT by two parts, a constructorand a destructor,which are essentially functions to/from a common representation. Then a fold can work on an ADT by applying parameter functions to values that are delivered by the ADT's own destructor. Fold operations that use as a parameter the constructor of another ADT, called ADT transformers,play an important role and offer a concise programming style. Several laws for ADT folds and transformers exist that can be used for program optimization and verification.
Datatype-Generic Programming Roland Backhouse at the University of Nottingham and Jeremy Gibbons at the University of Oxford have a joint EPSRC-supported project entitled Datatype-Generic Programming, running for three years and starting on 1st October 2003. Aim The project is to develop a novel mechanism for parametrizing programs, namely parametrization by a datatype or type constructor. The mechanism is related to parametric polymorphism, but of higher order. We aim to develop a calculus for constructing datatype-generic programs, with the ultimate goal of improving the state of the art in generic object-oriented programming, as occurs for example in the C++ Standard Template Library. further details of the project can be obtained from the contacts listed below.