7 %% http://www.michaelshell.org/
8 %% for current contact information.
10 %% This is a skeleton file demonstrating the use of IEEEtran.cls
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42 %% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
43 %% bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex
44 %%*************************************************************************
46 % *** Authors should verify (and, if needed, correct) their LaTeX system ***
47 % *** with the testflow diagnostic prior to trusting their LaTeX platform ***
48 % *** with production work. IEEE's font choices can trigger bugs that do ***
49 % *** not appear when using other class files. ***
50 % The testflow support page is at:
51 % http://www.michaelshell.org/tex/testflow/
55 % Note that the a4paper option is mainly intended so that authors in
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62 % Also note that the "draftcls" or "draftclsnofoot", not "draft", option
63 % should be used if it is desired that the figures are to be displayed in
66 \documentclass[conference,pdf,a4paper,10pt,final,twoside,twocolumn]{IEEEtran}
67 % Add the compsoc option for Computer Society conferences.
69 % If IEEEtran.cls has not been installed into the LaTeX system files,
70 % manually specify the path to it like:
71 % \documentclass[conference]{../sty/IEEEtran}
73 % Some very useful LaTeX packages include:
74 % (uncomment the ones you want to load)
76 % *** MISC UTILITY PACKAGES ***
79 % Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
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102 % cite.sty was written by Donald Arseneau
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104 % \cite{} output to follow that of IEEE. Loading the cite package will
105 % result in citation numbers being automatically sorted and properly
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108 % \cite will automatically add leading space, if needed. Use cite.sty's
109 % noadjust option (cite.sty V3.8 and later) if you want to turn this off.
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130 % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
132 % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
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159 % You can find documentation about the pdfTeX application at:
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166 % *** MATH PACKAGES ***
168 %\usepackage[cmex10]{amsmath}
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211 % *** ALIGNMENT PACKAGES ***
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234 % IEEEtran contains the IEEEeqnarray family of commands that can be used to
235 % generate multiline equations as well as matrices, tables, etc., of high
239 %\usepackage{eqparbox}
240 % Also of notable interest is Scott Pakin's eqparbox package for creating
241 % (automatically sized) equal width boxes - aka "natural width parboxes".
243 % http://www.ctan.org/tex-archive/macros/latex/contrib/eqparbox/
249 % *** SUBFIGURE PACKAGES ***
250 %\usepackage[tight,footnotesize]{subfigure}
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252 % easy to put subfigures in your figures. e.g., "Figure 1a and 1b". For IEEE
253 % work, it is a good idea to load it with the tight package option to reduce
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257 % http://www.ctan.org/tex-archive/obsolete/macros/latex/contrib/subfigure/
258 % subfigure.sty has been superceeded by subfig.sty.
262 %\usepackage[caption=false]{caption}
263 %\usepackage[font=footnotesize]{subfig}
264 % subfig.sty, also written by Steven Douglas Cochran, is the modern
265 % replacement for subfigure.sty. However, subfig.sty requires and
266 % automatically loads Axel Sommerfeldt's caption.sty which will override
267 % IEEEtran.cls handling of captions and this will result in nonIEEE style
268 % figure/table captions. To prevent this problem, be sure and preload
269 % caption.sty with its "caption=false" package option. This is will preserve
270 % IEEEtran.cls handing of captions. Version 1.3 (2005/06/28) and later
271 % (recommended due to many improvements over 1.2) of subfig.sty supports
272 % the caption=false option directly:
273 %\usepackage[caption=false,font=footnotesize]{subfig}
275 % The latest version and documentation can be obtained at:
276 % http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/
277 % The latest version and documentation of caption.sty can be obtained at:
278 % http://www.ctan.org/tex-archive/macros/latex/contrib/caption/
283 % *** FLOAT PACKAGES ***
285 %\usepackage{fixltx2e}
286 % fixltx2e, the successor to the earlier fix2col.sty, was written by
287 % Frank Mittelbach and David Carlisle. This package corrects a few problems
288 % in the LaTeX2e kernel, the most notable of which is that in current
289 % LaTeX2e releases, the ordering of single and double column floats is not
290 % guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
291 % single column figure to be placed prior to an earlier double column
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293 % http://www.ctan.org/tex-archive/macros/latex/base/
297 %\usepackage{stfloats}
298 % stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
299 % the ability to do double column floats at the bottom of the page as well
300 % as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
301 % LaTeX2e). It also provides a command:
303 % to enable the placement of footnotes below bottom floats (the standard
304 % LaTeX2e kernel puts them above bottom floats). This is an invasive package
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309 % Documentation is contained in the stfloats.sty comments as well as in the
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311 % does not allow \baselineskip to stretch. Authors submitting work to the
312 % IEEE should note that IEEE rarely uses double column equations and
313 % that authors should try to avoid such use. Do not be tempted to use the
314 % cuted.sty or midfloat.sty packages (also by Sigitas Tolusis) as IEEE does
315 % not format its papers in such ways.
321 % *** PDF, URL AND HYPERLINK PACKAGES ***
324 % url.sty was written by Donald Arseneau. It provides better support for
325 % handling and breaking URLs. url.sty is already installed on most LaTeX
326 % systems. The latest version can be obtained at:
327 % http://www.ctan.org/tex-archive/macros/latex/contrib/misc/
328 % Read the url.sty source comments for usage information. Basically,
335 % *** Do not adjust lengths that control margins, column widths, etc. ***
336 % *** Do not use packages that alter fonts (such as pslatex). ***
337 % There should be no need to do such things with IEEEtran.cls V1.6 and later.
338 % (Unless specifically asked to do so by the journal or conference you plan
339 % to submit to, of course. )
341 % correct bad hyphenation here
342 \hyphenation{op-tical net-works semi-conduc-tor}
344 % Macro for certain acronyms in small caps. Doesn't work with the
345 % default font, though (it contains no smallcaps it seems).
346 \def\acro#1{{\small{#1}}}
347 \def\VHDL{\acro{VHDL}}
349 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
351 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
352 % we'll get something more complex later on.
353 \def\hs#1{\texttt{#1}}
354 \def\quote#1{``{#1}"}
356 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
358 \settowidth{\labelwidth}{#1:}
359 \setlength{\labelsep}{0.5cm}
360 \setlength{\leftmargin}{\labelwidth}
361 \addtolength{\leftmargin}{\labelsep}
362 \setlength{\rightmargin}{0pt}
363 \setlength{\listparindent}{\parindent}
364 \setlength{\itemsep}{0 ex plus 0.2ex}
365 \renewcommand{\makelabel}[1]{##1:\hfil}
370 \usepackage{paralist}
372 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
374 %include polycode.fmt
380 % can use linebreaks \\ within to get better formatting as desired
381 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
384 % author names and affiliations
385 % use a multiple column layout for up to three different
387 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
388 \IEEEauthorblockA{University of Twente, Department of EEMCS\\
389 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
390 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl}}
392 % \IEEEauthorblockN{Homer Simpson}
393 % \IEEEauthorblockA{Twentieth Century Fox\\
395 % Email: homer@thesimpsons.com}
397 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
398 % \IEEEauthorblockA{Starfleet Academy\\
399 % San Francisco, California 96678-2391\\
400 % Telephone: (800) 555--1212\\
401 % Fax: (888) 555--1212}}
403 % conference papers do not typically use \thanks and this command
404 % is locked out in conference mode. If really needed, such as for
405 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
406 % after \documentclass
408 % for over three affiliations, or if they all won't fit within the width
409 % of the page, use this alternative format:
411 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
412 %Homer Simpson\IEEEauthorrefmark{2},
413 %James Kirk\IEEEauthorrefmark{3},
414 %Montgomery Scott\IEEEauthorrefmark{3} and
415 %Eldon Tyrell\IEEEauthorrefmark{4}}
416 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
417 %Georgia Institute of Technology,
418 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
419 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
420 %Email: homer@thesimpsons.com}
421 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
422 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
423 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
428 % use for special paper notices
429 %\IEEEspecialpapernotice{(Invited Paper)}
434 % make the title area
440 The abstract goes here.
442 % IEEEtran.cls defaults to using nonbold math in the Abstract.
443 % This preserves the distinction between vectors and scalars. However,
444 % if the conference you are submitting to favors bold math in the abstract,
445 % then you can use LaTeX's standard command \boldmath at the very start
446 % of the abstract to achieve this. Many IEEE journals/conferences frown on
447 % math in the abstract anyway.
454 % For peer review papers, you can put extra information on the cover
456 % \ifCLASSOPTIONpeerreview
457 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
460 % For peerreview papers, this IEEEtran command inserts a page break and
461 % creates the second title. It will be ignored for other modes.
462 \IEEEpeerreviewmaketitle
465 \section{Introduction}
466 Hardware description languages has allowed the productivity of hardware
467 engineers to keep pace with the development of chip technology. Standard
468 Hardware description languages, like \VHDL\ and Verilog, allowed an engineer
469 to describe circuits using a programming language. These standard languages
470 are very good at describing detailed hardware properties such as timing
471 behavior, but are generally cumbersome in expressing higher-level
472 abstractions. These languages also tend to have a complex syntax and a lack of
473 formal semantics. To overcome these complexities, and raise the abstraction
474 level, a great number of approaches based on functional languages has been
475 proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,ForSyDe1,Wired,reFLect}. The idea
476 of using functional languages started in the early 1980s \cite{Cardelli1981,
477 muFP,DAISY,FHDL}, a time which also saw the birth of the currently popular
478 hardware description languages such as \VHDL. What gives functional languages
479 as hardware description languages their merits is the fact that basic
480 combinatorial circuits are equivalent to mathematical function, and that
481 functional languages lend themselves very well to describe and compose these
482 mathematical functions.
484 In an attempt to decrease the amount of work involved with creating all the
485 required tooling, such as parsers and type-checkers, many functional hardware
486 description languages are embedded as a domain specific language inside the
487 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. What this
488 means is that a developer is given a library of Haskell functions and types
489 that together form the language primitives of the domain specific language.
490 Using these functions, the designer does not only describes a circuit, but
491 actually builds a large domain-specific datatype which can be further
492 processed by an embedded compiler. This compiler actually runs in the same
493 environment as the description; as a result compile-time and run-time become
494 hard to define, as the embedded compiler is usually compiled by the same
495 Haskell compiler as the circuit description itself.
497 The approach taken in this research is not to make another domain specific
498 language embedded in Haskell, but to use (a subset) of the Haskell language
499 itself to be used as hardware description language. By taking this approach,
500 we can capture certain language constructs, such as Haskell's choice elements
501 (if-statement, case-statment, etc.), which are not available in the functional
502 hardware description languages that are embedded in Haskell. As far as the
503 authors know, such extensive support for choice-elements is new in the domain
504 of functional hardware description language. As the hardware descriptions are
505 plain Haskell functions, these descriptions can be compiled for simulation
506 using using the optimizing Haskell compiler \GHC.
508 Like the standard hardware description languages, descriptions made in a
509 functional hardware description languages must eventually be converted into a
510 netlist. This research also features an a prototype translater called \CLaSH\
511 (pronounced: Clash), which converts the Haskell code to equivalently behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist format by optimizing \VHDL\ synthesis tools.
513 \section{Hardware description in Haskell}
515 \subsection{Function application}
516 The basic syntactic elements of a functional program are functions
517 and function application. These have a single obvious \VHDL\
518 translation: each top level function becomes a hardware component,
519 where each argument is an input port and the result value is the
520 (single) output port. This output port can have a complex type (such
521 as a tuple), so having just a single output port does not create a
524 Each function application in turn becomes component instantiation.
525 Here, the result of each argument expression is assigned to a
526 signal, which is mapped to the corresponding input port. The output
527 port of the function is also mapped to a signal, which is used as
528 the result of the application itself.
530 Since every top level function generates its own component, the
531 hierarchy of of function calls is reflected in the final \VHDL\
532 output as well, creating a hierarchical \VHDL\ description of the
533 hardware. This separation in different components makes the
534 resulting \VHDL\ output easier to read and debug.
536 Example that defines the \texttt{mac} function by applying the
537 \texttt{add} and \texttt{mul} functions to calculate $a * b + c$:
540 mac a b c = add (mul a b) c
543 \comment{TODO: Pretty picture}
546 Although describing components and connections allows describing a
547 lot of hardware designs already, there is an obvious thing missing:
548 choice. We need some way to be able to choose between values based
549 on another value. In Haskell, choice is achieved by \hs{case}
550 expressions, \hs{if} expressions, pattern matching and guards.
552 The easiest of these are of course case expressions (and \hs{if}
553 expressions, which can be very directly translated to \hs{case}
554 expressions). A \hs{case} expression can in turn simply be
555 translated to a conditional assignment in \VHDL, where the
556 conditions use equality comparisons against the constructors in the
557 \hs{case} expressions.
559 A slightly more complex (but very powerful) form of choice is
560 pattern matching. A function can be defined in multiple clauses,
561 where each clause specifies a pattern. When the arguments match the
562 pattern, the corresponding clause will be used.
564 A pattern match (with optional guards) can also be implemented using
565 conditional assignments in \VHDL, where the condition is the logical
566 and of comparison results of each part of the pattern as well as the
569 Contrived example that sums two values when they are equal or
570 non-equal (depending on the predicate given) and returns 0
571 otherwise. This shows three implementations, one using and if
572 expression, one using only case expressions and one using pattern
576 sumif pred a b = if pred == Eq && a == b ||
577 pred == Neq && a != b
581 sumif pred a b = case pred of
585 Neq -> case a != b of
589 sumif Eq a b | a == b = a + b
590 sumif Neq a b | a != b = a + b
594 \comment{TODO: Pretty picture}
597 Translation of two most basic functional concepts has been
598 discussed: function application and choice. Before looking further
599 into less obvious concepts like higher-order expressions and
600 polymorphism, the possible types that can be used in hardware
601 descriptions will be discussed.
603 Some way is needed to translate every value used to its hardware
604 equivalents. In particular, this means a hardware equivalent for
605 every \emph{type} used in a hardware description is needed.
607 The following types are \emph{built-in}, meaning that their hardware
608 translation is fixed into the \CLaSH compiler. A designer can also
609 define his own types, which will be translated into hardware types
610 using translation rules that are discussed later on.
612 \subsection{Built-in types}
615 This is the most basic type available. It can have two values:
616 \hs{Low} and \hs{High}. It is mapped directly onto the
617 \texttt{std\_logic} \VHDL\ type.
619 This is a basic logic type. It can have two values: \hs{True}
620 and \hs{False}. It is translated to \texttt{std\_logic} exactly
621 like the \hs{Bit} type (where a value of \hs{True} corresponds
622 to a value of \hs{High}). Supporting the Bool type is
623 particularly useful to support \hs{if ... then ... else ...}
624 expressions, which always have a \hs{Bool} value for the
626 \item[\hs{SizedWord}, \hs{SizedInt}]
627 These are types to represent integers. A \hs{SizedWord} is unsigned,
628 while a \hs{SizedInt} is signed. These types are parametrized by a
629 length type, so you can define an unsigned word of 32 bits wide as
633 type Word32 = SizedWord D32
636 Here, a type synonym \hs{Word32} is defined that is equal to the
637 \hs{SizedWord} type constructor applied to the type \hs{D32}. \hs{D32}
638 is the \emph{type level representation} of the decimal number 32,
639 making the \hs{Word32} type a 32-bit unsigned word. These types are
640 translated to the \VHDL\ \texttt{unsigned} and \texttt{signed}
643 This is a vector type, that can contain elements of any other type and
644 has a fixed length. The \hs{Vector} type constructor takes two type
645 arguments: the length of the vector and the type of the elements
646 contained in it. The state type of an 8 element register bank would
650 type RegisterState = Vector D8 Word32
653 Here, a type synonym \hs{RegisterState} is defined that is equal to
654 the \hs{Vector} type constructor applied to the types \hs{D8} (The
655 type level representation of the decimal number 8) and \hs{Word32}
656 (The 32 bit word type as defined above). In other words, the
657 \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
658 vector is translated to a \VHDL\ array type.
659 \item[\hs{RangedWord}]
660 This is another type to describe integers, but unlike the previous
661 two it has no specific bit-width, but an upper bound. This means that
662 its range is not limited to powers of two, but can be any number.
663 A \hs{RangedWord} only has an upper bound, its lower bound is
664 implicitly zero. The main purpose of the \hs{RangedWord} type is to be
665 used as an index to a \hs{Vector}.
667 \comment{TODO: Perhaps remove this example?} To define an index for
668 the 8 element vector above, we would do:
671 type RegisterIndex = RangedWord D7
674 Here, a type synonym \hs{RegisterIndex} is defined that is equal to
675 the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
676 other words, this defines an unsigned word with values from
677 0 to 7 (inclusive). This word can be be used to index the
678 8 element vector \hs{RegisterState} above. This type is translated to
679 the \texttt{unsigned} \VHDL type.
682 \subsection{User-defined types}
683 There are three ways to define new types in Haskell: algebraic
684 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
685 keyword and type renamings with the \hs{newtype} keyword. \GHC\
686 offers a few more advanced ways to introduce types (type families,
687 existential typing, {\small{GADT}}s, etc.) which are not standard
688 Haskell. These are not currently supported.
690 Only an algebraic datatype declaration actually introduces a
691 completely new type, for which we provide the \VHDL\ translation
692 below. Type synonyms and renamings only define new names for
693 existing types (where synonyms are completely interchangeable and
694 renamings need explicit conversion). Therefore, these do not need
695 any particular \VHDL\ translation, a synonym or renamed type will
696 just use the same representation as the original type. The
697 distinction between a renaming and a synonym does no longer matter
698 in hardware and can be disregarded in the generated \VHDL.
700 For algebraic types, we can make the following distinction:
703 \item[\bf{Single constructor}]
704 Algebraic datatypes with a single constructor with one or more
705 fields, are essentially a way to pack a few values together in a
706 record-like structure. An example of such a type is the following pair
710 data IntPair = IntPair Int Int
713 Haskell's builtin tuple types are also defined as single
714 constructor algebraic types and are translated according to this
715 rule by the \CLaSH compiler. These types are translated to \VHDL\
716 record types, with one field for every field in the constructor.
717 \item[\bf{No fields}]
718 Algebraic datatypes with multiple constructors, but without any
719 fields are essentially a way to get an enumeration-like type
720 containing alternatives. Note that Haskell's \hs{Bool} type is also
721 defined as an enumeration type, but we have a fixed translation for
722 that. These types are translated to \VHDL\ enumerations, with one
723 value for each constructor. This allows references to these
724 constructors to be translated to the corresponding enumeration value.
725 \item[\bf{Multiple constructors with fields}]
726 Algebraic datatypes with multiple constructors, where at least
727 one of these constructors has one or more fields are not
732 A very important concept in hardware it the concept of state. In a
733 stateful design, the outputs depend on the history of the inputs, or the
734 state. State is usually stored in registers, which retain their value
735 during a clock cycle. As we want to describe more than simple
736 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
738 An important property in Haskell, and in most other functional languages,
739 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
742 \item given the same arguments twice, it should return the same value in
744 \item when the function is called, it should not have observable
747 This purity property is important for functional languages, since it
748 enables all kinds of mathematical reasoning that could not be guaranteed
749 correct for impure functions. Pure functions are as such a perfect match
750 for a combinatorial circuit, where the output solely depends on the
751 inputs. When a circuit has state however, it can no longer be simply
752 described by a pure function. Simply removing the purity property is not a
753 valid option, as the language would then lose many of it mathematical
754 properties. In an effort to include the concept of state in pure
755 functions, the current value of the state is made an argument of the
756 function; the updated state becomes part of the result.
758 A simple example is the description of an accumulator circuit:
760 acc :: Word -> State Word -> (State Word, Word)
761 acc inp (State s) = (State s', outp)
766 This approach makes the state of a function very explicit: which variables
767 are part of the state is completely determined by the type signature. This
768 approach to state is well suited to be used in combination with the
769 existing code and language features, such as all the choice constructs, as
770 state values are just normal values.
771 \section{\CLaSH\ prototype}
775 \section{Related work}
776 Many functional hardware description languages have been developed over the
777 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
778 extension of Backus' \acro{FP} language to synchronous streams, designed
779 particularly for describing and reasoning about regular circuits. The
780 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
781 circuits, and has a particular focus on layout. \acro{HML}~\cite{HML2} is a
782 hardware modeling language based on the strict functional language
783 \acro{ML}, and has support for polymorphic types and higher-order functions.
784 Published work suggests that there is no direct simulation support for
785 \acro{HML}, and that the translation to \VHDL\ is only partial.
787 Like this work, many functional hardware description languages have some sort
788 of foundation in the functional programming language Haskell.
789 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
790 specifications used to model the behavior of superscalar microprocessors. Hawk
791 specifications can be simulated, but there seems to be no support for
792 automated circuit synthesis. The ForSyDe~\cite{ForSyDe2} system uses Haskell
793 to specify abstract system models, which can (manually) be transformed into an
794 implementation model using semantic preserving transformations. ForSyDe has
795 several simulation and synthesis backends, though synthesis is restricted to
796 the synchronous subset of the ForSyDe language.
798 Lava~\cite{Lava} is a hardware description language that focuses on the
799 structural representation of hardware. Besides support for simulation and
800 circuit synthesis, Lava descriptions can be interfaced with formal method
801 tools for formal verification. Lava descriptions are actually circuit
802 generators when viewed from a synthesis viewpoint, in that the language
803 elements of Haskell, such as choice, can be used to guide the circuit
804 generation. If a developer wants to insert a choice element inside an actual
805 circuit he will have to specify this explicitly as a component. In this
806 respect \CLaSH\ differs from Lava, in that all the choice elements, such as
807 case-statements and pattern matching, are synthesized to choice elements in the
808 eventual circuit. As such, richer control structures can both be specified and
809 synthesized in \CLaSH\ compared to any of the languages mentioned in this
812 The merits of polymorphic typing, combined with higher-order functions, are
813 now also recognized in the `main-stream' hardware description languages,
814 exemplified by the new \VHDL\-2008 standard~\cite{VHDL2008}. \VHDL-2008 has
815 support to specify types as generics, thus allowing a developer to describe
816 polymorphic components. Note that those types still require an explicit
817 generic map, whereas type-inference and type-specialization are implicit in
820 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
822 % A functional language designed specifically for hardware design is
823 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
824 % language called \acro{FL}~\cite{FL} to la
826 % An example of a floating figure using the graphicx package.
827 % Note that \label must occur AFTER (or within) \caption.
828 % For figures, \caption should occur after the \includegraphics.
829 % Note that IEEEtran v1.7 and later has special internal code that
830 % is designed to preserve the operation of \label within \caption
831 % even when the captionsoff option is in effect. However, because
832 % of issues like this, it may be the safest practice to put all your
833 % \label just after \caption rather than within \caption{}.
835 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
836 % option should be used if it is desired that the figures are to be
837 % displayed while in draft mode.
841 %\includegraphics[width=2.5in]{myfigure}
842 % where an .eps filename suffix will be assumed under latex,
843 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
844 % via \DeclareGraphicsExtensions.
845 %\caption{Simulation Results}
849 % Note that IEEE typically puts floats only at the top, even when this
850 % results in a large percentage of a column being occupied by floats.
853 % An example of a double column floating figure using two subfigures.
854 % (The subfig.sty package must be loaded for this to work.)
855 % The subfigure \label commands are set within each subfloat command, the
856 % \label for the overall figure must come after \caption.
857 % \hfil must be used as a separator to get equal spacing.
858 % The subfigure.sty package works much the same way, except \subfigure is
859 % used instead of \subfloat.
862 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
863 %\label{fig_first_case}}
865 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
866 %\label{fig_second_case}}}
867 %\caption{Simulation results}
871 % Note that often IEEE papers with subfigures do not employ subfigure
872 % captions (using the optional argument to \subfloat), but instead will
873 % reference/describe all of them (a), (b), etc., within the main caption.
876 % An example of a floating table. Note that, for IEEE style tables, the
877 % \caption command should come BEFORE the table. Table text will default to
878 % \footnotesize as IEEE normally uses this smaller font for tables.
879 % The \label must come after \caption as always.
882 %% increase table row spacing, adjust to taste
883 %\renewcommand{\arraystretch}{1.3}
884 % if using array.sty, it might be a good idea to tweak the value of
885 % \extrarowheight as needed to properly center the text within the cells
886 %\caption{An Example of a Table}
887 %\label{table_example}
889 %% Some packages, such as MDW tools, offer better commands for making tables
890 %% than the plain LaTeX2e tabular which is used here.
891 %\begin{tabular}{|c||c|}
901 % Note that IEEE does not put floats in the very first column - or typically
902 % anywhere on the first page for that matter. Also, in-text middle ("here")
903 % positioning is not used. Most IEEE journals/conferences use top floats
904 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
905 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
906 % command of the stfloats package.
911 The conclusion goes here.
916 % conference papers do not normally have an appendix
919 % use section* for acknowledgement
920 \section*{Acknowledgment}
923 The authors would like to thank...
929 % trigger a \newpage just before the given reference
930 % number - used to balance the columns on the last page
931 % adjust value as needed - may need to be readjusted if
932 % the document is modified later
933 %\IEEEtriggeratref{8}
934 % The "triggered" command can be changed if desired:
935 %\IEEEtriggercmd{\enlargethispage{-5in}}
939 % can use a bibliography generated by BibTeX as a .bbl file
940 % BibTeX documentation can be easily obtained at:
941 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
942 % The IEEEtran BibTeX style support page is at:
943 % http://www.michaelshell.org/tex/ieeetran/bibtex/
944 \bibliographystyle{IEEEtran}
945 % argument is your BibTeX string definitions and bibliography database(s)
946 \bibliography{IEEEabrv,clash.bib}
948 % <OR> manually copy in the resultant .bbl file
949 % set second argument of \begin to the number of references
950 % (used to reserve space for the reference number labels box)
951 % \begin{thebibliography}{1}
953 % \bibitem{IEEEhowto:kopka}
954 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
955 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
957 % \end{thebibliography}
965 % vim: set ai sw=2 sts=2 expandtab: