Higher-Order Strictness Typing

We extend an existing first-order typing system for strictness analysis to the fully higher-order case. The resulting fully higher-order strictness typing system has an expressivity beyond that of traditional strictness analysis systems. This extension is developed with the explicit aim to formally prove that the higher-order strictness typing is sound with respect to a natural operational semantics. A key aspect of our approach is that we introduce the proof assistant in an early stage, namely during development of the proof, and as such the language theoretic concepts are designed with the aid of the theorem prover. The combination of reporting on a new result together with its formal proof, can be seen as a case study towards the achievement of the long term PoplMark Challenge. The proof framework developed for this case study can be used further in other typing systems case studies.

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