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337 % (Unless specifically asked to do so by the journal or conference you plan
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{Christiaan P.R. Baaij, Matthijs Kooijman, 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 c.p.r.baaij@@utwente.nl, matthijs@@stdin.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,
516 T-Ruby,HML2,Hydra,Hawk1,Lava,Wired,ForSyDe1,reFLect}. The idea of using
517 functional languages for hardware descriptions started in the early 1980s
518 \cite{Cardelli1981,muFP,DAISY}, a time which also saw the birth of the
519 currently popular \acrop{HDL}, 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
525 In an attempt to ease the prototyping process of the language, such as
526 creating all the required tooling, like parsers and type-checkers, many
527 functional \acrop{HDL} \cite{Hydra,Hawk1,Lava,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 graph
533 (which is usually hidden from the designer). This graph 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{case}-expressions,
536 pattern-matching etc.) are evaluated at the time the domain-specific graph is
537 being build, they are no longer visible to the embedded compiler that
538 processes the datatype. Consequently, it is impossible to capture Haskell's
539 choice elements within a circuit description when taking the embedded language
540 approach. This does not mean that circuits specified in an embedded language
541 can not contain choice, just that choice elements only exists as functions,
542 e.g. a multiplexer function, and not as language elements.
544 The approach taken in this research is to use (a subset of) the Haskell
545 language \emph{itself} for the purpose of describing hardware. By taking this
546 approach, this research \emph{can} capture certain language constructs, like
547 all of Haskell's choice elements, within circuit descriptions. The more
548 advanced features of Haskel, such as polymorphic typing and higher-order
549 function, are also supported.
551 % supporting polymorphism, higher-order functions and such an extensive array
552 % of choice-elements, combined with a very concise way of specifying circuits
553 % is new in the domain of (functional) \acrop{HDL}.
554 % As the hardware descriptions are plain Haskell
555 % functions, these descriptions can be compiled to an executable binary
556 % for simulation using an optimizing Haskell compiler such as the Glasgow
557 % Haskell Compiler (\GHC)~\cite{ghc}.
559 Where descriptions in a conventional \acro{HDL} have an explicit clock for the
560 purposes state and synchronicity, the clock is implicit for the descriptions and research presented in this paper. A circuit designer describes the behavior of the hardware between clock cycles. Many functional \acrop{HDL} model signals as a stream of all values over time; state is then modeled as a delay on this stream of values. Descriptions presented in this research make the current state an additional input and the updated state a part of their output. This abstraction of state and time limits the descriptions to synchronous hardware, there is however room within the language to eventually add a different abstraction mechanism that will allow for the modeling of asynchronous systems.
562 Like the traditional \acrop{HDL}, descriptions made in a functional \acro{HDL}
563 must eventually be converted into a netlist. This research also features a
564 prototype translator, which has the same name as the language:
565 \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES} Language for Synchronous Hardware}
566 (pronounced: clash). This compiler converts the Haskell code to equivalently
567 behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist
568 format by an (optimizing) \VHDL\ synthesis tool.
570 Besides simple circuits such as variants of both the \acro{FIR} filter and
571 the higher-order \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler
572 has also been able to translate non-trivial functional descriptions such as a
573 streaming reduction circuit~\cite{reductioncircuit} for floating point
576 To the best knowledge of the authors, \CLaSH\ is the only (functional)
577 \acro{HDL} that allows circuit specification to be written in a very concise
578 way and at the same time support such advanced features as polymorphic typing,
579 higher order functions and pattern matching.
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 elements of a functional program are functions and function
589 application. These have a single obvious translation to a netlist format:
591 \item every function is translated to a component,
592 \item every function argument is translated to an input port,
593 \item the result value of a function is translated to an output port,
595 \item function applications are translated to component instantiations.
597 The result value can have a composite type (such as a tuple), so having
598 just a single result value does not pose any limitation. The actual
599 arguments of a function application are assigned to signals, which are
600 then mapped to the corresponding input ports of the component. The output
601 port of the function is also mapped to a signal, which is used as the
602 result of the application itself. Since every top level function generates
603 its own component, the hierarchy of function calls is reflected in the
604 final netlist. %, creating a hierarchical description of the hardware.
605 % The separation in different components makes it easier for a developer
606 % to understand and possibly hand-optimize the resulting \VHDL\ output of
607 % the \CLaSH\ compiler.
609 The short example (\ref{lst:code1}) demonstrated below gives an indication
610 of the level of conciseness that can be achieved with functional hardware
611 description languages when compared with the more traditional hardware
612 description languages. The example is a combinational multiply-accumulate
613 circuit that works for \emph{any} word length (this type of polymorphism
614 will be further elaborated in \Cref{sec:polymorhpism}). The corresponding
615 netlist is depicted in \Cref{img:mac-comb}.
618 \begin{minipage}{0.93\linewidth}
620 mac a b c = add (mul a b) c
623 \begin{minipage}{0.07\linewidth}
630 \centerline{\includegraphics{mac.svg}}
631 \caption{Combinational Multiply-Accumulate}
636 The use of a composite result value is demonstrated in the next example
637 (\ref{lst:code2}), where the multiply-accumulate circuit not only returns
638 the accumulation result, but also the intermediate multiplication result.
639 Its corresponding netlist can be seen in \Cref{img:mac-comb-composite}.
642 \begin{minipage}{0.93\linewidth}
644 mac a b c = (z, add z c)
649 \begin{minipage}{0.07\linewidth}
656 \centerline{\includegraphics{mac-nocurry.svg}}
657 \caption{Combinational Multiply-Accumulate (composite output)}
658 \label{img:mac-comb-composite}
663 In Haskell, choice can be achieved by a large set of syntactic elements,
664 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
665 pattern matching, and guards. The most general of these are the \hs{case}
666 expressions (\hs{if} expressions can be directly translated to
667 \hs{case} expressions). When transforming a \CLaSH\ description to a
668 netlist, a \hs{case} expression is translated to a multiplexer. The
669 control value of the \hs{case} expression is fed into a number of
670 comparators and their combined output forms the selection port of the
671 multiplexer. The result of each alternative in the \hs{case} expression is
672 linked to the corresponding input port of the multiplexer.
673 % A \hs{case} expression can in turn simply be translated to a conditional
674 % assignment in \VHDL, where the conditions use equality comparisons
675 % against the constructors in the \hs{case} expressions.
677 % Two versions of a contrived example are displayed below, the first
678 % (\ref{lst:code3}) using a \hs{case} expression and the second
679 % (\ref{lst:code4}) using an \hs{if-then-else} expression. Both examples
680 % sum two values when they are equal or non-equal (depending on the given
681 % predicate, the \hs{pred} variable) and return 0 otherwise.
683 An code example (\ref{lst:code3}) that uses a \hs{case} expression and
684 \hs{if-then-else} expressions is shown below. The function counts up or
685 down depending on the \hs{direction} variable, and has a \hs{wrap}
686 variable that determines both the upper bound and wrap-around point of the
687 counter. The \hs{direction} variable is of the following, user-defined,
688 enumeration datatype:
691 data Direction = Up | Down
694 The naive netlist corresponding to this example is depicted in
695 \Cref{img:choice}. Note that the \hs{direction} variable is only
696 compared to \hs{Up}, as an inequality immediately implies that
697 \hs{direction} is \hs{Down}.
700 \begin{minipage}{0.93\linewidth}
702 counter direction wrap x = case direction of
703 Up -> if x < wrap then
706 Down -> if x > 0 then
711 \begin{minipage}{0.07\linewidth}
718 % \begin{minipage}{0.93\linewidth}
721 % if pred == Equal then
722 % if a == b then a + b else 0
724 % if a != b then a + b else 0
727 % \begin{minipage}{0.07\linewidth}
735 \centerline{\includegraphics{choice-case.svg}}
736 \caption{Choice - sumif}
741 A user-friendly and also very powerful form of choice that is not found in
742 the traditional hardware description languages is pattern matching. A
743 function can be defined in multiple clauses, where each clause corresponds
744 to a pattern. When an argument matches a pattern, the corresponding clause
745 will be used. Expressions can also contain guards, where the expression is
746 only executed if the guard evaluates to true, and continues with the next
747 clause if the guard evaluates to false. Like \hs{if-then-else}
748 expressions, pattern matching and guards have a (straightforward)
749 translation to \hs{case} expressions and can as such be mapped to
750 multiplexers. A second version (\ref{lst:code5}) of the earlier example,
751 now using both pattern matching and guards, can be seen below. The guard
752 is the expression that follows the vertical bar (\hs{|}) and precedes the
753 assignment operator (\hs{=}). The \hs{otherwise} guards always evaluate to
756 The version using pattern matching and guards corresponds to the same
757 naive netlist representation (\Cref{img:choice}) as the earlier example.
760 \begin{minipage}{0.93\linewidth}
762 counter Up wrap x | x < wrap = x + 1
764 counter Down wrap x | x > 0 = x - 1
768 \begin{minipage}{0.07\linewidth}
775 % \centerline{\includegraphics{choice-ifthenelse}}
776 % \caption{Choice - \emph{if-then-else}}
781 Haskell is a statically-typed language, meaning that the type of a
782 variable or function is determined at compile-time. Not all of Haskell's
783 typing constructs have a clear translation to hardware, this section will
784 therefore only deal with the types that do have a clear correspondence
785 to hardware. The translatable types are divided into two categories:
786 \emph{built-in} types and \emph{user-defined} types. Built-in types are
787 those types for which a fixed translation is defined within the \CLaSH\
788 compiler. The \CLaSH\ compiler has generic translation rules to
789 translate the user-defined types, which are described later on.
791 The \CLaSH\ compiler is able to infer unspecified (polymorphic) types,
792 meaning that a developer does not have to annotate every function with a
793 type signature. % (even if it is good practice to do so).
794 Given that the top-level entity of a circuit design is annotated with
795 concrete/monomorphic types, the \CLaSH\ compiler can specialize
796 polymorphic functions to functions with concrete types.
798 % Translation of two most basic functional concepts has been
799 % discussed: function application and choice. Before looking further
800 % into less obvious concepts like higher-order expressions and
801 % polymorphism, the possible types that can be used in hardware
802 % descriptions will be discussed.
804 % Some way is needed to translate every value used to its hardware
805 % equivalents. In particular, this means a hardware equivalent for
806 % every \emph{type} used in a hardware description is needed.
808 % The following types are \emph{built-in}, meaning that their hardware
809 % translation is fixed into the \CLaSH\ compiler. A designer can also
810 % define his own types, which will be translated into hardware types
811 % using translation rules that are discussed later on.
813 \subsubsection{Built-in types}
814 The following types have fixed translations defined within the \CLaSH\
818 the most basic type available. It can have two values:
819 \hs{Low} or \hs{High}.
820 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
822 this is a basic logic type. It can have two values: \hs{True}
824 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
825 % type (where a value of \hs{True} corresponds to a value of
827 Supporting the Bool type is required in order to support the
828 \hs{if-then-else} expression, which requires a \hs{Bool} value for
830 \item[\bf{Signed}, \bf{Unsigned}]
831 these are types to represent integers and both are parametrizable in
832 their size. The overflow behavior of the numeric operators defined for
833 these types is \emph{wrap-around}.
834 % , so you can define an unsigned word of 32 bits wide as follows:
837 % type Word32 = SizedWord D32
840 % Here, a type synonym \hs{Word32} is defined that is equal to the
841 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
842 % \hs{D32} is the \emph{type level representation} of the decimal
843 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
844 % types are translated to the \VHDL\ \texttt{unsigned} and
845 % \texttt{signed} respectively.
847 this is a vector type that can contain elements of any other type and
848 has a static length. The \hs{Vector} type constructor takes two type
849 arguments: the length of the vector and the type of the elements
850 contained in it. The short-hand notation used for the vector type in
851 the rest of paper is: \hs{[a|n]}, where \hs{a} is the element
852 type, and \hs{n} is the length of the vector. Note that this is
853 a notation used in this paper only, vectors are slightly more
854 verbose in real \CLaSH\ descriptions.
855 % The state type of an 8 element register bank would then for example
859 % type RegisterState = Vector D8 Word32
862 % Here, a type synonym \hs{RegisterState} is defined that is equal to
863 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
864 % type level representation of the decimal number 8) and \hs{Word32}
865 % (The 32 bit word type as defined above). In other words, the
866 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
867 % vector is translated to a \VHDL\ array type.
869 the main purpose of the \hs{Index} type is to be used as an index into
870 a \hs{Vector}, and has no specified bit-size, but a specified upper
871 bound. This means that its range is not limited to powers of two, but
872 can be any number. An \hs{Index} only has an upper bound, its lower
873 bound is implicitly zero. If a value of this type exceeds either
874 bounds, an error will be thrown at simulation-time.
876 % \comment{TODO: Perhaps remove this example?} To define an index for
877 % the 8 element vector above, we would do:
880 % type RegisterIndex = RangedWord D7
883 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
884 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
885 % other words, this defines an unsigned word with values from
886 % 0 to 7 (inclusive). This word can be be used to index the
887 % 8 element vector \hs{RegisterState} above. This type is translated
888 % to the \texttt{unsigned} \VHDL type.
891 \subsubsection{User-defined types}
892 % There are three ways to define new types in Haskell: algebraic
893 % data-types with the \hs{data} keyword, type synonyms with the \hs{type}
894 % keyword and datatype renaming constructs with the \hs{newtype} keyword.
895 % \GHC\ offers a few more advanced ways to introduce types (type families,
896 % existential typing, {\acro{GADT}}s, etc.) which are not standard
897 % Haskell. As it is currently unclear how these advanced type constructs
898 % correspond to hardware, they are for now unsupported by the \CLaSH\
900 A completely new type is introduced by an algebraic datatype declaration
901 which is defined using the \hs{data} keyword. Type synonyms can be
902 introduced using the \hs{type} keyword.
903 % Only an algebraic datatype declaration actually introduces a
904 % completely new type. Type synonyms and type renaming only define new
905 % names for existing types, where synonyms are completely interchangeable
906 % and a type renaming requires an explicit conversion.
907 Type synonyms do not need any particular translation, as a synonym will
908 just use the same representation as the original type.
910 For algebraic types, we can make the following distinctions:
912 \item[\bf{Single constructor}]
913 Algebraic datatypes with a single constructor with one or more
914 fields, are essentially a way to pack a few values together in a
915 record-like structure. Haskell's built-in tuple types are also defined
916 as single constructor algebraic types (but with a bit of
917 syntactic sugar). An example of a single constructor type with
918 multiple fields is the following pair of integers:
920 data IntPair = IntPair Int Int
922 % These types are translated to \VHDL\ record types, with one field
923 % for every field in the constructor.
924 \item[\bf{No fields}]
925 Algebraic datatypes with multiple constructors, but without any
926 fields are essentially a way to get an enumeration-like type
927 containing alternatives. Note that Haskell's \hs{Bool} type is also
928 defined as an enumeration type, but that there is a fixed translation
929 for that type within the \CLaSH\ compiler. An example of such an
930 enumeration type is the type that represents the colors in a traffic
933 data TrafficLight = Red | Orange | Green
935 % These types are translated to \VHDL\ enumerations, with one
936 % value for each constructor. This allows references to these
937 % constructors to be translated to the corresponding enumeration
939 \item[\bf{Multiple constructors with fields}]
940 Algebraic datatypes with multiple constructors, where at least
941 one of these constructors has one or more fields are currently not
945 \subsection{Polymorphism}\label{sec:polymorhpism}
946 A powerful feature of most (functional) programming languages is
947 polymorphism, it allows a function to handle values of different data
948 types in a uniform way. Haskell supports \emph{parametric
949 polymorphism}~\cite{polymorphism}, meaning functions can be written
950 without mention of any specific type and can be used transparently with
951 any number of new types.
953 As an example of a parametric polymorphic function, consider the type of
954 the following \hs{append} function, which appends an element to a
955 vector:\footnote{The \hs{::} operator is used to annotate a function
959 append :: [a|n] -> a -> [a|n+1]
962 This type is parameterized by \hs{a}, which can contain any type at
963 all. This means that \hs{append} can append an element to a vector,
964 regardless of the type of the elements in the list (as long as the type of
965 the value to be added is of the same type as the values in the vector).
966 This kind of polymorphism is extremely useful in hardware designs to make
967 operations work on a vector without knowing exactly what elements are
968 inside, routing signals without knowing exactly what kinds of signals
969 these are, or working with a vector without knowing exactly how long it
970 is. Polymorphism also plays an important role in most higher order
971 functions, as we will see in the next section.
973 Another type of polymorphism is \emph{ad-hoc
974 polymorphism}~\cite{polymorphism}, which refers to polymorphic
975 functions which can be applied to arguments of different types, but which
976 behave differently depending on the type of the argument to which they are
977 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
978 type classes, where a class definition provides the general interface of a
979 function, and class instances define the functionality for the specific
980 types. An example of such a type class is the \hs{Num} class, which
981 contains all of Haskell's numerical operations. A designer can make use
982 of this ad-hoc polymorphism by adding a constraint to a parametrically
983 polymorphic type variable. Such a constraint indicates that the type
984 variable can only be instantiated to a type whose members supports the
985 overloaded functions associated with the type class.
987 An example of a type signature that includes such a constraint if the
988 signature of the \hs{sum} function, which sums the values in a vector:
990 sum :: Num a => [a|n] -> a
993 This type is again parameterized by \hs{a}, but it can only contain
994 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
995 the compiler knows that the addition (+) operator is defined for that
997 % \CLaSH's built-in numerical types are also instances of the \hs{Num}
999 % so we can use the addition operator (and thus the \hs{sum}
1000 % function) with \hs{Signed} as well as with \hs{Unsigned}.
1002 \CLaSH\ supports both parametric polymorphism and ad-hoc polymorphism. Any
1003 function defined can have any number of unconstrained type parameters. A
1004 developer can also specify his own type classes and corresponding
1005 instances. The \CLaSH\ compiler will infer the type of every polymorphic
1006 argument depending on how the function is applied. There is however one
1007 constraint: the top level function that is being translated can not have
1008 any polymorphic arguments. The arguments of the top-level can not be
1009 polymorphic as the function is never applied and consequently there is no
1010 way to determine the actual types for the type parameters.
1012 With regard to the built-in types, it should be noted that members of
1013 some of the standard Haskell type classes are supported as built-in
1014 functions. These include: the numerial operators of \hs{Num}, the equality
1015 operators of \hs{Eq}, and the comparison/order operators of \hs{Ord}.
1017 \subsection{Higher-order functions \& values}
1018 Another powerful abstraction mechanism in functional languages, is
1019 the concept of \emph{functions as a first class value}, also called
1020 \emph{higher-order functions}. This allows a function to be treated as a
1021 value and be passed around, even as the argument of another
1022 function. The following example should clarify this concept:
1025 \begin{minipage}{0.93\linewidth}
1026 %format not = "\mathit{not}"
1028 negateVector xs = map not xs
1031 \begin{minipage}{0.07\linewidth}
1037 The code above defines the \hs{negateVector} function, which takes a
1038 vector of booleans, \hs{xs}, and returns a vector where all the values are
1039 negated. It achieves this by calling the \hs{map} function, and passing it
1040 \emph{another function}, boolean negation, and the vector of booleans,
1041 \hs{xs}. The \hs{map} function applies the negation function to all the
1042 elements in the vector.
1044 The \hs{map} function is called a higher-order function, since it takes
1045 another function as an argument. Also note that \hs{map} is again a
1046 parametric polymorphic function: it does not pose any constraints on the
1047 type of the input vector, other than that its elements must have the same
1048 type as the first argument of the function passed to \hs{map}. The element
1049 type of the resulting vector is equal to the return type of the function
1050 passed, which need not necessarily be the same as the element type of the
1051 input vector. All of these characteristics can readily be inferred from
1052 the type signature belonging to \hs{map}:
1055 map :: (a -> b) -> [a|n] -> [b|n]
1058 So far, only functions have been used as higher-order values. In
1059 Haskell, there are two more ways to obtain a function-typed value:
1060 partial application and lambda abstraction. Partial application
1061 means that a function that takes multiple arguments can be applied
1062 to a single argument, and the result will again be a function (but
1063 that takes one argument less). As an example, consider the following
1064 expression, that adds one to every element of a vector:
1067 \begin{minipage}{0.93\linewidth}
1072 \begin{minipage}{0.07\linewidth}
1078 Here, the expression \hs{(add 1)} is the partial application of the
1079 addition function to the value \hs{1}, which is again a function that
1080 adds one to its (next) argument. A lambda expression allows one to
1081 introduce an anonymous function in any expression. Consider the following
1082 expression, which again adds one to every element of a vector:
1085 \begin{minipage}{0.93\linewidth}
1087 map (\x -> x + 1) xs
1090 \begin{minipage}{0.07\linewidth}
1096 Finally, not only built-in functions can have higher order arguments (such
1097 as the \hs{map} function), but any function defined in \CLaSH\ may have
1098 functions as arguments. This allows the circuit designer to use a
1099 powerful amount of code reuse. The only exception is again the top-level
1100 function: if a function-typed argument is not applied with an actual
1101 function, no hardware can be generated.
1103 % \comment{TODO: Describe ALU example (no code)}
1106 A very important concept in hardware is the concept of state. In a
1107 stateful design, the outputs depend on the history of the inputs, or the
1108 state. State is usually stored in registers, which retain their value
1109 during a clock cycle. As we want to describe more than simple
1110 combinational designs, \CLaSH\ needs an abstraction mechanism for state.
1112 An important property in Haskell, and in most other functional languages,
1113 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1116 \item given the same arguments twice, it should return the same value in
1118 \item that the function has no observable side-effects.
1120 % This purity property is important for functional languages, since it
1121 % enables all kinds of mathematical reasoning that could not be guaranteed
1122 % correct for impure functions.
1123 Pure functions are as such a perfect match for combinational circuits,
1124 where the output solely depends on the inputs. When a circuit has state
1125 however, it can no longer be simply described by a pure function.
1126 % Simply removing the purity property is not a valid option, as the
1127 % language would then lose many of it mathematical properties.
1128 In \CLaSH\ we deal with the concept of state in pure functions by making
1129 the current state an additional argument of the function, and the
1130 updated state part of result. In this sense the descriptions made in
1131 \CLaSH\ are the combinational parts of a mealy machine.
1133 A simple example is adding an accumulator register to the earlier
1134 multiply-accumulate circuit, of which the resulting netlist can be seen in
1135 \Cref{img:mac-state}:
1138 \begin{minipage}{0.93\linewidth}
1140 macS (State c) a b = (State c', c')
1145 \begin{minipage}{0.07\linewidth}
1152 \centerline{\includegraphics{mac-state.svg}}
1153 \caption{Stateful Multiply-Accumulate}
1154 \label{img:mac-state}
1158 Note that the \hs{macS} function returns both the new state and the value
1159 of the output port. The \hs{State} keyword indicates which arguments are
1160 part of the current state, and what part of the output is part of the
1161 updated state. This aspect will also be reflected in the type signature of
1162 the function. Abstracting the state of a circuit in this way makes it very
1163 explicit: which variables are part of the state is completely determined
1164 by the type signature. This approach to state is well suited to be used in
1165 combination with the existing code and language features, such as all the
1166 choice elements, as state values are just normal values. We can simulate
1167 stateful descriptions using the recursive \hs{run} function:
1170 \begin{minipage}{0.93\linewidth}
1172 run f s (i : inps) = o : (run f s' inps)
1177 \begin{minipage}{0.07\linewidth}
1183 The \hs{(:)} operator is the list concatenation operator, where the
1184 left-hand side is the head of a list and the right-hand side is the
1185 remainder of the list. The \hs{run} function applies the function the
1186 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1187 first input value, \hs{i}. The result is the first output value, \hs{o},
1188 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1189 is then called with the updated state, \hs{s'}, and the rest of the
1190 inputs, \hs{inps}. For the time being, and in the context of this paper,
1191 it is assumed that there is one input per clock cycle. Also note how the
1192 order of the input, output, and state in the \hs{run} function corresponds
1193 with the order of the input, output and state of the \hs{macS} function
1196 As the \hs{run} function, the hardware description, and the test
1197 inputs are also valid Haskell, the complete simulation can be compiled to
1198 an executable binary by an optimizing Haskell compiler, or executed in an
1199 Haskell interpreter. Both simulation paths are much faster than first
1200 translating the description to \VHDL\ and then running a \VHDL\
1203 \section{The \CLaSH\ compiler}
1204 An important aspect in this research is the creation of the prototype
1205 compiler, which allows us to translate descriptions made in the \CLaSH\
1206 language as described in the previous section to synthesizable \VHDL.
1207 % , allowing a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1209 The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open-source Haskell
1210 compiler that also provides a high level API to most of its internals. The
1211 availability of this high-level API obviated the need to design many of the
1212 tedious parts of the prototype compiler, such as the parser, semantics
1213 checker, and especially the type-checker. These parts together form the
1214 front-end of the prototype compiler pipeline, as seen in
1215 \Cref{img:compilerpipeline}.
1218 \centerline{\includegraphics{compilerpipeline.svg}}
1219 \caption{\CLaSHtiny\ compiler pipeline}
1220 \label{img:compilerpipeline}
1224 The output of the \GHC\ front-end consists of the translation of the original
1225 Haskell description in \emph{Core}~\cite{Sulzmann2007}, which is a smaller,
1226 typed, functional language. This \emph{Core} language is relatively easy to
1227 process compared to the larger Haskell language. A description in \emph{Core}
1228 can still contain elements which have no direct translation to hardware, such
1229 as polymorphic types and function-valued arguments. Such a description needs
1230 to be transformed to a \emph{normal form}, which only contains elements that
1231 have a direct translation. The second stage of the compiler, the
1232 \emph{normalization} phase, exhaustively applies a set of
1233 \emph{meaning-preserving} transformations on the \emph{Core} description until
1234 this description is in a \emph{normal form}. This set of transformations
1235 includes transformations typically found in reduction systems and lambda
1236 calculus~\cite{lambdacalculus}, such as $\beta$-reduction and
1237 $\eta$-expansion. It also includes self-defined transformations that are
1238 responsible for the reduction of higher-order functions to `regular'
1239 first-order functions, and specializing polymorphic types to concrete types.
1241 The final step in the compiler pipeline is the translation to a \VHDL\
1242 \emph{netlist}, which is a straightforward process due to resemblance of a
1243 normalized description and a set of concurrent signal assignments. We call the
1244 end-product of the \CLaSH\ compiler a \VHDL\ \emph{netlist} as the resulting
1245 \VHDL\ resembles an actual netlist description and not idiomatic \VHDL.
1248 \label{sec:usecases}
1249 \subsection{FIR Filter}
1250 As an example of a common hardware design where the use of higher-order
1251 functions leads to a very natural description is a \acro{FIR} filter, which is
1252 basically the dot-product of two vectors:
1255 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1258 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1259 and a few previous input samples ($x$). Each of these multiplications
1260 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1261 filter is indeed equivalent to the equation of the dot-product, which is
1265 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1268 We can easily and directly implement the equation for the dot-product
1269 using higher-order functions:
1272 \begin{minipage}{0.93\linewidth}
1274 as *+* bs = foldl1 (+) (zipWith (*) as bs)
1277 \begin{minipage}{0.07\linewidth}
1283 The \hs{zipWith} function is very similar to the \hs{map} function seen
1284 earlier: It takes a function, two vectors, and then applies the function to
1285 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1286 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1288 The \hs{foldl1} function takes a binary function, a single vector, and applies
1289 the function to the first two elements of the vector. It then applies the
1290 function to the result of the first application and the next element in the
1291 vector. This continues until the end of the vector is reached. The result of
1292 the \hs{foldl1} function is the result of the last application. It is obvious
1293 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1294 \hs{foldl1 (+)} function is summation.
1295 % Returning to the actual \acro{FIR} filter, we will slightly change the
1296 % equation describing it, so as to make the translation to code more obvious and
1297 % concise. What we do is change the definition of the vector of input samples
1298 % and delay the computation by one sample. Instead of having the input sample
1299 % received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1300 % sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1301 % to the following (note that this is completely equivalent to the original
1302 % equation, just with a different definition of $x$ that will better suit the
1303 % transformation to code):
1306 % y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1308 The complete definition of the \acro{FIR} filter in code then becomes:
1311 \begin{minipage}{0.93\linewidth}
1313 fir (State (xs,hs)) x =
1314 (State (x >> xs,hs), (x +> xs) *+* hs)
1317 \begin{minipage}{0.07\linewidth}
1323 Where the vector \hs{xs} contains the previous input samples, the vector
1324 \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input
1325 sample. The concatenate operator (\hs{+>}) creates a new vector by placing the
1326 current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The
1327 code for the shift (\hs{>>}) operator, that adds the new input sample (\hs{x})
1328 to the list of previous input samples (\hs{xs}) and removes the oldest sample,
1332 \begin{minipage}{0.93\linewidth}
1334 x >> xs = x +> init xs
1337 \begin{minipage}{0.07\linewidth}
1343 Where the \hs{init} function returns all but the last element of a vector.
1344 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1345 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1349 \centerline{\includegraphics{4tapfir.svg}}
1350 \caption{4-taps \acrotiny{FIR} Filter}
1355 \subsection{Higher-order CPU}
1356 The following simple \acro{CPU} is an example of user-defined higher order
1357 functions and pattern matching. The \acro{CPU} consists of four function
1358 units, of which three have a fixed function and one can perform certain less
1361 The \acro{CPU} contains a number of data sources, represented by the
1362 horizontal wires in \Cref{img:highordcpu}. These data sources offer the
1363 previous outputs of each function units, along with the single data input the
1364 \acro{CPU} has and two fixed initialization values.
1366 Each of the function units has both its operands connected to all data
1367 sources, and can be programmed to select any data source for either
1368 operand. In addition, the leftmost function unit has an additional
1369 opcode input to select the operation it performs. The output of the rightmost
1370 function unit is also the output of the entire \acro{CPU}.
1372 Looking at the code, the function unit (\hs{fu}) is the most simple. It
1373 arranges the operand selection for the function unit. Note that it does not
1374 define the actual operation that takes place inside the function unit,
1375 but simply accepts the (higher-order) argument \hs{op} which is a function
1376 of two arguments that defines the operation.
1379 \begin{minipage}{0.93\linewidth}
1381 fu op inputs (addr1, addr2) = regIn
1388 \begin{minipage}{0.07\linewidth}
1394 The \hs{multiop} function defines the operation that takes place in the
1395 leftmost function unit. It is essentially a simple three operation \acro{ALU}
1396 that makes good use of pattern matching and guards in its description.
1397 The \hs{shift} function used here shifts its first operand by the number
1398 of bits indicated in the second operand, the \hs{xor} function produces
1399 the bitwise xor of its operands.
1402 \begin{minipage}{0.93\linewidth}
1404 data Opcode = Shift | Xor | Equal
1406 multiop :: Opcode -> Word -> Word -> Word
1407 multiop Shift a b = shift a b
1408 multiop Xor a b = xor a b
1409 multiop Equal a b | a == b = 1
1413 \begin{minipage}{0.07\linewidth}
1419 The \acro{CPU} function ties everything together. It applies the \hs{fu}
1420 function four times, to create a different function unit each time. The
1421 first application is interesting, because it does not just pass a
1422 function to \hs{fu}, but a partial application of \hs{multiop}. This
1423 shows how the first function unit effectively gets an extra input,
1424 compared to the others.
1426 The vector \hs{inputs} is the set of data sources, which is passed to
1427 each function unit as a set of possible operants. The \acro{CPU} also receives
1428 a vector of address pairs, which are used by each function unit to select
1429 their operand. The application of the function units to the \hs{inputs} and
1430 \hs{addrs} arguments seems quite repetitive and could be rewritten to use
1431 a combination of the \hs{map} and \hs{zipwith} functions instead.
1432 However, the prototype compiler does not currently support working with lists
1433 of functions, so a more explicit version of the code is given instead.
1436 \begin{minipage}{0.93\linewidth}
1438 type CpuState = State [Word | 4]
1440 cpu :: CpuState -> Word -> [(Index 6, Index 6) | 4]
1441 -> Opcode -> (CpuState, Word)
1442 cpu (State s) input addrs opc = (State s', out)
1444 s' = [ fu (multiop opc) inputs (addrs!0)
1445 , fu add inputs (addrs!1)
1446 , fu sub inputs (addrs!2)
1447 , fu mul inputs (addrs!3)
1449 inputs = 0 +> (1 +> (input +> s))
1453 \begin{minipage}{0.07\linewidth}
1459 This is still a simple example, but it could form the basis
1460 of an actual design, in which the same techniques can be reused.
1462 \section{Related work}
1463 This section describes the features of existing (functional) hardware
1464 description languages and highlights the advantages that this research has
1467 % Many functional hardware description languages have been developed over the
1468 % years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1469 % extension of Backus' \acro{FP} language to synchronous streams, designed
1470 % particularly for describing and reasoning about regular circuits. The
1471 % Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1472 % circuits, and has a particular focus on layout.
1474 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1475 functional language \acro{ML}, and has support for polymorphic types and
1476 higher-order functions. Published work suggests that there is no direct
1477 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1478 be translated to \VHDL\ and that the translated description can then be
1479 simulated in a \VHDL\ simulator. Certain aspects of HML, such as higher-order
1480 functions are however not supported by the \VHDL\ translator~\cite{HML3}. The
1481 \CLaSH\ compiler on the other hand can correctly translate all of the language
1482 constructs mentioned in this paper. % to a netlist format.
1485 \centerline{\includegraphics{highordcpu.svg}}
1486 \caption{CPU with higher-order Function Units}
1487 \label{img:highordcpu}
1491 Like the research presented in this paper, many functional hardware
1492 description languages have some sort of foundation in the functional
1493 programming language Haskell. Hawk~\cite{Hawk1} uses Haskell to describe
1494 system-level executable specifications used to model the behavior of
1495 superscalar microprocessors. Hawk specifications can be simulated; to the best
1496 knowledge of the authors there is however no support for automated circuit
1499 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1500 models. A designer can model systems using heterogeneous models of
1501 computation, which include continuous time, synchronous and untimed models of
1502 computation. Using so-called domain interfaces a designer can simulate
1503 electronic systems which have both analog as digital parts. ForSyDe has
1504 several backends including simulation and automated synthesis, though
1505 automated synthesis is restricted to the synchronous model of computation.
1506 Though ForSyDe offers higher-order functions and polymorphism, ForSyDe's
1507 choice elements are limited to \hs{if} and \hs{case} expressions. ForSyDe's
1508 explicit conversions, where function have to be wrapped in processes and
1509 processes have to be wrapped in systems, combined with the explicit
1510 instantiations of components, also makes ForSyDe more verbose than \CLaSH.
1512 Lava~\cite{Lava} is a hardware description language, embedded in Haskell, and
1513 focuses on the structural representation of hardware. Like \CLaSH, Lava has
1514 support for polymorphic types and higher-order functions. Besides support for
1515 simulation and circuit synthesis, Lava descriptions can be interfaced with
1516 formal method tools for formal verification. As discussed in the introduction,
1517 taking the embedded language approach does not allow for Haskell's choice
1518 elements to be captured within the circuit descriptions. In this respect
1519 \CLaSH\ differs from Lava, in that all of Haskell's choice elements, such as
1520 \hs{case}-expressions and pattern matching, are synthesized to choice elements
1521 in the eventual circuit. Consequently, descriptions containing rich control
1522 structures can be specified in a more user-friendly way in \CLaSH\ than possible within Lava, and are hence less error-prone.
1524 Bluespec~\cite{Bluespec} is a high-level synthesis language that features
1525 guarded atomic transactions and allows for the automated derivation of control
1526 structures based on these atomic transactions. Bluespec, like \CLaSH, supports
1527 polymorphic typing and function-valued arguments. Bluespec's syntax and
1528 language features \emph{had} their basis in Haskell. However, in order to
1529 appeal to the users of the traditional \acrop{HDL}, Bluespec has adapted
1530 imperative features and a syntax that resembles Verilog. As a result, Bluespec
1531 is (unnecessarily) verbose when compared to \CLaSH.
1533 The merits of polymorphic typing and function-valued arguments are now also
1534 recognized in the traditional \acrop{HDL}, exemplified by the new \VHDL-2008
1535 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to
1536 types and subprograms, allowing a designer to describe components with
1537 polymorphic ports and function-valued arguments. Note that the types and
1538 subprograms still require an explicit generic map, whereas types can be
1539 automatically inferred, and function-values can be automatically propagated
1540 by the \CLaSH\ compiler. There are also no (generally available) \VHDL\
1541 synthesis tools that currently support the \VHDL-2008 standard.
1543 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1545 % A functional language designed specifically for hardware design is
1546 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1547 % language called \acro{FL}~\cite{FL} to la
1549 % An example of a floating figure using the graphicx package.
1550 % Note that \label must occur AFTER (or within) \caption.
1551 % For figures, \caption should occur after the \includegraphics.
1552 % Note that IEEEtran v1.7 and later has special internal code that
1553 % is designed to preserve the operation of \label within \caption
1554 % even when the captionsoff option is in effect. However, because
1555 % of issues like this, it may be the safest practice to put all your
1556 % \label just after \caption rather than within \caption{}.
1558 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1559 % option should be used if it is desired that the figures are to be
1560 % displayed while in draft mode.
1564 %\includegraphics[width=2.5in]{myfigure}
1565 % where an .eps filename suffix will be assumed under latex,
1566 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1567 % via \DeclareGraphicsExtensions.
1568 %\caption{Simulation Results}
1572 % Note that IEEE typically puts floats only at the top, even when this
1573 % results in a large percentage of a column being occupied by floats.
1576 % An example of a double column floating figure using two subfigures.
1577 % (The subfig.sty package must be loaded for this to work.)
1578 % The subfigure \label commands are set within each subfloat command, the
1579 % \label for the overall figure must come after \caption.
1580 % \hfil must be used as a separator to get equal spacing.
1581 % The subfigure.sty package works much the same way, except \subfigure is
1582 % used instead of \subfloat.
1584 %\begin{figure*}[!t]
1585 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1586 %\label{fig_first_case}}
1588 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1589 %\label{fig_second_case}}}
1590 %\caption{Simulation results}
1594 % Note that often IEEE papers with subfigures do not employ subfigure
1595 % captions (using the optional argument to \subfloat), but instead will
1596 % reference/describe all of them (a), (b), etc., within the main caption.
1599 % An example of a floating table. Note that, for IEEE style tables, the
1600 % \caption command should come BEFORE the table. Table text will default to
1601 % \footnotesize as IEEE normally uses this smaller font for tables.
1602 % The \label must come after \caption as always.
1605 %% increase table row spacing, adjust to taste
1606 %\renewcommand{\arraystretch}{1.3}
1607 % if using array.sty, it might be a good idea to tweak the value of
1608 % \extrarowheight as needed to properly center the text within the cells
1609 %\caption{An Example of a Table}
1610 %\label{table_example}
1612 %% Some packages, such as MDW tools, offer better commands for making tables
1613 %% than the plain LaTeX2e tabular which is used here.
1614 %\begin{tabular}{|c||c|}
1624 % Note that IEEE does not put floats in the very first column - or typically
1625 % anywhere on the first page for that matter. Also, in-text middle ("here")
1626 % positioning is not used. Most IEEE journals/conferences use top floats
1627 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1628 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1629 % command of the stfloats package.
1633 \section{Conclusion}
1634 This research demonstrates once more that functional languages are well suited
1635 for hardware descriptions: function applications provide an elegant notation
1636 for component instantiation. Where this research goes beyond the existing
1637 (functional) hardware descriptions languages is the inclusion of various
1638 choice elements, such as pattern matching, that are well suited to describe
1639 the conditional assignments in control-oriented circuits. Besides being able
1640 to translate these basic constructs to synthesizable \VHDL, the prototype
1641 compiler can also correctly translate descriptions that contain both
1642 polymorphic types and function-valued arguments.
1644 Where recent functional hardware description languages have mostly opted to
1645 embed themselves in an existing functional language, this research features a
1646 `true' compiler. As a result there is a clear distinction between compile-time
1647 and run-time, which allows a myriad of choice constructs to be part of the
1648 actual circuit description; a feature the embedded hardware description
1649 languages do not offer.
1651 \section{Future Work}
1652 The choice of describing state explicitly as extra arguments and results can
1653 be seen as a mixed blessing. Even though the description that use state are
1654 usually very clear, one finds that dealing with unpacking, passing, receiving
1655 and repacking can become tedious and even error-prone, especially in the case
1656 of sub-states. Removing this boilerplate, or finding a more suitable
1657 abstraction mechanism would make \CLaSH\ easier to use.
1659 The transformations in normalization phase of the prototype compiler were
1660 developed in an ad-hoc manner, which makes the existence of many desirable
1661 properties unclear. Such properties include whether the complete set of
1662 transformations will always lead to a normal form or if the normalization
1663 process always terminates. Though various use cases suggests that these
1664 properties usually hold, they have not been formally proven. A systematic
1665 approach to defining the set of transformations allows one to proof that the
1666 earlier mentioned properties do indeed exist.
1668 % conference papers do not normally have an appendix
1671 % use section* for acknowledgement
1672 % \section*{Acknowledgment}
1674 % The authors would like to thank...
1676 % trigger a \newpage just before the given reference
1677 % number - used to balance the columns on the last page
1678 % adjust value as needed - may need to be readjusted if
1679 % the document is modified later
1680 % \IEEEtriggeratref{14}
1681 % The "triggered" command can be changed if desired:
1682 %\IEEEtriggercmd{\enlargethispage{-5in}}
1684 % references section
1686 % can use a bibliography generated by BibTeX as a .bbl file
1687 % BibTeX documentation can be easily obtained at:
1688 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1689 % The IEEEtran BibTeX style support page is at:
1690 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1691 \bibliographystyle{IEEEtran}
1692 % argument is your BibTeX string definitions and bibliography database(s)
1693 \bibliography{clash}
1695 % <OR> manually copy in the resultant .bbl file
1696 % set second argument of \begin to the number of references
1697 % (used to reserve space for the reference number labels box)
1698 % \begin{thebibliography}{1}
1700 % \bibitem{IEEEhowto:kopka}
1701 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1702 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1704 % \end{thebibliography}
1712 % vim: set ai sw=2 sts=2 expandtab: