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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 Baaij, Matthijs Kooijman, Jan Kuper, Arjan Boeijink, Marco 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 \author{\IEEEauthorblockN{Blind Review}%, Bert Molenkamp, Sabih H. Gerez}
427 \thanks{Supported through: ``Hidden for blind review''}
431 % \IEEEauthorblockN{Homer Simpson}
432 % \IEEEauthorblockA{Twentieth Century Fox\\
434 % Email: homer@thesimpsons.com}
436 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
437 % \IEEEauthorblockA{Starfleet Academy\\
438 % San Francisco, California 96678-2391\\
439 % Telephone: (800) 555--1212\\
440 % Fax: (888) 555--1212}}
442 % conference papers do not typically use \thanks and this command
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444 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
445 % after \documentclass
447 % for over three affiliations, or if they all won't fit within the width
448 % of the page, use this alternative format:
450 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
451 %Homer Simpson\IEEEauthorrefmark{2},
452 %James Kirk\IEEEauthorrefmark{3},
453 %Montgomery Scott\IEEEauthorrefmark{3} and
454 %Eldon Tyrell\IEEEauthorrefmark{4}}
455 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
456 %Georgia Institute of Technology,
457 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
458 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
459 %Email: homer@thesimpsons.com}
460 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
461 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
462 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
467 % use for special paper notices
468 %\IEEEspecialpapernotice{(Invited Paper)}
473 % make the title area
478 \CLaSH\ is a functional hardware description language that borrows both its syntax and semantics from the functional programming language Haskell. Polymorphism and higher-order functions provide a level of abstraction and generality that allow a circuit designer to describe circuits in a more natural way than possible with the language elements found in the traditional hardware description languages.
480 Circuit descriptions can be translated to synthesizable \VHDL\ using the prototype \CLaSH\ compiler. As the circuit descriptions, simulation code, and test input are also valid Haskell, complete simulations can be done by a Haskell compiler or interpreter, allowing high-speed simulation and analysis.
482 % \CLaSH\ supports stateful descriptions by explicitly making the current
483 % state an argument of the function, and the updated state part of the result.
484 % This makes \CLaSH\ descriptions in essence the combinational parts of a
487 % IEEEtran.cls defaults to using nonbold math in the Abstract.
488 % This preserves the distinction between vectors and scalars. However,
489 % if the conference you are submitting to favors bold math in the abstract,
490 % then you can use LaTeX's standard command \boldmath at the very start
491 % of the abstract to achieve this. Many IEEE journals/conferences frown on
492 % math in the abstract anyway.
499 % For peer review papers, you can put extra information on the cover
501 % \ifCLASSOPTIONpeerreview
502 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
505 % For peerreview papers, this IEEEtran command inserts a page break and
506 % creates the second title. It will be ignored for other modes.
507 \IEEEpeerreviewmaketitle
509 \section{Introduction}
510 Hardware description languages (\acrop{HDL}) have not allowed the productivity
511 of hardware engineers to keep pace with the development of chip technology.
512 While traditional \acrop{HDL}, like \VHDL~\cite{VHDL2008} and
513 Verilog~\cite{Verilog}, are very good at describing detailed hardware
514 properties such as timing behavior, they are generally cumbersome in
515 expressing the higher-level abstractions needed for today's large and complex
516 circuit designs. In an attempt to raise the abstraction level of the
517 descriptions, a great number of approaches based on functional languages have
518 been proposed \cite{Cardelli1981,muFP,DAISY,FHDL,T-Ruby,HML2,Hydra,Hawk1,Lava,
519 Wired,ForSyDe1,reFLect}. The idea of using functional languages for hardware
520 descriptions started in the early 1980s \cite{Cardelli1981,muFP,DAISY,FHDL}, a
521 time which also saw the birth of the currently popular \acrop{HDL}, such as
522 \VHDL. Functional languages are especially well suited to describe hardware
523 because combinational circuits can be directly modeled as mathematical
524 functions and functional languages are very good at describing and composing
527 In an attempt to reduce the effort involved with prototyping a new
528 language, such as creating all the required tooling like parsers and
529 type-checkers, many functional \acrop{HDL} \cite{Hydra,Hawk1,Lava,Wired} are
530 embedded as a domain specific language (\acro{DSL}) within the functional
531 language Haskell \cite{Haskell}. This means that a developer is given a
532 library of Haskell functions and types that together form the language
533 primitives of the \acro{DSL}. The primitive functions used to describe a
534 circuit do not actually process any signals, they instead compose a large
535 graph (which is usually hidden from the designer). This graph is then further
536 processed by an embedded circuit compiler which can perform e.g. simulation or
537 synthesis. As Haskell's choice elements (\hs{case}-expressions,
538 pattern-matching, etc.) are evaluated at the time the graph is being build,
539 they are no longer visible to the embedded compiler that processes the graph.
540 Consequently, it is impossible to capture Haskell's choice elements within a
541 circuit description when taking the embedded language approach. This does not
542 mean that circuits specified in an embedded language can not contain choice,
543 just that choice elements only exist as functions, e.g. a multiplexer
544 function, and not as syntactic elements of the language itself.
546 This research uses (a subset of) the Haskell language \emph{itself} for the
547 purpose of describing hardware. As a result, certain language constructs, like
548 all of Haskell's choice elements, \emph{can} now be captured within circuit
549 descriptions. Advanced features of Haskell, such as polymorphic typing and
550 higher-order functions, are also supported.
552 % supporting polymorphism, higher-order functions and such an extensive array
553 % of choice-elements, combined with a very concise way of specifying circuits
554 % is new in the domain of (functional) \acrop{HDL}.
555 % As the hardware descriptions are plain Haskell
556 % functions, these descriptions can be compiled to an executable binary
557 % for simulation using an optimizing Haskell compiler such as the Glasgow
558 % Haskell Compiler (\GHC)~\cite{ghc}.
560 Where descriptions in a conventional \acro{HDL} have an explicit clock for the
561 purposes state and synchronicity, the clock is implicit for the descriptions
562 and research presented in this paper. A circuit designer describes the
563 behavior of the hardware between clock cycles, as a transition from the
564 current state to the next. Many functional \acrop{HDL} model signals as a
565 stream of values over time; state is then modeled as a delay on this stream of
566 values. Descriptions presented in this research make the current state an
567 additional input and the updated state a part of their output. This
568 abstraction of state and time limits the descriptions to synchronous hardware.
569 However, work is in progress to add an abstraction mechanism that allows the
570 modeling of asynchronous and multi-clock systems.
572 Likewise as with the traditional \acrop{HDL}, descriptions made in a
573 functional \acro{HDL} must eventually be converted into a netlist. This
574 research also features a prototype compiler, which has the same name as the
575 language: \CLaSH\footnote{\CLaSHtiny:
576 % \acrotiny{CAES} Language for Synchronous Hardware.
577 ``Hidden for blind review'' Language for Synchronous Hardware
579 (pronounced: clash). This compiler converts the Haskell code to equivalently
580 behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist
581 format by an (optimizing) \VHDL\ synthesis tool.
583 To the best knowledge of the authors, \CLaSH\ is the only (functional)
584 \acro{HDL} that allows circuit specification to be written in a very concise
585 way and at the same time support such advanced features as polymorphic typing,
586 user-defined higher-order functions and pattern matching.
589 \noindent The next section will describe the language elements of \CLaSH, and
590 \Cref{sec:compiler} gives a high-level overview of the \CLaSH\ compiler.
591 \Cref{sec:usecases} discusses two use-cases, a \acro{FIR} filter, and a
592 higher-order \acro{CPU} design. The related work section
593 (\Cref{sec:relatedwork}) is placed towards the end, as the features of \CLaSH\
594 should be presented before comparing \CLaSH\ to existing (functional)
595 \acrop{HDL}. Conclusions are presented in \Cref{sec:conclusion}, and future
596 work is discussed in \Cref{sec:futurework}.
598 \section{Hardware description in Haskell}
599 This section describes the basic language elements of \CLaSH\ and the support
600 of these elements within the \CLaSH\ compiler. In various subsections, the
601 relation between the language elements and their eventual netlist
602 representation is also highlighted.
604 \subsection{Function application}
605 Two basic elements of a functional program are functions and function
606 application. These have a single obvious translation to a netlist format:
608 \item every function is translated to a component,
609 \item every function argument is translated to an input port,
610 \item the result value of a function is translated to an output port,
612 \item function applications are translated to component instantiations.
614 The result value can have a composite type (such as a tuple), so the fact
615 that a function has just a single result value does not pose any
616 limitation. The actual arguments of a function application are assigned to
617 signals, which are then mapped to the corresponding input ports of the
618 component. The output port of the function is also mapped to a signal,
619 which is used as the result of the application itself. Since every
620 function generates its own component, the hierarchy of function calls is
621 reflected in the final netlist.
622 %, creating a hierarchical description of the hardware.
623 % The separation in different components makes it easier for a developer
624 % to understand and possibly hand-optimize the resulting \VHDL\ output of
625 % the \CLaSH\ compiler.
627 The short example below (\ref{code:mac}) gives a demonstration of
628 the conciseness that can be achieved with \CLaSH\ when compared to
629 other (more traditional) \acrop{HDL}. The example is a combinational
630 multiply-accumulate circuit that works for \emph{any} word length (this
631 type of polymorphism will be further elaborated in
632 \Cref{sec:polymorhpism}). The corresponding netlist is depicted in
636 \begin{minipage}{0.93\linewidth}
638 mac a b c = add (mul a b) c
641 \begin{minipage}{0.07\linewidth}
648 \centerline{\includegraphics{mac.svg}}
649 \caption{Combinational Multiply-Accumulate}
654 The use of a composite result value is demonstrated in the next example
655 (\ref{code:mac-composite}), where the multiply-accumulate circuit returns
656 not only the accumulation result, but also the intermediate multiplication
657 result (see \Cref{img:mac-comb-composite}, where the double arrow suggests
658 the composite output).
661 \begin{minipage}{0.93\linewidth}
663 mac a b c = (z, add z c)
668 \begin{minipage}{0.07\linewidth}
670 \label{code:mac-composite}
676 \centerline{\includegraphics{mac-nocurry.svg}}
677 \caption{Combinational Multiply-Accumulate (composite output)}
678 \label{img:mac-comb-composite}
683 In Haskell, choice can be achieved by a large set of syntactic elements,
684 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
685 pattern matching, and guards. The most general of these are the \hs{case}
686 expressions (\hs{if} expressions can be directly translated to
687 \hs{case} expressions). When transforming a \CLaSH\ description to a
688 netlist, a \hs{case} expression is translated to a multiplexer. The
689 control value of the \hs{case} expression is fed into a number of
690 comparators, and their combined output forms the selection port of the
691 multiplexer. The result of each alternative in the \hs{case} expression is
692 linked to the corresponding input port of the multiplexer.
693 % A \hs{case} expression can in turn simply be translated to a conditional
694 % assignment in \VHDL, where the conditions use equality comparisons
695 % against the constructors in the \hs{case} expressions.
697 % Two versions of a contrived example are displayed below, the first
698 % (\ref{lst:code3}) using a \hs{case} expression and the second
699 % (\ref{lst:code4}) using an \hs{if-then-else} expression. Both examples
700 % sum two values when they are equal or non-equal (depending on the given
701 % predicate, the \hs{pred} variable) and return 0 otherwise.
703 A code example (\ref{code:counter1}) that uses a \hs{case} expression and
704 \hs{if-then-else} expressions is shown below. The function counts up or
705 down depending on the \hs{direction} variable, and has a \hs{bound}
706 variable that determines both the upper bound and wrap-around point of the
707 counter. The \hs{direction} variable is of the following, user-defined,
708 enumeration datatype:
711 data Direction = Up | Down
714 The naive netlist corresponding to this example is depicted in
715 \Cref{img:counter}. Note that the \hs{direction} variable is only
716 compared to \hs{Up}, as an inequality immediately implies that
717 \hs{direction} is \hs{Down} (as derived by the compiler).
720 \begin{minipage}{0.93\linewidth}
722 counter bound direction x = case direction of
723 Up -> if x < bound then
726 Down -> if x > 0 then
731 \begin{minipage}{0.07\linewidth}
733 \label{code:counter1}
738 % \begin{minipage}{0.93\linewidth}
741 % if pred == Equal then
742 % if a == b then a + b else 0
744 % if a != b then a + b else 0
747 % \begin{minipage}{0.07\linewidth}
755 % \centerline{\includegraphics{choice-case.svg}}
756 % \caption{Choice - sumif}
762 \centerline{\includegraphics{counter.svg}}
763 \caption{Counter netlist}
768 A \emph{user-friendly} and also powerful form of choice that is not found
769 in the traditional \acrop{HDL} is pattern matching. A function can be
770 defined in multiple clauses, where each clause corresponds to a pattern.
771 When an argument matches a pattern, the corresponding clause will be used.
772 Expressions can also contain guards, where the expression is only executed
773 if the guard evaluates to true, and continues with the next clause if the
774 guard evaluates to false. Like \hs{if-then-else} expressions, pattern
775 matching and guards have a (straightforward) translation to \hs{case}
776 expressions and can as such be mapped to multiplexers. A second version
777 (\ref{code:counter2}) of the earlier example, now using both pattern
778 matching and guards, can be seen below. The guard is the expression that
779 follows the vertical bar (\hs{|}) and precedes the assignment operator
780 (\hs{=}). The \hs{otherwise} guards always evaluate to \hs{true}.
782 The second version corresponds to the same naive netlist representation
783 (\Cref{img:counter}) as the earlier example.
786 \begin{minipage}{0.93\linewidth}
788 counter bound Up x | x < bound = x + 1
791 counter bound Down x | x > 0 = x - 1
795 \begin{minipage}{0.07\linewidth}
797 \label{code:counter2}
802 % \centerline{\includegraphics{choice-ifthenelse}}
803 % \caption{Choice - \emph{if-then-else}}
808 Haskell is a statically-typed language, meaning that the type of a
809 variable or function is determined at compile-time. Not all of
810 Haskell's typing constructs have a clear translation to hardware,
811 therefore this section only deals with the types that do have a clear
812 correspondence to hardware. The translatable types are divided into two
813 categories: \emph{built-in} types and \emph{user-defined} types. Built-in
814 types are those types for which a fixed translation is defined within the
815 \CLaSH\ compiler. The \CLaSH\ compiler has generic translation rules to
816 translate the user-defined types, which are described later on.
818 Type annotations (entities in \VHDL) are optional, since the \CLaSH\
819 compiler can derive them when the top-level function \emph{is} annotated
822 % Translation of two most basic functional concepts has been
823 % discussed: function application and choice. Before looking further
824 % into less obvious concepts like higher-order expressions and
825 % polymorphism, the possible types that can be used in hardware
826 % descriptions will be discussed.
828 % Some way is needed to translate every value used to its hardware
829 % equivalents. In particular, this means a hardware equivalent for
830 % every \emph{type} used in a hardware description is needed.
832 % The following types are \emph{built-in}, meaning that their hardware
833 % translation is fixed into the \CLaSH\ compiler. A designer can also
834 % define his own types, which will be translated into hardware types
835 % using translation rules that are discussed later on.
837 \subsubsection{Built-in types}
838 The following types have fixed translations defined within the \CLaSH\
842 the most basic type available. It can have two values:
843 \hs{Low} or \hs{High}.
844 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
846 this is a basic logic type. It can have two values: \hs{True}
848 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
849 % type (where a value of \hs{True} corresponds to a value of
851 Supporting the Bool type is required in order to support the
852 \hs{if-then-else} expression.
853 \item[\bf{Signed}, \bf{Unsigned}]
854 these are types to represent integers, and both are parametrizable in
855 their size. The overflow behavior of the numeric operators defined for
856 these types is \emph{wrap-around}.
857 % , so you can define an unsigned word of 32 bits wide as follows:
860 % type Word32 = SizedWord D32
863 % Here, a type synonym \hs{Word32} is defined that is equal to the
864 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
865 % \hs{D32} is the \emph{type level representation} of the decimal
866 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
867 % types are translated to the \VHDL\ \texttt{unsigned} and
868 % \texttt{signed} respectively.
870 this type can contain elements of any type and has a static length.
871 The \hs{Vector} type constructor takes two arguments: the length of
872 the vector and the type of the elements contained in it. The
873 short-hand notation used for the vector type in the rest of paper is:
874 \hs{[a|n]}, where \hs{a} is the element type, and \hs{n} is the length
876 % Note that this is a notation used in this paper only, vectors are
877 % slightly more verbose in real \CLaSH\ descriptions.
878 % The state type of an 8 element register bank would then for example
882 % type RegisterState = Vector D8 Word32
885 % Here, a type synonym \hs{RegisterState} is defined that is equal to
886 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
887 % type level representation of the decimal number 8) and \hs{Word32}
888 % (The 32 bit word type as defined above). In other words, the
889 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
890 % vector is translated to a \VHDL\ array type.
892 the main purpose of the \hs{Index} type is to be used as an index into
893 a \hs{Vector}, and has an integer range from zero to a specified upper
895 % This means that its range is not limited to powers of two, but
897 If a value of this type exceeds either bounds, an error will be thrown
900 % \comment{TODO: Perhaps remove this example?} To define an index for
901 % the 8 element vector above, we would do:
904 % type RegisterIndex = RangedWord D7
907 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
908 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
909 % other words, this defines an unsigned word with values from
910 % 0 to 7 (inclusive). This word can be be used to index the
911 % 8 element vector \hs{RegisterState} above. This type is translated
912 % to the \texttt{unsigned} \VHDL type.
915 \subsubsection{User-defined types}
916 % There are three ways to define new types in Haskell: algebraic
917 % data-types with the \hs{data} keyword, type synonyms with the \hs{type}
918 % keyword and datatype renaming constructs with the \hs{newtype} keyword.
919 % \GHC\ offers a few more advanced ways to introduce types (type families,
920 % existential typing, {\acro{GADT}}s, etc.) which are not standard
921 % Haskell. As it is currently unclear how these advanced type constructs
922 % correspond to hardware, they are for now unsupported by the \CLaSH\
924 A designer may define a completely new type by an algebraic datatype
925 declaration using the \hs{data} keyword. Type synonyms can be introduced
926 using the \hs{type} keyword.
927 % Only an algebraic datatype declaration actually introduces a
928 % completely new type. Type synonyms and type renaming only define new
929 % names for existing types, where synonyms are completely interchangeable
930 % and a type renaming requires an explicit conversion.
931 Type synonyms do not need any particular translation, as a synonym will
932 use the same representation as the original type.
934 Algebraic datatypes can be categorized as follows:
936 \item[\bf{Single constructor}]
937 datatypes with a single constructor with one or more fields allow
938 values to be packed together in a record-like structure. Haskell's
939 built-in tuple types are also defined as single constructor algebraic
940 types (using some syntactic sugar). An example of a single constructor
941 type with multiple fields is the following pair of integers:
943 data IntPair = IntPair Int Int
945 % These types are translated to \VHDL\ record types, with one field
946 % for every field in the constructor.
947 \item[\bf{Multiple constructors, No fields}]
948 datatypes with multiple constructors, but without any fields are
950 % Note that Haskell's \hs{Bool} type is also defined as an enumeration
951 % type, but that there is a fixed translation for that type within the
953 An example of an enumeration type definition is:
955 data TrafficLight = Red | Orange | Green
957 % These types are translated to \VHDL\ enumerations, with one
958 % value for each constructor. This allows references to these
959 % constructors to be translated to the corresponding enumeration
961 \item[\bf{Multiple constructors with fields}]
962 datatypes with multiple constructors, where at least
963 one of these constructors has one or more fields are currently not
964 supported. Additional research is required to optimize the overlap of
965 fields belonging to the different constructors.
968 \subsection{Polymorphism}\label{sec:polymorhpism}
969 A powerful feature of some programming languages is polymorphism, it
970 allows a function to handle values of different data types in a uniform
971 way. Haskell supports \emph{parametric polymorphism}, meaning that
972 functions can be written without mentioning specific types, and that those
973 functions can be used for arbitrary types.
975 As an example of a parametric polymorphic function, consider the type of
976 the \hs{first} function, which returns the first element of a
977 tuple:\footnote{The \hs{::} operator is used to annotate a function
984 This type is parameterized in \hs{a} and \hs{b}, which can both
985 represent any type that is supported by the \CLaSH\ compiler. This means
986 that \hs{first} works for any tuple, regardless of what elements it
987 contains. This kind of polymorphism is extremely useful in hardware
988 designs, for example when routing signals without knowing their exact
989 type, or specifying vector operations that work on vectors of any length
990 and element type. Polymorphism also plays an important role in most higher
991 order functions, as will be shown in the next section.
993 % Another type of polymorphism is \emph{ad-hoc
994 % polymorphism}~\cite{polymorphism}, which refers to polymorphic
995 % functions which can be applied to arguments of different types, but
996 % which behave differently depending on the type of the argument to which
997 % they are applied. In Haskell, ad-hoc polymorphism is achieved through
998 % the use of \emph{type classes}, where a class definition provides the
999 % general interface of a function, and class \emph{instances} define the
1000 % functionality for the specific types. An example of such a type class is
1001 % the \hs{Num} class, which contains all of Haskell's numerical
1002 % operations. A designer can make use of this ad-hoc polymorphism by
1003 % adding a \emph{constraint} to a parametrically polymorphic type
1004 % variable. Such a constraint indicates that the type variable can only be
1005 % instantiated to a type whose members supports the overloaded functions
1006 % associated with the type class.
1008 Another type of polymorphism is \emph{ad-hoc polymorphism}, which refers
1009 to functions that can be applied to arguments of a limited set to types.
1010 Furthermore, how such functions work may depend on the type of their
1011 arguments. For instance, multiplication only works for numeric types, and
1012 it works differently for e.g. integers and complex numbers.
1014 In Haskell, ad-hoc polymorphism is achieved through the use of \emph{type
1015 classes}, where a class definition provides the general interface of a
1016 function, and class \emph{instances} define the functionality for the
1017 specific types. For example, all numeric operators are gathered in the
1018 \hs{Num} class, so every type that wants to use those operators must be
1019 made an instance of \hs{Num}.
1021 By prefixing a type signature with class constraints, the constrained type
1022 parameters are forced to belong to that type class. For example, the
1023 arguments of the \hs{add} function must belong to the \hs{Num} type class
1024 because the \hs{add} function adds them with the (\hs{+}) operator:
1027 \begin{minipage}{0.93\linewidth}
1029 add :: Num a => a -> a -> a
1033 \begin{minipage}{0.07\linewidth}
1039 % An example of a type signature that includes such a constraint if the
1040 % signature of the \hs{sum} function, which sums the values in a vector:
1042 % sum :: Num a => [a|n] -> a
1045 % This type is again parameterized by \hs{a}, but it can only contain
1046 % types that are \emph{instances} of the \emph{type class} \hs{Num}, so
1047 % that the compiler knows that the addition (+) operator is defined for
1050 % A place where class constraints also play a role is in the size and
1051 % range parameters of the \hs{Vector} and numeric types. The reason being
1052 % that these parameters have to be limited to types that can represent
1053 % \emph{natural} numbers. The complete type of for example the \hs{Vector}
1056 % Natural n => Vector n a
1059 % \CLaSH's built-in numerical types are also instances of the \hs{Num}
1061 % so we can use the addition operator (and thus the \hs{sum}
1062 % function) with \hs{Signed} as well as with \hs{Unsigned}.
1064 \CLaSH\ supports both parametric polymorphism and ad-hoc polymorphism. A
1065 circuit designer can specify his own type classes and corresponding
1066 instances. The \CLaSH\ compiler will infer the type of every polymorphic
1067 argument depending on how the function is applied. There is however one
1068 constraint: the top level function that is being translated can not have
1069 polymorphic arguments. The arguments of the top-level can not be
1070 polymorphic as there is no way to infer the \emph{specific} types of the
1073 With regard to the built-in types, it should be noted that members of
1074 some of the standard Haskell type classes are supported as built-in
1075 functions. These include: the numerial operators of \hs{Num}, the equality
1076 operators of \hs{Eq}, and the comparison (order) operators of \hs{Ord}.
1078 \subsection{Higher-order functions \& values}
1079 Another powerful abstraction mechanism in functional languages, is
1080 the concept of \emph{functions as a first class value} and
1081 \emph{higher-order functions}. These concepts allows a function to be
1082 treated as a value and be passed around, even as the argument of another
1083 function. The following example clarifies this concept:
1086 \begin{minipage}{0.93\linewidth}
1087 %format not = "\mathit{not}"
1089 negate{-"\!\!\!"-}Vector xs = map not xs
1092 \begin{minipage}{0.07\linewidth}
1094 \label{code:negatevector}
1098 The code above defines the \hs{negate{-"\!\!\!"-}Vector} function, which
1099 takes a vector of booleans, \hs{xs}, and returns a vector where all the
1100 values are negated. It achieves this by calling the \hs{map} function, and
1101 passing it another \emph{function}, boolean negation, and the vector of
1102 booleans, \hs{xs}. The \hs{map} function applies the negation function to
1103 all the elements in the vector.
1105 The \hs{map} function is called a higher-order function, since it takes
1106 another function as an argument. Also note that \hs{map} is again a
1107 parametric polymorphic function: it does not pose any constraints on the
1108 type of the input vector, other than that its elements must have the same
1109 type as the first argument of the function passed to \hs{map}. The element
1110 type of the resulting vector is equal to the return type of the function
1111 passed, which need not necessarily be the same as the element type of the
1112 input vector. All of these characteristics can be inferred from the type
1113 signature of \hs{map}:
1116 map :: (a -> b) -> [a|n] -> [b|n]
1119 In Haskell, there are two more ways to obtain a function-typed value:
1120 partial application and lambda abstraction. Partial application means that
1121 a function that takes multiple arguments can be applied to a single
1122 argument, and the result will again be a function, but takes one argument
1123 less. As an example, consider the following expression, that adds one to
1124 every element of a vector:
1127 \begin{minipage}{0.93\linewidth}
1132 \begin{minipage}{0.07\linewidth}
1134 \label{code:partialapplication}
1138 Here, the expression \hs{(add 1)} is the partial application of the
1139 addition function to the value \hs{1}, which is again a function that
1140 adds 1 to its (next) argument.
1142 A lambda expression allows a designer to introduce an anonymous function
1143 in any expression. Consider the following expression, which again adds 1
1144 to every element of a vector:
1147 \begin{minipage}{0.93\linewidth}
1149 map (\x -> x + 1) xs
1152 \begin{minipage}{0.07\linewidth}
1154 \label{code:lambdaexpression}
1158 Finally, not only built-in functions can have higher-order arguments (such
1159 as the \hs{map} function), but any function defined in \CLaSH\ may have
1160 functions as arguments. This allows the circuit designer to apply a
1161 large amount of code reuse. The only exception is again the top-level
1162 function: if a function-typed argument is not instantiated with an actual
1163 function, no hardware can be generated.
1165 An example of a common circuit where higher-order functions and partial
1166 application lead to a very concise and natural description is a crossbar.
1167 The code (\ref{code:crossbar}) for this example can be seen below:
1170 \begin{minipage}{0.93\linewidth}
1172 crossbar inputs selects = map (mux inputs) selects
1174 mux inp x = (inp ! x)
1177 \begin{minipage}{0.07\linewidth}
1179 \label{code:crossbar}
1183 The \hs{crossbar} function selects those values from \hs{inputs} that
1184 are indicated by the indexes in the vector \hs{selects}. The crossbar is
1185 polymorphic in the width of the input (defined by the length of
1186 \hs{inputs}), the width of the output (defined by the length of
1187 \hs{selects}), and the signal type (defined by the element type of
1188 \hs{inputs}). The type-checker can also automatically infer that
1189 \hs{selects} is a vector of \hs{Index} values due to the use of the vector
1190 indexing operator (\hs{!}).
1193 In a stateful design, the outputs depend on the history of the inputs, or
1194 the state. State is usually stored in registers, which retain their value
1195 during a clock cycle.
1196 % As \CLaSH\ has to be able to describe more than plain combinational
1197 % designs, there is a need for an abstraction mechanism for state.
1199 An important property in Haskell, and in many other functional languages,
1200 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1203 \item given the same arguments twice, it should return the same value in
1205 \item that the function has no observable side-effects.
1207 % This purity property is important for functional languages, since it
1208 % enables all kinds of mathematical reasoning that could not be guaranteed
1209 % correct for impure functions.
1210 Pure functions are a perfect match for combinational circuits, where the
1211 output solely depends on the inputs. When a circuit has state however, it
1212 can no longer be described by a pure function.
1213 % Simply removing the purity property is not a valid option, as the
1214 % language would then lose many of it mathematical properties.
1215 \CLaSH\ deals with the concept of state by making the current state an
1216 additional argument of the function, and the updated state part of the
1217 result. In this sense the descriptions made in \CLaSH\ are the
1218 combinational parts of a mealy machine.
1220 A simple example is adding an accumulator register to the earlier
1221 multiply-accumulate circuit, of which the resulting netlist can be seen in
1222 \Cref{img:mac-state}:
1225 \begin{minipage}{0.93\linewidth}
1227 macS (State c) (a, b) = (State c', c')
1232 \begin{minipage}{0.07\linewidth}
1234 \label{code:macstate}
1238 Note that the \hs{macS} function returns both the new state and the value
1239 of the output port. The \hs{State} wrapper indicates which arguments are
1240 part of the current state, and what part of the output is part of the
1241 updated state. This aspect will also be reflected in the type signature of
1242 the function. Abstracting the state of a circuit in this way makes it very
1243 explicit: which variables are part of the state is completely determined
1244 by the type signature. This approach to state is well suited to be used in
1245 combination with the existing code and language features, such as all the
1246 choice elements, as state values are just normal values from Haskell's
1247 point of view. Stateful descriptions are simulated using the recursive
1251 \begin{minipage}{0.93\linewidth}
1253 run f s (i : inps) = o : (run f s' inps)
1258 \begin{minipage}{0.07\linewidth}
1264 The \hs{(:)} operator is the list concatenation operator, where the
1265 left-hand side is the head of a list and the right-hand side is the
1266 remainder of the list. The \hs{run} function applies the function the
1267 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1268 first input value, \hs{i}. The result is the first output value, \hs{o},
1269 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1270 is then called with the updated state, \hs{s'}, and the rest of the
1271 inputs, \hs{inps}. In the context of this paper, it is assumed that there
1272 is one input per clock cycle. Note that the order of \hs{s',o,s,i} in the
1273 \hs{where} clause of the \hs{run} functions corresponds with the order of
1274 the input, output and state of the \hs{macS} function
1275 (\ref{code:macstate}). Thus, the expression below (\ref{code:runmacs})
1276 simulates \hs{macS} on \hs{inputpairs} starting with the value \hs{0}:
1279 \begin{minipage}{0.93\linewidth}
1281 run macS 0 inputpairs
1284 \begin{minipage}{0.07\linewidth}
1286 \label{code:runmacs}
1291 \centerline{\includegraphics{mac-state.svg}}
1292 \caption{Stateful Multiply-Accumulate}
1293 \label{img:mac-state}
1297 The complete simulation can be compiled to an executable binary by a
1298 Haskell compiler, or executed in a Haskell interpreter. Both
1299 simulation paths require less effort from a circuit designer than first
1300 translating the description to \VHDL\ and then running a \VHDL\
1301 simulation; it is also very likely that both simulation paths are much
1304 \section{The \CLaSH\ compiler}
1305 \label{sec:compiler}
1306 The prototype \CLaSH\ compiler translates descriptions made in the \CLaSH\
1307 language as described in the previous section to synthesizable \VHDL.
1308 % , allowing a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1310 The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open source Haskell
1311 compiler that also provides a high level \acro{API} to most of its internals.
1312 Furthermore, it provides several parts of the prototype compiler for free,
1313 such as the parser, the semantics checker, and the type checker. These parts
1314 together form the front-end of the prototype compiler pipeline, as seen in
1315 \Cref{img:compilerpipeline}.
1319 \centerline{\includegraphics{compilerpipeline.svg}}
1320 \caption{\CLaSHtiny\ compiler pipeline}
1321 \label{img:compilerpipeline}
1325 The output of the \GHC\ front-end consists of the translation of the original
1326 Haskell description to \emph{Core}~\cite{Sulzmann2007}, which is a small
1327 typed functional language. This \emph{Core} language is relatively easy to
1328 process compared to the larger Haskell language. A description in \emph{Core}
1329 can still contain elements which have no direct translation to hardware, such
1330 as polymorphic types and function-valued arguments. Such a description needs
1331 to be transformed to a \emph{normal form}, which corresponds directly to
1332 hardware. The second stage of the compiler, the \emph{normalization} phase,
1333 exhaustively applies a set of \emph{meaning-preserving} transformations on the
1334 \emph{Core} description until this description is in a \emph{normal form}.
1335 This set of transformations includes transformations typically found in
1336 reduction systems and lambda calculus~\cite{lambdacalculus}, such as
1337 $\beta$-reduction and $\eta$-expansion. It also includes transformations that
1338 are responsible for the specialization of higher-order functions to `regular'
1339 first-order functions, and specializing polymorphic types to concrete types.
1341 The final step in the compiler pipeline is the translation to a \VHDL\
1342 \emph{netlist}, which is a straightforward process due to the resemblance of a
1343 normalized description and a set of concurrent signal assignments. The
1344 end-product of the \CLaSH\ compiler is called a \VHDL\ \emph{netlist} as the
1345 result resembles an actual netlist description, and the fact that it is \VHDL\
1346 is only an implementation detail; e.g., the output could have been Verilog or
1350 \label{sec:usecases}
1351 \subsection{FIR Filter}
1352 As an example of a common hardware design where the relation between
1353 functional languages and mathematical functions, combined with the use of
1354 higher-order functions leads to a very natural description is a \acro{FIR}
1358 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1361 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1362 and a few previous input samples ($x$). Each of these multiplications
1363 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1364 filter is equivalent to the equation of the dot-product of two vectors, which
1368 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1371 The equation for the dot-product is easily and directly implemented using
1372 higher-order functions:
1375 \begin{minipage}{0.93\linewidth}
1377 as *+* bs = fold (+) (zip{-"\!\!\!"-}With (*) as bs)
1380 \begin{minipage}{0.07\linewidth}
1382 \label{code:dotproduct}
1386 The \hs{zip{-"\!\!\!"-}With} function is very similar to the \hs{map} function
1387 seen earlier: It takes a function, two vectors, and then applies the function
1388 to each of the elements in the two vectors pairwise (\emph{e.g.},
1389 \hs{zip{-"\!\!\!"-}With (*) [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1391 The \hs{fold} function takes a binary function, a single vector, and applies
1392 the function to the first two elements of the vector. It then applies the
1393 function to the result of the first application and the next element in the
1394 vector. This continues until the end of the vector is reached. The result of
1395 the \hs{fold} function is the result of the last application. It is obvious
1396 that the \hs{zip{-"\!\!\!\!"-}With (*)} function is pairwise multiplication
1397 and that the \hs{fold (+)} function is summation.
1398 % Returning to the actual \acro{FIR} filter, we will slightly change the
1399 % equation describing it, so as to make the translation to code more obvious and
1400 % concise. What we do is change the definition of the vector of input samples
1401 % and delay the computation by one sample. Instead of having the input sample
1402 % received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1403 % sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1404 % to the following (note that this is completely equivalent to the original
1405 % equation, just with a different definition of $x$ that will better suit the
1406 % transformation to code):
1409 % y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1411 The complete definition of the \acro{FIR} filter in \CLaSH\ is:
1414 \begin{minipage}{0.93\linewidth}
1416 fir (State (xs,hs)) x =
1417 (State (shiftInto x xs,hs), (x +> xs) *+* hs)
1420 \begin{minipage}{0.07\linewidth}
1426 where the vector \hs{xs} contains the previous input samples, the vector
1427 \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input
1428 sample. The concatenate operator (\hs{+>}) creates a new vector by placing the
1429 current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The
1430 code for the \hs{shiftInto} function, that adds the new input sample (\hs{x})
1431 to the list of previous input samples (\hs{xs}) and removes the oldest sample,
1435 \begin{minipage}{0.93\linewidth}
1437 shiftInto x xs = x +> init xs
1440 \begin{minipage}{0.07\linewidth}
1442 \label{code:shiftinto}
1446 where the \hs{init} function returns all but the last element of a vector.
1447 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1448 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1452 \centerline{\includegraphics{4tapfir.svg}}
1453 \caption{4-taps \acrotiny{FIR} Filter}
1458 \subsection{Higher-order CPU}
1459 %format fun x = "\textit{fu}_" x
1460 This section discusses a somewhat more elaborate example in which user-defined
1461 higher-order function, partial application, lambda expressions, and pattern
1462 matching are exploited. The example concerns a \acro{CPU} which consists of
1463 four function units, \hs{fun 0,{-"\ldots"-},fun 3}, (see
1464 \Cref{img:highordcpu}) that each perform some binary operation.
1467 \centerline{\includegraphics{highordcpu.svg}}
1468 \caption{CPU with higher-order Function Units}
1469 \label{img:highordcpu}
1473 Every function unit has seven data inputs (of type \hs{Signed 16}), and two
1474 address inputs (of type \hs{Index 6}). The latter two addresses indicate
1475 which of the seven data inputs are to be used as operands for the binary
1476 operation the function unit performs.
1478 These seven data inputs consist of one external input \hs{x}, two fixed
1479 initialization values (0 and 1), and the previous outputs of the four function
1480 units. The output of the \acro{CPU} as a whole is the previous output of
1483 Function units \hs{fun 1}, \hs{fun 2}, and \hs{fun 3} can perform a fixed
1484 binary operation, whereas \hs{fun 0} has an additional input for an opcode to
1485 choose a binary operation out of a few possibilities. Each function unit
1486 outputs its result into a register, i.e., the state of the \acro{CPU}. This
1487 state can e.g. be defined as follows:
1490 type CpuState = State [Signed 16 | 4]
1493 Every function unit can now be defined by the following higher-order function,
1494 \hs{fu}, which takes three arguments: the operation \hs{op} that the function
1495 unit should perform, the seven \hs{inputs}, and the address pair
1496 \hs{({-"a_0"-},{-"a_1"-})}. It selects two inputs, based on the
1497 addresses, and applies the given operation to them, returning the
1501 \begin{minipage}{0.93\linewidth}
1503 fu op inputs ({-"a_0"-}, {-"a_1"-}) =
1504 op (inputs!{-"a_0"-}) (inputs!{-"a_1"-})
1507 \begin{minipage}{0.07\linewidth}
1509 \label{code:functionunit}
1513 \noindent Using partial application we now define:
1516 \begin{minipage}{0.93\linewidth}
1523 \begin{minipage}{0.07\linewidth}
1525 \label{code:functionunits1to3}
1529 In order to define \hs{fun 0}, the \hs{Opcode} type and the \hs{multiop}
1530 function that chooses a specific operation given the opcode, are defined
1531 first. It is assumed that the binary functions \hs{shift} (where \hs{shift a
1532 b} shifts \hs{a} by the number of bits indicated by \hs{b}) and \hs{xor} (for
1533 the bitwise \hs{xor}) exist.
1536 \begin{minipage}{0.93\linewidth}
1538 data Opcode = Shift | Xor | Equal
1540 multiop Shift = shift
1542 multiop Equal = \a b -> if a == b then 1 else 0
1545 \begin{minipage}{0.07\linewidth}
1547 \label{code:multiop}
1551 Note that the result of \hs{multiop} is a binary function; this is supported
1552 by \CLaSH. The complete definition of \hs{fun 0}, which takes an opcode as
1553 additional argument, is:
1556 \begin{minipage}{0.93\linewidth}
1558 fun 0 c = fu (multiop c)
1561 \begin{minipage}{0.07\linewidth}
1563 \label{code:functionunit0}
1567 \noindent Now comes the definition of the full \acro{CPU}. Its type is:
1571 -> (Signed 16, Opcode, [(Index 6, Index 6) | 4])
1572 -> (CpuState, Signed 16)
1575 \noindent Note that this type fits the requirements of the \hs{run}
1576 function (meaning it can be simulated and synthesized). The actual
1577 definition of the \hs{cpu} function is:
1580 \begin{minipage}{0.93\linewidth}
1582 cpu (State s) (x,opc,addrs) = (State s', out)
1584 inputs = x +> (0 +> (1 +> s))
1585 s' = [{-"\;"-}fun 0 opc inputs (addrs!0)
1586 ,{-"\;"-}fun 1 inputs (addrs!1)
1587 ,{-"\;"-}fun 2 inputs (addrs!2)
1588 ,{-"\;"-}fun 3 inputs (addrs!3)
1593 \begin{minipage}{0.07\linewidth}
1599 Due to space restrictions, \Cref{img:highordcpu} does not show the
1600 internals of each function unit, but note that e.g. \hs{multiop} is a
1601 subcomponent of \hs{fun 0}.
1603 While the \acro{CPU} has a simple (and maybe not very useful) design, it
1604 illustrates some possibilities that \CLaSH\ offers and suggests how to write
1607 % Each of the function units has both its operands connected to all data
1608 % sources, and can be programmed to select any data source for either
1609 % operand. In addition, the leftmost function unit has an additional
1610 % opcode input to select the operation it performs. The previous output of the
1611 % rightmost function unit is the output of the entire \acro{CPU}.
1613 % The code of the function unit (\ref{code:functionunit}), which arranges the
1614 % operand selection for the function unit, is shown below. Note that the actual
1615 % operation that takes place inside the function unit is supplied as the
1616 % (higher-order) argument \hs{op}, which is a function that takes two arguments.
1620 % The \hs{multiop} function (\ref{code:multiop}) defines the operation that takes place in the leftmost function unit. It is essentially a simple three operation \acro{ALU} that makes good use of pattern matching and guards in its description. The \hs{shift} function used here shifts its first operand by the number of bits indicated in the second operand, the \hs{xor} function produces
1621 % the bitwise xor of its operands.
1624 % The \acro{CPU} function (\ref{code:cpu}) ties everything together. It applies
1625 % the function unit (\hs{fu}) to several operations, to create a different
1626 % function unit each time. The first application is interesting, as it does not
1627 % just pass a function to \hs{fu}, but a partial application of \hs{multiop}.
1628 % This demonstrates how one function unit can effectively get extra inputs
1629 % compared to the others.
1631 % The vector \hs{inputs} is the set of data sources, which is passed to
1632 % each function unit as a set of possible operants. The \acro{CPU} also receives
1633 % a vector of address pairs, which are used by each function unit to select
1635 % The application of the function units to the \hs{inputs} and
1636 % \hs{addrs} arguments seems quite repetitive and could be rewritten to use
1637 % a combination of the \hs{map} and \hs{zipwith} functions instead.
1638 % However, the prototype compiler does not currently support working with
1639 % lists of functions, so a more explicit version of the code is given instead.
1641 % While this is still a simple example, it could form the basis of an actual
1642 % design, in which the same techniques can be reused.
1644 \section{Related work}
1645 \label{sec:relatedwork}
1646 This section describes the features of existing (functional) hardware
1647 description languages and highlights the advantages that \CLaSH\ has
1650 % Many functional hardware description languages have been developed over the
1651 % years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1652 % extension of Backus' \acro{FP} language to synchronous streams, designed
1653 % particularly for describing and reasoning about regular circuits. The
1654 % Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1655 % circuits, and has a particular focus on layout.
1657 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1658 functional language \acro{ML}, and has support for polymorphic types and
1659 higher-order functions. There is no direct simulation support for \acro{HML},
1660 so a description in \acro{HML} has to be translated to \VHDL\ and the
1661 translated description can then be simulated in a \VHDL\ simulator. Certain
1662 aspects of HML, such as higher-order functions are however not supported by
1663 the \VHDL\ translator~\cite{HML3}. The \CLaSH\ compiler on the other hand can
1664 correctly translate all of its language constructs.
1666 Like the research presented in this paper, many functional hardware
1667 description languages have a foundation in the functional programming language
1668 Haskell. Hawk~\cite{Hawk1} is a hardware modeling language embedded in Haskell
1669 and has sequential environments that make it easier to specify stateful
1670 computation (by using the \acro{ST} monad). Hawk specifications can be
1671 simulated; to the best knowledge of the authors there is however no support
1672 for automated circuit synthesis.
1674 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1675 models. A designer can model systems using heterogeneous models of
1676 computation, which include continuous time, synchronous and untimed models of
1677 computation. Using so-called domain interfaces a designer can simulate
1678 electronic systems which have both analog and digital parts. ForSyDe has
1679 several backends including simulation and automated synthesis, though
1680 automated synthesis is restricted to the synchronous model of computation.
1681 Although ForSyDe offers higher-order functions and polymorphism, ForSyDe's
1682 choice elements are limited to \hs{if-then-else} and \hs{case} expressions.
1683 ForSyDe's explicit conversions, where functions have to be wrapped in
1684 processes and processes have to be wrapped in systems, combined with the
1685 explicit instantiations of components, also makes ForSyDe far more verbose
1688 Lava~\cite{Lava,kansaslava} is a \acro{HDL} embedded in Haskell which focuses
1689 on the structural representation of hardware. Like \CLaSH, Lava has support
1690 for polymorphic types and higher-order functions. Besides support for
1691 simulation and circuit synthesis, Lava descriptions can be interfaced with
1692 formal method tools for formal verification. As discussed in the introduction,
1693 taking the embedded language approach does not allow for Haskell's choice
1694 elements to be captured within the circuit descriptions. In this respect
1695 \CLaSH\ differs from Lava, in that all of Haskell's choice elements, such as
1696 \hs{case}-expressions and pattern matching, are synthesized to choice elements
1697 in the eventual circuit. Consequently, descriptions containing rich control
1698 structures can be specified in a more user-friendly way in \CLaSH\ than
1699 possible within Lava, and hence are less error-prone.
1701 Bluespec~\cite{Bluespec} is a high-level synthesis language that features
1702 guarded atomic transactions and allows for the automated derivation of control
1703 structures based on these atomic transactions. Bluespec, like \CLaSH, supports
1704 polymorphic typing and function-valued arguments. Bluespec's syntax and
1705 language features \emph{had} their basis in Haskell. However, in order to
1706 appeal to the users of the traditional \acrop{HDL}, Bluespec has adapted
1707 imperative features and a syntax that resembles Verilog. As a result, Bluespec
1708 is (unnecessarily) verbose when compared to \CLaSH.
1710 The merits of polymorphic typing and function-valued arguments are now also
1711 recognized in the traditional \acrop{HDL}, exemplified by the new \VHDL-2008
1712 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to
1713 types and subprograms, allowing a designer to describe components with
1714 polymorphic ports and function-valued arguments. Note that the types and
1715 subprograms still require an explicit generic map, while the \CLaSH\ compiler
1716 automatically infers types, and automatically propagates function-valued
1717 arguments. There are also no (generally available) \VHDL\ synthesis tools that
1718 currently support the \VHDL-2008 standard.
1720 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1722 % A functional language designed specifically for hardware design is
1723 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1724 % language called \acro{FL}~\cite{FL} to la
1726 % An example of a floating figure using the graphicx package.
1727 % Note that \label must occur AFTER (or within) \caption.
1728 % For figures, \caption should occur after the \includegraphics.
1729 % Note that IEEEtran v1.7 and later has special internal code that
1730 % is designed to preserve the operation of \label within \caption
1731 % even when the captionsoff option is in effect. However, because
1732 % of issues like this, it may be the safest practice to put all your
1733 % \label just after \caption rather than within \caption{}.
1735 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1736 % option should be used if it is desired that the figures are to be
1737 % displayed while in draft mode.
1741 %\includegraphics[width=2.5in]{myfigure}
1742 % where an .eps filename suffix will be assumed under latex,
1743 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1744 % via \DeclareGraphicsExtensions.
1745 %\caption{Simulation Results}
1749 % Note that IEEE typically puts floats only at the top, even when this
1750 % results in a large percentage of a column being occupied by floats.
1753 % An example of a double column floating figure using two subfigures.
1754 % (The subfig.sty package must be loaded for this to work.)
1755 % The subfigure \label commands are set within each subfloat command, the
1756 % \label for the overall figure must come after \caption.
1757 % \hfil must be used as a separator to get equal spacing.
1758 % The subfigure.sty package works much the same way, except \subfigure is
1759 % used instead of \subfloat.
1761 %\begin{figure*}[!t]
1762 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1763 %\label{fig_first_case}}
1765 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1766 %\label{fig_second_case}}}
1767 %\caption{Simulation results}
1771 % Note that often IEEE papers with subfigures do not employ subfigure
1772 % captions (using the optional argument to \subfloat), but instead will
1773 % reference/describe all of them (a), (b), etc., within the main caption.
1776 % An example of a floating table. Note that, for IEEE style tables, the
1777 % \caption command should come BEFORE the table. Table text will default to
1778 % \footnotesize as IEEE normally uses this smaller font for tables.
1779 % The \label must come after \caption as always.
1782 %% increase table row spacing, adjust to taste
1783 %\renewcommand{\arraystretch}{1.3}
1784 % if using array.sty, it might be a good idea to tweak the value of
1785 % \extrarowheight as needed to properly center the text within the cells
1786 %\caption{An Example of a Table}
1787 %\label{table_example}
1789 %% Some packages, such as MDW tools, offer better commands for making tables
1790 %% than the plain LaTeX2e tabular which is used here.
1791 %\begin{tabular}{|c||c|}
1801 % Note that IEEE does not put floats in the very first column - or typically
1802 % anywhere on the first page for that matter. Also, in-text middle ("here")
1803 % positioning is not used. Most IEEE journals/conferences use top floats
1804 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1805 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1806 % command of the stfloats package.
1810 \section{Conclusion}
1811 \label{sec:conclusion}
1812 This research demonstrates once more that functional languages are well suited
1813 for hardware descriptions: function applications provide an elegant notation
1814 for component instantiation. While circuit descriptions made in \CLaSH\ are
1815 very concise when compared to other (traditional) \acrop{HDL}, their intended
1816 functionality remains clear. \CLaSH\ goes beyond the existing (functional)
1817 \acrop{HDL} by including advanced choice elements, such as pattern matching
1818 and guards, which are well suited to describe the conditional assignments in
1819 control-oriented circuits. Besides being able to translate these basic
1820 constructs to synthesizable \VHDL, the prototype compiler can also translate
1821 descriptions that contain both polymorphic types and user-defined higher-order
1824 % Where recent functional hardware description languages have mostly opted to
1825 % embed themselves in an existing functional language, this research features
1826 % a `true' compiler. As a result there is a clear distinction between
1827 % compile-time and run-time, which allows a myriad of choice constructs to be
1828 % part of the actual circuit description; a feature the embedded hardware
1829 % description languages do not offer.
1831 Besides simple circuits such as variants of both the \acro{FIR} filter and
1832 the higher-order \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler
1833 has also been able to translate non-trivial functional descriptions such as a
1834 streaming reduction circuit~\cite{blindreview} %~\cite{reductioncircuit}
1835 for floating point numbers.
1837 \section{Future Work}
1838 \label{sec:futurework}
1839 The choice of describing state explicitly as an extra argument and result can
1840 be seen as a mixed blessing. Even though descriptions that use state are
1841 usually very clear, distributing and collecting substate can become tedious
1842 and even error-prone. Automating the required distribution and collection, or
1843 finding a more suitable abstraction mechanism for state would make \CLaSH\
1844 easier to use. Currently, one of the examined approaches to suppress state in
1845 the specification is by using Haskell's arrow-abstraction.
1847 The transformations in the normalization phase of the prototype compiler are
1848 developed in an ad-hoc manner, which makes the existence of many desirable
1849 properties unclear. Such properties include whether the complete set of
1850 transformations will always lead to a normal form or whether the normalization
1851 process always terminates. Although extensive use of the compiler suggests
1852 that these properties usually hold, they have not been formally proven. A
1853 systematic approach to defining the set of transformations allows one to proof
1854 that the earlier mentioned properties do indeed hold.
1856 % conference papers do not normally have an appendix
1859 % use section* for acknowledgement
1860 % \section*{Acknowledgment}
1862 % The authors would like to thank...
1864 % trigger a \newpage just before the given reference
1865 % number - used to balance the columns on the last page
1866 % adjust value as needed - may need to be readjusted if
1867 % the document is modified later
1868 % \IEEEtriggeratref{14}
1869 % The "triggered" command can be changed if desired:
1870 %\IEEEtriggercmd{\enlargethispage{-5in}}
1872 % references section
1874 % can use a bibliography generated by BibTeX as a .bbl file
1875 % BibTeX documentation can be easily obtained at:
1876 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1877 % The IEEEtran BibTeX style support page is at:
1878 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1879 \bibliographystyle{IEEEtran}
1880 % argument is your BibTeX string definitions and bibliography database(s)
1881 \bibliography{clash}
1883 % <OR> manually copy in the resultant .bbl file
1884 % set second argument of \begin to the number of references
1885 % (used to reserve space for the reference number labels box)
1886 % \begin{thebibliography}{1}
1888 % \bibitem{IEEEhowto:kopka}
1889 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1890 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1892 % \end{thebibliography}
1900 % vim: set ai sw=2 sts=2 expandtab: