Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 5. SPECIALISATION 119
Modifications are necessary to the type system to provide this kind of support. One possibility
is to provide a full system of dependent types, where the type of a signal could depend on a
variable value. This complicates type inference - making it undecidable - and would require
the designer to write complex type declarations.
A better alternative is to achieve the same power by introducing the much simpler construct
of enumerated types. These are standard constructs in many programming languages, which
allow programmers to specify their own types using type constructors. Functional program-
ming languages usually provide easy-to-use support for recursive types and these are used to
define recursive data structures such as linked lists and trees. We do not require recursive
types – merely the ability for a value that can have multiple interpretations to have a simple
type.
We could define a data type which could be declared by (in pseudo-code):
type data =
Known of bool
Wire of wire.
Values of type data would then be used in circuit descriptions, rather than wire or bool, and
the specific value would be extracted by the block itself. Figure 5.9 illustrates what an or2
block that used this mechanism could look like. Because static and dynamic values now have
the same type we are no longer able to use the overloading mechanism to select between
instances and instead this or2 block contains code to generate the correct output regardless
of whether zero, one or both inputs are known. This block with specialising code can however
be overloaded with the hardware primitive with type wire wire ∼ wire and the type system
can determine which block to instantiate.
In this description “Wire” and “Known” are used as both an access function, to retrieve the
wire value attached to the data inputs a and b and as a constructor, and a constructor, to
be pattern matched. It may be that there is a more appropriate syntax, however it is the
concept that matters.
This system can be used to achieve optimal constant propagation results and verification is
still relatively easy using a suitable model in an automatic theorem prover.