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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 done by a
476 Haskell compiler allowing high-speed simulation and analysis.
478 % \CLaSH\ supports stateful descriptions by explicitly making the current
479 % state an argument of the function, and the updated state part of the result.
480 % This makes \CLaSH\ descriptions in essence the combinational parts of a
483 % IEEEtran.cls defaults to using nonbold math in the Abstract.
484 % This preserves the distinction between vectors and scalars. However,
485 % if the conference you are submitting to favors bold math in the abstract,
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487 % of the abstract to achieve this. Many IEEE journals/conferences frown on
488 % math in the abstract anyway.
495 % For peer review papers, you can put extra information on the cover
497 % \ifCLASSOPTIONpeerreview
498 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
501 % For peerreview papers, this IEEEtran command inserts a page break and
502 % creates the second title. It will be ignored for other modes.
503 \IEEEpeerreviewmaketitle
505 \section{Introduction}
506 Hardware description languages (\acrop{HDL}) have not allowed the productivity
507 of hardware engineers to keep pace with the development of chip technology.
508 While traditional \acrop{HDL}, like \VHDL~\cite{VHDL2008} and
509 Verilog~\cite{Verilog}, are very good at describing detailed hardware
510 properties such as timing behavior, they are generally cumbersome in
511 expressing the higher-level abstractions needed for today's large and complex
512 circuit designs. In an attempt to raise the abstraction level of the
513 descriptions, a great number of approaches based on functional languages has
514 been proposed \cite{Cardelli1981,muFP,DAISY,T-Ruby,HML2,Hydra,Hawk1,Lava,
515 Wired,ForSyDe1,reFLect}. The idea of using functional languages for hardware
516 descriptions started in the early 1980s \cite{Cardelli1981,muFP,DAISY}, a
517 time which also saw the birth of the currently popular \acrop{HDL}, such as
518 \VHDL. Functional languages are especially well suited to describe hardware
519 because combinational circuits can be directly modeled as mathematical
520 functions and functional languages are very good at describing and composing
523 In an attempt to ease the prototyping process of the language, such as
524 creating all the required tooling like parsers and type-checkers, many
525 functional \acrop{HDL} \cite{Hydra,Hawk1,Lava,Wired} are embedded as a domain
526 specific language (\acro{DSL}) within the functional language Haskell
527 \cite{Haskell}. This means that a developer is given a library of Haskell
528 functions and types that together form the language primitives of the
529 \acro{DSL}. The primitive functions used to describe a circuit do not actually
530 process any signals, they instead compose a large domain-specific graph
531 (which is usually hidden from the designer). This graph is then further
532 processed by an embedded circuit compiler which can perform e.g. simulation or
533 synthesis. As Haskell's choice elements (\hs{case}-expressions,
534 pattern-matching, etc.) are evaluated at the time the domain-specific graph is
535 being build, they are no longer visible to the embedded compiler that
536 processes the datatype. Consequently, it is impossible to capture Haskell's
537 choice elements within a circuit description when taking the embedded language
538 approach. This does not mean that circuits specified in an embedded language
539 can not contain choice, just that choice elements only exists as functions,
540 e.g. a multiplexer function, and not as syntactic elements of the language
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 Haskell, such as polymorphic typing and higher-order
548 functions, 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
560 and research presented in this paper. A circuit designer describes the
561 behavior of the hardware between clock cycles. Many functional \acrop{HDL}
562 model signals as a stream of all values over time; state is then modeled as a
563 delay on this stream of values. Descriptions presented in this research make
564 the current state an additional input and the updated state a part of their
565 output. This abstraction of state and time limits the descriptions to
566 synchronous hardware, there is however room within the language to eventually
567 add a different abstraction mechanism that will allow for the modeling of
568 asynchronous systems.
570 Likewise as with the traditional \acrop{HDL}, descriptions made in a functional \acro{HDL} must eventually be converted into a netlist. This research also features a prototype compiler, which has the same name as the language: \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES} Language for Synchronous Hardware, where \acrotiny{CAES} is the acronyom of our chair.} (pronounced: clash). This compiler converts the Haskell code to equivalently behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist format by an (optimizing) \VHDL\ synthesis tool.
572 To the best knowledge of the authors, \CLaSH\ is the only (functional)
573 \acro{HDL} that allows circuit specification to be written in a very concise
574 way and at the same time support such advanced features as polymorphic typing,
575 user-defined higher-order functions and pattern matching.
577 \section{Hardware description in Haskell}
578 This section describes the basic language elements of \CLaSH\ and the support
579 of these elements within the \CLaSH\ compiler. In various subsections, the
580 relation between the language elements and their eventual netlist
581 representation is also highlighted.
583 \subsection{Function application}
584 Two basic elements of a functional program are functions and function
585 application. These have a single obvious translation to a netlist format:
587 \item every function is translated to a component,
588 \item every function argument is translated to an input port,
589 \item the result value of a function is translated to an output port,
591 \item function applications are translated to component instantiations.
593 The result value can have a composite type (such as a tuple), so having
594 just a single result value does not pose any limitation. The actual
595 arguments of a function application are assigned to signals, which are
596 then mapped to the corresponding input ports of the component. The output
597 port of the function is also mapped to a signal, which is used as the
598 result of the application itself. Since every top level function generates
599 its own component, the hierarchy of function calls is reflected in the
600 final netlist. %, creating a hierarchical description of the hardware.
601 % The separation in different components makes it easier for a developer
602 % to understand and possibly hand-optimize the resulting \VHDL\ output of
603 % the \CLaSH\ compiler.
605 The short example below (\ref{code:mac}) gives a demonstration of
606 the conciseness that can be achieved with \CLaSH\ when compared with
607 other (more traditional) \acrop{HDL}. The example is a combinational
608 multiply-accumulate circuit that works for \emph{any} word length (this
609 type of polymorphism will be further elaborated in
610 \Cref{sec:polymorhpism}). The corresponding netlist is depicted in
614 \begin{minipage}{0.93\linewidth}
616 mac a b c = add (mul a b) c
619 \begin{minipage}{0.07\linewidth}
626 \centerline{\includegraphics{mac.svg}}
627 \caption{Combinational Multiply-Accumulate}
632 The use of a composite result value is demonstrated in the next example
633 (\ref{code:mac-composite}), where the multiply-accumulate circuit not only
634 returns the accumulation result, but also the intermediate multiplication
635 result (see \Cref{img:mac-comb-composite}, where the double arrow suggests
636 the composite output).
639 \begin{minipage}{0.93\linewidth}
641 mac a b c = (z, add z c)
646 \begin{minipage}{0.07\linewidth}
648 \label{code:mac-composite}
655 \centerline{\includegraphics{mac-nocurry.svg}}
656 \caption{Combinational Multiply-Accumulate (composite output)}
657 \label{img:mac-comb-composite}
662 In Haskell, choice can be achieved by a large set of syntactic elements,
663 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
664 pattern matching, and guards. The most general of these are the \hs{case}
665 expressions (\hs{if} expressions can be directly translated to
666 \hs{case} expressions). When transforming a \CLaSH\ description to a
667 netlist, a \hs{case} expression is translated to a multiplexer. The
668 control value of the \hs{case} expression is fed into a number of
669 comparators, and their combined output forms the selection port of the
670 multiplexer. The result of each alternative in the \hs{case} expression is
671 linked to the corresponding input port of the multiplexer.
672 % A \hs{case} expression can in turn simply be translated to a conditional
673 % assignment in \VHDL, where the conditions use equality comparisons
674 % against the constructors in the \hs{case} expressions.
676 % Two versions of a contrived example are displayed below, the first
677 % (\ref{lst:code3}) using a \hs{case} expression and the second
678 % (\ref{lst:code4}) using an \hs{if-then-else} expression. Both examples
679 % sum two values when they are equal or non-equal (depending on the given
680 % predicate, the \hs{pred} variable) and return 0 otherwise.
682 A code example (\ref{code:counter1}) that uses a \hs{case} expression and
683 \hs{if-then-else} expressions is shown below. The function counts up or
684 down depending on the \hs{direction} variable, and has a \hs{bound}
685 variable that determines both the upper bound and wrap-around point of the
686 counter. The \hs{direction} variable is of the following, user-defined,
687 enumeration datatype:
690 data Direction = Up | Down
693 The naive netlist corresponding to this example is depicted in
694 \Cref{img:counter}. Note that the \hs{direction} variable is only
695 compared to \hs{Up}, as an inequality immediately implies that
696 \hs{direction} is \hs{Down} (as derived by the compiler).
699 \begin{minipage}{0.93\linewidth}
701 counter bound direction x = case direction of
702 Up -> if x < bound then
705 Down -> if x > 0 then
710 \begin{minipage}{0.07\linewidth}
712 \label{code:counter1}
717 % \begin{minipage}{0.93\linewidth}
720 % if pred == Equal then
721 % if a == b then a + b else 0
723 % if a != b then a + b else 0
726 % \begin{minipage}{0.07\linewidth}
734 % \centerline{\includegraphics{choice-case.svg}}
735 % \caption{Choice - sumif}
741 \centerline{\includegraphics{counter.svg}}
742 \caption{Counter netlist}
747 A user-friendly and also very powerful form of choice that is not found in
748 the traditional hardware description languages is pattern matching. A
749 function can be defined in multiple clauses, where each clause corresponds
750 to a pattern. When an argument matches a pattern, the corresponding clause
751 will be used. Expressions can also contain guards, where the expression is
752 only executed if the guard evaluates to true, and continues with the next
753 clause if the guard evaluates to false. Like \hs{if-then-else}
754 expressions, pattern matching and guards have a (straightforward)
755 translation to \hs{case} expressions and can as such be mapped to
756 multiplexers. A second version (\ref{code:counter2}) of the earlier
757 example, now using both pattern matching and guards, can be seen below.
758 The guard is the expression that follows the vertical bar (\hs{|}) and
759 precedes the assignment operator (\hs{=}). The \hs{otherwise} guards
760 always evaluate to \hs{true}.
762 The second version corresponds to the same naive netlist representation
763 (\Cref{img:counter}) as the earlier example.
766 \begin{minipage}{0.93\linewidth}
768 counter bound Up x | x < bound = x + 1
771 counter bound Down x | x > 0 = x - 1
775 \begin{minipage}{0.07\linewidth}
777 \label{code:counter2}
782 % \centerline{\includegraphics{choice-ifthenelse}}
783 % \caption{Choice - \emph{if-then-else}}
788 Haskell is a statically-typed language, meaning that the type of a
789 variable or function is determined at compile-time. Not all of
790 Haskell's typing constructs have a clear translation to hardware, this
791 section therefor only deals with the types that do have a clear
792 correspondence to hardware. The translatable types are divided into two
793 categories: \emph{built-in} types and \emph{user-defined} types. Built-in
794 types are those types for which a fixed translation is defined within the
795 \CLaSH\ compiler. The \CLaSH\ compiler has generic translation rules to
796 translate the user-defined types, which are described later on.
798 The \CLaSH\ compiler is able to infer unspecified (polymorphic) types,
799 meaning that a developer does not have to annotate every function with a
800 type signature. Given that the top-level entity of a circuit design is
801 annotated with specific types, the \CLaSH\ compiler can specialize
802 polymorphic functions to functions with specific types.
804 % Translation of two most basic functional concepts has been
805 % discussed: function application and choice. Before looking further
806 % into less obvious concepts like higher-order expressions and
807 % polymorphism, the possible types that can be used in hardware
808 % descriptions will be discussed.
810 % Some way is needed to translate every value used to its hardware
811 % equivalents. In particular, this means a hardware equivalent for
812 % every \emph{type} used in a hardware description is needed.
814 % The following types are \emph{built-in}, meaning that their hardware
815 % translation is fixed into the \CLaSH\ compiler. A designer can also
816 % define his own types, which will be translated into hardware types
817 % using translation rules that are discussed later on.
819 \subsubsection{Built-in types}
820 The following types have fixed translations defined within the \CLaSH\
824 the most basic type available. It can have two values:
825 \hs{Low} or \hs{High}.
826 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
828 this is a basic logic type. It can have two values: \hs{True}
830 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
831 % type (where a value of \hs{True} corresponds to a value of
833 Supporting the Bool type is required in order to support the
834 \hs{if-then-else} expression.
835 \item[\bf{Signed}, \bf{Unsigned}]
836 these are types to represent integers, and both are parametrizable in
837 their size. The overflow behavior of the numeric operators defined for
838 these types is \emph{wrap-around}.
839 % , so you can define an unsigned word of 32 bits wide as follows:
842 % type Word32 = SizedWord D32
845 % Here, a type synonym \hs{Word32} is defined that is equal to the
846 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
847 % \hs{D32} is the \emph{type level representation} of the decimal
848 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
849 % types are translated to the \VHDL\ \texttt{unsigned} and
850 % \texttt{signed} respectively.
852 this type can contain elements of any type and has a static length.
853 The \hs{Vector} type constructor takes two arguments: the length of
854 the vector and the type of the elements contained in it. The
855 short-hand notation used for the vector type in the rest of paper is:
856 \hs{[a|n]}, where \hs{a} is the element type, and \hs{n} is the length
858 % Note that this is a notation used in this paper only, vectors are
859 % slightly more verbose in real \CLaSH\ descriptions.
860 % The state type of an 8 element register bank would then for example
864 % type RegisterState = Vector D8 Word32
867 % Here, a type synonym \hs{RegisterState} is defined that is equal to
868 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
869 % type level representation of the decimal number 8) and \hs{Word32}
870 % (The 32 bit word type as defined above). In other words, the
871 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
872 % vector is translated to a \VHDL\ array type.
874 the main purpose of the \hs{Index} type is to be used as an index into
875 a \hs{Vector}, and has an integer range from zero to a specified upper
877 % This means that its range is not limited to powers of two, but
879 If a value of this type exceeds either bounds, an error will be thrown
882 % \comment{TODO: Perhaps remove this example?} To define an index for
883 % the 8 element vector above, we would do:
886 % type RegisterIndex = RangedWord D7
889 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
890 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
891 % other words, this defines an unsigned word with values from
892 % 0 to 7 (inclusive). This word can be be used to index the
893 % 8 element vector \hs{RegisterState} above. This type is translated
894 % to the \texttt{unsigned} \VHDL type.
897 \subsubsection{User-defined types}
898 % There are three ways to define new types in Haskell: algebraic
899 % data-types with the \hs{data} keyword, type synonyms with the \hs{type}
900 % keyword and datatype renaming constructs with the \hs{newtype} keyword.
901 % \GHC\ offers a few more advanced ways to introduce types (type families,
902 % existential typing, {\acro{GADT}}s, etc.) which are not standard
903 % Haskell. As it is currently unclear how these advanced type constructs
904 % correspond to hardware, they are for now unsupported by the \CLaSH\
906 A designer may define a completely new type by an algebraic datatype
907 declaration using the \hs{data} keyword. Type synonyms can be introduced
908 using the \hs{type} keyword.
909 % Only an algebraic datatype declaration actually introduces a
910 % completely new type. Type synonyms and type renaming only define new
911 % names for existing types, where synonyms are completely interchangeable
912 % and a type renaming requires an explicit conversion.
913 Type synonyms do not need any particular translation, as a synonym will
914 use the same representation as the original type.
916 Algebraic datatypes can be categorized as follows:
918 \item[\bf{Single constructor}]
919 datatypes with a single constructor with one or more fields allow
920 values to be packed together in a record-like structure. Haskell's
921 built-in tuple types are also defined as single constructor algebraic
922 types (using a bit of syntactic sugar). An example of a single
923 constructor type with multiple fields is the following pair of
926 data IntPair = IntPair Int Int
928 % These types are translated to \VHDL\ record types, with one field
929 % for every field in the constructor.
930 \item[\bf{Multiple constructors, No fields}]
931 datatypes with multiple constructors, but without any
932 fields are essentially enumeration types.
933 % Note that Haskell's \hs{Bool} type is also defined as an enumeration
934 % type, but that there is a fixed translation for that type within the
936 An example of an enumeration type definition is:
938 data TrafficLight = Red | Orange | Green
940 % These types are translated to \VHDL\ enumerations, with one
941 % value for each constructor. This allows references to these
942 % constructors to be translated to the corresponding enumeration
944 \item[\bf{Multiple constructors with fields}]
945 datatypes with multiple constructors, where at least
946 one of these constructors has one or more fields are currently not
947 supported. Additional research is required to optimize the overlap of
948 fields belonging to the different constructors.
951 \subsection{Polymorphism}\label{sec:polymorhpism}
952 A powerful feature of some programming languages is polymorphism, it
953 allows a function to handle values of different data types in a uniform
954 way. Haskell supports \emph{parametric polymorphism}, meaning that
955 functions can be written without mentioning specific types, and they can
956 be used for arbitrary types.
958 As an example of a parametric polymorphic function, consider the type of
959 the following \hs{first} function, which returns the first element of a
960 tuple:\footnote{The \hs{::} operator is used to annotate a function
967 This type is parameterized in \hs{a} and \hs{b}, which can both
968 represent any type at all, as long as that type is supported by the
969 \CLaSH\ compiler. This means that \hs{first} works for any tuple,
970 regardless of what elements it contains. This kind of polymorphism is
971 extremely useful in hardware designs, for example when routing signals
972 without knowing their exact type, or specifying vector operations that
973 work on vectors of any length and element type. Polymorphism also plays an
974 important role in most higher order functions, as will be shown in the
977 % Another type of polymorphism is \emph{ad-hoc
978 % polymorphism}~\cite{polymorphism}, which refers to polymorphic
979 % functions which can be applied to arguments of different types, but
980 % which behave differently depending on the type of the argument to which
981 % they are applied. In Haskell, ad-hoc polymorphism is achieved through
982 % the use of \emph{type classes}, where a class definition provides the
983 % general interface of a function, and class \emph{instances} define the
984 % functionality for the specific types. An example of such a type class is
985 % the \hs{Num} class, which contains all of Haskell's numerical
986 % operations. A designer can make use of this ad-hoc polymorphism by
987 % adding a \emph{constraint} to a parametrically polymorphic type
988 % variable. Such a constraint indicates that the type variable can only be
989 % instantiated to a type whose members supports the overloaded functions
990 % associated with the type class.
992 Another type of polymorphism is \emph{ad-hoc polymorphism}, which refers
993 to function that can be applied to arguments of a limited set to types.
994 Furthermore, how such functions work may depend on the type of their
995 arguments. For example, addition only works for numeric types, and it
996 works differently for e.g. integers and complex numbers.
998 In Haskell, ad-hoc polymorphism is achieved through the use of \emph{type
999 classes}, where a class definition provides the general interface of a
1000 function, and class \emph{instances} define the functionality for the
1001 specific types. For example, all numeric operators are gathered in the
1002 \hs{Num} class, so every type that wants to use those operators must be
1003 made an instance of \hs{Num}.
1005 By prefixing a type signature with class constraints, the constrained type
1006 parameters are forced to belong to that type class. For example, the
1007 arguments of the \hs{add} function must belong to the \hs{Num} type class
1008 because the \hs{add} function adds them with the (+) operator:
1011 add :: Num a => a -> a -> a
1015 % An example of a type signature that includes such a constraint if the
1016 % signature of the \hs{sum} function, which sums the values in a vector:
1018 % sum :: Num a => [a|n] -> a
1021 % This type is again parameterized by \hs{a}, but it can only contain
1022 % types that are \emph{instances} of the \emph{type class} \hs{Num}, so
1023 % that the compiler knows that the addition (+) operator is defined for
1026 % A place where class constraints also play a role is in the size and
1027 % range parameters of the \hs{Vector} and numeric types. The reason being
1028 % that these parameters have to be limited to types that can represent
1029 % \emph{natural} numbers. The complete type of for example the \hs{Vector}
1032 % Natural n => Vector n a
1035 % \CLaSH's built-in numerical types are also instances of the \hs{Num}
1037 % so we can use the addition operator (and thus the \hs{sum}
1038 % function) with \hs{Signed} as well as with \hs{Unsigned}.
1040 \CLaSH\ supports both parametric polymorphism and ad-hoc polymorphism. A
1041 circuit designer can specify his own type classes and corresponding
1042 instances. The \CLaSH\ compiler will infer the type of every polymorphic
1043 argument depending on how the function is applied. There is however one
1044 constraint: the top level function that is being translated can not have
1045 polymorphic arguments. The arguments of the top-level can not be
1046 polymorphic as there is no way to infer the \emph{specific} types of the
1049 With regard to the built-in types, it should be noted that members of
1050 some of the standard Haskell type classes are supported as built-in
1051 functions. These include: the numerial operators of \hs{Num}, the equality
1052 operators of \hs{Eq}, and the comparison (order) operators of \hs{Ord}.
1054 \subsection{Higher-order functions \& values}
1055 Another powerful abstraction mechanism in functional languages, is
1056 the concept of \emph{functions as a first class value} and
1057 \emph{higher-order functions}. These concepts allows a function to be
1058 treated as a value and be passed around, even as the argument of another
1059 function. The following example clarifies this concept:
1062 \begin{minipage}{0.93\linewidth}
1063 %format not = "\mathit{not}"
1065 negate{-"\!\!\!"-}Vector xs = map not xs
1068 \begin{minipage}{0.07\linewidth}
1070 \label{code:negatevector}
1074 The code above defines the \hs{negate{-"\!\!\!"-}Vector} function, which
1075 takes a vector of booleans, \hs{xs}, and returns a vector where all the
1076 values are negated. It achieves this by calling the \hs{map} function, and
1077 passing it another \emph{function}, boolean negation, and the vector of
1078 booleans, \hs{xs}. The \hs{map} function applies the negation function to
1079 all the elements in the vector.
1081 The \hs{map} function is called a higher-order function, since it takes
1082 another function as an argument. Also note that \hs{map} is again a
1083 parametric polymorphic function: it does not pose any constraints on the
1084 type of the input vector, other than that its elements must have the same
1085 type as the first argument of the function passed to \hs{map}. The element
1086 type of the resulting vector is equal to the return type of the function
1087 passed, which need not necessarily be the same as the element type of the
1088 input vector. All of these characteristics can be inferred from the type
1089 signature belonging to \hs{map}:
1092 map :: (a -> b) -> [a|n] -> [b|n]
1095 In Haskell, there are two more ways to obtain a function-typed value:
1096 partial application and lambda abstraction. Partial application means that
1097 a function that takes multiple arguments can be applied to a single
1098 argument, and the result will again be a function, but takes one argument
1099 less. As an example, consider the following expression, that adds one to
1100 every element of a vector:
1103 \begin{minipage}{0.93\linewidth}
1108 \begin{minipage}{0.07\linewidth}
1110 \label{code:partialapplication}
1114 Here, the expression \hs{(add 1)} is the partial application of the
1115 addition function to the value \hs{1}, which is again a function that
1116 adds 1 to its (next) argument.
1118 A lambda expression allows a designer to introduce an anonymous function
1119 in any expression. Consider the following expression, which again adds 1
1120 to every element of a vector:
1123 \begin{minipage}{0.93\linewidth}
1125 map (\x -> x + 1) xs
1128 \begin{minipage}{0.07\linewidth}
1130 \label{code:lambdaexpression}
1134 Finally, not only built-in functions can have higher order arguments (such
1135 as the \hs{map} function), but any function defined in \CLaSH\ may have
1136 functions as arguments. This allows the circuit designer to apply a
1137 large amount of code reuse. The only exception is again the top-level
1138 function: if a function-typed argument is not instantiated with an actual
1139 function, no hardware can be generated.
1141 An example of a common circuit where higher-order functions and partial
1142 application lead to a very concise and natural description is a crossbar.
1143 The code (\ref{code:crossbar}) for this example can be seen below:
1146 \begin{minipage}{0.93\linewidth}
1148 crossbar inputs selects = map (mux inputs) selects
1150 mux inp x = (inp ! x)
1153 \begin{minipage}{0.07\linewidth}
1155 \label{code:crossbar}
1159 The the \hs{crossbar} function selects those values from \hs{inputs} that
1160 are indicated by the indexes in the vector \hs{selects}. The crossbar is
1161 polymorphic in the width of the input (defined by the length of
1162 \hs{inputs}), the width of the output (defined by the length of
1163 \hs{selects}), and the signal type (defined by the element type of
1164 \hs{inputs}). The type-checker can also automatically infer that
1165 \hs{selects} is a vector of \hs{Index} values due to the use of the vector
1166 indexing operator (\hs{!}).
1169 In a stateful design, the outputs depend on the history of the inputs, or
1170 the state. State is usually stored in registers, which retain their value
1171 during a clock cycle. As \CLaSH\ has to be able to describe more than
1172 plain combinational designs, there is a need for an abstraction mechanism
1175 An important property in Haskell, and in many other functional languages,
1176 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1179 \item given the same arguments twice, it should return the same value in
1181 \item that the function has no observable side-effects.
1183 % This purity property is important for functional languages, since it
1184 % enables all kinds of mathematical reasoning that could not be guaranteed
1185 % correct for impure functions.
1186 Pure functions are as such a perfect match for combinational circuits,
1187 where the output solely depends on the inputs. When a circuit has state
1188 however, it can no longer be described by a pure function.
1189 % Simply removing the purity property is not a valid option, as the
1190 % language would then lose many of it mathematical properties.
1191 \CLaSH\ deals with the concept of state by making the current state an
1192 additional argument of the function, and the updated state part of the
1193 result. In this sense the descriptions made in \CLaSH\ are the
1194 combinational parts of a mealy machine.
1196 A simple example is adding an accumulator register to the earlier
1197 multiply-accumulate circuit, of which the resulting netlist can be seen in
1198 \Cref{img:mac-state}:
1201 \begin{minipage}{0.93\linewidth}
1203 macS (State c) a b = (State c', c')
1208 \begin{minipage}{0.07\linewidth}
1210 \label{code:macstate}
1214 Note that the \hs{macS} function returns both the new state and the value
1215 of the output port. The \hs{State} wrapper indicates which arguments are
1216 part of the current state, and what part of the output is part of the
1217 updated state. This aspect will also be reflected in the type signature of
1218 the function. Abstracting the state of a circuit in this way makes it very
1219 explicit: which variables are part of the state is completely determined
1220 by the type signature. This approach to state is well suited to be used in
1221 combination with the existing code and language features, such as all the
1222 choice elements, as state values are just normal values from Haskell's
1223 point of view. Stateful descriptions are simulated using the recursive
1227 \begin{minipage}{0.93\linewidth}
1229 run f s (i : inps) = o : (run f s' inps)
1234 \begin{minipage}{0.07\linewidth}
1240 The \hs{(:)} operator is the list concatenation operator, where the
1241 left-hand side is the head of a list and the right-hand side is the
1242 remainder of the list. The \hs{run} function applies the function the
1243 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1244 first input value, \hs{i}. The result is the first output value, \hs{o},
1245 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1246 is then called with the updated state, \hs{s'}, and the rest of the
1247 inputs, \hs{inps}. For the time being, and in the context of this paper,
1248 it is assumed that there is one input per clock cycle. Note that the order
1249 of \hs{s',o,s,i} in the where clause of the \hs{run} functions corresponds
1250 with the order of the input, output and state of the \hs{macS} function
1251 described earlier. Thus, in Haskell the expression \hs{run macS 0 inputs}
1252 simulates \hs{macS} on \hs{inputs} starting with the value \hs{0}
1255 \centerline{\includegraphics{mac-state.svg}}
1256 \caption{Stateful Multiply-Accumulate}
1257 \label{img:mac-state}
1261 The complete simulation can be compiled to an executable binary by a
1262 Haskell compiler, or executed in an Haskell interpreter. Both
1263 simulation paths require less effort from a circuit designer than first
1264 translating the description to \VHDL\ and then running a \VHDL\
1265 simulation; it is also very likely that both simulation paths are much
1268 \section{The \CLaSH\ compiler}
1269 An important aspect in this research is the creation of the prototype
1270 compiler, which allows us to translate descriptions made in the \CLaSH\
1271 language as described in the previous section to synthesizable \VHDL.
1272 % , allowing a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1274 The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open-source Haskell
1275 compiler that also provides a high level \acro{API} to most of its internals.
1276 The availability of this high-level \acro{API} obviated the need to design
1277 many of the tedious parts of the prototype compiler, such as the parser,
1278 semantics checker, and especially the type-checker. These parts together form
1279 the front-end of the prototype compiler pipeline, as seen in
1280 \Cref{img:compilerpipeline}.
1284 \centerline{\includegraphics{compilerpipeline.svg}}
1285 \caption{\CLaSHtiny\ compiler pipeline}
1286 \label{img:compilerpipeline}
1290 The output of the \GHC\ front-end consists of the translation of the original
1291 Haskell description to \emph{Core}~\cite{Sulzmann2007}, which is a small
1292 typed functional language. This \emph{Core} language is relatively easy to
1293 process compared to the larger Haskell language. A description in \emph{Core}
1294 can still contain elements which have no direct translation to hardware, such
1295 as polymorphic types and function-valued arguments. Such a description needs
1296 to be transformed to a \emph{normal form}, which only contains elements that
1297 have a direct translation. The second stage of the compiler, the
1298 \emph{normalization} phase, exhaustively applies a set of
1299 \emph{meaning-preserving} transformations on the \emph{Core} description until
1300 this description is in a \emph{normal form}. This set of transformations
1301 includes transformations typically found in reduction systems and lambda
1302 calculus~\cite{lambdacalculus}, such as $\beta$-reduction and
1303 $\eta$-expansion. It also includes self-defined transformations that are
1304 responsible for the reduction of higher-order functions to `regular'
1305 first-order functions, and specializing polymorphic types to concrete types.
1307 The final step in the compiler pipeline is the translation to a \VHDL\
1308 \emph{netlist}, which is a straightforward process due to the resemblance of a
1309 normalized description and a set of concurrent signal assignments. The
1310 end-product of the \CLaSH\ compiler is called a \VHDL\ \emph{netlist} as the
1311 result resembles an actual netlist description, and the fact that it is \VHDL\
1312 is only an implementation detail; e.g., the output could have been Verilog.
1315 \label{sec:usecases}
1316 \subsection{FIR Filter}
1317 As an example of a common hardware design where the relation between
1318 functional languages and mathematical functions, combined with the use of
1319 higher-order functions leads to a very natural description is a \acro{FIR}
1323 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1326 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1327 and a few previous input samples ($x$). Each of these multiplications
1328 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1329 filter is equivalent to the equation of the dot-product of two vectors, which
1333 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1336 The equation for the dot-product is easily and directly implemented using
1337 higher-order functions:
1340 \begin{minipage}{0.93\linewidth}
1342 as *+* bs = fold (+) (zipWith (*) as bs)
1345 \begin{minipage}{0.07\linewidth}
1347 \label{code:dotproduct}
1351 The \hs{zipWith} function is very similar to the \hs{map} function seen
1352 earlier: It takes a function, two vectors, and then applies the function to
1353 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1354 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1356 The \hs{fold} function takes a binary function, a single vector, and applies
1357 the function to the first two elements of the vector. It then applies the
1358 function to the result of the first application and the next element in the
1359 vector. This continues until the end of the vector is reached. The result of
1360 the \hs{fold} function is the result of the last application. It is obvious
1361 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1362 \hs{fold (+)} function is summation.
1363 % Returning to the actual \acro{FIR} filter, we will slightly change the
1364 % equation describing it, so as to make the translation to code more obvious and
1365 % concise. What we do is change the definition of the vector of input samples
1366 % and delay the computation by one sample. Instead of having the input sample
1367 % received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1368 % sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1369 % to the following (note that this is completely equivalent to the original
1370 % equation, just with a different definition of $x$ that will better suit the
1371 % transformation to code):
1374 % y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1376 The complete definition of the \acro{FIR} filter in \CLaSH\ is:
1379 \begin{minipage}{0.93\linewidth}
1381 fir (State (xs,hs)) x =
1382 (State (shiftInto x xs,hs), (x +> xs) *+* hs)
1385 \begin{minipage}{0.07\linewidth}
1391 where the vector \hs{xs} contains the previous input samples, the vector
1392 \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input
1393 sample. The concatenate operator (\hs{+>}) creates a new vector by placing the
1394 current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The
1395 code for the \hs{shiftInto} function, that adds the new input sample (\hs{x})
1396 to the list of previous input samples (\hs{xs}) and removes the oldest sample,
1400 \begin{minipage}{0.93\linewidth}
1402 shiftInto x xs = x +> init xs
1405 \begin{minipage}{0.07\linewidth}
1407 \label{code:shiftinto}
1411 where the \hs{init} function returns all but the last element of a vector.
1412 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1413 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1417 \centerline{\includegraphics{4tapfir.svg}}
1418 \caption{4-taps \acrotiny{FIR} Filter}
1423 \subsection{Higher-order CPU}
1424 %format fun x = "\textit{fu}_" x
1425 In this section discusses a somewhat more serious example in which
1426 user-defined higher-order function, partial application, lambda expressions,
1427 and pattern matching are exploited. The example concerns a \acro{CPU} which
1428 consists of four function unites \hs{fun 0,{-"\ldots"-},fun 3} (see
1429 \Cref{img:highordcpu}) that each perform some binary operation.
1432 \centerline{\includegraphics{highordcpu.svg}}
1433 \caption{CPU with higher-order Function Units}
1434 \label{img:highordcpu}
1438 Every function unit has seven data inputs (of type \hs{Word}), and two address
1439 inputs (of type \hs{Index 6}) which indicate which data inputs have to be
1440 chosen as arguments for the the binary operation that the unit performs. These
1441 data inputs consists of one external input \hs{x}, two fixed initialization
1442 values (0 and 1), and the previous outputs of the four function units. The
1443 output of the \acro{CPU} as a whole is the previous output of \hs{fun 3}.
1445 The function units \hs{fun 1, fun 2, fun 3} can perform a fixed binary
1446 operation, whereas \hs{fun 0} has an additional input for an opcode to choose
1447 a binary operation out of a few possibilities.
1449 Each function unit outputs its result into a register, i.e., the state of the
1450 \acro{CPU}. This can can e.g. be defined as follows:
1453 type CpuState = State [Word | 4]
1456 Every function unit can now be defined by the following higher-order function
1457 \hs{fu}, which takes three arguments: the operation \hs{op} that the function
1458 unit performs, the seven \hs{inputs}, and the pair \hs{(a1,a2)} of two
1462 \begin{minipage}{0.93\linewidth}
1464 fu op inputs (a1, a2) = regIn
1468 regIn = op arg1 arg2
1471 \begin{minipage}{0.07\linewidth}
1473 \label{code:functionunit}
1477 Using partial application we now define:
1480 \begin{minipage}{0.93\linewidth}
1487 \begin{minipage}{0.07\linewidth}
1489 \label{code:functionunits1to3}
1493 In order to define \hs{fun 0} we first define the type \hs{Opcode} for the
1494 opcode and the function \hs{multiop} that chooses a specific operation given
1495 the opcode. We assume that the functions \hs{shifts} (which shifts its first
1496 operand by the number of bits indicate in the second operand), \hs{xor} (for
1497 the bitwise \hs{xor}), and (==) (for equality) already exits.
1500 \begin{minipage}{0.93\linewidth}
1502 data Opcode = Shift | Xor | Equal
1504 multiop Shift = shift
1506 multiop Equal = \a b -> if a == b then 1 else 0
1509 \begin{minipage}{0.07\linewidth}
1511 \label{code:multiop}
1515 Note that the result of \hs{multiop} is a binary function; this is supported
1516 by \CLaSH. We can now define \hs{fun 0} as a function which takes an opcode as
1517 additional argument:
1520 \begin{minipage}{0.93\linewidth}
1522 fun 0 c = fu (multiop c)
1525 \begin{minipage}{0.07\linewidth}
1527 \label{code:functionunit0}
1531 Now we come to the definition \hs{cpu} of the full \acro{CPU}. Its type is:
1535 -> (Word, Opcode, [(Index 6, Index 6) | 4])
1539 Note that this type fits the requirements of the function \hs{run}. The
1540 definition of the \hs{cpu} now is:
1543 \begin{minipage}{0.93\linewidth}
1545 cpu (State s) (x,opc,addrs) = (State s', out)
1547 inputs = x +> (0 +> (1 +> s))
1548 s' = [{-"\;"-}fun 0 opc inputs (addrs!0)
1549 ,{-"\;"-}fun 1 inputs (addrs!1)
1550 ,{-"\;"-}fun 2 inputs (addrs!2)
1551 ,{-"\;"-}fun 3 inputs (addrs!3)
1556 \begin{minipage}{0.07\linewidth}
1562 While this is still a simple (and maybe not very useful) design, it
1563 illustrates some possibilities that \CLaSH\ offers and suggests how to write
1566 % Each of the function units has both its operands connected to all data
1567 % sources, and can be programmed to select any data source for either
1568 % operand. In addition, the leftmost function unit has an additional
1569 % opcode input to select the operation it performs. The previous output of the
1570 % rightmost function unit is the output of the entire \acro{CPU}.
1572 % The code of the function unit (\ref{code:functionunit}), which arranges the
1573 % operand selection for the function unit, is shown below. Note that the actual
1574 % operation that takes place inside the function unit is supplied as the
1575 % (higher-order) argument \hs{op}, which is a function that takes two arguments.
1579 % 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
1580 % the bitwise xor of its operands.
1583 % The \acro{CPU} function (\ref{code:cpu}) ties everything together. It applies
1584 % the function unit (\hs{fu}) to several operations, to create a different
1585 % function unit each time. The first application is interesting, as it does not
1586 % just pass a function to \hs{fu}, but a partial application of \hs{multiop}.
1587 % This demonstrates how one function unit can effectively get extra inputs
1588 % compared to the others.
1590 % The vector \hs{inputs} is the set of data sources, which is passed to
1591 % each function unit as a set of possible operants. The \acro{CPU} also receives
1592 % a vector of address pairs, which are used by each function unit to select
1594 % The application of the function units to the \hs{inputs} and
1595 % \hs{addrs} arguments seems quite repetitive and could be rewritten to use
1596 % a combination of the \hs{map} and \hs{zipwith} functions instead.
1597 % However, the prototype compiler does not currently support working with
1598 % lists of functions, so a more explicit version of the code is given instead.
1600 % While this is still a simple example, it could form the basis of an actual
1601 % design, in which the same techniques can be reused.
1603 \section{Related work}
1604 This section describes the features of existing (functional) hardware
1605 description languages and highlights the advantages that this research has
1608 % Many functional hardware description languages have been developed over the
1609 % years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1610 % extension of Backus' \acro{FP} language to synchronous streams, designed
1611 % particularly for describing and reasoning about regular circuits. The
1612 % Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1613 % circuits, and has a particular focus on layout.
1615 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1616 functional language \acro{ML}, and has support for polymorphic types and
1617 higher-order functions. There is no direct simulation support for \acro{HML},
1618 so a description in \acro{HML} has to be translated to \VHDL\ and the
1619 translated description can then be simulated in a \VHDL\ simulator. Certain
1620 aspects of HML, such as higher-order functions are however not supported by
1621 the \VHDL\ translator~\cite{HML3}. The \CLaSH\ compiler on the other hand can
1622 correctly translate all of its language constructs.
1624 Like the research presented in this paper, many functional hardware
1625 description languages have some sort of foundation in the functional
1626 programming language Haskell. Hawk~\cite{Hawk1} is a hardware modeling
1627 language embedded in Haskell and has sequential environments that make it
1628 easier to specify stateful computation (by using the \acro{ST} monad). Hawk
1629 specifications can be simulated; to the best knowledge of the authors there is
1630 however no support for automated circuit synthesis.
1632 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1633 models. A designer can model systems using heterogeneous models of
1634 computation, which include continuous time, synchronous and untimed models of
1635 computation. Using so-called domain interfaces a designer can simulate
1636 electronic systems which have both analog and digital parts. ForSyDe has
1637 several backends including simulation and automated synthesis, though
1638 automated synthesis is restricted to the synchronous model of computation.
1639 Though ForSyDe offers higher-order functions and polymorphism, ForSyDe's
1640 choice elements are limited to \hs{if} and \hs{case} expressions. ForSyDe's
1641 explicit conversions, where functions have to be wrapped in processes and
1642 processes have to be wrapped in systems, combined with the explicit
1643 instantiations of components, also makes ForSyDe far more verbose than \CLaSH.
1645 Lava~\cite{Lava,kansaslava} is a hardware description language embedded in
1646 Haskell which focuses on the structural representation of hardware. Like
1647 \CLaSH, Lava has support for polymorphic types and higher-order functions.
1648 Besides support for simulation and circuit synthesis, Lava descriptions can be
1649 interfaced with formal method tools for formal verification. As discussed in
1650 the introduction, taking the embedded language approach does not allow for
1651 Haskell's choice elements to be captured within the circuit descriptions. In
1652 this respect \CLaSH\ differs from Lava, in that all of Haskell's choice
1653 elements, such as \hs{case}-expressions and pattern matching, are synthesized
1654 to choice elements in the eventual circuit. Consequently, descriptions
1655 containing rich control structures can be specified in a more user-friendly
1656 way in \CLaSH\ than possible within Lava, and hence are less error-prone.
1658 Bluespec~\cite{Bluespec} is a high-level synthesis language that features
1659 guarded atomic transactions and allows for the automated derivation of control
1660 structures based on these atomic transactions. Bluespec, like \CLaSH, supports
1661 polymorphic typing and function-valued arguments. Bluespec's syntax and
1662 language features \emph{had} their basis in Haskell. However, in order to
1663 appeal to the users of the traditional \acrop{HDL}, Bluespec has adapted
1664 imperative features and a syntax that resembles Verilog. As a result, Bluespec
1665 is (unnecessarily) verbose when compared to \CLaSH.
1667 The merits of polymorphic typing and function-valued arguments are now also
1668 recognized in the traditional \acrop{HDL}, exemplified by the new \VHDL-2008
1669 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to
1670 types and subprograms, allowing a designer to describe components with
1671 polymorphic ports and function-valued arguments. Note that the types and
1672 subprograms still require an explicit generic map, while the \CLaSH\ compiler
1673 automatically infers types, and automatically propagates function-valued
1674 arguments. There are also no (generally available) \VHDL\ synthesis tools that
1675 currently support the \VHDL-2008 standard.
1677 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1679 % A functional language designed specifically for hardware design is
1680 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1681 % language called \acro{FL}~\cite{FL} to la
1683 % An example of a floating figure using the graphicx package.
1684 % Note that \label must occur AFTER (or within) \caption.
1685 % For figures, \caption should occur after the \includegraphics.
1686 % Note that IEEEtran v1.7 and later has special internal code that
1687 % is designed to preserve the operation of \label within \caption
1688 % even when the captionsoff option is in effect. However, because
1689 % of issues like this, it may be the safest practice to put all your
1690 % \label just after \caption rather than within \caption{}.
1692 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1693 % option should be used if it is desired that the figures are to be
1694 % displayed while in draft mode.
1698 %\includegraphics[width=2.5in]{myfigure}
1699 % where an .eps filename suffix will be assumed under latex,
1700 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1701 % via \DeclareGraphicsExtensions.
1702 %\caption{Simulation Results}
1706 % Note that IEEE typically puts floats only at the top, even when this
1707 % results in a large percentage of a column being occupied by floats.
1710 % An example of a double column floating figure using two subfigures.
1711 % (The subfig.sty package must be loaded for this to work.)
1712 % The subfigure \label commands are set within each subfloat command, the
1713 % \label for the overall figure must come after \caption.
1714 % \hfil must be used as a separator to get equal spacing.
1715 % The subfigure.sty package works much the same way, except \subfigure is
1716 % used instead of \subfloat.
1718 %\begin{figure*}[!t]
1719 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1720 %\label{fig_first_case}}
1722 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1723 %\label{fig_second_case}}}
1724 %\caption{Simulation results}
1728 % Note that often IEEE papers with subfigures do not employ subfigure
1729 % captions (using the optional argument to \subfloat), but instead will
1730 % reference/describe all of them (a), (b), etc., within the main caption.
1733 % An example of a floating table. Note that, for IEEE style tables, the
1734 % \caption command should come BEFORE the table. Table text will default to
1735 % \footnotesize as IEEE normally uses this smaller font for tables.
1736 % The \label must come after \caption as always.
1739 %% increase table row spacing, adjust to taste
1740 %\renewcommand{\arraystretch}{1.3}
1741 % if using array.sty, it might be a good idea to tweak the value of
1742 % \extrarowheight as needed to properly center the text within the cells
1743 %\caption{An Example of a Table}
1744 %\label{table_example}
1746 %% Some packages, such as MDW tools, offer better commands for making tables
1747 %% than the plain LaTeX2e tabular which is used here.
1748 %\begin{tabular}{|c||c|}
1758 % Note that IEEE does not put floats in the very first column - or typically
1759 % anywhere on the first page for that matter. Also, in-text middle ("here")
1760 % positioning is not used. Most IEEE journals/conferences use top floats
1761 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1762 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1763 % command of the stfloats package.
1767 \section{Conclusion}
1768 This research demonstrates once more that functional languages are well suited
1769 for hardware descriptions: function applications provide an elegant notation
1770 for component instantiation. While circuit descriptions made in \CLaSH\ are
1771 very concise when compared to other (traditional) \acrop{HDL}, their intended
1772 functionality remains clear. \CLaSH\ goes beyond the existing (functional)
1773 hardware descriptions languages by including advanced choice elements, such as
1774 pattern matching and guards, which are well suited to describe the conditional
1775 assignments in control-oriented circuits. Besides being able to translate
1776 these basic constructs to synthesizable \VHDL, the prototype compiler can also
1777 correctly translate descriptions that contain both polymorphic types and
1778 user-defined higher-order functions.
1780 % Where recent functional hardware description languages have mostly opted to
1781 % embed themselves in an existing functional language, this research features
1782 % a `true' compiler. As a result there is a clear distinction between
1783 % compile-time and run-time, which allows a myriad of choice constructs to be
1784 % part of the actual circuit description; a feature the embedded hardware
1785 % description languages do not offer.
1787 Besides simple circuits such as variants of both the \acro{FIR} filter and
1788 the higher-order \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler
1789 has also been able to translate non-trivial functional descriptions such as a
1790 streaming reduction circuit~\cite{reductioncircuit} for floating point
1793 \section{Future Work}
1794 The choice of describing state explicitly as and extra argument and result can
1795 be seen as a mixed blessing. Even though descriptions that use state are
1796 usually very clear, distributing and collecting substate can become tedious
1797 and even error-prone. Automating the required distribution and collection, or
1798 finding a more suitable abstraction mechanism for state would make \CLaSH\
1799 easier to use. Currently, one of the examined approaches to suppress state in
1800 the specification is by using Haskell's arrow-abstraction.
1802 The transformations in the normalization phase of the prototype compiler are
1803 developed in an ad-hoc manner, which makes the existence of many desirable
1804 properties unclear. Such properties include whether the complete set of
1805 transformations will always lead to a normal form or whether the normalization
1806 process always terminates. Though extensive use of the compiler suggests that
1807 these properties usually hold, they have not been formally proven. A
1808 systematic approach to defining the set of transformations allows one to proof
1809 that the earlier mentioned properties do indeed hold.
1811 % conference papers do not normally have an appendix
1814 % use section* for acknowledgement
1815 % \section*{Acknowledgment}
1817 % The authors would like to thank...
1819 % trigger a \newpage just before the given reference
1820 % number - used to balance the columns on the last page
1821 % adjust value as needed - may need to be readjusted if
1822 % the document is modified later
1823 % \IEEEtriggeratref{14}
1824 % The "triggered" command can be changed if desired:
1825 %\IEEEtriggercmd{\enlargethispage{-5in}}
1827 % references section
1829 % can use a bibliography generated by BibTeX as a .bbl file
1830 % BibTeX documentation can be easily obtained at:
1831 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1832 % The IEEEtran BibTeX style support page is at:
1833 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1834 \bibliographystyle{IEEEtran}
1835 % argument is your BibTeX string definitions and bibliography database(s)
1836 \bibliography{clash}
1838 % <OR> manually copy in the resultant .bbl file
1839 % set second argument of \begin to the number of references
1840 % (used to reserve space for the reference number labels box)
1841 % \begin{thebibliography}{1}
1843 % \bibitem{IEEEhowto:kopka}
1844 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1845 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1847 % \end{thebibliography}
1855 % vim: set ai sw=2 sts=2 expandtab: