Verification of Parameterised FPGA Circuit Descriptions with Layout ...

APPENDIX B. THEORETICAL BASIS FOR LAYOUT REASONING 188
ParallelComposition defines the semantics and layout interpretation of Quartz parallel
composition. The theory includes AST rewriting functions to allow Isabelle to parse and
pretty-print parallel compositions and also contains proofs of useful properties of parallel
composition layouts.
Functions defines the maxf and sum functions and includes their correctness proofs and
theorems describing a wide range of useful properties.
Structures contains theorems that are particularly useful for simplifying proof goals that
are formed by certain circuit structures (e.g. horizontal arrays).
CompilerSimps contains the proofs of simplification rules used in the Quartz compiler to
simplify maxf and sum functions.
QuartzLayout is a dummy theory which brings together all dependent theories to be used
as the root library.
Minf is not included in the QuartzLayout library. It contains definitions and correspon-
dance theorems between min and max functions and minf and maxf functions. If expressions
using these minimum operators are desired these theorems can be used to rewrite expressions
into forms which use purely the max and maxf functions.
B.1 IntAlgebra
header {* Useful theorems about integers for use in size function reasoning *}
theory IntAlgebra = Main:
section {* Additional ordering operators *}
constdefs
grthn:: "[’a::ord, ’a]=>bool" ("(_/ > _)" [50, 51] 50)
"grthn == % a b. (b < a)"
geq:: "[’a::ord, ’a]=>bool" ("(_/ >= _)" [50, 51] 50)
"geq == % a b. (b