Abstract
Some existing systems for supporting reasoning about functional programs have been constructed without first formalising the semantics of the language. This paper discusses how a reasoning system can be built, within the HOL theorem proving environment, based on an operational semantics for the language and using a fully definitional approach. The theoretical structure of the system is based on work by Andrew Gordon, where applicative bisimulation is used to define program equivalence. We discuss how this theory can be embedded in HOL and the type of tools which can be built on top of this theoretical framework to make reasoning possible in practice.
Highlights
It is often stated that one advantage of functional programming languages, in particular pure functional languages, is that they are suitable for formal reasoning
One style used for reasoning about functional programs is equational reasoning
There is a tradition in the HOL community of taking a purely definitional approach to using logic; instead of postulating axioms to give meaning to new notations, as is typical in the use of theorem provers such as LP, new concepts are defined in terms of existing ones that already have the required semantics
Summary
It is often stated that one advantage of functional programming languages, in particular pure functional languages, is that they are suitable for formal reasoning. With lazy languages many programs exhibit infinite behaviour and a proof method such as co-induction is required. Such proofs method are not yet widely understood and theorem proving support can help introduce them to a wider community and give greater confidence to a programmer using an unfamiliar method. The exact formulation of the syntax and semantics and the definition of program equality is taken from work by Andrew Gordon that provides a rigorous development, on paper, of a theory for a number of languages [7]. This paper does not attempt to provide all the details of the system developed but concentrates on how a system can be structured
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