Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 3. GENERATING PARAMETERISED LIBRARIES WITH LAYOUT 54
Proof Pointwise, by expanding the definition of surround to give the proposition:
∃l2, t2, b2, r2. l ; map n B ; l2 ∧ t ; map m B ; t2 ∧ (l2, t2) ; grid m,n A ; (b2, r2)
∧ b2 ; D ; b ∧ r2 ; E ; r =
[map n B, map m B] ; grid m,n A ; [map m C, map n C]
Then by expanding the definitions of series and parallel composition.
The placement co-ordinates of the C block in this combinator are particularly worthy of
interest. The max function is used to describe the y co-ordinate that C is placed at, this
ensures that the layout is truly general and independent of the sizes of each block. The
verification of this combinator’s layout is discussed further in Section 4.7.
3.6.2 Combinators
Another key problem is that the map n R combinator block itself has been given a layout
interpretation - with its elements arranged vertically. However, in this example we require
both a vertically and horizontally arranged map . One possibility is to require designers to
choose between vmap and hmap blocks, however this reduces the link between the original
pure-functional description and the placed version. It also ignores the fact that most of the
time the map combinator is used in manner where vertical layout is the most appropriate.
The Quartz overloading mechanism can be used to handle circumstances where multiple
blocks are required which have the same basic functional properties but differ in some other
way. Figure 3.15 illustrates how this system can be used to provide a map n R combinator
which has a default vertical layout but can also be configured to be laid out horizontally.
A simple usage of map n R will be resolved to refer to the default case map block which then
instantiates the general combinator with the specific default layout (vertical, for map). If
horizontal layout is desired then the fully flexible map block can be invoked specifically by
adding an additional orientation parameter to the instantiation.
In Figure 3.15 we have used an integer parameter to control the orientation of the map block
however if the Quartz type system were extended to support enumerated types then this could