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338 % to submit to, of course. )
340 % correct bad hyphenation here
341 \hyphenation{op-tical net-works semi-conduc-tor}
343 % Macro for certain acronyms in small caps. Doesn't work with the
344 % default font, though (it contains no smallcaps it seems).
345 \def\acro#1{{\small{#1}}}
346 \def\acrop#1{\acro{#1}s}
347 \def\acrotiny#1{{\scriptsize{#1}}}
348 \def\VHDL{\acro{VHDL}}
350 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
351 \def\CLaSHtiny{{\scriptsize{C}}$\lambda$a{\scriptsize{SH}}}
353 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
354 % we'll get something more complex later on.
355 \def\hs#1{\texttt{#1}}
356 \def\quote#1{``{#1}"}
358 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
360 \settowidth{\labelwidth}{#1:}
361 \setlength{\labelsep}{0.5em}
362 \setlength{\leftmargin}{\labelwidth}
363 \addtolength{\leftmargin}{\labelsep}
364 \addtolength{\leftmargin}{\parindent}
365 \setlength{\rightmargin}{0pt}
366 \setlength{\listparindent}{\parindent}
367 \setlength{\itemsep}{0 ex plus 0.2ex}
368 \renewcommand{\makelabel}[1]{##1:\hfil}
373 \usepackage{paralist}
375 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
377 \usepackage{cleveref}
378 \crefname{figure}{figure}{figures}
379 \newcommand{\fref}[1]{\cref{#1}}
380 \newcommand{\Fref}[1]{\Cref{#1}}
382 \usepackage{epstopdf}
384 \epstopdfDeclareGraphicsRule{.svg}{pdf}{.pdf}{rsvg-convert --format=pdf < #1 > \noexpand\OutputFile}
386 %include polycode.fmt
389 \newcounter{Codecount}
390 \setcounter{Codecount}{0}
392 \newenvironment{example}
394 \refstepcounter{equation}
405 % can use linebreaks \\ within to get better formatting as desired
406 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
409 % author names and affiliations
410 % use a multiple column layout for up to three different
412 \author{\IEEEauthorblockN{Matthijs Kooijman, Christiaan P.R. Baaij, Jan Kuper, Marco E.T. Gerards}%, Bert Molenkamp, Sabih H. Gerez}
413 \IEEEauthorblockA{%Computer Architecture for Embedded Systems (CAES)\\
414 Department of EEMCS, University of Twente\\
415 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
416 matthijs@@stdin.nl, c.p.r.baaij@@utwente.nl, j.kuper@@utwente.nl}
417 % \thanks{Supported through the FP7 project: S(o)OS (248465)}
420 % \IEEEauthorblockN{Homer Simpson}
421 % \IEEEauthorblockA{Twentieth Century Fox\\
423 % Email: homer@thesimpsons.com}
425 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
426 % \IEEEauthorblockA{Starfleet Academy\\
427 % San Francisco, California 96678-2391\\
428 % Telephone: (800) 555--1212\\
429 % Fax: (888) 555--1212}}
431 % conference papers do not typically use \thanks and this command
432 % is locked out in conference mode. If really needed, such as for
433 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
434 % after \documentclass
436 % for over three affiliations, or if they all won't fit within the width
437 % of the page, use this alternative format:
439 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
440 %Homer Simpson\IEEEauthorrefmark{2},
441 %James Kirk\IEEEauthorrefmark{3},
442 %Montgomery Scott\IEEEauthorrefmark{3} and
443 %Eldon Tyrell\IEEEauthorrefmark{4}}
444 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
445 %Georgia Institute of Technology,
446 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
447 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
448 %Email: homer@thesimpsons.com}
449 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
450 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
451 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
456 % use for special paper notices
457 %\IEEEspecialpapernotice{(Invited Paper)}
462 % make the title area
467 \CLaSH\ is a functional hardware description language that borrows both its
468 syntax and semantics from the functional programming language Haskell.
469 Polymorphism and higher-order functions provide a level of abstraction and
470 generality that allow a circuit designer to describe circuits in a more
471 natural way than possible in a traditional hardware description language.
473 Circuit descriptions can be translated to synthesizable VHDL using the
474 prototype \CLaSH\ compiler. As the circuit descriptions, simulation code, and
475 test input are also valid Haskell, complete simulations can be compiled as an
476 executable binary by a Haskell compiler allowing high-speed simulation and
479 % \CLaSH\ supports stateful descriptions by explicitly making the current
480 % state an argument of the function, and the updated state part of the result.
481 % This makes \CLaSH\ descriptions in essence the combinational parts of a
484 % IEEEtran.cls defaults to using nonbold math in the Abstract.
485 % This preserves the distinction between vectors and scalars. However,
486 % if the conference you are submitting to favors bold math in the abstract,
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488 % of the abstract to achieve this. Many IEEE journals/conferences frown on
489 % math in the abstract anyway.
496 % For peer review papers, you can put extra information on the cover
498 % \ifCLASSOPTIONpeerreview
499 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
502 % For peerreview papers, this IEEEtran command inserts a page break and
503 % creates the second title. It will be ignored for other modes.
504 \IEEEpeerreviewmaketitle
506 \section{Introduction}
507 Hardware description languages (\acrop{HDL}) have allowed the productivity of
508 hardware engineers to keep pace with the development of chip technology.
509 Traditional \acrop{HDL}, like \VHDL~\cite{VHDL2008} and
510 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
511 `programming' language. These standard languages are very good at describing
512 detailed hardware properties such as timing behavior, but are generally
513 cumbersome in expressing higher-level abstractions. In an attempt to raise the
514 abstraction level of the descriptions, a great number of approaches based on
515 functional languages has been proposed \cite{Cardelli1981,muFP,DAISY,FHDL,
516 T-Ruby,Hydra,HML2,Hawk1,Lava,ForSyDe1,Wired,reFLect}. The idea of using
517 functional languages for hardware descriptions started in the early 1980s
518 \cite{Cardelli1981,muFP,DAISY,FHDL}, a time which also saw the birth of the
519 currently popular hardware description languages, such as \VHDL. Functional
520 languages are especially well suited to describe hardware because
521 combinational circuits can be directly modeled as mathematical functions and
522 functional languages are very good at describing and composing these
523 mathematical functions.
525 In an attempt to decrease the amount of work involved in creating all the
526 required tooling, such as parsers and type-checkers, many functional
527 \acrop{HDL} \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired} are embedded as a domain
528 specific language (\acro{DSL}) within the functional language Haskell
529 \cite{Haskell}. This means that a developer is given a library of Haskell
530 functions and types that together form the language primitives of the
531 \acro{DSL}. The primitive functions used to describe a circuit do not actually
532 process any signals, they instead compose a large domain-specific datatype
533 (which is usually hidden from the designer). This datatype is then further
534 processed by an embedded circuit compiler which can perform for example
535 simulation or synthesis. As Haskell's choice elements (\hs{if}-expressions,
536 \hs{case}-expressions, etc.) are evaluated at the time the domain-specific
537 datatype is being build, they are no longer visible to the embedded compiler
538 that processes the datatype. Consequently, it is impossible the capture
539 Haskell's choice elements within a circuit description when taking the
540 embedded language approach. Descriptions can however still contain
541 polymorphism and higher-order functions.
543 The approach taken in this research is not to make another \acro{DSL} embedded
544 in Haskell, but to use (a subset of) the Haskell language \emph{itself} for
545 the purpose of describing hardware. By taking this approach, this research
546 \emph{can} capture certain language constructs, such as Haskell's choice
547 elements, within circuit descriptions. To the best knowledge of the authors,
548 supporting polymorphism, higher-order functions and such an extensive array of
549 choice-elements is new in the domain of (functional) \acrop{HDL}.
550 % As the hardware descriptions are plain Haskell
551 % functions, these descriptions can be compiled to an executable binary
552 % for simulation using an optimizing Haskell compiler such as the Glasgow
553 % Haskell Compiler (\GHC)~\cite{ghc}.
555 Where descriptions in a conventional \acro{HDL} have an explicit clock for the
556 purposes state and synchronicity, the clock is implied in the context of the
557 research presented in this paper. A circuit designer describes the behavior of
558 the hardware between clock cycles. Many functional \acrop{HDL} model signals
559 as a stream of all values over time; state is then modeled as a delay on this
560 stream of values. The approach taken in this research is to make the current
561 state an additional input and the updated state a part of the output of a
562 function. This abstraction of state and time limits the descriptions to
563 synchronous hardware, there is however room within the language to eventually
564 add a different abstraction mechanism that will allow for the modeling of
565 asynchronous systems.
567 Like the traditional \acrop{HDL}, descriptions made in a functional \acro{HDL}
568 must eventually be converted into a netlist. This research also features a
569 prototype translator, which has the same name as the language:
570 \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES} Language for Synchronous Hardware}
571 (pronounced: clash). This compiler converts the Haskell code to equivalently
572 behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist
573 format by an (optimizing) \VHDL\ synthesis tool.
575 Besides trivial circuits such as variants of both the \acro{FIR} filter and
576 the simple \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler has
577 also been able to successfully translate non-trivial functional descriptions
578 such as a streaming reduction circuit~\cite{reductioncircuit} for floating
581 \section{Hardware description in Haskell}
582 The following section describes the basic language elements of \CLaSH\ and the
583 extensiveness of the support of these elements within the \CLaSH\ compiler. In
584 various subsections, the relation between the language elements and their
585 eventual netlist representation is also highlighted.
587 \subsection{Function application}
588 Two basic syntactic elements of a functional program are functions
589 and function application. These have a single obvious translation to a
592 \item every function is translated to a component,
593 \item every function argument is translated to an input port,
594 \item the result value of a function is translated to an output port,
596 \item function applications are translated to component instantiations.
598 The result value can have a composite type (such as a tuple), so having
599 just a single result value does not pose any limitation. The actual
600 arguments of a function application are assigned to signals, which are
601 then mapped to the corresponding input ports of the component. The output
602 port of the function is also mapped to a signal, which is used as the
603 result of the application itself. Since every top level function generates
604 its own component, the hierarchy of function calls is reflected in the
605 final netlist. %, creating a hierarchical description of the hardware.
606 % The separation in different components makes it easier for a developer
607 % to understand and possibly hand-optimize the resulting \VHDL\ output of
608 % the \CLaSH\ compiler.
610 The short example (\ref{lst:code1}) demonstrated below gives an indication
611 of the level of conciseness that can be achieved with functional hardware
612 description languages when compared with the more traditional hardware
613 description languages. The example is a combinational multiply-accumulate
614 circuit that works for \emph{any} word length (this type of polymorphism
615 will be further elaborated in \Cref{sec:polymorhpism}). The corresponding
616 netlist is depicted in \Cref{img:mac-comb}.
619 \begin{minipage}{0.93\linewidth}
621 mac a b c = add (mul a b) c
624 \begin{minipage}{0.07\linewidth}
631 \centerline{\includegraphics{mac.svg}}
632 \caption{Combinational Multiply-Accumulate}
637 The use of a composite result value is demonstrated in the next example
638 (\ref{lst:code2}), where the multiply-accumulate circuit not only returns
639 the accumulation result, but also the intermediate multiplication result.
640 Its corresponding netlist can be seen in \Cref{img:mac-comb-composite}.
643 \begin{minipage}{0.93\linewidth}
645 mac a b c = (z, add z c)
650 \begin{minipage}{0.07\linewidth}
658 \centerline{\includegraphics{mac-nocurry.svg}}
659 \caption{Combinational Multiply-Accumulate (composite output)}
660 \label{img:mac-comb-composite}
665 In Haskell, choice can be achieved by a large set of syntactic elements,
666 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
667 pattern matching, and guards. The most general of these are the \hs{case}
668 expressions (\hs{if} expressions can be directly translated to
669 \hs{case} expressions). When transforming a \CLaSH\ description to a
670 netlist, a \hs{case} expression is translated to a multiplexer. The
671 control value of the \hs{case} expression is fed into a number of
672 comparators and their combined output forms the selection port of the
673 multiplexer. The result of each alternative in the \hs{case} expression is
674 linked to the corresponding input port of the multiplexer.
675 % A \hs{case} expression can in turn simply be translated to a conditional
676 % assignment in \VHDL, where the conditions use equality comparisons
677 % against the constructors in the \hs{case} expressions.
678 Two versions of a contrived example are displayed below, the first
679 (\ref{lst:code3}) using a \hs{case} expression and the second
680 (\ref{lst:code4}) using an \hs{if-then-else} expression. Both examples
681 sum two values when they are equal or non-equal (depending on the given
682 predicate, the \hs{pred} variable) and return 0 otherwise. The \hs{pred}
683 variable is of the following, user-defined, enumeration datatype:
686 data Pred = Equal | NotEqual
689 The naive netlist corresponding to both versions of the example is
690 depicted in \Cref{img:choice}. Note that the \hs{pred} variable is only
691 compared to \hs{Equal}, as an inequality immediately implies that the
692 \hs{pred} variable is \hs{NotEqual}.
695 \begin{minipage}{0.93\linewidth}
697 sumif pred a b = case pred of
698 Equal -> case a == b of
701 NotEqual -> case a != b of
706 \begin{minipage}{0.07\linewidth}
713 \begin{minipage}{0.93\linewidth}
716 if pred == Equal then
717 if a == b then a + b else 0
719 if a != b then a + b else 0
722 \begin{minipage}{0.07\linewidth}
729 \centerline{\includegraphics{choice-case.svg}}
730 \caption{Choice - sumif}
735 A user-friendly and also very powerful form of choice that is not found in
736 the traditional hardware description languages is pattern matching. A
737 function can be defined in multiple clauses, where each clause corresponds
738 to a pattern. When an argument matches a pattern, the corresponding clause
739 will be used. Expressions can also contain guards, where the expression is
740 only executed if the guard evaluates to true, and continues with the next
741 clause if the guard evaluates to false. Like \hs{if-then-else}
742 expressions, pattern matching and guards have a (straightforward)
743 translation to \hs{case} expressions and can as such be mapped to
744 multiplexers. A third version (\ref{lst:code5}) of the earlier example,
745 now using both pattern matching and guards, can be seen below. The guard
746 is the expression that follows the vertical bar (\hs{|}) and precedes the
747 assignment operator (\hs{=}). The \hs{otherwise} guards always evaluate to
750 The version using pattern matching and guards corresponds to the same
751 naive netlist representation (\Cref{img:choice}) as the earlier two
752 versions of the example.
755 \begin{minipage}{0.93\linewidth}
757 sumif Equal a b | a == b = a + b
759 sumif NotEqual a b | a != b = a + b
763 \begin{minipage}{0.07\linewidth}
770 % \centerline{\includegraphics{choice-ifthenelse}}
771 % \caption{Choice - \emph{if-then-else}}
776 Haskell is a statically-typed language, meaning that the type of a
777 variable or function is determined at compile-time. Not all of Haskell's
778 typing constructs have a clear translation to hardware, this section will
779 therefore only deal with the types that do have a clear correspondence
780 to hardware. The translatable types are divided into two categories:
781 \emph{built-in} types and \emph{user-defined} types. Built-in types are
782 those types for which a fixed translation is defined within the \CLaSH\
783 compiler. The \CLaSH\ compiler has generic translation rules to
784 translate the user-defined types described later on.
786 The \CLaSH\ compiler is able to infer unspecified (polymorphic) types,
787 meaning that a developer does not have to annotate every function with a
788 type signature. % (even if it is good practice to do so).
789 Given that the top-level entity of a circuit design is annotated with
790 concrete types, the \CLaSH\ compiler can specialize polymorphic functions
791 to functions with concrete types.
793 % Translation of two most basic functional concepts has been
794 % discussed: function application and choice. Before looking further
795 % into less obvious concepts like higher-order expressions and
796 % polymorphism, the possible types that can be used in hardware
797 % descriptions will be discussed.
799 % Some way is needed to translate every value used to its hardware
800 % equivalents. In particular, this means a hardware equivalent for
801 % every \emph{type} used in a hardware description is needed.
803 % The following types are \emph{built-in}, meaning that their hardware
804 % translation is fixed into the \CLaSH\ compiler. A designer can also
805 % define his own types, which will be translated into hardware types
806 % using translation rules that are discussed later on.
808 \subsubsection{Built-in types}
809 The following types have fixed translations defined within the \CLaSH\
813 the most basic type available. It can have two values:
814 \hs{Low} or \hs{High}.
815 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
817 this is a basic logic type. It can have two values: \hs{True}
819 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
820 % type (where a value of \hs{True} corresponds to a value of
822 Supporting the Bool type is required in order to support the
823 \hs{if-then-else} expression, which requires a \hs{Bool} value for
825 \item[\bf{Signed}, \bf{Unsigned}]
826 these are types to represent integers and both are parametrizable in
827 their size. The overflow behavior of the numeric operators defined for
828 these types is \emph{wrap-around}.
829 % , so you can define an unsigned word of 32 bits wide as follows:
832 % type Word32 = SizedWord D32
835 % Here, a type synonym \hs{Word32} is defined that is equal to the
836 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
837 % \hs{D32} is the \emph{type level representation} of the decimal
838 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
839 % types are translated to the \VHDL\ \texttt{unsigned} and
840 % \texttt{signed} respectively.
842 this is a vector type that can contain elements of any other type and
843 has a fixed length. The \hs{Vector} type constructor takes two type
844 arguments: the length of the vector and the type of the elements
845 contained in it. The short-hand notation used for the vector type in
846 the rest of paper is: \hs{[a|n]}, where \hs{a} is the element
847 type, and \hs{n} is the length of the vector. Note that this is
848 a notation used in this paper only, vectors are slightly more
849 verbose in real \CLaSH\ descriptions.
850 % The state type of an 8 element register bank would then for example
854 % type RegisterState = Vector D8 Word32
857 % Here, a type synonym \hs{RegisterState} is defined that is equal to
858 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
859 % type level representation of the decimal number 8) and \hs{Word32}
860 % (The 32 bit word type as defined above). In other words, the
861 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
862 % vector is translated to a \VHDL\ array type.
864 this is another type to describe integers, but unlike the previous
865 two it has no specific bit-width, but an upper bound. This means that
866 its range is not limited to powers of two, but can be any number.
867 An \hs{Index} only has an upper bound, its lower bound is
868 implicitly zero. If a value of this type exceeds either bounds, an
869 error will be thrown at simulation-time. The main purpose of the
870 \hs{Index} type is to be used as an index into a \hs{Vector}.
872 % \comment{TODO: Perhaps remove this example?} To define an index for
873 % the 8 element vector above, we would do:
876 % type RegisterIndex = RangedWord D7
879 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
880 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
881 % other words, this defines an unsigned word with values from
882 % 0 to 7 (inclusive). This word can be be used to index the
883 % 8 element vector \hs{RegisterState} above. This type is translated
884 % to the \texttt{unsigned} \VHDL type.
887 \subsubsection{User-defined types}
888 There are three ways to define new types in Haskell: algebraic
889 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
890 keyword and datatype renaming constructs with the \hs{newtype} keyword.
891 % \GHC\ offers a few more advanced ways to introduce types (type families,
892 % existential typing, {\acro{GADT}}s, etc.) which are not standard
893 % Haskell. As it is currently unclear how these advanced type constructs
894 % correspond to hardware, they are for now unsupported by the \CLaSH\
897 Only an algebraic datatype declaration actually introduces a
898 completely new type. Type synonyms and type renaming only define new
899 names for existing types, where synonyms are completely interchangeable
900 and a type renaming requires an explicit conversion. Type synonyms and
901 type renaming do not need any particular translation, a synonym or
902 renamed type will just use the same representation as the original type.
904 For algebraic types, we can make the following distinctions:
906 \item[\bf{Single constructor}]
907 Algebraic datatypes with a single constructor with one or more
908 fields, are essentially a way to pack a few values together in a
909 record-like structure. Haskell's built-in tuple types are also defined
910 as single constructor algebraic types (but with a bit of
911 syntactic sugar). An example of a single constructor type with
912 multiple fields is the following pair of integers:
914 data IntPair = IntPair Int Int
916 % These types are translated to \VHDL\ record types, with one field
917 % for every field in the constructor.
918 \item[\bf{No fields}]
919 Algebraic datatypes with multiple constructors, but without any
920 fields are essentially a way to get an enumeration-like type
921 containing alternatives. Note that Haskell's \hs{Bool} type is also
922 defined as an enumeration type, but that there is a fixed translation
923 for that type within the \CLaSH\ compiler. An example of such an
924 enumeration type is the type that represents the colors in a traffic
927 data TrafficLight = Red | Orange | Green
929 % These types are translated to \VHDL\ enumerations, with one
930 % value for each constructor. This allows references to these
931 % constructors to be translated to the corresponding enumeration
933 \item[\bf{Multiple constructors with fields}]
934 Algebraic datatypes with multiple constructors, where at least
935 one of these constructors has one or more fields are currently not
939 \subsection{Polymorphism}\label{sec:polymorhpism}
940 A powerful feature of most (functional) programming languages is
941 polymorphism, it allows a function to handle values of different data
942 types in a uniform way. Haskell supports \emph{parametric
943 polymorphism}~\cite{polymorphism}, meaning functions can be written
944 without mention of any specific type and can be used transparently with
945 any number of new types.
947 As an example of a parametric polymorphic function, consider the type of
948 the following \hs{append} function, which appends an element to a
949 vector:\footnote{The \hs{::} operator is used to annotate a function
953 append :: [a|n] -> a -> [a|n + 1]
956 This type is parameterized by \hs{a}, which can contain any type at
957 all. This means that \hs{append} can append an element to a vector,
958 regardless of the type of the elements in the list (as long as the type of
959 the value to be added is of the same type as the values in the vector).
960 This kind of polymorphism is extremely useful in hardware designs to make
961 operations work on a vector without knowing exactly what elements are
962 inside, routing signals without knowing exactly what kinds of signals
963 these are, or working with a vector without knowing exactly how long it
964 is. Polymorphism also plays an important role in most higher order
965 functions, as we will see in the next section.
967 Another type of polymorphism is \emph{ad-hoc
968 polymorphism}~\cite{polymorphism}, which refers to polymorphic
969 functions which can be applied to arguments of different types, but which
970 behave differently depending on the type of the argument to which they are
971 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
972 type classes, where a class definition provides the general interface of a
973 function, and class instances define the functionality for the specific
974 types. An example of such a type class is the \hs{Num} class, which
975 contains all of Haskell's numerical operations. A designer can make use
976 of this ad-hoc polymorphism by adding a constraint to a parametrically
977 polymorphic type variable. Such a constraint indicates that the type
978 variable can only be instantiated to a type whose members supports the
979 overloaded functions associated with the type class.
981 As an example we will take a look at type signature of the function
982 \hs{sum}, which sums the values in a vector:
984 sum :: Num a => [a|n] -> a
987 This type is again parameterized by \hs{a}, but it can only contain
988 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
989 we know that the addition (+) operator is defined for that type.
990 \CLaSH's built-in numerical types are also instances of the \hs{Num}
992 % so we can use the addition operator (and thus the \hs{sum}
993 % function) with \hs{Signed} as well as with \hs{Unsigned}.
995 \CLaSH\ supports both parametric polymorphism and ad-hoc polymorphism. Any
996 function defined can have any number of unconstrained type parameters. A
997 developer can also specify his own type classes and corresponding
998 instances. The \CLaSH\ compiler will infer the type of every polymorphic
999 argument depending on how the function is applied. There is however one
1000 constraint: the top level function that is being translated can not have
1001 any polymorphic arguments. The arguments can not be polymorphic as the
1002 function is never applied and consequently there is no way to determine
1003 the actual types for the type parameters. The members of some standard
1004 Haskell type classes are supported as built-in functions, including:
1005 \hs{Num} for numerical operations, \hs{Eq} for the equality operators, and
1006 \hs{Ord} for the comparison/order operators.
1008 \subsection{Higher-order functions \& values}
1009 Another powerful abstraction mechanism in functional languages, is
1010 the concept of \emph{functions as a first class value}, also called
1011 \emph{higher-order functions}. This allows a function to be treated as a
1012 value and be passed around, even as the argument of another
1013 function. The following example should clarify this concept:
1016 \begin{minipage}{0.93\linewidth}
1017 %format not = "\mathit{not}"
1019 negateVector xs = map not xs
1022 \begin{minipage}{0.07\linewidth}
1028 The code above defines the \hs{negateVector} function, which takes a
1029 vector of booleans, \hs{xs}, and returns a vector where all the values are
1030 negated. It achieves this by calling the \hs{map} function, and passing it
1031 \emph{another function}, boolean negation, and the vector of booleans,
1032 \hs{xs}. The \hs{map} function applies the negation function to all the
1033 elements in the vector.
1035 The \hs{map} function is called a higher-order function, since it takes
1036 another function as an argument. Also note that \hs{map} is again a
1037 parametric polymorphic function: it does not pose any constraints on the
1038 type of the input vector, other than that its elements must have the same
1039 type as the first argument of the function passed to \hs{map}. The element
1040 type of the resulting vector is equal to the return type of the function
1041 passed, which need not necessarily be the same as the element type of the
1042 input vector. All of these characteristics can readily be inferred from
1043 the type signature belonging to \hs{map}:
1046 map :: (a -> b) -> [a|n] -> [b|n]
1049 So far, only functions have been used as higher-order values. In
1050 Haskell, there are two more ways to obtain a function-typed value:
1051 partial application and lambda abstraction. Partial application
1052 means that a function that takes multiple arguments can be applied
1053 to a single argument, and the result will again be a function (but
1054 that takes one argument less). As an example, consider the following
1055 expression, that adds one to every element of a vector:
1058 \begin{minipage}{0.93\linewidth}
1063 \begin{minipage}{0.07\linewidth}
1069 Here, the expression \hs{(add 1)} is the partial application of the
1070 addition function to the value \hs{1}, which is again a function that
1071 adds one to its (next) argument. A lambda expression allows one to
1072 introduce an anonymous function in any expression. Consider the following
1073 expression, which again adds one to every element of a vector:
1076 \begin{minipage}{0.93\linewidth}
1078 map (\x -> x + 1) xs
1081 \begin{minipage}{0.07\linewidth}
1087 Finally, not only built-in functions can have higher order
1088 arguments, but any function defined in \CLaSH\ may have functions as
1089 arguments. This allows the hardware designer to use a powerful
1090 abstraction mechanism in his designs and have an optimal amount of
1091 code reuse. The only exception is again the top-level function: if a
1092 function-typed argument is not applied with an actual function, no
1093 hardware can be generated.
1095 % \comment{TODO: Describe ALU example (no code)}
1098 A very important concept in hardware is the concept of state. In a
1099 stateful design, the outputs depend on the history of the inputs, or the
1100 state. State is usually stored in registers, which retain their value
1101 during a clock cycle. As we want to describe more than simple
1102 combinational designs, \CLaSH\ needs an abstraction mechanism for state.
1104 An important property in Haskell, and in most other functional languages,
1105 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1108 \item given the same arguments twice, it should return the same value in
1110 \item that the function has no observable side-effects.
1112 % This purity property is important for functional languages, since it
1113 % enables all kinds of mathematical reasoning that could not be guaranteed
1114 % correct for impure functions.
1115 Pure functions are as such a perfect match for combinational circuits,
1116 where the output solely depends on the inputs. When a circuit has state
1117 however, it can no longer be simply described by a pure function.
1118 % Simply removing the purity property is not a valid option, as the
1119 % language would then lose many of it mathematical properties.
1120 In \CLaSH\ we deal with the concept of state in pure functions by making
1121 the current state an additional argument of the function, and the
1122 updated state part of result. In this sense the descriptions made in
1123 \CLaSH\ are the combinational parts of a mealy machine.
1125 A simple example is adding an accumulator register to the earlier
1126 multiply-accumulate circuit, of which the resulting netlist can be seen in
1127 \Cref{img:mac-state}:
1130 \begin{minipage}{0.93\linewidth}
1132 macS (State c) a b = (State c', c')
1137 \begin{minipage}{0.07\linewidth}
1144 \centerline{\includegraphics{mac-state.svg}}
1145 \caption{Stateful Multiply-Accumulate}
1146 \label{img:mac-state}
1150 Note that the \hs{macS} function returns both the new state and the value
1151 of the output port. The \hs{State} keyword indicates which arguments are
1152 part of the current state, and what part of the output is part of the
1153 updated state. This aspect will also be reflected in the type signature of
1154 the function. Abstracting the state of a circuit in this way makes it very
1155 explicit: which variables are part of the state is completely determined
1156 by the type signature. This approach to state is well suited to be used in
1157 combination with the existing code and language features, such as all the
1158 choice elements, as state values are just normal values. We can simulate
1159 stateful descriptions using the recursive \hs{run} function:
1162 \begin{minipage}{0.93\linewidth}
1164 run f s (i : inps) = o : (run f s' inps)
1169 \begin{minipage}{0.07\linewidth}
1175 The \hs{(:)} operator is the list concatenation operator, where the
1176 left-hand side is the head of a list and the right-hand side is the
1177 remainder of the list. The \hs{run} function applies the function the
1178 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1179 first input value, \hs{i}. The result is the first output value, \hs{o},
1180 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1181 is then called with the updated state, \hs{s'}, and the rest of the
1182 inputs, \hs{inps}. For the time being, and in the context of this paper,
1183 it is assumed that there is one input per clock cycle. Also note how the
1184 order of the input, output, and state in the \hs{run} function corresponds
1185 with the order of the input, output and state of the \hs{macS} function
1188 As the \hs{run} function, the hardware description, and the test
1189 inputs are also valid Haskell, the complete simulation can be compiled to
1190 an executable binary by an optimizing Haskell compiler, or executed in an
1191 Haskell interpreter. Both simulation paths are much faster than first
1192 translating the description to \VHDL\ and then running a \VHDL\
1195 \section{The \CLaSH\ compiler}
1196 An important aspect in this research is the creation of the prototype
1197 compiler, which allows us to translate descriptions made in the \CLaSH\
1198 language as described in the previous section to synthesizable \VHDL.
1199 % , allowing a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1201 The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open-source Haskell
1202 compiler that also provides a high level API to most of its internals. The
1203 availability of this high-level API obviated the need to design many of the
1204 tedious parts of the prototype compiler, such as the parser, semantics
1205 checker, and especially the type-checker. These parts together form the
1206 front-end of the prototype compiler pipeline, as seen in
1207 \Cref{img:compilerpipeline}.
1210 \centerline{\includegraphics{compilerpipeline.svg}}
1211 \caption{\CLaSHtiny\ compiler pipeline}
1212 \label{img:compilerpipeline}
1216 The output of the \GHC\ front-end consists of the translation of the original
1217 Haskell description in \emph{Core}~\cite{Sulzmann2007}, which is a smaller,
1218 typed, functional language. This \emph{Core} language is relatively easy to
1219 process compared to the larger Haskell language. A description in \emph{Core}
1220 can still contain elements which have no direct translation to hardware, such
1221 as polymorphic types and function-valued arguments. Such a description needs
1222 to be transformed to a \emph{normal form}, which only contains elements that
1223 have a direct translation. The second stage of the compiler, the
1224 \emph{normalization} phase, exhaustively applies a set of
1225 \emph{meaning-preserving} transformations on the \emph{Core} description until
1226 this description is in a \emph{normal form}. This set of transformations
1227 includes transformations typically found in reduction systems and lambda
1228 calculus~\cite{lambdacalculus}, such as $\beta$-reduction and
1229 $\eta$-expansion. It also includes self-defined transformations that are
1230 responsible for the reduction of higher-order functions to `regular'
1231 first-order functions, and specializing polymorphic types to concrete types.
1233 The final step in the compiler pipeline is the translation to a \VHDL\
1234 \emph{netlist}, which is a straightforward process due to resemblance of a
1235 normalized description and a set of concurrent signal assignments. We call the
1236 end-product of the \CLaSH\ compiler a \VHDL\ \emph{netlist} as the resulting
1237 \VHDL\ resembles an actual netlist description and not idiomatic \VHDL.
1240 \label{sec:usecases}
1241 \subsection{FIR Filter}
1242 As an example of a common hardware design where the use of higher-order
1243 functions leads to a very natural description is a \acro{FIR} filter, which is
1244 basically the dot-product of two vectors:
1247 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1250 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1251 and a few previous input samples ($x$). Each of these multiplications
1252 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1253 filter is indeed equivalent to the equation of the dot-product, which is
1257 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1260 We can easily and directly implement the equation for the dot-product
1261 using higher-order functions:
1264 \begin{minipage}{0.93\linewidth}
1266 as *+* bs = foldl1 (+) (zipWith (*) as bs)
1269 \begin{minipage}{0.07\linewidth}
1275 The \hs{zipWith} function is very similar to the \hs{map} function seen
1276 earlier: It takes a function, two vectors, and then applies the function to
1277 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1278 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1280 The \hs{foldl1} function takes a binary function, a single vector, and applies
1281 the function to the first two elements of the vector. It then applies the
1282 function to the result of the first application and the next element in the
1283 vector. This continues until the end of the vector is reached. The result of
1284 the \hs{foldl1} function is the result of the last application. It is obvious
1285 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1286 \hs{foldl1 (+)} function is summation.
1287 % Returning to the actual \acro{FIR} filter, we will slightly change the
1288 % equation describing it, so as to make the translation to code more obvious and
1289 % concise. What we do is change the definition of the vector of input samples
1290 % and delay the computation by one sample. Instead of having the input sample
1291 % received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1292 % sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1293 % to the following (note that this is completely equivalent to the original
1294 % equation, just with a different definition of $x$ that will better suit the
1295 % transformation to code):
1298 % y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1300 The complete definition of the \acro{FIR} filter in code then becomes:
1303 \begin{minipage}{0.93\linewidth}
1305 fir (State (xs,hs)) x =
1306 (State (x >> xs,hs), (x +> xs) *+* hs)
1309 \begin{minipage}{0.07\linewidth}
1315 Where the vector \hs{xs} contains the previous input samples, the vector
1316 \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input
1317 sample. The concatenate operator (\hs{+>}) creates a new vector by placing the
1318 current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The
1319 code for the shift (\hs{>>}) operator, that adds the new input sample (\hs{x})
1320 to the list of previous input samples (\hs{xs}) and removes the oldest sample,
1324 \begin{minipage}{0.93\linewidth}
1326 x >> xs = x +> init xs
1329 \begin{minipage}{0.07\linewidth}
1335 Where the \hs{init} function returns all but the last element of a vector.
1336 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1337 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1341 \centerline{\includegraphics{4tapfir.svg}}
1342 \caption{4-taps \acrotiny{FIR} Filter}
1347 \subsection{Higher-order CPU}
1348 The following simple \acro{CPU} is an example of user-defined higher order
1349 functions and pattern matching. The \acro{CPU} consists of four function
1350 units, of which three have a fixed function and one can perform certain less
1353 The \acro{CPU} contains a number of data sources, represented by the
1354 horizontal wires in \Cref{img:highordcpu}. These data sources offer the
1355 previous outputs of each function units, along with the single data input the
1356 \acro{CPU} has and two fixed initialization values.
1358 Each of the function units has both its operands connected to all data
1359 sources, and can be programmed to select any data source for either
1360 operand. In addition, the leftmost function unit has an additional
1361 opcode input to select the operation it performs. The output of the rightmost
1362 function unit is also the output of the entire \acro{CPU}.
1364 Looking at the code, the function unit (\hs{fu}) is the most simple. It
1365 arranges the operand selection for the function unit. Note that it does not
1366 define the actual operation that takes place inside the function unit,
1367 but simply accepts the (higher-order) argument \hs{op} which is a function
1368 of two arguments that defines the operation.
1371 \begin{minipage}{0.93\linewidth}
1373 fu op inputs (addr1, addr2) = regIn
1380 \begin{minipage}{0.07\linewidth}
1386 The \hs{multiop} function defines the operation that takes place in the
1387 leftmost function unit. It is essentially a simple three operation \acro{ALU}
1388 that makes good use of pattern matching and guards in its description.
1389 The \hs{shift} function used here shifts its first operand by the number
1390 of bits indicated in the second operand, the \hs{xor} function produces
1391 the bitwise xor of its operands.
1394 \begin{minipage}{0.93\linewidth}
1396 data Opcode = Shift | Xor | Equal
1398 multiop :: Opcode -> Word -> Word -> Word
1399 multiop Shift a b = shift a b
1400 multiop Xor a b = xor a b
1401 multiop Equal a b | a == b = 1
1405 \begin{minipage}{0.07\linewidth}
1411 The \acro{CPU} function ties everything together. It applies the \hs{fu}
1412 function four times, to create a different function unit each time. The
1413 first application is interesting, because it does not just pass a
1414 function to \hs{fu}, but a partial application of \hs{multiop}. This
1415 shows how the first function unit effectively gets an extra input,
1416 compared to the others.
1418 The vector \hs{inputs} is the set of data sources, which is passed to
1419 each function unit as a set of possible operants. The \acro{CPU} also receives
1420 a vector of address pairs, which are used by each function unit to select
1421 their operand. The application of the function units to the \hs{inputs} and
1422 \hs{addrs} arguments seems quite repetitive and could be rewritten to use
1423 a combination of the \hs{map} and \hs{zipwith} functions instead.
1424 However, the prototype compiler does not currently support working with lists
1425 of functions, so a more explicit version of the code is given instead.
1428 \begin{minipage}{0.93\linewidth}
1430 type CpuState = State [Word | 4]
1432 cpu :: CpuState -> Word -> [(Index 6, Index 6) | 4]
1433 -> Opcode -> (CpuState, Word)
1434 cpu (State s) input addrs opc = (State s', out)
1436 s' = [ fu (multiop opc) inputs (addrs!0)
1437 , fu add inputs (addrs!1)
1438 , fu sub inputs (addrs!2)
1439 , fu mul inputs (addrs!3)
1441 inputs = 0 +> (1 +> (input +> s))
1445 \begin{minipage}{0.07\linewidth}
1451 This is still a simple example, but it could form the basis
1452 of an actual design, in which the same techniques can be reused.
1454 \section{Related work}
1455 This section describes the features of existing (functional) hardware
1456 description languages and highlights the advantages that this research has
1459 Many functional hardware description languages have been developed over the
1460 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1461 extension of Backus' \acro{FP} language to synchronous streams, designed
1462 particularly for describing and reasoning about regular circuits. The
1463 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1464 circuits, and has a particular focus on layout.
1467 \centerline{\includegraphics{highordcpu.svg}}
1468 \caption{CPU with higher-order Function Units}
1469 \label{img:highordcpu}
1473 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1474 functional language \acro{ML}, and has support for polymorphic types and
1475 higher-order functions. Published work suggests that there is no direct
1476 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1477 be translated to \VHDL\ and that the translated description can then be
1478 simulated in a \VHDL\ simulator. Certain aspects of HML, such as higher-order
1479 functions are however not supported by the \VHDL\ translator~\cite{HML3}. The
1480 \CLaSH\ compiler on the other hand can correctly translate all of the language
1481 constructs mentioned in this paper. % to a netlist format.
1483 Like the work presented in this paper, many functional hardware description
1484 languages have some sort of foundation in the functional programming language
1485 Haskell. Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1486 specifications used to model the behavior of superscalar microprocessors. Hawk
1487 specifications can be simulated; to the best knowledge of the authors there is
1488 however no support for automated circuit synthesis.
1490 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1491 models. A designer can model systems using heterogeneous models of
1492 computation, which include continuous time, synchronous and untimed models of
1493 computation. Using so-called domain interfaces a designer can simulate
1494 electronic systems which have both analog as digital parts. ForSyDe has
1495 several backends including simulation and automated synthesis, though
1496 automated synthesis is restricted to the synchronous model of computation.
1497 Unlike \CLaSH\ there is no support for the automated synthesis of descriptions
1498 that contain polymorphism or higher-order functions.
1500 Lava~\cite{Lava} is a hardware description language that focuses on the
1501 structural representation of hardware. Besides support for simulation and
1502 circuit synthesis, Lava descriptions can be interfaced with formal method
1503 tools for formal verification. Lava descriptions are actually circuit
1504 generators when viewed from a synthesis viewpoint, in that the language
1505 elements of Haskell, such as choice, can be used to guide the circuit
1506 generation. If a developer wants to insert a choice element inside an actual
1507 circuit he will have to explicitly instantiate a multiplexer-like component.
1509 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1510 such as case-statements and pattern matching, are synthesized to choice
1511 elements in the eventual circuit. As such, richer control structures can both
1512 be specified and synthesized in \CLaSH\ compared to any of the embedded
1513 languages, such as: Hawk, ForSyDe, or Lava.
1515 The merits of polymorphic typing, combined with higher-order functions, are
1516 now also recognized in the `main-stream' hardware description languages,
1517 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support
1518 for generics has been extended to types and subprograms, allowing a developer
1519 to describe components with polymorphic ports and function-valued arguments.
1520 Note that the types and subprograms still require an explicit generic map,
1521 whereas types can be automatically inferred, and function-values can be
1522 automatically propagated by the \CLaSH\ compiler. There are also no (generally
1523 available) \VHDL\ synthesis tools that currently support the \VHDL-2008
1524 standard, and thus the synthesis of polymorphic types and function-valued
1527 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1529 % A functional language designed specifically for hardware design is
1530 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1531 % language called \acro{FL}~\cite{FL} to la
1533 % An example of a floating figure using the graphicx package.
1534 % Note that \label must occur AFTER (or within) \caption.
1535 % For figures, \caption should occur after the \includegraphics.
1536 % Note that IEEEtran v1.7 and later has special internal code that
1537 % is designed to preserve the operation of \label within \caption
1538 % even when the captionsoff option is in effect. However, because
1539 % of issues like this, it may be the safest practice to put all your
1540 % \label just after \caption rather than within \caption{}.
1542 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1543 % option should be used if it is desired that the figures are to be
1544 % displayed while in draft mode.
1548 %\includegraphics[width=2.5in]{myfigure}
1549 % where an .eps filename suffix will be assumed under latex,
1550 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1551 % via \DeclareGraphicsExtensions.
1552 %\caption{Simulation Results}
1556 % Note that IEEE typically puts floats only at the top, even when this
1557 % results in a large percentage of a column being occupied by floats.
1560 % An example of a double column floating figure using two subfigures.
1561 % (The subfig.sty package must be loaded for this to work.)
1562 % The subfigure \label commands are set within each subfloat command, the
1563 % \label for the overall figure must come after \caption.
1564 % \hfil must be used as a separator to get equal spacing.
1565 % The subfigure.sty package works much the same way, except \subfigure is
1566 % used instead of \subfloat.
1568 %\begin{figure*}[!t]
1569 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1570 %\label{fig_first_case}}
1572 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1573 %\label{fig_second_case}}}
1574 %\caption{Simulation results}
1578 % Note that often IEEE papers with subfigures do not employ subfigure
1579 % captions (using the optional argument to \subfloat), but instead will
1580 % reference/describe all of them (a), (b), etc., within the main caption.
1583 % An example of a floating table. Note that, for IEEE style tables, the
1584 % \caption command should come BEFORE the table. Table text will default to
1585 % \footnotesize as IEEE normally uses this smaller font for tables.
1586 % The \label must come after \caption as always.
1589 %% increase table row spacing, adjust to taste
1590 %\renewcommand{\arraystretch}{1.3}
1591 % if using array.sty, it might be a good idea to tweak the value of
1592 % \extrarowheight as needed to properly center the text within the cells
1593 %\caption{An Example of a Table}
1594 %\label{table_example}
1596 %% Some packages, such as MDW tools, offer better commands for making tables
1597 %% than the plain LaTeX2e tabular which is used here.
1598 %\begin{tabular}{|c||c|}
1608 % Note that IEEE does not put floats in the very first column - or typically
1609 % anywhere on the first page for that matter. Also, in-text middle ("here")
1610 % positioning is not used. Most IEEE journals/conferences use top floats
1611 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1612 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1613 % command of the stfloats package.
1617 \section{Conclusion}
1618 This research demonstrates once more that functional languages are well suited
1619 for hardware descriptions: function applications provide an elegant notation
1620 for component instantiation. Where this research goes beyond the existing
1621 (functional) hardware descriptions languages is the inclusion of various
1622 choice elements, such as pattern matching, that are well suited to describe
1623 the conditional assignments in control-oriented circuits. Besides being able
1624 to translate these basic constructs to synthesizable \VHDL, the prototype
1625 compiler can also correctly translate descriptions that contain both
1626 polymorphic types and function-valued arguments.
1628 Where recent functional hardware description languages have mostly opted to
1629 embed themselves in an existing functional language, this research features a
1630 `true' compiler. As a result there is a clear distinction between compile-time
1631 and run-time, which allows a myriad of choice constructs to be part of the
1632 actual circuit description; a feature the embedded hardware description
1633 languages do not offer.
1635 \section{Future Work}
1636 The choice of describing state explicitly as extra arguments and results can
1637 be seen as a mixed blessing. Even though the description that use state are
1638 usually very clear, one finds that dealing with unpacking, passing, receiving
1639 and repacking can become tedious and even error-prone, especially in the case
1640 of sub-states. Removing this boilerplate, or finding a more suitable
1641 abstraction mechanism would make \CLaSH\ easier to use.
1643 The transformations in normalization phase of the prototype compiler were
1644 developed in an ad-hoc manner, which makes the existence of many desirable
1645 properties unclear. Such properties include whether the complete set of
1646 transformations will always lead to a normal form or if the normalization
1647 process always terminates. Though various use cases suggests that these
1648 properties usually hold, they have not been formally proven. A systematic
1649 approach to defining the set of transformations allows one to proof that the
1650 earlier mentioned properties do indeed exist.
1652 % conference papers do not normally have an appendix
1655 % use section* for acknowledgement
1656 % \section*{Acknowledgment}
1658 % The authors would like to thank...
1660 % trigger a \newpage just before the given reference
1661 % number - used to balance the columns on the last page
1662 % adjust value as needed - may need to be readjusted if
1663 % the document is modified later
1664 % \IEEEtriggeratref{14}
1665 % The "triggered" command can be changed if desired:
1666 %\IEEEtriggercmd{\enlargethispage{-5in}}
1668 % references section
1670 % can use a bibliography generated by BibTeX as a .bbl file
1671 % BibTeX documentation can be easily obtained at:
1672 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1673 % The IEEEtran BibTeX style support page is at:
1674 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1675 \bibliographystyle{IEEEtran}
1676 % argument is your BibTeX string definitions and bibliography database(s)
1677 \bibliography{clash}
1679 % <OR> manually copy in the resultant .bbl file
1680 % set second argument of \begin to the number of references
1681 % (used to reserve space for the reference number labels box)
1682 % \begin{thebibliography}{1}
1684 % \bibitem{IEEEhowto:kopka}
1685 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1686 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1688 % \end{thebibliography}
1696 % vim: set ai sw=2 sts=2 expandtab: