Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 2. BACKGROUND AND RELATED WORK 17
Quartz also supports overloading. Overloading, or ad-hoc polymorphism, describes the use
of a single identifier to produce different implementations depending on context, the standard
example being the use of “+” to represent addition of both integers and floating point num-
bers in most programming languages. Quartz blocks can be overloaded by defining multiple
blocks with the same name, a mechanism that has a number of uses, including:
• Primitive blocks can be overloaded when multiple hardware primitives are available
which essentially carry out the same operation but with different types.
• Higher-order combinators can be overloaded when multiple blocks have the same basic
function but different parameterisations, or different non-functional properties.
• Composite blocks can be overloaded with primitive ones as “wrappers” around the
primitives e.g. to provide multiple different interfaces to the same functionality.
The inclusion of overloading allows the designer to work at a higher level of abstraction than
would otherwise be possible. In order to maintain type inference and permit the automatic
resolution of overloading without requiring explicit annotations by the designer Quartz uses
a type inference algorithm based on satisfiability matrix predicates [63, 64] – matrices that
represent possible values of a type and relationships between type variables. This system
minimises ambiguity and can express n-ary constraints between type variables clearly and
easily.
A key feature of the Quartz overloading system is that it permits overloading of blocks
with overlapping types. This means, for example, that it is possible to overload a fully
polymorphic block with type τ ∼ τ with specific instances for wire ∼ wire and int ∼ int.
The overloading mechanism will select the most specific matching block to use, so for this
example the instance with type wire ∼ wire would be used if wire types were supplied, even
though the polymorphic instance also matches.
Satisfiability matrices can also support blocks with different numbers of parameters by using
an empty/void type Ω, which can be used to “pad” matrices and block types so that they
are all the same length. Ω only unifies with itself so blocks with the wrong number of
parameters are eliminated from the matrix when unification fails. This is a particularly
useful mechanism for overloading blocks with versions that are have the same function but