\subsection[sec:normalization:intendednormalform]{Intended normal form definition}
Now we have some intuition for the normal form, we can describe how we want
- the normal form to look like in a slightly more formal manner. The following
- EBNF-like description captures most of the intended structure (and
- generates a subset of \GHC's core format).
+ the normal form to look like in a slightly more formal manner. The
+ EBNF-like description in \in{definition}[def:IntendedNormal] captures
+ most of the intended structure (and generates a subset of \GHC's core
+ format).
- There are two things missing: cast expressions are sometimes
- allowed by the prototype, but not specified here and the below
+ There are two things missing from this definition: cast expressions are
+ sometimes allowed by the prototype, but not specified here and the below
definition allows uses of state that cannot be translated to \VHDL\
properly. These two problems are discussed in
\in{section}[sec:normalization:castproblems] and
{\defref{intended normal form definition}
\typebufferlam{IntendedNormal}}
- When looking at such a program from a hardware perspective, the
- top level lambda abstractions define the input ports. Lambda
- abstractions cannot appear anywhere else. The variable reference
- in the body of the recursive let expression is the output port.
- Most function applications bound by the let expression define a
- component instantiation, where the input and output ports are
- mapped to local signals or arguments. Some of the others use a
- built-in construction (\eg\ the \lam{case} expression) or call a
- built-in function (\eg\ \lam{+} or \lam{map}). For these, a
- hardcoded \small{VHDL} translation is available.
+ When looking at such a program from a hardware perspective, the top
+ level lambda abstractions (\italic{lambda}) define the input ports.
+ Lambda abstractions cannot appear anywhere else. The variable reference
+ in the body of the recursive let expression (\italic{toplet}) is the
+ output port. Most binders bound by the let expression define a
+ component instantiation (\italic{userapp}), where the input and output
+ ports are mapped to local signals (\italic{userarg}). Some of the others
+ use a built-in construction (\eg\ the \lam{case} expression) or call a
+ built-in function (\italic{builtinapp}) such as \lam{+} or \lam{map}.
+ For these, a hardcoded \small{VHDL} translation is available.
\section[sec:normalization:transformation]{Transformation notation}
To be able to concisely present transformations, we use a specific format
dictionaries, functions.
\defref{representable}
- A \emph{built-in function} is a function supplied by the Cλash framework, whose
- implementation is not valid Cλash. The implementation is of course valid
- Haskell, for simulation, but it is not expressable in Cλash.
- \defref{built-in function} \defref{user-defined function}
+ A \emph{built-in function} is a function supplied by the Cλash
+ framework, whose implementation is not used to generate \VHDL. This is
+ either because it is no valid Cλash (like most list functions that need
+ recursion) or because a Cλash implementation would be unwanted (for the
+ addition operator, for example, we would rather use the \VHDL addition
+ operator to let the synthesis tool decide what kind of adder to use
+ instead of explicitly describing one in Cλash). \defref{built-in
+ function}
- For these functions, Cλash has a \emph{built-in hardware translation}, so calls
- to these functions can still be translated. These are functions like
- \lam{map}, \lam{hwor} and \lam{length}.
+ These are functions like \lam{map}, \lam{hwor}, \lam{+} and \lam{length}.
- A \emph{user-defined} function is a function for which we do have a Cλash
- implementation available.
+ For these functions, Cλash has a \emph{built-in hardware translation},
+ so calls to these functions can still be translated. Built-in functions
+ must have a valid Haskell implementation, of course, to allow
+ simulation.
+
+ A \emph{user-defined} function is a function for which no built-in
+ translation is available and whose definition will thus need to be
+ translated to Cλash. \defref{user-defined function}
\subsubsection[sec:normalization:predicates]{Predicates}
Here, we define a number of predicates that can be used below to concisely
\todo{Define β-reduction and η-reduction?}
- Note that the normal form of such a system consists of the set of nodes
- (expressions) without outgoing edges, since those are the expressions to which
- no transformation applies anymore. We call this set of nodes the \emph{normal
- set}. The set of nodes containing expressions in intended normal
- form \refdef{intended normal form} is called the \emph{intended
- normal set}.
+ In such a graph a node (expression) is in normal form if it has no
+ outgoing edges (meaning no transformation applies to it). The set of
+ nodes without outgoing edges is called the \emph{normal set}. Similarly,
+ the set of nodes containing expressions in intended normal form
+ \refdef{intended normal form} is called the \emph{intended normal set}.
From such a graph, we can derive some properties easily:
\startitemize[KR]
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