Mechanizing the metatheory of rewire

Abstract

The [lambda]-calculus provides a simple, well-established framework for research in functional programming languages that readily lends itself to the use offormal methods--that is, the use of mathematically sound techniques and supporting tools--to describe and verify properties of programming languages, as well. This is no coincidence. After all, the [lambda]-calculus formalizes the concept of effective computability, for all computable functions are definable in the untyped [lambda]-calculus, making it expressively equivalent torecursive functions. In software, the expressiveness of functional languages is considereda strength. Functional approaches to language design, however, needn't be limited to soft-ware. In hardware, the expressiveness of functional languages becomes a major obstacle to successful hardware synthesis, for the reason that such languages are usually capable of expressing general recursion. The presence of general recursion makes it possible to generate expressions that run forever, never producing a well-defined value. In this dissertation, we study two novel variants of the simply typed [lambda]-calculus, representing fragments of functional hardware description languages. The first variant extends the type system, using natural numbers representing time. This addition, though simple, is non-trivial. We prove that this calculus possesses bounded variants of type-safety and strong normalization. That is to say, we show that all well-typed expressions evaluate to values within a bound determined by the natural number index of their corresponding types. The second variant is a computational [lambda]-calculus that formalizes the core fragment of the hardware description language known as ReWire. We prove that the language has type-safety and is strongly normalizing -- the proof of strong normalizationis the first mechanized proof of its kind. We define an equational theory with respect to this language. This allows us to prove that the language has desirable security properties by construction. This work supports a full-edged, formal methodology for producing high assurance hardware.