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This paper considers random testing of a compiler, using randomly generated programs as inputs, and comparing their behaviour with and without optimisation. Since the generated programs must compile, then we need to take into account syntax, scope rules, and type checking during our random generation. Doing so, while attaining a good distribution of test data, proves surprisingly subtle; the main contribution of this paper is a workable solution to this problem. We used it to generate typed functions on lists, which we compiled using the Glasgow Haskell compiler, a mature production quality Haskell compiler. After around 20,000 tests we triggered an optimiser failure, and automatically simplified it to a program with just a few constructs.

HipSpec is a system for automatically deriving and proving properties about functional programs. It uses a novel approach, combining theory exploration, counterexample testing and inductive theorem proving. HipSpec automatically generates a set of equational theorems about the available recursive functions of a program. These equational properties make up an algebraic specification for the program and can in addition be used as a background theory for proving additional user-stated properties. Experimental results are encouraging: HipSpec compares favourably to other inductive theorem provers and theory exploration systems.

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Abstract. We present QuickSpec, a tool that automatically generates algebraic specifications for sets of pure functions. The tool is based on testing, rather than static analysis or theorem proving. The main challenge QuickSpec faces is to keep the number of generated equations to a minimum while maintaining completeness. We demonstrate how QuickSpec can improve one's understanding of a program module by exploring the laws that are generated using two case studies: a heap library for Haskell and a fixed-point arithmetic library for Erlang.