A Calculus for Hardware Description Languages

In efforts to overcome the complexity of the syntax and the lack of formal semantics in conventional hardware description languages (most notably Verilog and VHDL), a number of approaches based on functional languages have been proposed. The merits of functional languages as hardware description languages can be attributed to the fact that basic building blocks for hardware circuits are equivalent to mathematical functions while functional languages lend themselves to creating and composing mathematical functions. Functional hardware description languages are typically embedded into existing functional languages such as Haskell and ML, or into new functional languages designed specifically for hardware design such as reFL ect. Since its semantics is unaware of hardware circuits, a host language represents hardware circuits as a special datatype. Eventually we convert such a datatype into netlists which describe connections in hardware circuits at the lowest level. Converting a datatype representing hardware circuits into netlists is certainly a necessary step, but makes it an unnecessarily low level task to prove properties of hardware circuits. The reason is that netlists conceal high level descriptions written into a source program and are thus correspondingly more complex to analyze. Such an indirect analysis via netlists can be compared to an analysis of an ordinary functional program in which we first compile it into an assembly language and then analyze the output assembly program instead. We present a new calculus, called l λ, which may serve as a " high level assembly language " for functional hardware description languages. l λ is an assembly language in the sense that its definition consists only of a minimal set of primitive constructs each of which corresponds to a specific method of combining hardware components, e.g., linking two separate hardware components or building feedback circuits. l λ is still a high level language in that it makes no explicit use of low level constructs, such as ports and wires, characterizing netlists. As it extends the syntax and the type system of the standard lambda calculus, l λ is particularly suitable as a substitute for netlists when designing functional hardware description languages. Two characteristic features of l λ are a denotational semantics and a linear type system. The denotational semantics enables us to translate an expression, without evaluating it, into a structural description of hardware components and their connections. It is sound in the sense that it maps expressions only to realiz-able hardware circuits which …