I declare that this thesis is my own account of my research and contains as its main content work which has not previously been submitted for a degree at any tertiary education institution. Joel Kelso ii The purported advantages of Visual Programming, as applied to general purpose programming languages, have remained largely unfulfilled. The essence of this thesis is that functional programming languages have at least one natural visual representation, and that a useful programming environment can be based upon this representation. This thesis describes the implementation of a Visual Functional Programming Environment (VFPE). The programming environment has several significant features. • The environment includes a program editor that is inherently

Abstract. Developing dependently typed functional programs can be difficult because the user may be required to write proofs and program errors are often hard to identify and fix. We describe a framework, implemented in Coq, that combines testing with user-assisted proof automation to make development easier. Testing occurs within Coq and is used to give user feedback to program errors and faulty conjectures, as well as guiding automated proof search. Dependently typed functional programming languages, such as Epigram [1] and ATS [2], offer an approach for developing verified software. These languages use dependent types to assign more accurate typing to terms, compared to simple typing, thereby enabling program properties to be verified at compile-time. However, programming with dependent types can be difficult. The user can be expected to write proofs for the proof obligations that arise and program errors can be hard to identify and fix. In this paper, we describe techniques that use a combination of testing and user-assisted proof automation for making dependently typed functional programming easier. These techniques are generic enough to support user-defined types and functions. We have implemented our ideas in the Coq theorem prover [3]. Coq can be used as a dependently typed programming language. The contributions of this paper are: – A description of how to provide useful counterexample-based program error feedback (see Section 2). – A description of the important role of testing in our user-assisted proof automation (see Section 3). – A small-scale usability study examining the utility of our counterexamplebased program error feedback (see Section 4). 1

Like other software engineering activities, formal modelling needs to deal with change: bugs and omissions need to be corrected, and changes from the outside need to be dealt with. In the context of axiomatic specifications and (partly) interactive proofs, the main obstacle is that changes invalidate proofs, which then need to be rebuilt using an inhibitive amount of resources. This thesis proposes to solve the problem by considering the state of a formal development consisting of (potentially buggy) specification and (potentially partial) proofs as one entity and transforming it using preconceived transformations. These transformations are operationally motivated: how would one patch the proofs on paper given a consistent transformation for the specification? They are formulated in terms of the specification and logic language, so as to be usable for several application domains. In order to make the approach compatible with the architecture of existing