Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 6. LAYOUT CASE STUDIES 156
x_in
y_in
R
x_out
z_in z_out
y_out
Figure 6.21: The cube cell wiring block
have implemented tplapl and tplapr using the Quartz compiler infrastructure for defining new
experimental language constructs.
The tuple-append operations do exhibit some interesting behaviour because of the way they
interact with other aspects of the Quartz type system, in particular the typing rule which
treats a singleton as equivalent to a single-element tuple. For example, the operation tplapl
1 or tplapr 1 applied to a pair leaves the pair unchanged – the effect is to append the left or
right element to the single element tuple of the other element forming a new pair within the
original tuple, which is then eliminated because it only contains a single element (the pair).
For tplapl the process looks a little like:
(a, b) −→ ((a), b) −→ ((a, b)) −→ (a, b)
The tuple-append operators allow us to decompose an n-tuple into a pair of the leftmost/right-
most element and the rest of the tuple. Once this has been done we can use standard oper-
ations on pairs to manipulate the tuple. They are vital in allowing us to generalise the 3D
combinator we have developed in this section into an n-dimensional meta-combinator, nd .
We describe this as a meta-combinator because it is not itself a valid Quartz combinator
since it is parameterised in its number of dimensions and utilises tuples of parameterisable
lengths, something that is not valid in the Quartz type system. Each possible instance is a
valid combinator but must be described individually. It has been designed to use point-free
wiring constructs in order to achieve its generality and thus could be a valid construct in the
untyped Ruby calculus. The limiting influence of type systems in specification languages has