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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,
487 % then you can use LaTeX's standard command \boldmath at the very start
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 not allowed the productivity
508 of hardware engineers to keep pace with the development of chip technology.
509 While traditional \acrop{HDL}, like \VHDL~\cite{VHDL2008} and
510 Verilog~\cite{Verilog}, are very good at describing detailed hardware
511 properties such as timing behavior, they are generally cumbersome in
512 expressing the higher-level abstractions needed for today's large and complex
513 circuit designs. In an attempt to raise the abstraction level of the
514 descriptions, a great number of approaches based on functional languages has
515 been proposed \cite{Cardelli1981,muFP,DAISY,T-Ruby,HML2,Hydra,Hawk1,Lava,
516 Wired,ForSyDe1,reFLect}. The idea of using functional languages for hardware
517 descriptions started in the early 1980s \cite{Cardelli1981,muFP,DAISY}, a
518 time which also saw the birth of the currently popular \acrop{HDL}, such as
519 \VHDL. Functional languages are especially well suited to describe hardware
520 because combinational circuits can be directly modeled as mathematical
521 functions and functional languages are very good at describing and composing
524 In an attempt to ease the prototyping process of the language, such as
525 creating all the required tooling, like parsers and type-checkers, many
526 functional \acrop{HDL} \cite{Hydra,Hawk1,Lava,Wired} are embedded as a domain
527 specific language (\acro{DSL}) within the functional language Haskell
528 \cite{Haskell}. This means that a developer is given a library of Haskell
529 functions and types that together form the language primitives of the
530 \acro{DSL}. The primitive functions used to describe a circuit do not actually
531 process any signals, they instead compose a large domain-specific graph
532 (which is usually hidden from the designer). This graph is then further
533 processed by an embedded circuit compiler which can perform for example
534 simulation or synthesis. As Haskell's choice elements (\hs{case}-expressions,
535 pattern-matching etc.) are evaluated at the time the domain-specific graph is
536 being build, they are no longer visible to the embedded compiler that
537 processes the datatype. Consequently, it is impossible to capture Haskell's
538 choice elements within a circuit description when taking the embedded language
539 approach. This does not mean that circuits specified in an embedded language
540 can not contain choice, just that choice elements only exists as functions,
541 e.g. a multiplexer function, and not as language elements.
543 The approach taken in this research is to use (a subset of) the Haskell
544 language \emph{itself} for the purpose of describing hardware. By taking this
545 approach, this research \emph{can} capture certain language constructs, like
546 all of Haskell's choice elements, within circuit descriptions. The more
547 advanced features of Haskel, such as polymorphic typing and higher-order
548 function, are also supported.
550 % supporting polymorphism, higher-order functions and such an extensive array
551 % of choice-elements, combined with a very concise way of specifying circuits
552 % is new in the domain of (functional) \acrop{HDL}.
553 % As the hardware descriptions are plain Haskell
554 % functions, these descriptions can be compiled to an executable binary
555 % for simulation using an optimizing Haskell compiler such as the Glasgow
556 % Haskell Compiler (\GHC)~\cite{ghc}.
558 Where descriptions in a conventional \acro{HDL} have an explicit clock for the
559 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.
561 Like the traditional \acrop{HDL}, descriptions made in a functional \acro{HDL}
562 must eventually be converted into a netlist. This research also features a
563 prototype translator, which has the same name as the language:
564 \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES} Language for Synchronous Hardware}
565 (pronounced: clash). This compiler converts the Haskell code to equivalently
566 behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist
567 format by an (optimizing) \VHDL\ synthesis tool.
569 To the best knowledge of the authors, \CLaSH\ is the only (functional)
570 \acro{HDL} that allows circuit specification to be written in a very concise
571 way and at the same time support such advanced features as polymorphic typing,
572 user-defined higher-order functions and pattern matching.
574 \section{Hardware description in Haskell}
575 The following section describes the basic language elements of \CLaSH\ and the
576 extensiveness of the support of these elements within the \CLaSH\ compiler. In
577 various subsections, the relation between the language elements and their
578 eventual netlist representation is also highlighted.
580 \subsection{Function application}
581 Two basic elements of a functional program are functions and function
582 application. These have a single obvious translation to a netlist format:
584 \item every function is translated to a component,
585 \item every function argument is translated to an input port,
586 \item the result value of a function is translated to an output port,
588 \item function applications are translated to component instantiations.
590 The result value can have a composite type (such as a tuple), so having
591 just a single result value does not pose any limitation. The actual
592 arguments of a function application are assigned to signals, which are
593 then mapped to the corresponding input ports of the component. The output
594 port of the function is also mapped to a signal, which is used as the
595 result of the application itself. Since every top level function generates
596 its own component, the hierarchy of function calls is reflected in the
597 final netlist. %, creating a hierarchical description of the hardware.
598 % The separation in different components makes it easier for a developer
599 % to understand and possibly hand-optimize the resulting \VHDL\ output of
600 % the \CLaSH\ compiler.
602 The short example (\ref{code:mac}) seen below gives a demonstration of
603 the conciseness that can be achieved with \CLaSH\ when compared with
604 other (more traditional) \acrop{HDL}. The example is a combinational
605 multiply-accumulate circuit that works for \emph{any} word length (this
606 type of polymorphism will be further elaborated in
607 \Cref{sec:polymorhpism}). The corresponding netlist is depicted in
611 \begin{minipage}{0.93\linewidth}
613 mac a b c = add (mul a b) c
616 \begin{minipage}{0.07\linewidth}
623 \centerline{\includegraphics{mac.svg}}
624 \caption{Combinational Multiply-Accumulate}
629 The use of a composite result value is demonstrated in the next example
630 (\ref{code:mac-composite}), where the multiply-accumulate circuit not only
631 returns the accumulation result, but also the intermediate multiplication
632 result. Its corresponding netlist can be seen in
633 \Cref{img:mac-comb-composite}.
636 \begin{minipage}{0.93\linewidth}
638 mac a b c = (z, add z c)
643 \begin{minipage}{0.07\linewidth}
645 \label{code:mac-composite}
652 \centerline{\includegraphics{mac-nocurry.svg}}
653 \caption{Combinational Multiply-Accumulate (composite output)}
654 \label{img:mac-comb-composite}
659 In Haskell, choice can be achieved by a large set of syntactic elements,
660 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
661 pattern matching, and guards. The most general of these are the \hs{case}
662 expressions (\hs{if} expressions can be directly translated to
663 \hs{case} expressions). When transforming a \CLaSH\ description to a
664 netlist, a \hs{case} expression is translated to a multiplexer. The
665 control value of the \hs{case} expression is fed into a number of
666 comparators and their combined output forms the selection port of the
667 multiplexer. The result of each alternative in the \hs{case} expression is
668 linked to the corresponding input port of the multiplexer.
669 % A \hs{case} expression can in turn simply be translated to a conditional
670 % assignment in \VHDL, where the conditions use equality comparisons
671 % against the constructors in the \hs{case} expressions.
673 % Two versions of a contrived example are displayed below, the first
674 % (\ref{lst:code3}) using a \hs{case} expression and the second
675 % (\ref{lst:code4}) using an \hs{if-then-else} expression. Both examples
676 % sum two values when they are equal or non-equal (depending on the given
677 % predicate, the \hs{pred} variable) and return 0 otherwise.
679 An code example (\ref{code:counter1}) that uses a \hs{case} expression and
680 \hs{if-then-else} expressions is shown below. The function counts up or
681 down depending on the \hs{direction} variable, and has a \hs{wrap}
682 variable that determines both the upper bound and wrap-around point of the
683 counter. The \hs{direction} variable is of the following, user-defined,
684 enumeration datatype:
687 data Direction = Up | Down
690 The naive netlist corresponding to this example is depicted in
691 \Cref{img:counter}. Note that the \hs{direction} variable is only
692 compared to \hs{Up}, as an inequality immediately implies that
693 \hs{direction} is \hs{Down}.
696 \begin{minipage}{0.93\linewidth}
698 counter direction wrap x = case direction of
699 Up -> if x < wrap then
702 Down -> if x > 0 then
707 \begin{minipage}{0.07\linewidth}
709 \label{code:counter1}
714 % \begin{minipage}{0.93\linewidth}
717 % if pred == Equal then
718 % if a == b then a + b else 0
720 % if a != b then a + b else 0
723 % \begin{minipage}{0.07\linewidth}
731 % \centerline{\includegraphics{choice-case.svg}}
732 % \caption{Choice - sumif}
738 \centerline{\includegraphics{counter.svg}}
739 \caption{Counter netlist}
744 A user-friendly and also very powerful form of choice that is not found in
745 the traditional hardware description languages is pattern matching. A
746 function can be defined in multiple clauses, where each clause corresponds
747 to a pattern. When an argument matches a pattern, the corresponding clause
748 will be used. Expressions can also contain guards, where the expression is
749 only executed if the guard evaluates to true, and continues with the next
750 clause if the guard evaluates to false. Like \hs{if-then-else}
751 expressions, pattern matching and guards have a (straightforward)
752 translation to \hs{case} expressions and can as such be mapped to
753 multiplexers. A second version (\ref{code:counter2}) of the earlier
754 example, now using both pattern matching and guards, can be seen below.
755 The guard is the expression that follows the vertical bar (\hs{|}) and
756 precedes the assignment operator (\hs{=}). The \hs{otherwise} guards
757 always evaluate to \hs{true}.
759 The version using pattern matching and guards corresponds to the same
760 naive netlist representation (\Cref{img:counter}) as the earlier example.
763 \begin{minipage}{0.93\linewidth}
765 counter Up wrap x | x < wrap = x + 1
767 counter Down wrap x | x > 0 = x - 1
771 \begin{minipage}{0.07\linewidth}
773 \label{code:counter2}
778 % \centerline{\includegraphics{choice-ifthenelse}}
779 % \caption{Choice - \emph{if-then-else}}
784 Haskell is a statically-typed language, meaning that the type of a
785 variable or function is determined at compile-time. Not all of Haskell's
786 typing constructs have a clear translation to hardware, this section will
787 therefore only deal with the types that do have a clear correspondence
788 to hardware. The translatable types are divided into two categories:
789 \emph{built-in} types and \emph{user-defined} types. Built-in types are
790 those types for which a fixed translation is defined within the \CLaSH\
791 compiler. The \CLaSH\ compiler has generic translation rules to
792 translate the user-defined types, which are described later on.
794 The \CLaSH\ compiler is able to infer unspecified (polymorphic) types,
795 meaning that a developer does not have to annotate every function with a
796 type signature. % (even if it is good practice to do so).
797 Given that the top-level entity of a circuit design is annotated with
798 concrete/monomorphic types, the \CLaSH\ compiler can specialize
799 polymorphic functions to functions with concrete types.
801 % Translation of two most basic functional concepts has been
802 % discussed: function application and choice. Before looking further
803 % into less obvious concepts like higher-order expressions and
804 % polymorphism, the possible types that can be used in hardware
805 % descriptions will be discussed.
807 % Some way is needed to translate every value used to its hardware
808 % equivalents. In particular, this means a hardware equivalent for
809 % every \emph{type} used in a hardware description is needed.
811 % The following types are \emph{built-in}, meaning that their hardware
812 % translation is fixed into the \CLaSH\ compiler. A designer can also
813 % define his own types, which will be translated into hardware types
814 % using translation rules that are discussed later on.
816 \subsubsection{Built-in types}
817 The following types have fixed translations defined within the \CLaSH\
821 the most basic type available. It can have two values:
822 \hs{Low} or \hs{High}.
823 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
825 this is a basic logic type. It can have two values: \hs{True}
827 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
828 % type (where a value of \hs{True} corresponds to a value of
830 Supporting the Bool type is required in order to support the
831 \hs{if-then-else} expression, which requires a \hs{Bool} value for
833 \item[\bf{Signed}, \bf{Unsigned}]
834 these are types to represent integers and both are parametrizable in
835 their size. The overflow behavior of the numeric operators defined for
836 these types is \emph{wrap-around}.
837 % , so you can define an unsigned word of 32 bits wide as follows:
840 % type Word32 = SizedWord D32
843 % Here, a type synonym \hs{Word32} is defined that is equal to the
844 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
845 % \hs{D32} is the \emph{type level representation} of the decimal
846 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
847 % types are translated to the \VHDL\ \texttt{unsigned} and
848 % \texttt{signed} respectively.
850 this is a vector type that can contain elements of any other type and
851 has a static length. The \hs{Vector} type constructor takes two type
852 arguments: the length of the vector and the type of the elements
853 contained in it. The short-hand notation used for the vector type in
854 the rest of paper is: \hs{[a|n]}, where \hs{a} is the element
855 type, and \hs{n} is the length of the vector. Note that this is
856 a notation used in this paper only, vectors are slightly more
857 verbose in real \CLaSH\ descriptions.
858 % The state type of an 8 element register bank would then for example
862 % type RegisterState = Vector D8 Word32
865 % Here, a type synonym \hs{RegisterState} is defined that is equal to
866 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
867 % type level representation of the decimal number 8) and \hs{Word32}
868 % (The 32 bit word type as defined above). In other words, the
869 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
870 % vector is translated to a \VHDL\ array type.
872 the main purpose of the \hs{Index} type is to be used as an index into
873 a \hs{Vector}, and has no specified bit-size, but a specified upper
874 bound. This means that its range is not limited to powers of two, but
875 can be any number. An \hs{Index} only has an upper bound, its lower
876 bound is implicitly zero. If a value of this type exceeds either
877 bounds, an error will be thrown at \emph{simulation}-time.
879 % \comment{TODO: Perhaps remove this example?} To define an index for
880 % the 8 element vector above, we would do:
883 % type RegisterIndex = RangedWord D7
886 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
887 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
888 % other words, this defines an unsigned word with values from
889 % 0 to 7 (inclusive). This word can be be used to index the
890 % 8 element vector \hs{RegisterState} above. This type is translated
891 % to the \texttt{unsigned} \VHDL type.
894 \subsubsection{User-defined types}
895 % There are three ways to define new types in Haskell: algebraic
896 % data-types with the \hs{data} keyword, type synonyms with the \hs{type}
897 % keyword and datatype renaming constructs with the \hs{newtype} keyword.
898 % \GHC\ offers a few more advanced ways to introduce types (type families,
899 % existential typing, {\acro{GADT}}s, etc.) which are not standard
900 % Haskell. As it is currently unclear how these advanced type constructs
901 % correspond to hardware, they are for now unsupported by the \CLaSH\
903 A completely new type is introduced by an algebraic datatype declaration
904 which is defined using the \hs{data} keyword. Type synonyms can be
905 introduced using the \hs{type} keyword.
906 % Only an algebraic datatype declaration actually introduces a
907 % completely new type. Type synonyms and type renaming only define new
908 % names for existing types, where synonyms are completely interchangeable
909 % and a type renaming requires an explicit conversion.
910 Type synonyms do not need any particular translation, as a synonym will
911 just use the same representation as the original type.
913 Algebraic datatypes can be categorized as follows:
915 \item[\bf{Single constructor}]
916 Algebraic datatypes with a single constructor with one or more
917 fields allow values to be packed together in a record-like structure.
918 Haskell's built-in tuple types are also defined as single constructor
919 algebraic types (using a bit of syntactic sugar). An example of a
920 single constructor type with multiple fields is the following pair of
923 data IntPair = IntPair Int Int
925 % These types are translated to \VHDL\ record types, with one field
926 % for every field in the constructor.
927 \item[\bf{No fields}]
928 Algebraic datatypes with multiple constructors, but without any
929 fields are essentially enumeration types. Note that Haskell's
930 \hs{Bool} type is also defined as an enumeration type, but that there
931 is a fixed translation for that type within the \CLaSH\ compiler. An
932 example of an enumeration type definition is the definition for a
935 data TrafficLight = Red | Orange | Green
937 % These types are translated to \VHDL\ enumerations, with one
938 % value for each constructor. This allows references to these
939 % constructors to be translated to the corresponding enumeration
941 \item[\bf{Multiple constructors with fields}]
942 Algebraic datatypes with multiple constructors, where at least
943 one of these constructors has one or more fields are currently not
944 supported. Additional research is required to allow for the overlap of
945 the fields belonging to the different constructors.
948 \subsection{Polymorphism}\label{sec:polymorhpism}
949 A powerful feature of most (functional) programming languages is
950 polymorphism, it allows a function to handle values of different data
951 types in a uniform way. Haskell supports \emph{parametric
952 polymorphism}~\cite{polymorphism}, meaning functions can be written
953 without mention of any specific type and can be used transparently with
954 any number of new types.
956 As an example of a parametric polymorphic function, consider the type of
957 the following \hs{first} function, which returns the first element of a
958 tuple:\footnote{The \hs{::} operator is used to annotate a function
965 This type is parameterized in both \hs{a} and \hs{b}, which can both
966 represent any type at all (as long as that type is supported by the
967 \CLaSH\ compiler). This means that \hs{first} works for any tuple,
968 regardless of what elements it contains. This kind of polymorphism is
969 extremely useful in hardware designs, for example when routing signals
970 without knowing their exact type, or specifying vector operations that
971 work on vectors of any length and element type. Polymorphism also plays an
972 important role in most higher order functions, as will be shown in the
975 Another type of polymorphism is \emph{ad-hoc
976 polymorphism}~\cite{polymorphism}, which refers to polymorphic
977 functions which can be applied to arguments of different types, but which
978 behave differently depending on the type of the argument to which they are
979 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
980 \emph{type classes}, where a class definition provides the general
981 interface of a function, and class \emph{instances} define the
982 functionality for the specific types. An example of such a type class is
983 the \hs{Num} class, which contains all of Haskell's numerical operations.
984 A designer can make use of this ad-hoc polymorphism by adding a
985 \emph{constraint} to a parametrically polymorphic type variable. Such a
986 constraint indicates that the type variable can only be instantiated to a
987 type whose members supports the overloaded functions associated with the
990 An example of a type signature that includes such a constraint if the
991 signature of the \hs{sum} function, which sums the values in a vector:
993 sum :: Num a => [a|n] -> a
996 This type is again parameterized by \hs{a}, but it can only contain
997 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
998 the compiler knows that the addition (+) operator is defined for that
1001 A place where class constraints also play a role is in the size and range
1002 parameters of the \hs{Vector} and numeric types. The reason being that
1003 these parameters have to be limited to types that can represent
1004 \emph{natural} numbers. The complete type of for example the \hs{Vector}
1007 Natural n => Vector n a
1010 % \CLaSH's built-in numerical types are also instances of the \hs{Num}
1012 % so we can use the addition operator (and thus the \hs{sum}
1013 % function) with \hs{Signed} as well as with \hs{Unsigned}.
1015 \CLaSH\ supports both parametric polymorphism and ad-hoc polymorphism. Any
1016 function defined can have any number of unconstrained type parameters. A
1017 circuit designer can also specify his own type classes and corresponding
1018 instances. The \CLaSH\ compiler will infer the type of every polymorphic
1019 argument depending on how the function is applied. There is however one
1020 constraint: the top level function that is being translated can not have
1021 any polymorphic arguments. The arguments of the top-level can not be
1022 polymorphic as the function is never applied and consequently there is no
1023 way to determine the actual types for the type parameters.
1025 With regard to the built-in types, it should be noted that members of
1026 some of the standard Haskell type classes are supported as built-in
1027 functions. These include: the numerial operators of \hs{Num}, the equality
1028 operators of \hs{Eq}, and the comparison/order operators of \hs{Ord}.
1030 \subsection{Higher-order functions \& values}
1031 Another powerful abstraction mechanism in functional languages, is
1032 the concept of \emph{functions as a first class value}, also called
1033 \emph{higher-order functions}. This allows a function to be treated as a
1034 value and be passed around, even as the argument of another
1035 function. The following example should clarify this concept:
1038 \begin{minipage}{0.93\linewidth}
1039 %format not = "\mathit{not}"
1041 negateVector xs = map not xs
1044 \begin{minipage}{0.07\linewidth}
1046 \label{code:negatevector}
1050 The code above defines the \hs{negateVector} function, which takes a
1051 vector of booleans, \hs{xs}, and returns a vector where all the values are
1052 negated. It achieves this by calling the \hs{map} function, and passing it
1053 \emph{another function}, boolean negation, and the vector of booleans,
1054 \hs{xs}. The \hs{map} function applies the negation function to all the
1055 elements in the vector.
1057 The \hs{map} function is called a higher-order function, since it takes
1058 another function as an argument. Also note that \hs{map} is again a
1059 parametric polymorphic function: it does not pose any constraints on the
1060 type of the input vector, other than that its elements must have the same
1061 type as the first argument of the function passed to \hs{map}. The element
1062 type of the resulting vector is equal to the return type of the function
1063 passed, which need not necessarily be the same as the element type of the
1064 input vector. All of these characteristics can be inferred from the type
1065 signature belonging to \hs{map}:
1068 map :: (a -> b) -> [a|n] -> [b|n]
1071 So far, only functions have been used as higher-order values. In
1072 Haskell, there are two more ways to obtain a function-typed value:
1073 partial application and lambda abstraction. Partial application
1074 means that a function that takes multiple arguments can be applied
1075 to a single argument, and the result will again be a function (but
1076 that takes one argument less). As an example, consider the following
1077 expression, that adds one to every element of a vector:
1080 \begin{minipage}{0.93\linewidth}
1085 \begin{minipage}{0.07\linewidth}
1087 \label{code:partialapplication}
1091 Here, the expression \hs{(add 1)} is the partial application of the
1092 addition function to the value \hs{1}, which is again a function that
1093 adds one to its (next) argument. A lambda expression allows one to
1094 introduce an anonymous function in any expression. Consider the following
1095 expression, which again adds one to every element of a vector:
1098 \begin{minipage}{0.93\linewidth}
1100 map (\x -> x + 1) xs
1103 \begin{minipage}{0.07\linewidth}
1105 \label{code:lambdaexpression}
1109 Finally, not only built-in functions can have higher order arguments (such
1110 as the \hs{map} function), but any function defined in \CLaSH\ may have
1111 functions as arguments. This allows the circuit designer to use a
1112 powerful amount of code reuse. The only exception is again the top-level
1113 function: if a function-typed argument is not applied with an actual
1114 function, no hardware can be generated.
1116 An example of a common circuit where higher-order functions and partial
1117 application lead to a very concise and natural description is a crossbar.
1118 The code (\ref{code:crossbar}) for this example can be seen below:
1121 \begin{minipage}{0.93\linewidth}
1123 crossbar inputs selects = map (mux inputs) selects
1125 mux inp x = (inp ! x)
1128 \begin{minipage}{0.07\linewidth}
1130 \label{code:crossbar}
1134 The crossbar is polymorphic in the width of the input (defined by the
1135 length of \hs{inputs}), the width of the output (defined by the length of
1136 \hs{selects}), and the signal type (defined by the element type of
1137 \hs{inputs}). The type-checker can also automatically infer that
1138 \hs{selects} is a vector of \hs{Index} values due to the use of the vector
1139 indexing operator (\hs{!}).
1142 In a stateful design, the outputs depend on the history of the inputs, or
1143 the state. State is usually stored in registers, which retain their value
1144 during a clock cycle. As \CLaSH\ has to be able to describe more than
1145 simple combinational designs, there is a need for an abstraction mechanism
1148 An important property in Haskell, and in many other functional languages,
1149 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1152 \item given the same arguments twice, it should return the same value in
1154 \item that the function has no observable side-effects.
1156 % This purity property is important for functional languages, since it
1157 % enables all kinds of mathematical reasoning that could not be guaranteed
1158 % correct for impure functions.
1159 Pure functions are as such a perfect match for combinational circuits,
1160 where the output solely depends on the inputs. When a circuit has state
1161 however, it can no longer be simply described by a pure function.
1162 % Simply removing the purity property is not a valid option, as the
1163 % language would then lose many of it mathematical properties.
1164 In \CLaSH\ deals with the concept of state in pure functions by making
1165 the current state an additional argument of the function, and the
1166 updated state part of result. In this sense the descriptions made in
1167 \CLaSH\ are the combinational parts of a mealy machine.
1169 A simple example is adding an accumulator register to the earlier
1170 multiply-accumulate circuit, of which the resulting netlist can be seen in
1171 \Cref{img:mac-state}:
1174 \begin{minipage}{0.93\linewidth}
1176 macS (State c) a b = (State c', c')
1181 \begin{minipage}{0.07\linewidth}
1183 \label{code:macstate}
1187 Note that the \hs{macS} function returns both the new state and the value
1188 of the output port. The \hs{State} wrapper indicates which arguments are
1189 part of the current state, and what part of the output is part of the
1190 updated state. This aspect will also be reflected in the type signature of
1191 the function. Abstracting the state of a circuit in this way makes it very
1192 explicit: which variables are part of the state is completely determined
1193 by the type signature. This approach to state is well suited to be used in
1194 combination with the existing code and language features, such as all the
1195 choice elements, as state values are just normal values. Stateful
1196 descriptions are simulated using the recursive \hs{run} function:
1199 \begin{minipage}{0.93\linewidth}
1201 run f s (i : inps) = o : (run f s' inps)
1206 \begin{minipage}{0.07\linewidth}
1212 The \hs{(:)} operator is the list concatenation operator, where the
1213 left-hand side is the head of a list and the right-hand side is the
1214 remainder of the list. The \hs{run} function applies the function the
1215 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1216 first input value, \hs{i}. The result is the first output value, \hs{o},
1217 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1218 is then called with the updated state, \hs{s'}, and the rest of the
1219 inputs, \hs{inps}. For the time being, and in the context of this paper,
1220 it is assumed that there is one input per clock cycle. Also note how the
1221 order of the input, output, and state in the \hs{run} function corresponds
1222 with the order of the input, output and state of the \hs{macS} function
1226 \centerline{\includegraphics{mac-state.svg}}
1227 \caption{Stateful Multiply-Accumulate}
1228 \label{img:mac-state}
1232 As the \hs{run} function, the hardware description, and the test
1233 inputs are also valid Haskell, the complete simulation can be compiled to
1234 an executable binary by an optimizing Haskell compiler, or executed in an
1235 Haskell interpreter. Both simulation paths require less effort from a
1236 circuit designer than first translating the description to \VHDL\ and then
1237 running a \VHDL\ simulation; it is also very likely that both simulation
1238 paths are much faster.
1240 \section{The \CLaSH\ compiler}
1241 An important aspect in this research is the creation of the prototype
1242 compiler, which allows us to translate descriptions made in the \CLaSH\
1243 language as described in the previous section to synthesizable \VHDL.
1244 % , allowing a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1246 The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open-source Haskell
1247 compiler that also provides a high level API to most of its internals. The
1248 availability of this high-level API obviated the need to design many of the
1249 tedious parts of the prototype compiler, such as the parser, semantics
1250 checker, and especially the type-checker. These parts together form the
1251 front-end of the prototype compiler pipeline, as seen in
1252 \Cref{img:compilerpipeline}.
1256 \centerline{\includegraphics{compilerpipeline.svg}}
1257 \caption{\CLaSHtiny\ compiler pipeline}
1258 \label{img:compilerpipeline}
1262 The output of the \GHC\ front-end consists of the translation of the original
1263 Haskell description to \emph{Core}~\cite{Sulzmann2007}, which is a smaller,
1264 typed, functional language. This \emph{Core} language is relatively easy to
1265 process compared to the larger Haskell language. A description in \emph{Core}
1266 can still contain elements which have no direct translation to hardware, such
1267 as polymorphic types and function-valued arguments. Such a description needs
1268 to be transformed to a \emph{normal form}, which only contains elements that
1269 have a direct translation. The second stage of the compiler, the
1270 \emph{normalization} phase, exhaustively applies a set of
1271 \emph{meaning-preserving} transformations on the \emph{Core} description until
1272 this description is in a \emph{normal form}. This set of transformations
1273 includes transformations typically found in reduction systems and lambda
1274 calculus~\cite{lambdacalculus}, such as $\beta$-reduction and
1275 $\eta$-expansion. It also includes self-defined transformations that are
1276 responsible for the reduction of higher-order functions to `regular'
1277 first-order functions, and specializing polymorphic types to concrete types.
1279 The final step in the compiler pipeline is the translation to a \VHDL\
1280 \emph{netlist}, which is a straightforward process due to resemblance of a
1281 normalized description and a set of concurrent signal assignments. The
1282 end-product of the \CLaSH\ compiler is called a \VHDL\ \emph{netlist} as the
1283 result resembles an actual netlist description, and the fact that it is \VHDL\
1284 is only an implementation detail; the output could for example also be in
1288 \label{sec:usecases}
1289 \subsection{FIR Filter}
1290 As an example of a common hardware design where the relation between functional languages and mathematical functions, combined with the use of higher-order functions leads to a very natural description is a \acro{FIR} filter; which is basically the dot-product of two vectors:
1293 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1296 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1297 and a few previous input samples ($x$). Each of these multiplications
1298 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1299 filter is indeed equivalent to the equation of the dot-product, which is
1303 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1306 The equation for the dot-product is easily and directly implemented using
1307 higher-order functions:
1310 \begin{minipage}{0.93\linewidth}
1312 as *+* bs = fold (+) (zipWith (*) as bs)
1315 \begin{minipage}{0.07\linewidth}
1317 \label{code:dotproduct}
1321 The \hs{zipWith} function is very similar to the \hs{map} function seen
1322 earlier: It takes a function, two vectors, and then applies the function to
1323 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1324 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1326 The \hs{fold} function takes a binary function, a single vector, and applies
1327 the function to the first two elements of the vector. It then applies the
1328 function to the result of the first application and the next element in the
1329 vector. This continues until the end of the vector is reached. The result of
1330 the \hs{fold} function is the result of the last application. It is obvious
1331 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1332 \hs{fold (+)} function is summation.
1333 % Returning to the actual \acro{FIR} filter, we will slightly change the
1334 % equation describing it, so as to make the translation to code more obvious and
1335 % concise. What we do is change the definition of the vector of input samples
1336 % and delay the computation by one sample. Instead of having the input sample
1337 % received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1338 % sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1339 % to the following (note that this is completely equivalent to the original
1340 % equation, just with a different definition of $x$ that will better suit the
1341 % transformation to code):
1344 % y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1346 The complete definition of the \acro{FIR} filter in \CLaSH\ is:
1349 \begin{minipage}{0.93\linewidth}
1351 fir (State (xs,hs)) x =
1352 (State (shiftInto x xs,hs), (x +> xs) *+* hs)
1355 \begin{minipage}{0.07\linewidth}
1361 Where the vector \hs{xs} contains the previous input samples, the vector
1362 \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input
1363 sample. The concatenate operator (\hs{+>}) creates a new vector by placing the
1364 current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The
1365 code for the \hs{shiftInto} function, that adds the new input sample (\hs{x})
1366 to the list of previous input samples (\hs{xs}) and removes the oldest sample,
1370 \begin{minipage}{0.93\linewidth}
1372 shiftInto x xs = x +> init xs
1375 \begin{minipage}{0.07\linewidth}
1377 \label{code:shiftinto}
1381 Where the \hs{init} function returns all but the last element of a vector.
1382 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1383 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1387 \centerline{\includegraphics{4tapfir.svg}}
1388 \caption{4-taps \acrotiny{FIR} Filter}
1393 \subsection{Higher-order CPU}
1394 The following simple \acro{CPU} is an example of user-defined higher-order
1395 functions and pattern matching. The \acro{CPU} consists of four function
1396 units, of which three have a fixed function and one can perform certain less
1397 common operations. The \acro{CPU} contains a number of data sources, represented by the horizontal wires in \Cref{img:highordcpu}. These data sources offer the previous output of every function unit, along with the single data input of the \acro{CPU} and two fixed initialization values.
1398 Each of the function units has both its operands connected to all data
1399 sources, and can be programmed to select any data source for either
1400 operand. In addition, the leftmost function unit has an additional
1401 opcode input to select the operation it performs. The previous output of the
1402 rightmost function unit is the output of the entire \acro{CPU}.
1404 The code of the function unit (\ref{code:functionunit}), which arranges the operand selection for the function unit, is shown below. Note that the actual operation that takes place inside the function unit is supplied as the (higher-order) argument \hs{op}, which is a function that takes two arguments.
1407 \begin{minipage}{0.93\linewidth}
1409 fu op inputs (addr1, addr2) = regIn
1416 \begin{minipage}{0.07\linewidth}
1418 \label{code:functionunit}
1422 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
1423 the bitwise xor of its operands.
1426 \begin{minipage}{0.93\linewidth}
1428 data Opcode = Shift | Xor | Equal
1430 multiop :: Opcode -> Word -> Word -> Word
1431 multiop Shift a b = shift a b
1432 multiop Xor a b = xor a b
1433 multiop Equal a b | a == b = 1
1437 \begin{minipage}{0.07\linewidth}
1439 \label{code:multiop}
1443 The \acro{CPU} function (\ref{code:cpu}) ties everything together. It applies
1444 the function unit (\hs{fu}) to several operations, to create a different
1445 function unit each time. The first application is interesting, as it does not
1446 just pass a function to \hs{fu}, but a partial application of \hs{multiop}.
1447 This demonstrates how one function unit can effectively get extra inputs
1448 compared to the others.
1450 The vector \hs{inputs} is the set of data sources, which is passed to
1451 each function unit as a set of possible operants. The \acro{CPU} also receives
1452 a vector of address pairs, which are used by each function unit to select
1454 % The application of the function units to the \hs{inputs} and
1455 % \hs{addrs} arguments seems quite repetitive and could be rewritten to use
1456 % a combination of the \hs{map} and \hs{zipwith} functions instead.
1457 % However, the prototype compiler does not currently support working with
1458 % lists of functions, so a more explicit version of the code is given instead.
1461 \begin{minipage}{0.93\linewidth}
1463 type CpuState = State [Word | 4]
1465 cpu :: CpuState -> Word -> [(Index 6, Index 6) | 4]
1466 -> Opcode -> (CpuState, Word)
1467 cpu (State s) input addrs opc = (State s', out)
1469 s' = [ fu (multiop opc) inputs (addrs!0)
1470 , fu add inputs (addrs!1)
1471 , fu sub inputs (addrs!2)
1472 , fu mul inputs (addrs!3)
1474 inputs = 0 +> (1 +> (input +> s))
1478 \begin{minipage}{0.07\linewidth}
1484 While this is still a simple example, it could form the basis of an actual
1485 design, in which the same techniques can be reused.
1487 \section{Related work}
1488 This section describes the features of existing (functional) hardware
1489 description languages and highlights the advantages that this research has
1492 % Many functional hardware description languages have been developed over the
1493 % years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1494 % extension of Backus' \acro{FP} language to synchronous streams, designed
1495 % particularly for describing and reasoning about regular circuits. The
1496 % Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1497 % circuits, and has a particular focus on layout.
1499 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1500 functional language \acro{ML}, and has support for polymorphic types and
1501 higher-order functions. There is no direct simulation support for \acro{HML},
1502 so a description in \acro{HML} has to be translated to \VHDL\ and that the
1503 translated description can then be simulated in a \VHDL\ simulator. Certain
1504 aspects of HML, such as higher-order functions are however not supported by
1505 the \VHDL\ translator~\cite{HML3}. The \CLaSH\ compiler on the other hand can
1506 correctly translate all of the language constructs mentioned in this paper.
1509 \centerline{\includegraphics{highordcpu.svg}}
1510 \caption{CPU with higher-order Function Units}
1511 \label{img:highordcpu}
1515 Like the research presented in this paper, many functional hardware
1516 description languages have some sort of foundation in the functional
1517 programming language Haskell. Hawk~\cite{Hawk1} is a hardware modeling
1518 language embedded in Haskell and has sequential environments that make it
1519 easier to specify stateful computation. Hawk specifications can be simulated;
1520 to the best knowledge of the authors there is however no support for automated
1523 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1524 models. A designer can model systems using heterogeneous models of
1525 computation, which include continuous time, synchronous and untimed models of
1526 computation. Using so-called domain interfaces a designer can simulate
1527 electronic systems which have both analog as digital parts. ForSyDe has
1528 several backends including simulation and automated synthesis, though
1529 automated synthesis is restricted to the synchronous model of computation.
1530 Though ForSyDe offers higher-order functions and polymorphism, ForSyDe's
1531 choice elements are limited to \hs{if} and \hs{case} expressions. ForSyDe's
1532 explicit conversions, where function have to be wrapped in processes and
1533 processes have to be wrapped in systems, combined with the explicit
1534 instantiations of components, also makes ForSyDe more verbose than \CLaSH.
1536 Lava~\cite{Lava,kansaslava} is a hardware description language, embedded in
1537 Haskell, and focuses on the structural representation of hardware. Like
1538 \CLaSH, Lava has support for polymorphic types and higher-order functions.
1539 Besides support for simulation and circuit synthesis, Lava descriptions can be
1540 interfaced with formal method tools for formal verification. As discussed in
1541 the introduction, taking the embedded language approach does not allow for
1542 Haskell's choice elements to be captured within the circuit descriptions. In
1543 this respect \CLaSH\ differs from Lava, in that all of Haskell's choice
1544 elements, such as \hs{case}-expressions and pattern matching, are synthesized
1545 to choice elements in the eventual circuit. Consequently, descriptions
1546 containing rich control structures can be specified in a more user-friendly
1547 way in \CLaSH\ than possible within Lava, and are hence less error-prone.
1549 Bluespec~\cite{Bluespec} is a high-level synthesis language that features
1550 guarded atomic transactions and allows for the automated derivation of control
1551 structures based on these atomic transactions. Bluespec, like \CLaSH, supports
1552 polymorphic typing and function-valued arguments. Bluespec's syntax and
1553 language features \emph{had} their basis in Haskell. However, in order to
1554 appeal to the users of the traditional \acrop{HDL}, Bluespec has adapted
1555 imperative features and a syntax that resembles Verilog. As a result, Bluespec
1556 is (unnecessarily) verbose when compared to \CLaSH.
1558 The merits of polymorphic typing and function-valued arguments are now also
1559 recognized in the traditional \acrop{HDL}, exemplified by the new \VHDL-2008
1560 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to
1561 types and subprograms, allowing a designer to describe components with
1562 polymorphic ports and function-valued arguments. Note that the types and
1563 subprograms still require an explicit generic map, whereas types can be
1564 automatically inferred, and function-values can be automatically propagated
1565 by the \CLaSH\ compiler. There are also no (generally available) \VHDL\
1566 synthesis tools that currently support the \VHDL-2008 standard.
1568 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1570 % A functional language designed specifically for hardware design is
1571 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1572 % language called \acro{FL}~\cite{FL} to la
1574 % An example of a floating figure using the graphicx package.
1575 % Note that \label must occur AFTER (or within) \caption.
1576 % For figures, \caption should occur after the \includegraphics.
1577 % Note that IEEEtran v1.7 and later has special internal code that
1578 % is designed to preserve the operation of \label within \caption
1579 % even when the captionsoff option is in effect. However, because
1580 % of issues like this, it may be the safest practice to put all your
1581 % \label just after \caption rather than within \caption{}.
1583 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1584 % option should be used if it is desired that the figures are to be
1585 % displayed while in draft mode.
1589 %\includegraphics[width=2.5in]{myfigure}
1590 % where an .eps filename suffix will be assumed under latex,
1591 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1592 % via \DeclareGraphicsExtensions.
1593 %\caption{Simulation Results}
1597 % Note that IEEE typically puts floats only at the top, even when this
1598 % results in a large percentage of a column being occupied by floats.
1601 % An example of a double column floating figure using two subfigures.
1602 % (The subfig.sty package must be loaded for this to work.)
1603 % The subfigure \label commands are set within each subfloat command, the
1604 % \label for the overall figure must come after \caption.
1605 % \hfil must be used as a separator to get equal spacing.
1606 % The subfigure.sty package works much the same way, except \subfigure is
1607 % used instead of \subfloat.
1609 %\begin{figure*}[!t]
1610 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1611 %\label{fig_first_case}}
1613 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1614 %\label{fig_second_case}}}
1615 %\caption{Simulation results}
1619 % Note that often IEEE papers with subfigures do not employ subfigure
1620 % captions (using the optional argument to \subfloat), but instead will
1621 % reference/describe all of them (a), (b), etc., within the main caption.
1624 % An example of a floating table. Note that, for IEEE style tables, the
1625 % \caption command should come BEFORE the table. Table text will default to
1626 % \footnotesize as IEEE normally uses this smaller font for tables.
1627 % The \label must come after \caption as always.
1630 %% increase table row spacing, adjust to taste
1631 %\renewcommand{\arraystretch}{1.3}
1632 % if using array.sty, it might be a good idea to tweak the value of
1633 % \extrarowheight as needed to properly center the text within the cells
1634 %\caption{An Example of a Table}
1635 %\label{table_example}
1637 %% Some packages, such as MDW tools, offer better commands for making tables
1638 %% than the plain LaTeX2e tabular which is used here.
1639 %\begin{tabular}{|c||c|}
1649 % Note that IEEE does not put floats in the very first column - or typically
1650 % anywhere on the first page for that matter. Also, in-text middle ("here")
1651 % positioning is not used. Most IEEE journals/conferences use top floats
1652 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1653 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1654 % command of the stfloats package.
1658 \section{Conclusion}
1659 This research demonstrates once more that functional languages are well suited
1660 for hardware descriptions: function applications provide an elegant notation
1661 for component instantiation. While circuit descriptions made in \CLaSH\ are
1662 very concise when compared to other (traditional) \acrop{HDL}, their intended
1663 functionality remains clear. Where \CLaSH\ goes beyond the existing
1664 (functional) hardware descriptions languages is the inclusion of advanced
1665 choice elements, such as pattern matching and guards, that are well suited to
1666 describe the conditional assignments in control-oriented circuits. Besides
1667 being able to translate these basic constructs to synthesizable \VHDL, the
1668 prototype compiler can also correctly translate descriptions that contain both
1669 polymorphic types and user-defined higher-order functions.
1671 % Where recent functional hardware description languages have mostly opted to
1672 % embed themselves in an existing functional language, this research features
1673 % a `true' compiler. As a result there is a clear distinction between
1674 % compile-time and run-time, which allows a myriad of choice constructs to be
1675 % part of the actual circuit description; a feature the embedded hardware
1676 % description languages do not offer.
1678 Besides simple circuits such as variants of both the \acro{FIR} filter and
1679 the higher-order \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler
1680 has also been able to translate non-trivial functional descriptions such as a
1681 streaming reduction circuit~\cite{reductioncircuit} for floating point
1684 \section{Future Work}
1685 The choice of describing state explicitly as extra arguments and results can
1686 be seen as a mixed blessing. Even though the description that use state are
1687 usually very clear, one finds that distributing and collecting substate can
1688 become tedious and even error-prone. Removing the required boilerplate for
1689 distribution and collection, or finding a more suitable abstraction mechanism
1690 for state would make \CLaSH\ easier to use.
1692 The transformations in normalization phase of the prototype compiler are
1693 developed in an ad-hoc manner, which makes the existence of many desirable
1694 properties unclear. Such properties include whether the complete set of
1695 transformations will always lead to a normal form or if the normalization
1696 process always terminates. Though extensive use of the compiler suggests that
1697 these properties usually hold, they have not been formally proven. A
1698 systematic approach to defining the set of transformations allows one to proof
1699 that the earlier mentioned properties do indeed exist.
1701 % conference papers do not normally have an appendix
1704 % use section* for acknowledgement
1705 % \section*{Acknowledgment}
1707 % The authors would like to thank...
1709 % trigger a \newpage just before the given reference
1710 % number - used to balance the columns on the last page
1711 % adjust value as needed - may need to be readjusted if
1712 % the document is modified later
1713 % \IEEEtriggeratref{14}
1714 % The "triggered" command can be changed if desired:
1715 %\IEEEtriggercmd{\enlargethispage{-5in}}
1717 % references section
1719 % can use a bibliography generated by BibTeX as a .bbl file
1720 % BibTeX documentation can be easily obtained at:
1721 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1722 % The IEEEtran BibTeX style support page is at:
1723 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1724 \bibliographystyle{IEEEtran}
1725 % argument is your BibTeX string definitions and bibliography database(s)
1726 \bibliography{clash}
1728 % <OR> manually copy in the resultant .bbl file
1729 % set second argument of \begin to the number of references
1730 % (used to reserve space for the reference number labels box)
1731 % \begin{thebibliography}{1}
1733 % \bibitem{IEEEhowto:kopka}
1734 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1735 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1737 % \end{thebibliography}
1745 % vim: set ai sw=2 sts=2 expandtab: