Our universe description, generic traversals and proofs, and our examples have all been formalised in Agda and are available in the accompanying material available online at. We present an expressive universe of syntaxes with binding and demonstrate how to (1) implement scope-safe traversals once and for all by generic programming and (2) how to derive properties of these traversals by generic proving. Nevertheless, the programmer is still forced to write the same boilerplate over again for each new implementation of a scope-safe operation (e.g., renaming, substitution, desugaring, printing), and then again for correctness proofs. Modern programming languages include features that enable constraints like scope safety to be expressed in types. In the past, implementing and reasoning about programming languages required careful handling to maintain the correct behaviour of bound variables. The syntax of almost every programming language includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of α-equivalence, capture-avoiding substitution, typing contexts, runtime environments, and so on. We seek funding for an RA at Nottingham (Peter Morris, whose PhD laid much of the groundwork for this proposal), and two doctoral students (one each at Oxford and Strathclyde), together with appropriate support for equipment, coordination, travel, and dissimination (i.e. Our programme is to build new tools extending the Epigram2 framework, investigate the underlying theory using container types, and most importantly establish novel programming patterns and libraries. To achieve this, we intend to explore two alternative roads - reusability by structure and reusability by design - and express both within a dependently typed framework. Based on and inspired by recent research at Nottingham on dependently typed programming (EPSRC EP/C512022/1) and container types (EPSRC EP/C511964/2) and at Oxford on datatype-generic programming (EPSRC GR/S27078/01, EP/E02128X/1) we plan to explore the potential of dependent types to deliver reusable and reliable software components. Luckily, all is not lost: dependent types are expressive enough that they can talk about themselves reflectively, making meta- programming one of their potential killer applications (11), with the potential to combine expressive types and reusable software components. This phenomenon already shows up in the traditional Hindley-Milner style type system of ML and Haskell it becomes even more prevalent in a dependently typed setting. However, expressive type systems have their price: more specific types frequently reduce the reusability of code, whose too-specific implementation type may not fit its current application. This is witnessed by a recent surge of language proposals with the goal to harness the power of dependent types, e.g. Nowadays, we can and should go further: dependently typed pro- gramming exploits the power of very expressive type systems to deliver stronger guarantees but also additional support for software development, using types to guide the development process. Summary Robin Milner coined the slogan well typed programs cannot go wrong, advertising the power of types in functional lan- guages like ML and Haskell to catch runtime errors.
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