}
{\end{list}}
+\usepackage{paralist}
+
%include polycode.fmt
+%include clash.fmt
\begin{document}
%
\author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
\IEEEauthorblockA{University of Twente, Department of EEMCS\\
P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
-c.p.r.baaij@utwente.nl, matthijs@stdin.nl}}
+c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl}}
% \and
% \IEEEauthorblockN{Homer Simpson}
% \IEEEauthorblockA{Twentieth Century Fox\\
expression, one using only case expressions and one using pattern
matching and guards.
-\begin{verbatim}
-sumif pred a b = if pred == Eq && a == b || pred == Neq && a != b
- then a + b
- else 0
-\end{verbatim}
+\begin{code}
+sumif pred a b =
+ if pred == Eq && a == b || pred == Neq && a != b
+ then a + b
+ else 0
-\begin{verbatim}
sumif pred a b = case pred of
- Eq -> case a == b of
- True -> a + b
- False -> 0
- Neq -> case a != b of
- True -> a + b
- False -> 0
-\end{verbatim}
-
-\begin{verbatim}
-sumif Eq a b | a == b = a + b
-sumif Neq a b | a != b = a + b
-sumif _ _ _ = 0
-\end{verbatim}
+ Eq -> case a == b of
+ True -> a + b
+ False -> 0
+ Neq -> case a != b of
+ True -> a + b
+ False -> 0
+
+sumif Eq a b | a == b = a + b
+sumif Neq a b | a != b = a + b
+sumif _ _ _ = 0
+\end{code}
TODO: Pretty picture
For algebraic types, we can make the following distinction:
\begin{xlist}
- \item[Product types]
+ \item[\textbf{Product types}]
A product type is an algebraic datatype with a single constructor with
two or more fields, denoted in practice like (a,b), (a,b,c), etc. This
is essentially a way to pack a few values together in a record-like
constructor algebraic data-types, including those with just one
field (which are technically not a product, but generate a VHDL
record for implementation simplicity).
- \item[Enumerated types]
+ \item[\textbf{Enumerated types}]
An enumerated type is an algebraic datatype with multiple constructors, but
none of them have fields. This is essentially a way to get an
enumeration-like type containing alternatives.
These types are translated to \VHDL\ enumerations, with one value for
each constructor. This allows references to these constructors to be
translated to the corresponding enumeration value.
- \item[Sum types]
+ \item[\textbf{Sum types}]
A sum type is an algebraic datatype with multiple constructors, where
the constructors have one or more fields. Technically, a type with
more than one field per constructor is a sum of products type, but
during a clock cycle. As we want to describe more than simple
combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
+ An important property in Haskell, and in most other functional languages,
+ is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
+ conditions:
+ \begin{inparaenum}
+ \item given the same arguments twice, it should return the same value in
+ both cases, and
+ \item when the function is called, it should not have observable
+ side-effects.
+ \end{inparaenum}
+ This purity property is important for functional languages, since it
+ enables all kinds of mathematical reasoning that could not be guaranteed
+ correct for impure functions. Pure functions are as such a perfect match
+ for a combinatorial circuit, where the output solely depends on the
+ inputs. When a circuit has state however, it can no longer be simply
+ described by a pure function. Simply removing the purity property is not a
+ valid option, as the language would then lose many of it mathematical
+ properties. In an effort to include the concept of state in pure
+ functions, the current value of the state is made an argument of the
+ function; the updated state becomes part of the result.
+
+ A simple example is the description of an accumulator circuit:
+ \begin{code}
+ acc :: Word -> State Word -> (State Word, Word)
+ acc inp (State s) = (State s', outp)
+ where
+ outp = s + inp
+ s' = outp
+ \end{code}
+ This approach makes the state of a function very explicit: which variables
+ are part of the state is completely determined by the type signature. This
+ approach to state is well suited to be used in combination with the
+ existing code and language features, such as all the choice elements, as
+ state values are just normal values.
\section{\CLaSH\ prototype}
foo\par bar
projects / matthijs / master-project / dsd-paper.git / blobdiff