Proof Tool Support for Explicit Strictness

Abstract

Abstract. In programs written in lazy functional languages such as for example Clean and Haskell, the programmer can choose freely whether particular subexpressions will be evaluated lazily (the default) or strictly (must be specified explicitly). It is widely known that this choice affects program behavior, resource consumption and semantics in several ways. However, not much experience is available about the impact on logical program properties and formal reasoning. This paper aims to give a better understanding of the concept of explicit strictness. The impact of explicit strictness on formal reasoning will be investigated. It will be shown that this impact is bigger than expected and that tool support is needed for formal reasoning in the context of explicit strictness. We introduce the various ways in which strictness specific support is offered by the proof assistant Sparkle.

EditorArrow: An arrow-based model for editor-based programming

“…Implementing the EditorArrow model in Clean as EditorArrowCore allows us to use the integrated proof assistant Sparkle (Mol et al, 2002(Mol et al, , 2008Kesteren et al, 2004) and its proof tool support for strictness (Eekelen & Mol, 2005) to verify the correctness of the laws of Section 3 when translated to EditorArrowCore.…”

“…We use Clean because it comes with the interactive proof assistant Sparkle (Mol et al, 2002(Mol et al, , 2008Kesteren et al, 2004;Mol, 2009). We use Sparkle and its special support for reasoning about strictness (Eekelen & Mol, 2005) to determine and analyze the definedness properties of the EditorArrow framework.…”

Trends in Trends in Functional Programming 1999/2000 versus 2007/2008

“…This seminal paper [7] was the first to reason formally about the consequences of strictness (changing the order of evaluation). It inspired work to reason less formally, but still remain "morally correct" [31] and work to create a formal proof tool to support reasoning in the context of lazy evaluation combined with explicit strictness [124]. Other lines of research focused on comparing lazy and eager evaluation in a setting with explicit process creation and implicit message-passing communication [60] to assist in developing the best implementation strategy for languages such as Eden. Over the years the topics changed from formally defining the basic concepts of parallelism and graph reduction to the definition of the semantics of concepts that were related to extensions of type systems and to (the incorporation of) concepts from other declarative and imperative languages.…”

Proving Properties of Lazy Functional Programs with Sparkle

“…Below we present a small example to illustrate the propagation of L-values through expressions. For a full explanation of com putation in C lean we refer to [28] and [32]. It is very im portant th a t the starting point of formal reasoning is a logically correct property.…”

“…The SPARKLE-tactic 'Definedness' is therefore extremely useful, and can be applied often in proofs. More examples of the use of definedness can be found in [32].…”