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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{Matthijs Kooijman, Christiaan P.R. Baaij, Jan Kuper, Marco E.T. Gerards}%, Bert Molenkamp, Sabih H. Gerez}
413 \IEEEauthorblockA{%Computer Architecture for Embedded Systems (CAES)\\
414 Department of EEMCS, University of Twente\\
415 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
416 matthijs@@stdin.nl, c.p.r.baaij@@utwente.nl, j.kuper@@utwente.nl}
417 \thanks{Supported through the FP7 project: S(o)OS (248465)}
420 % \IEEEauthorblockN{Homer Simpson}
421 % \IEEEauthorblockA{Twentieth Century Fox\\
423 % Email: homer@thesimpsons.com}
425 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
426 % \IEEEauthorblockA{Starfleet Academy\\
427 % San Francisco, California 96678-2391\\
428 % Telephone: (800) 555--1212\\
429 % Fax: (888) 555--1212}}
431 % conference papers do not typically use \thanks and this command
432 % is locked out in conference mode. If really needed, such as for
433 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
434 % after \documentclass
436 % for over three affiliations, or if they all won't fit within the width
437 % of the page, use this alternative format:
439 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
440 %Homer Simpson\IEEEauthorrefmark{2},
441 %James Kirk\IEEEauthorrefmark{3},
442 %Montgomery Scott\IEEEauthorrefmark{3} and
443 %Eldon Tyrell\IEEEauthorrefmark{4}}
444 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
445 %Georgia Institute of Technology,
446 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
447 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
448 %Email: homer@thesimpsons.com}
449 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
450 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
451 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
456 % use for special paper notices
457 %\IEEEspecialpapernotice{(Invited Paper)}
462 % make the title area
467 \CLaSH\ is a functional hardware description language that borrows both its
468 syntax and semantics from the functional programming language Haskell.
469 Polymorphism and higher-order functions provide a level of abstraction and
470 generality that allow a circuit designer to describe circuits in a more
471 natural way than possible in a traditional hardware description language.
473 Circuit descriptions can be translated to synthesizable VHDL using the
474 prototype \CLaSH\ compiler. As the circuit descriptions, simulation code, and
475 test input are also valid Haskell, complete simulations can be compiled as an
476 executable binary by a Haskell compiler allowing high-speed simulation and
479 % \CLaSH\ supports stateful descriptions by explicitly making the current
480 % state an argument of the function, and the updated state part of the result.
481 % This makes \CLaSH\ descriptions in essence the combinational parts of a
484 % IEEEtran.cls defaults to using nonbold math in the Abstract.
485 % This preserves the distinction between vectors and scalars. However,
486 % if the conference you are submitting to favors bold math in the abstract,
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 allowed the productivity of
508 hardware engineers to keep pace with the development of chip technology.
509 Traditional \acrop{HDL}, like \VHDL~\cite{VHDL2008} and
510 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
511 `programming' language. These standard languages are very good at describing
512 detailed hardware properties such as timing behavior, but are generally
513 cumbersome in expressing higher-level abstractions. In an attempt to raise the
514 abstraction level of the descriptions, a great number of approaches based on
515 functional languages has been proposed \cite{Cardelli1981,muFP,DAISY,FHDL,
516 T-Ruby,Hydra,HML2,Hawk1,Lava,ForSyDe1,Wired,reFLect}. The idea of using
517 functional languages for hardware descriptions started in the early 1980s
518 \cite{Cardelli1981,muFP,DAISY,FHDL}, a time which also saw the birth of the
519 currently popular hardware description languages such as \VHDL. Functional
520 languages are especially well suited to describe hardware because
521 combinational circuits can be directly modeled as mathematical functions.
522 Functional languages are very good at describing and composing these
523 mathematical functions.
525 In an attempt to decrease the amount of work involved in creating all the
526 required tooling, such as parsers and type-checkers, many functional
527 \acrop{HDL} \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired} are embedded as a domain
528 specific language (\acro{DSL}) inside the functional language Haskell
529 \cite{Haskell}. This means that a developer is given a library of Haskell
530 functions and types that together form the language primitives of the
531 \acro{DSL}. The primitive functions used to describe a circuit do not actually
532 process any signals, but instead compose a large domain-specific datatype
533 (which is usually hidden from the designer). This datatype is then further
534 processed by an embedded circuit compiler. As Haskell's choice elements
535 (\hs{if}-expressions, \hs{case}-expressions, pattern matching, etc.) are
536 evaluated at the time the domain-specific datatype is being build, they are no
537 longer visible to the embedded compiler that processes the datatype.
538 Consequently, it is impossible the capture Haskell's choice elements within a
539 circuit description when taking the embedded language approach. However,
540 descriptions can still contain polymorphism and higher-order functions.
542 The approach taken in this research is not to make another \acro{DSL} embedded
543 in Haskell, but to use (a subset of) the Haskell language \emph{itself} for
544 the purpose of describing hardware. By taking this approach, we \emph{can}
545 capture certain language constructs, such as Haskell's choice elements, within
546 circuit descriptions. To the best knowledge of the authors, supporting
547 polymorphism, higher-order functions and such an extensive array of
548 choice-elements is new in the domain of (functional) \acrop{HDL}.
549 % As the hardware descriptions are plain Haskell
550 % functions, these descriptions can be compiled to an executable binary
551 % for simulation using an optimizing Haskell compiler such as the Glasgow
552 % Haskell Compiler (\GHC)~\cite{ghc}.
554 Where descriptions in a conventional \acro{HDL} have an explicit clock for the
555 purposes state and synchronicity, the clock is implied in the context of the
556 research presented in this paper. A circuit designer describes the behavior of
557 the hardware between clock cycles. Many functional \acrop{HDL} model signals
558 as a stream of all values over time; state is then modeled as a delay on this
559 stream of values. The approach taken in this research is to make the current
560 state an additional input and the updated state a part of the output of a
561 function. The current abstraction of state and time limits the descriptions to
562 synchronous hardware, there is however room within the language to eventually
563 add a different abstraction mechanism that will allow for the modeling of
564 asynchronous systems.
566 Like the traditional \acrop{HDL}, descriptions made in a functional \acro{HDL}
567 must eventually be converted into a netlist. This research also features a
568 prototype translator, which has the same name as the language:
569 \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES} Language for Synchronous Hardware}
570 (pronounced: clash). This compiler converts the Haskell code to equivalently
571 behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist
572 format by an (optimizing) \VHDL\ synthesis tool.
574 Besides trivial circuits such as variants of both the \acro{FIR} filter and
575 the simple \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler has
576 also been able to successfully translate non-trivial functional descriptions
577 such as a streaming reduction circuit~\cite{reductioncircuit} for floating
580 \section{Hardware description in Haskell}
581 The following section describes the basic language elements of \CLaSH\ and the
582 extensiveness of the support of these elements within the \CLaSH\ compiler. In
583 various subsections, the relation between the language elements and their
584 eventual netlist representation is also highlighted.
586 \subsection{Function application}
587 Two basic syntactic elements of a functional program are functions
588 and function application. These have a single obvious translation to a
591 \item every function is translated to a component,
592 \item every function argument is translated to an input port,
593 \item the result value of a function is translated to an output port,
595 \item function applications are translated to component instantiations.
597 The result value can have a composite type (such as a tuple), so having
598 just a single result value does not pose any limitation. The actual
599 arguments of a function application are assigned to signals, which are
600 then mapped to the corresponding input ports of the component. The output
601 port of the function is also mapped to a signal, which is used as the
602 result of the application itself. Since every top level function generates
603 its own component, the hierarchy of function calls is reflected in the
604 final netlist, creating a hierarchical description of the hardware.
605 % The separation in different components makes it easier for a developer
606 % to understand and possibly hand-optimize the resulting \VHDL\ output of
607 % the \CLaSH\ compiler.
609 The short example (\ref{lst:code1}) demonstrated below gives an indication
610 of the level of conciseness that can be achieved with functional hardware
611 description languages when compared with the more traditional hardware
612 description languages. The example is a combinational multiply-accumulate
613 circuit that works for \emph{any} word length (this type of polymorphism
614 will be further elaborated in \Cref{sec:polymorhpism}). The corresponding
615 netlist is depicted in \Cref{img:mac-comb}.
618 \begin{minipage}{0.93\linewidth}
620 mac a b c = add (mul a b) c
623 \begin{minipage}{0.07\linewidth}
630 \centerline{\includegraphics{mac.svg}}
631 \caption{Combinational Multiply-Accumulate}
636 The use of a composite result value is demonstrated in the next example
637 (\ref{lst:code2}), where the multiply-accumulate circuit not only returns
638 the accumulation result, but also the intermediate multiplication result.
639 Its corresponding netlist can be see in \Cref{img:mac-comb-composite}.
642 \begin{minipage}{0.93\linewidth}
644 mac a b c = (z, add z c)
649 \begin{minipage}{0.07\linewidth}
656 \centerline{\includegraphics{mac-nocurry.svg}}
657 \caption{Combinational Multiply-Accumulate (composite output)}
658 \label{img:mac-comb-composite}
663 In Haskell, choice can be achieved by a large set of syntactic elements,
664 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
665 pattern matching, and guards. The most general of these are the \hs{case}
666 expressions (\hs{if} expressions can be directly translated to
667 \hs{case} expressions). When transforming a \CLaSH\ description to a
668 netlist, a \hs{case} expression is translated to a multiplexer. The
669 control value is fed into a number of comparators and their output forms
670 the selection port of the multiplexer. The result of each alternative in
671 the \hs{case} expression is linked to the corresponding input port on the
673 % A \hs{case} expression can in turn simply be translated to a conditional
674 % assignment in \VHDL, where the conditions use equality comparisons
675 % against the constructors in the \hs{case} expressions.
676 We can see two versions of a contrived example below, the first
677 (\ref{lst:code3}) using a \hs{case} expression, and the other
678 (\ref{lst:code4}) using an \hs{if-then-else} expression . Both examples
679 sums two values when they are equal or non-equal (depending on the given
680 predicate, the \hs{pred} variable) and returns 0 otherwise. The \hs{pred}
681 variable if of the following, user-defined, enumeration datatype:
684 data Pred = Equal | NotEqual
687 The naive netlist corresponding to both versions of the example is
688 depicted in \Cref{img:choice}. Note that the \hs{pred} variable is only
689 compared to the \hs{Equal} value, as an inequality immediately implies
690 that the \hs{pred} variable has a \hs{NotEqual} value.
693 \begin{minipage}{0.93\linewidth}
695 sumif pred a b = case pred of
696 Equal -> case a == b of
699 NotEqual -> case a != b of
704 \begin{minipage}{0.07\linewidth}
711 \begin{minipage}{0.93\linewidth}
714 if pred == Equal then
715 if a == b then a + b else 0
717 if a != b then a + b else 0
720 \begin{minipage}{0.07\linewidth}
728 \centerline{\includegraphics{choice-case.svg}}
729 \caption{Choice - sumif}
734 A user-friendly and also very powerful form of choice that is not found in
735 the traditional hardware description languages is pattern matching. A
736 function can be defined in multiple clauses, where each clause corresponds
737 to a pattern. When an argument matches a pattern, the corresponding clause
738 will be used. Expressions can also contain guards, where the expression is
739 only executed if the guard evaluates to true, and continues with the next
740 clause if the guard evaluates to false. Like \hs{if-then-else}
741 expressions, pattern matching and guards have a (straightforward)
742 translation to \hs{case} expressions and can as such be mapped to
743 multiplexers. A third version (\ref{lst:code5}) of the earlier example,
744 now using both pattern matching and guards, can be seen below. The guard
745 is the expression that follows the vertical bar (\hs{|}) and precedes the
746 assignment operator (\hs{=}). The \hs{otherwise} guards always evaluate to
749 The version using pattern matching and guards corresponds to the same
750 naive netlist representation (\Cref{img:choice}) as the earlier two
751 versions of the example.
754 \begin{minipage}{0.93\linewidth}
756 sumif Equal a b | a == b = a + b
758 sumif NotEqual a b | a != b = a + b
762 \begin{minipage}{0.07\linewidth}
769 % \centerline{\includegraphics{choice-ifthenelse}}
770 % \caption{Choice - \emph{if-then-else}}
775 Haskell is a statically-typed language, meaning that the type of a
776 variable or function is determined at compile-time. Not all of Haskell's
777 typing constructs have a clear translation to hardware, this section will
778 therefore only deal with the types that do have a clear correspondence
779 to hardware. The translatable types are divided into two categories:
780 \emph{built-in} types and \emph{user-defined} types. Built-in types are
781 those types for which a fixed translation is defined within the \CLaSH\
782 compiler. The \CLaSH\ compiler has generic translation rules to
783 translate the user-defined types described later on.
785 The \CLaSH\ compiler is able to infer unspecified (polymorphic) types,
786 meaning that a developer does not have to annotate every function with a
787 type signature. % (even if it is good practice to do so).
788 Given that the top-level entity of a circuit design is annotated with
789 concrete types, the \CLaSH\ compiler can specialize polymorphic functions
790 to functions with concrete types.
792 % Translation of two most basic functional concepts has been
793 % discussed: function application and choice. Before looking further
794 % into less obvious concepts like higher-order expressions and
795 % polymorphism, the possible types that can be used in hardware
796 % descriptions will be discussed.
798 % Some way is needed to translate every value used to its hardware
799 % equivalents. In particular, this means a hardware equivalent for
800 % every \emph{type} used in a hardware description is needed.
802 % The following types are \emph{built-in}, meaning that their hardware
803 % translation is fixed into the \CLaSH\ compiler. A designer can also
804 % define his own types, which will be translated into hardware types
805 % using translation rules that are discussed later on.
807 \subsubsection{Built-in types}
808 The following types have fixed translations defined within the \CLaSH\
812 the most basic type available. It can have two values:
813 \hs{Low} or \hs{High}.
814 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
816 this is a basic logic type. It can have two values: \hs{True}
818 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
819 % type (where a value of \hs{True} corresponds to a value of
821 Supporting the Bool type is required in order to support the
822 \hs{if-then-else} expression, which requires a \hs{Bool} value for
824 \item[\bf{Signed}, \bf{Unsigned}]
825 these are types to represent integers and both are parametrizable in
826 their size. The overflow behavior of the numeric operators defined for
827 these types is \emph{wrap-around}.
828 % , so you can define an unsigned word of 32 bits wide as follows:
831 % type Word32 = SizedWord D32
834 % Here, a type synonym \hs{Word32} is defined that is equal to the
835 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
836 % \hs{D32} is the \emph{type level representation} of the decimal
837 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
838 % types are translated to the \VHDL\ \texttt{unsigned} and
839 % \texttt{signed} respectively.
841 this is a vector type that can contain elements of any other type and
842 has a fixed length. The \hs{Vector} type constructor takes two type
843 arguments: the length of the vector and the type of the elements
844 contained in it. The short-hand notation used for the vector type in
845 the rest of paper is: \hs{[a|n]}, where \hs{a} is the element
846 type, and \hs{n} is the length of the vector. Note that this is
847 a notation used in this paper only, vectors are slightly more
848 verbose in real \CLaSH\ descriptions.
849 % The state type of an 8 element register bank would then for example
853 % type RegisterState = Vector D8 Word32
856 % Here, a type synonym \hs{RegisterState} is defined that is equal to
857 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
858 % type level representation of the decimal number 8) and \hs{Word32}
859 % (The 32 bit word type as defined above). In other words, the
860 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
861 % vector is translated to a \VHDL\ array type.
863 this is another type to describe integers, but unlike the previous
864 two it has no specific bit-width, but an upper bound. This means that
865 its range is not limited to powers of two, but can be any number.
866 An \hs{Index} only has an upper bound, its lower bound is
867 implicitly zero. If a value of this type exceeds either bounds, an
868 error will be thrown at simulation-time. The main purpose of the
869 \hs{Index} type is to be used as an index to a \hs{Vector}.
871 % \comment{TODO: Perhaps remove this example?} To define an index for
872 % the 8 element vector above, we would do:
875 % type RegisterIndex = RangedWord D7
878 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
879 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
880 % other words, this defines an unsigned word with values from
881 % 0 to 7 (inclusive). This word can be be used to index the
882 % 8 element vector \hs{RegisterState} above. This type is translated
883 % to the \texttt{unsigned} \VHDL type.
886 \subsubsection{User-defined types}
887 There are three ways to define new types in Haskell: algebraic
888 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
889 keyword and datatype renaming constructs with the \hs{newtype} keyword.
890 % \GHC\ offers a few more advanced ways to introduce types (type families,
891 % existential typing, {\acro{GADT}}s, etc.) which are not standard
892 % Haskell. As it is currently unclear how these advanced type constructs
893 % correspond to hardware, they are for now unsupported by the \CLaSH\
896 Only an algebraic datatype declaration actually introduces a
897 completely new type. Type synonyms and type renaming only define new
898 names for existing types, where synonyms are completely interchangeable
899 and a type renaming requires an explicit conversion. Type synonyms and
900 type renaming do not need any particular translation, a synonym or
901 renamed type will just use the same representation as the original type.
903 For algebraic types, we can make the following distinctions:
905 \item[\bf{Single constructor}]
906 Algebraic datatypes with a single constructor with one or more
907 fields, are essentially a way to pack a few values together in a
908 record-like structure. Haskell's built-in tuple types are also defined
909 as single constructor algebraic types (but with a bit of
910 syntactic sugar). An example of a single constructor type with
911 multiple fields is the following pair of integers:
913 data IntPair = IntPair Int Int
915 % These types are translated to \VHDL\ record types, with one field
916 % for every field in the constructor.
917 \item[\bf{No fields}]
918 Algebraic datatypes with multiple constructors, but without any
919 fields are essentially a way to get an enumeration-like type
920 containing alternatives. Note that Haskell's \hs{Bool} type is also
921 defined as an enumeration type, but that there is a fixed translation
922 for that type within the \CLaSH\ compiler. An example of such an
923 enumeration type is the type that represents the colors in a traffic
926 data TrafficLight = Red | Orange | Green
928 % These types are translated to \VHDL\ enumerations, with one
929 % value for each constructor. This allows references to these
930 % constructors to be translated to the corresponding enumeration
932 \item[\bf{Multiple constructors with fields}]
933 Algebraic datatypes with multiple constructors, where at least
934 one of these constructors has one or more fields are currently not
938 \subsection{Polymorphism}\label{sec:polymorhpism}
939 A powerful feature of most (functional) programming languages is
940 polymorphism, it allows a function to handle values of different data
941 types in a uniform way. Haskell supports \emph{parametric
942 polymorphism}~\cite{polymorphism}, meaning functions can be written
943 without mention of any specific type and can be used transparently with
944 any number of new types.
946 As an example of a parametric polymorphic function, consider the type of
947 the following \hs{append} function, which appends an element to a
948 vector:\footnote{The \hs{::} operator is used to annotate a function
952 append :: [a|n] -> a -> [a|n + 1]
955 This type is parameterized by \hs{a}, which can contain any type at
956 all. This means that \hs{append} can append an element to a vector,
957 regardless of the type of the elements in the list (as long as the type of
958 the value to be added is of the same type as the values in the vector).
959 This kind of polymorphism is extremely useful in hardware designs to make
960 operations work on a vector without knowing exactly what elements are
961 inside, routing signals without knowing exactly what kinds of signals
962 these are, or working with a vector without knowing exactly how long it
963 is. Polymorphism also plays an important role in most higher order
964 functions, as we will see in the next section.
966 Another type of polymorphism is \emph{ad-hoc
967 polymorphism}~\cite{polymorphism}, which refers to polymorphic
968 functions which can be applied to arguments of different types, but which
969 behave differently depending on the type of the argument to which they are
970 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
971 type classes, where a class definition provides the general interface of a
972 function, and class instances define the functionality for the specific
973 types. An example of such a type class is the \hs{Num} class, which
974 contains all of Haskell's numerical operations. A designer can make use
975 of this ad-hoc polymorphism by adding a constraint to a parametrically
976 polymorphic type variable. Such a constraint indicates that the type
977 variable can only be instantiated to a type whose members supports the
978 overloaded functions associated with the type class.
980 As an example we will take a look at type signature of the function
981 \hs{sum}, which sums the values in a vector:
983 sum :: Num a => [a|n] -> a
986 This type is again parameterized by \hs{a}, but it can only contain
987 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
988 we know that the addition (+) operator is defined for that type.
989 \CLaSH's built-in numerical types are also instances of the \hs{Num}
990 class, so we can use the addition operator (and thus the \hs{sum}
991 function) with \hs{Signed} as well as with \hs{Unsigned}.
993 In \CLaSH, parametric polymorphism is completely supported. Any function
994 defined can have any number of unconstrained type parameters. The \CLaSH\
995 compiler will infer the type of every such argument depending on how the
996 function is applied. There is however one constraint: the top level
997 function that is being translated can not have any polymorphic arguments.
998 The arguments can not be polymorphic as the function is never applied and
999 consequently there is no way to determine the actual types for the type
1002 \CLaSH\ does \emph{currently} not support\emph{ user-defined} type
1003 classes, but does use some of the standard Haskell type classes for its
1004 built-in function, such as: \hs{Num} for numerical operations, \hs{Eq} for
1005 the equality operators, and \hs{Ord} for the comparison/order operators.
1007 \subsection{Higher-order functions \& values}
1008 Another powerful abstraction mechanism in functional languages, is
1009 the concept of \emph{functions as a first class value}, also called
1010 \emph{higher-order functions}. This allows a function to be treated as a
1011 value and be passed around, even as the argument of another
1012 function. The following example should clarify this concept:
1015 \begin{minipage}{0.93\linewidth}
1016 %format not = "\mathit{not}"
1018 negateVector xs = map not xs
1021 \begin{minipage}{0.07\linewidth}
1027 The code above defines the \hs{negateVector} function, which takes a
1028 vector of booleans, \hs{xs}, and returns a vector where all the values are
1029 negated. It achieves this by calling the \hs{map} function, and passing it
1030 \emph{another function}, boolean negation, and the vector of booleans,
1031 \hs{xs}. The \hs{map} function applies the negation function to all the
1032 elements in the vector.
1034 The \hs{map} function is called a higher-order function, since it takes
1035 another function as an argument. Also note that \hs{map} is again a
1036 parametric polymorphic function: it does not pose any constraints on the
1037 type of the input vector, other than that its elements must have the same
1038 type as the first argument of the function passed to \hs{map}. The element
1039 type of the resulting vector is equal to the return type of the function
1040 passed, which need not necessarily be the same as the element type of the
1041 input vector. All of these characteristics can readily be inferred from
1042 the type signature belonging to \hs{map}:
1045 map :: (a -> b) -> [a|n] -> [b|n]
1048 So far, only functions have been used as higher-order values. In
1049 Haskell, there are two more ways to obtain a function-typed value:
1050 partial application and lambda abstraction. Partial application
1051 means that a function that takes multiple arguments can be applied
1052 to a single argument, and the result will again be a function (but
1053 that takes one argument less). As an example, consider the following
1054 expression, that adds one to every element of a vector:
1057 \begin{minipage}{0.93\linewidth}
1062 \begin{minipage}{0.07\linewidth}
1068 Here, the expression \hs{(add 1)} is the partial application of the
1069 addition function to the value \hs{1}, which is again a function that
1070 adds one to its (next) argument. A lambda expression allows one to
1071 introduce an anonymous function in any expression. Consider the following
1072 expression, which again adds one to every element of a vector:
1075 \begin{minipage}{0.93\linewidth}
1077 map (\x -> x + 1) xs
1080 \begin{minipage}{0.07\linewidth}
1086 Finally, not only built-in functions can have higher order
1087 arguments, but any function defined in \CLaSH\ may have functions as
1088 arguments. This allows the hardware designer to use a powerful
1089 abstraction mechanism in his designs and have an optimal amount of
1090 code reuse. The only exception is again the top-level function: if a
1091 function-typed argument is not applied with an actual function, no
1092 hardware can be generated.
1094 % \comment{TODO: Describe ALU example (no code)}
1097 A very important concept in hardware is the concept of state. In a
1098 stateful design, the outputs depend on the history of the inputs, or the
1099 state. State is usually stored in registers, which retain their value
1100 during a clock cycle. As we want to describe more than simple
1101 combinational designs, \CLaSH\ needs an abstraction mechanism for state.
1103 An important property in Haskell, and in most other functional languages,
1104 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1107 \item given the same arguments twice, it should return the same value in
1109 \item that the function has no observable side-effects.
1111 % This purity property is important for functional languages, since it
1112 % enables all kinds of mathematical reasoning that could not be guaranteed
1113 % correct for impure functions.
1114 Pure functions are as such a perfect match for combinational circuits,
1115 where the output solely depends on the inputs. When a circuit has state
1116 however, it can no longer be simply described by a pure function.
1117 % Simply removing the purity property is not a valid option, as the
1118 % language would then lose many of it mathematical properties.
1119 In \CLaSH\ we deal with the concept of state in pure functions by making
1120 the current state an additional argument of the function, and the
1121 updated state part of result. In this sense the descriptions made in
1122 \CLaSH\ are the combinational parts of a mealy machine.
1124 A simple example is adding an accumulator register to the earlier
1125 multiply-accumulate circuit, of which the resulting netlist can be seen in
1126 \Cref{img:mac-state}:
1129 \begin{minipage}{0.93\linewidth}
1131 macS (State c) a b = (State c', c')
1136 \begin{minipage}{0.07\linewidth}
1143 \centerline{\includegraphics{mac-state.svg}}
1144 \caption{Stateful Multiply-Accumulate}
1145 \label{img:mac-state}
1149 Note that the \hs{macS} function returns both the new state and the value
1150 of the output port. The \hs{State} keyword indicates which arguments are
1151 part of the current state, and what part of the output is part of the
1152 updated state. This aspect will also be reflected in the type signature of
1153 the function. Abstracting the state of a circuit in this way makes it very
1154 explicit: which variables are part of the state is completely determined
1155 by the type signature. This approach to state is well suited to be used in
1156 combination with the existing code and language features, such as all the
1157 choice elements, as state values are just normal values. We can simulate
1158 stateful descriptions using the recursive \hs{run} function:
1161 \begin{minipage}{0.93\linewidth}
1163 run f s (i : inps) = o : (run f s' inps)
1168 \begin{minipage}{0.07\linewidth}
1174 The \hs{(:)} operator is the list concatenation operator, where the
1175 left-hand side is the head of a list and the right-hand side is the
1176 remainder of the list. The \hs{run} function applies the function the
1177 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1178 first input value, \hs{i}. The result is the first output value, \hs{o},
1179 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1180 is then called with the updated state, \hs{s'}, and the rest of the
1181 inputs, \hs{inps}. For the time being, and in the context of this paper,
1182 it is assumed that there is one input per clock cycle. Also note how the
1183 order of the input, output, and state in the \hs{run} function corresponds
1184 with the order of the input, output and state of the \hs{macS} function
1187 As the \hs{run} function, the hardware description, and the test
1188 inputs are also valid Haskell, the complete simulation can be compiled to
1189 an executable binary by an optimizing Haskell compiler, or executed in an
1190 Haskell interpreter. Both simulation paths are much faster than first
1191 translating the description to \VHDL\ and then running a \VHDL\
1194 \section{The \CLaSH\ compiler}
1195 An important aspect in this research is the creation of the prototype
1196 compiler, which allows us to translate descriptions made in the \CLaSH\
1197 language as described in the previous section to synthesizable \VHDL.
1198 % , allowing a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1200 The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open-source Haskell
1201 compiler that also provides a high level API to most of its internals. The
1202 availability of this high-level API obviated the need to design many of the
1203 tedious parts of the prototype compiler, such as the parser, semantics
1204 checker, and especially the type-checker. These parts together form the
1205 front-end of the prototype compiler pipeline, as seen in
1206 \Cref{img:compilerpipeline}.
1209 \centerline{\includegraphics{compilerpipeline.svg}}
1210 \caption{\CLaSHtiny\ compiler pipeline}
1211 \label{img:compilerpipeline}
1215 The output of the \GHC\ front-end consists of the translation of the original
1216 Haskell description in \emph{Core}~\cite{Sulzmann2007}, which is a smaller,
1217 typed, functional language. This \emph{Core} language is relatively easy to
1218 process compared to the larger Haskell language. A description in \emph{Core}
1219 can still contain elements which have no direct translation to hardware, such
1220 as polymorphic types and function-valued arguments. Such a description needs
1221 to be transformed to a \emph{normal form}, which only contains elements that
1222 have a direct translation. The second stage of the compiler, the
1223 \emph{normalization} phase, exhaustively applies a set of
1224 \emph{meaning-preserving} transformations on the \emph{Core} description until
1225 this description is in a \emph{normal form}. This set of transformations
1226 includes transformations typically found in reduction systems and lambda
1227 calculus~\cite{lambdacalculus}, such as $\beta$-reduction and
1228 $\eta$-expansion. It also includes self-defined transformations that are
1229 responsible for the reduction of higher-order functions to `regular'
1230 first-order functions, and specializing polymorphic types to concrete types.
1232 The final step in the compiler pipeline is the translation to a \VHDL\
1233 \emph{netlist}, which is a straightforward process due to resemblance of a
1234 normalized description and a set of concurrent signal assignments. We call the
1235 end-product of the \CLaSH\ compiler a \VHDL\ \emph{netlist} as the resulting
1236 \VHDL\ resembles an actual netlist description and not idiomatic \VHDL.
1239 \label{sec:usecases}
1240 \subsection{FIR Filter}
1241 As an example of a common hardware design where the use of higher-order
1242 functions leads to a very natural description is a \acro{FIR} filter, which is
1243 basically the dot-product of two vectors:
1246 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1249 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1250 and a few previous input samples ($x$). Each of these multiplications
1251 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1252 filter is indeed equivalent to the equation of the dot-product, which is
1256 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1259 We can easily and directly implement the equation for the dot-product
1260 using higher-order functions:
1263 \begin{minipage}{0.93\linewidth}
1265 as *+* bs = foldl1 (+) (zipWith (*) as bs)
1268 \begin{minipage}{0.07\linewidth}
1274 The \hs{zipWith} function is very similar to the \hs{map} function seen
1275 earlier: It takes a function, two vectors, and then applies the function to
1276 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1277 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1279 The \hs{foldl1} function takes a binary function, a single vector, and applies
1280 the function to the first two elements of the vector. It then applies the
1281 function to the result of the first application and the next element in the
1282 vector. This continues until the end of the vector is reached. The result of
1283 the \hs{foldl1} function is the result of the last application. It is obvious
1284 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1285 \hs{foldl1 (+)} function is summation.
1286 % Returning to the actual \acro{FIR} filter, we will slightly change the
1287 % equation describing it, so as to make the translation to code more obvious and
1288 % concise. What we do is change the definition of the vector of input samples
1289 % and delay the computation by one sample. Instead of having the input sample
1290 % received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1291 % sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1292 % to the following (note that this is completely equivalent to the original
1293 % equation, just with a different definition of $x$ that will better suit the
1294 % transformation to code):
1297 % y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1299 The complete definition of the \acro{FIR} filter in code then becomes:
1302 \begin{minipage}{0.93\linewidth}
1304 fir (State (xs,hs)) x =
1305 (State (x >> xs,hs), (x +> xs) *+* hs)
1308 \begin{minipage}{0.07\linewidth}
1314 Where the vector \hs{xs} contains the previous input samples, the vector
1315 \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input
1316 sample. The concatenate operator (\hs{+>}) creates a new vector by placing the
1317 current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The
1318 code for the shift (\hs{>>}) operator, that adds the new input sample (\hs{x})
1319 to the list of previous input samples (\hs{xs}) and removes the oldest sample,
1323 \begin{minipage}{0.93\linewidth}
1325 x >> xs = x +> init xs
1328 \begin{minipage}{0.07\linewidth}
1334 Where the \hs{init} function returns all but the last element of a vector.
1335 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1336 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1340 \centerline{\includegraphics{4tapfir.svg}}
1341 \caption{4-taps \acrotiny{FIR} Filter}
1346 \subsection{Higher-order CPU}
1347 The following simple \acro{CPU} is an example of user-defined higher order
1348 functions and pattern matching. The \acro{CPU} consists of four function
1349 units, of which three have a fixed function and one can perform certain less
1352 The \acro{CPU} contains a number of data sources, represented by the
1353 horizontal wires in \Cref{img:highordcpu}. These data sources offer the
1354 previous outputs of each function units, along with the single data input the
1355 \acro{CPU} has and two fixed initialization values.
1357 Each of the function units has both its operands connected to all data
1358 sources, and can be programmed to select any data source for either
1359 operand. In addition, the leftmost function unit has an additional
1360 opcode input to select the operation it performs. The output of the rightmost
1361 function unit is also the output of the entire \acro{CPU}.
1363 Looking at the code, the function unit (\hs{fu}) is the most simple. It
1364 arranges the operand selection for the function unit. Note that it does not
1365 define the actual operation that takes place inside the function unit,
1366 but simply accepts the (higher-order) argument \hs{op} which is a function
1367 of two arguments that defines the operation.
1370 \begin{minipage}{0.93\linewidth}
1372 fu op inputs (addr1, addr2) = regIn
1379 \begin{minipage}{0.07\linewidth}
1385 The \hs{multiop} function defines the operation that takes place in the
1386 leftmost function unit. It is essentially a simple three operation \acro{ALU}
1387 that makes good use of pattern matching and guards in its description.
1388 The \hs{shift} function used here shifts its first operand by the number
1389 of bits indicated in the second operand, the \hs{xor} function produces
1390 the bitwise xor of its operands.
1393 \begin{minipage}{0.93\linewidth}
1395 data Opcode = Shift | Xor | Equal
1397 multiop :: Opcode -> Word -> Word -> Word
1398 multiop Shift a b = shift a b
1399 multiop Xor a b = xor a b
1400 multiop Equal a b | a == b = 1
1404 \begin{minipage}{0.07\linewidth}
1410 The \acro{CPU} function ties everything together. It applies the \hs{fu}
1411 function four times, to create a different function unit each time. The
1412 first application is interesting, because it does not just pass a
1413 function to \hs{fu}, but a partial application of \hs{multiop}. This
1414 shows how the first function unit effectively gets an extra input,
1415 compared to the others.
1417 The vector \hs{inputs} is the set of data sources, which is passed to
1418 each function unit as a set of possible operants. The \acro{CPU} also receives
1419 a vector of address pairs, which are used by each function unit to select
1420 their operand. The application of the function units to the \hs{inputs} and
1421 \hs{addrs} arguments seems quite repetitive and could be rewritten to use
1422 a combination of the \hs{map} and \hs{zipwith} functions instead.
1423 However, the prototype compiler does not currently support working with lists
1424 of functions, so a more explicit version of the code is given instead.
1427 \begin{minipage}{0.93\linewidth}
1429 type CpuState = State [Word | 4]
1431 cpu :: CpuState -> Word -> [(Index 6, Index 6) | 4]
1432 -> Opcode -> (CpuState, Word)
1433 cpu (State s) input addrs opc = (State s', out)
1435 s' = [ fu (multiop opc) inputs (addrs!0)
1436 , fu add inputs (addrs!1)
1437 , fu sub inputs (addrs!2)
1438 , fu mul inputs (addrs!3)
1440 inputs = 0 +> (1 +> (input +> s))
1444 \begin{minipage}{0.07\linewidth}
1450 This is still a simple example, but it could form the basis
1451 of an actual design, in which the same techniques can be reused.
1453 \section{Related work}
1454 This section describes the features of existing (functional) hardware
1455 description languages and highlights the advantages that this research has
1458 Many functional hardware description languages have been developed over the
1459 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1460 extension of Backus' \acro{FP} language to synchronous streams, designed
1461 particularly for describing and reasoning about regular circuits. The
1462 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1463 circuits, and has a particular focus on layout.
1466 \centerline{\includegraphics{highordcpu.svg}}
1467 \caption{CPU with higher-order Function Units}
1468 \label{img:highordcpu}
1472 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1473 functional language \acro{ML}, and has support for polymorphic types and
1474 higher-order functions. Published work suggests that there is no direct
1475 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1476 be translated to \VHDL\ and that the translated description can then be
1477 simulated in a \VHDL\ simulator. Certain aspects of HML, such as higher-order
1478 functions are however not supported by the \VHDL\ translator~\cite{HML3}. The
1479 \CLaSH\ compiler on the other hand can correctly translate all of the language
1480 constructs mentioned in this paper. % to a netlist format.
1482 Like the work presented in this paper, many functional hardware description
1483 languages have some sort of foundation in the functional programming language
1484 Haskell. Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1485 specifications used to model the behavior of superscalar microprocessors. Hawk
1486 specifications can be simulated; to the best knowledge of the authors there is
1487 however no support for automated circuit synthesis.
1489 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1490 models. A designer can model systems using heterogeneous models of
1491 computation, which include continuous time, synchronous and untimed models of
1492 computation. Using so-called domain interfaces a designer can simulate
1493 electronic systems which have both analog as digital parts. ForSyDe has
1494 several backends including simulation and automated synthesis, though
1495 automated synthesis is restricted to the synchronous model of computation.
1496 Unlike \CLaSH\ there is no support for the automated synthesis of descriptions
1497 that contain polymorphism or higher-order functions.
1499 Lava~\cite{Lava} is a hardware description language that focuses on the
1500 structural representation of hardware. Besides support for simulation and
1501 circuit synthesis, Lava descriptions can be interfaced with formal method
1502 tools for formal verification. Lava descriptions are actually circuit
1503 generators when viewed from a synthesis viewpoint, in that the language
1504 elements of Haskell, such as choice, can be used to guide the circuit
1505 generation. If a developer wants to insert a choice element inside an actual
1506 circuit he will have to explicitly instantiate a multiplexer-like component.
1508 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1509 such as case-statements and pattern matching, are synthesized to choice
1510 elements in the eventual circuit. As such, richer control structures can both
1511 be specified and synthesized in \CLaSH\ compared to any of the embedded
1512 languages, such as: Hawk, ForSyDe, or Lava.
1514 The merits of polymorphic typing, combined with higher-order functions, are
1515 now also recognized in the `main-stream' hardware description languages,
1516 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support
1517 for generics has been extended to types and subprograms, allowing a developer
1518 to describe components with polymorphic ports and function-valued arguments.
1519 Note that the types and subprograms still require an explicit generic map,
1520 whereas types can be automatically inferred, and function-values can be
1521 automatically propagated by the \CLaSH\ compiler. There are also no (generally
1522 available) \VHDL\ synthesis tools that currently support the \VHDL-2008
1523 standard, and thus the synthesis of polymorphic types and function-valued
1526 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1528 % A functional language designed specifically for hardware design is
1529 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1530 % language called \acro{FL}~\cite{FL} to la
1532 % An example of a floating figure using the graphicx package.
1533 % Note that \label must occur AFTER (or within) \caption.
1534 % For figures, \caption should occur after the \includegraphics.
1535 % Note that IEEEtran v1.7 and later has special internal code that
1536 % is designed to preserve the operation of \label within \caption
1537 % even when the captionsoff option is in effect. However, because
1538 % of issues like this, it may be the safest practice to put all your
1539 % \label just after \caption rather than within \caption{}.
1541 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1542 % option should be used if it is desired that the figures are to be
1543 % displayed while in draft mode.
1547 %\includegraphics[width=2.5in]{myfigure}
1548 % where an .eps filename suffix will be assumed under latex,
1549 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1550 % via \DeclareGraphicsExtensions.
1551 %\caption{Simulation Results}
1555 % Note that IEEE typically puts floats only at the top, even when this
1556 % results in a large percentage of a column being occupied by floats.
1559 % An example of a double column floating figure using two subfigures.
1560 % (The subfig.sty package must be loaded for this to work.)
1561 % The subfigure \label commands are set within each subfloat command, the
1562 % \label for the overall figure must come after \caption.
1563 % \hfil must be used as a separator to get equal spacing.
1564 % The subfigure.sty package works much the same way, except \subfigure is
1565 % used instead of \subfloat.
1567 %\begin{figure*}[!t]
1568 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1569 %\label{fig_first_case}}
1571 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1572 %\label{fig_second_case}}}
1573 %\caption{Simulation results}
1577 % Note that often IEEE papers with subfigures do not employ subfigure
1578 % captions (using the optional argument to \subfloat), but instead will
1579 % reference/describe all of them (a), (b), etc., within the main caption.
1582 % An example of a floating table. Note that, for IEEE style tables, the
1583 % \caption command should come BEFORE the table. Table text will default to
1584 % \footnotesize as IEEE normally uses this smaller font for tables.
1585 % The \label must come after \caption as always.
1588 %% increase table row spacing, adjust to taste
1589 %\renewcommand{\arraystretch}{1.3}
1590 % if using array.sty, it might be a good idea to tweak the value of
1591 % \extrarowheight as needed to properly center the text within the cells
1592 %\caption{An Example of a Table}
1593 %\label{table_example}
1595 %% Some packages, such as MDW tools, offer better commands for making tables
1596 %% than the plain LaTeX2e tabular which is used here.
1597 %\begin{tabular}{|c||c|}
1607 % Note that IEEE does not put floats in the very first column - or typically
1608 % anywhere on the first page for that matter. Also, in-text middle ("here")
1609 % positioning is not used. Most IEEE journals/conferences use top floats
1610 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1611 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1612 % command of the stfloats package.
1616 \section{Conclusion}
1617 This research demonstrates once more that functional languages are well suited
1618 for hardware descriptions: function applications provide an elegant notation
1619 for component instantiation. Where this research goes beyond the existing
1620 (functional) hardware descriptions languages is the inclusion of various
1621 choice elements, such as pattern matching, that are well suited to describe
1622 the conditional assignments in control-oriented circuits. Besides being able
1623 to translate these basic constructs to synthesizable \VHDL, the prototype
1624 compiler can also correctly translate descriptions that contain both
1625 polymorphic types and function-valued arguments.
1627 Where recent functional hardware description languages have mostly opted to
1628 embed themselves in an existing functional language, this research features a
1629 `true' compiler. As a result there is a clear distinction between compile-time
1630 and run-time, which allows a myriad of choice constructs to be part of the
1631 actual circuit description; a feature the embedded hardware description
1632 languages do not offer.
1634 \section{Future Work}
1635 The choice of describing state explicitly as extra arguments and results can
1636 be seen as a mixed blessing. Even though the description that use state are
1637 usually very clear, one finds that dealing with unpacking, passing, receiving
1638 and repacking can become tedious and even error-prone, especially in the case
1639 of sub-states. Removing this boilerplate, or finding a more suitable
1640 abstraction mechanism would make \CLaSH\ easier to use.
1642 The transformations in normalization phase of the prototype compiler were
1643 developed in an ad-hoc manner, which makes the existence of many desirable
1644 properties unclear. Such properties include whether the complete set of
1645 transformations will always lead to a normal form or if the normalization
1646 process always terminates. Though various use cases suggests that these
1647 properties usually hold, they have not been formally proven. A systematic
1648 approach to defining the set of transformations allows one to proof that the
1649 earlier mentioned properties do indeed exist.
1651 % conference papers do not normally have an appendix
1654 % use section* for acknowledgement
1655 % \section*{Acknowledgment}
1657 % The authors would like to thank...
1659 % trigger a \newpage just before the given reference
1660 % number - used to balance the columns on the last page
1661 % adjust value as needed - may need to be readjusted if
1662 % the document is modified later
1663 % \IEEEtriggeratref{14}
1664 % The "triggered" command can be changed if desired:
1665 %\IEEEtriggercmd{\enlargethispage{-5in}}
1667 % references section
1669 % can use a bibliography generated by BibTeX as a .bbl file
1670 % BibTeX documentation can be easily obtained at:
1671 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1672 % The IEEEtran BibTeX style support page is at:
1673 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1674 \bibliographystyle{IEEEtran}
1675 % argument is your BibTeX string definitions and bibliography database(s)
1676 \bibliography{clash}
1678 % <OR> manually copy in the resultant .bbl file
1679 % set second argument of \begin to the number of references
1680 % (used to reserve space for the reference number labels box)
1681 % \begin{thebibliography}{1}
1683 % \bibitem{IEEEhowto:kopka}
1684 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1685 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1687 % \end{thebibliography}
1695 % vim: set ai sw=2 sts=2 expandtab: