Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 4. VERIFYING CIRCUIT LAYOUTS 88
4.6 Proving the Prelude Library
One set of Quartz blocks it is essential to prove is the prelude library, the basic set of
operations that encode a variety of useful functions. The majority of the blocks in the
prelude are actually wiring constructs rather than combinators, however it is still necessary
to give them all a layout interpretation. We have done this according to the following rules:
1. Wiring blocks, which simply re-arrange signals, are given size 0 × 0.
2. Repeated composition (R n /rcomp) is laid out horizontally. /tri and ˜ /irt blocks
which both use repeated composition are laid out vertically. map is laid out vertically,
as are col and rdr .
3. All other blocks are laid out horizontally, with the exception of grid which is two
dimensional.
The prelude library provides a fairly comprehensive set of blocks with different signal arrange-
ments and is thus useful for experimenting with how automatic proof tools can be tuned to
minimise the human intervention in proofs.
4.6.1 Proofs with Tacticals
Our initial approach to automating proof of the Prelude library involves generating proof
tacticals in the Quartz compiler Isabelle module. Tacticals combine elementary proof steps
and automated tactics with basic repetition or choice operations.
We design tacticals based on experience with hand-proof of a variety of prelude blocks. These
tacticals are based on invocations of Isabelle’s simplifier with specific simplification rules,
interspersed with uses of the primitive rule method to decompose goals into multiple simpler
sub-goals using theorems such as Theorems 13 and 17. Auto-generating proof scripts for all
prelude blocks we find that many theories run correctly with the automatically generated
tacticals without any human intervention, however some require intervention.
The conjugate and conjugate2 blocks (defined in Figure 4.12) require additional intervention
to prove the validity of their size functions due to the use of series composition. We de-