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Random testing is increasingly popular and successful, but tends to spend most time rediscovering the ``most probable bugs'' again and again, reducing the value of long test runs on buggy software. We present a new automated method to adapt random test case generation so that already-discovered bugs are avoided, and further test effort can be devoted to searching for new bugs instead. We evaluate our method primarily against RANDOOP-style testing, in three different settings our method avoids rediscovering bugs more successfully than RANDOOP and in some cases finds bugs that RANDOOP did not find at all

Safe functional reactive programming through dependent types

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals. FRP is based on the synchronous dataflow paradigm and supports both continuous-time and discrete-time signals (hybrid systems).What sets FRP apart from most other languages for similar applications is its support for systems with dynamic structure and for higher-order reactive constructs. Statically guaranteeing correctness properties of programs is an attractive proposition. This is true in particular for typical application domains for reactive programming such as embedded systems. To that end, many existing reactive languages have type systems or other static checks that guarantee domain-specific properties, such as feedback loops always being well-formed. However, they are limited in their capabilities to support dynamism and higher-order data-flow compared with FRP. Thus, the onus of ensuring such properties of FRP programs has so far been on the programmer as established static techniques do not suffice. In this paper, we show how dependent types allow this concern to be addressed. We present an implementation of FRP embedded in the dependently-typed language Agda, leveraging the type system of the host language to craft a domain-specific (dependent) type system for FRP. The implementation constitutes a discrete, operational semantics of FRP, and as it passes the Agda type, coverage, and termination checks, we know the operational semantics is total, which means our type system is safe

Explicit Substitutions for Contextual Type Theory

In this paper, we present an explicit substitution calculus which distinguishes between ordinary bound variables and meta-variables. Its typing discipline is derived from contextual modal type theory. We first present a dependently typed lambda calculus with explicit substitutions for ordinary variables and explicit meta-substitutions for meta-variables. We then present a weak head normalization procedure which performs both substitutions lazily and in a single pass thereby combining substitution walks for the two different classes of variables. Finally, we describe a bidirectional type checking algorithm which uses weak head normalization and prove soundness.Comment: In Proceedings LFMTP 2010, arXiv:1009.218

A Lambda Term Representation Inspired by Linear Ordered Logic

We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional information where to cut the variable context into function and argument part. This way, complete information about free variable occurrence is available at each subterm without requiring a traversal, and environments can be kept exact such that they only assign values to variables that actually occur in the associated term. Our approach avoids space leaks in interpreters that build function closures. In this article, we prove correctness of the new representation and present an experimental evaluation of its performance in a proof checker for the Edinburgh Logical Framework. Keywords: representation of binders, explicit substitutions, ordered contexts, space leaks, Logical Framework.Comment: In Proceedings LFMTP 2011, arXiv:1110.668

A Type and Scope Safe Universe of Syntaxes with Binding: Their Semantics and Proofs

Almost every programming language’s syntax 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. In the past, implementing and reasoning about programming languages required careful handling to maintain the correct behaviour of bound variables. Modern programming languages include features that enable constraints like scope safety to be expressed in types. 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, etc.), and then again for correctness proofs. 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. Our universe description, generic traversals and proofs, and our examples have all been formalised in Agda and are available in the accompanying material

Step-Indexed Normalization for a Language with General Recursion

The Trellys project has produced several designs for practical dependently typed languages. These languages are broken into two fragments-a_logical_fragment where every term normalizes and which is consistent when interpreted as a logic, and a_programmatic_fragment with general recursion and other convenient but unsound features. In this paper, we present a small example language in this style. Our design allows the programmer to explicitly mention and pass information between the two fragments. We show that this feature substantially complicates the metatheory and present a new technique, combining the traditional Girard-Tait method with step-indexed logical relations, which we use to show normalization for the logical fragment.Comment: In Proceedings MSFP 2012, arXiv:1202.240

Dependently-Typed Formalisation of Typed Term Graphs

We employ the dependently-typed programming language Agda2 to explore formalisation of untyped and typed term graphs directly as set-based graph structures, via the gs-monoidal categories of Corradini and Gadducci, and as nested let-expressions using Pouillard and Pottier's NotSoFresh library of variable-binding abstractions.Comment: In Proceedings TERMGRAPH 2011, arXiv:1102.226

Implementing Functional Generic Programming

Functional generic programming extends functional programming with the ability to parameterize functions on the structure of a datatype. This allows a programmer to implement certain algorithms once and for all, instead of re-implementing them for each datatype they apply to. Examples of such algorithms include simple traversals and pretty printing as well as more complex XML processing tools. The topic of this dissertation is the implementation of functional generic programming. More precisely we address two particular questions: how can we reduce the amount of work required to implement generic programming languages, and how can we embed generic programming in an existing functional language. To answer the rst question we show how meta-programming can be used to quickly prototype generic programming languages. In particular we describe prototype implementations of two generic programming languages: PolyP [15] and Generic Haskell [4]. The prototypes are extremely light-weight while still retaining most of the functionality of the original languages. One thing that is missing, though, is a way of adding type systems to the prototypes. I

Towards a practical programming language based on dependent type theory

Dependent type theories have a long history of being used for theorem proving. One aspect of type theory which makes it very powerful as a proof language is that it mixes deduction with computation. This also makes type theory a good candidate for programming---the strength of the type system allows properties of programs to be stated and established, and the computational properties provide semantics for the programs. This thesis is concerned with bridging the gap between the theoretical presentations of type theory and the requirements on a practical programming language. Although there are many challenging research problems left to solve before we have an industrial scale programming language based on type theory, this thesis takes us a good step along the way