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67 \documentclass[conference,pdf,a4paper,10pt,final,twoside,twocolumn]{IEEEtran}
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263 % replacement for subfigure.sty. However, subfig.sty requires and
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267 % caption.sty with its "caption=false" package option. This is will preserve
268 % IEEEtran.cls handing of captions. Version 1.3 (2005/06/28) and later
269 % (recommended due to many improvements over 1.2) of subfig.sty supports
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281 % *** FLOAT PACKAGES ***
283 %\usepackage{fixltx2e}
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333 % *** Do not adjust lengths that control margins, column widths, etc. ***
334 % *** Do not use packages that alter fonts (such as pslatex). ***
335 % There should be no need to do such things with IEEEtran.cls V1.6 and later.
336 % (Unless specifically asked to do so by the journal or conference you plan
337 % to submit to, of course. )
339 % correct bad hyphenation here
340 \hyphenation{op-tical net-works semi-conduc-tor}
342 % Macro for certain acronyms in small caps. Doesn't work with the
343 % default font, though (it contains no smallcaps it seems).
344 \def\acro#1{{\small{#1}}}
345 \def\VHDL{\acro{VHDL}}
347 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
349 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
350 % we'll get something more complex later on.
351 \def\hs#1{\texttt{#1}}
352 \def\quote#1{``{#1}"}
354 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
356 \settowidth{\labelwidth}{#1:}
357 \setlength{\labelsep}{0.5cm}
358 \setlength{\leftmargin}{\labelwidth}
359 \addtolength{\leftmargin}{\labelsep}
360 \setlength{\rightmargin}{0pt}
361 \setlength{\listparindent}{\parindent}
362 \setlength{\itemsep}{0 ex plus 0.2ex}
363 \renewcommand{\makelabel}[1]{##1:\hfil}
368 \usepackage{paralist}
370 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
372 \usepackage{cleveref}
373 \crefname{figure}{figure}{figures}
374 \newcommand{\fref}[1]{\cref{#1}}
375 \newcommand{\Fref}[1]{\Cref{#1}}
378 %include polycode.fmt
384 % can use linebreaks \\ within to get better formatting as desired
385 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
388 % author names and affiliations
389 % use a multiple column layout for up to three different
391 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
392 \IEEEauthorblockA{University of Twente, Department of EEMCS\\
393 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
394 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl}}
396 % \IEEEauthorblockN{Homer Simpson}
397 % \IEEEauthorblockA{Twentieth Century Fox\\
399 % Email: homer@thesimpsons.com}
401 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
402 % \IEEEauthorblockA{Starfleet Academy\\
403 % San Francisco, California 96678-2391\\
404 % Telephone: (800) 555--1212\\
405 % Fax: (888) 555--1212}}
407 % conference papers do not typically use \thanks and this command
408 % is locked out in conference mode. If really needed, such as for
409 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
410 % after \documentclass
412 % for over three affiliations, or if they all won't fit within the width
413 % of the page, use this alternative format:
415 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
416 %Homer Simpson\IEEEauthorrefmark{2},
417 %James Kirk\IEEEauthorrefmark{3},
418 %Montgomery Scott\IEEEauthorrefmark{3} and
419 %Eldon Tyrell\IEEEauthorrefmark{4}}
420 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
421 %Georgia Institute of Technology,
422 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
423 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
424 %Email: homer@thesimpsons.com}
425 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
426 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
427 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
432 % use for special paper notices
433 %\IEEEspecialpapernotice{(Invited Paper)}
438 % make the title area
444 The abstract goes here.
446 % IEEEtran.cls defaults to using nonbold math in the Abstract.
447 % This preserves the distinction between vectors and scalars. However,
448 % if the conference you are submitting to favors bold math in the abstract,
449 % then you can use LaTeX's standard command \boldmath at the very start
450 % of the abstract to achieve this. Many IEEE journals/conferences frown on
451 % math in the abstract anyway.
458 % For peer review papers, you can put extra information on the cover
460 % \ifCLASSOPTIONpeerreview
461 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
464 % For peerreview papers, this IEEEtran command inserts a page break and
465 % creates the second title. It will be ignored for other modes.
466 \IEEEpeerreviewmaketitle
469 \section{Introduction}
470 Hardware description languages has allowed the productivity of hardware
471 engineers to keep pace with the development of chip technology. Standard
472 Hardware description languages, like \VHDL~\cite{VHDL2008} and
473 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
474 programming language. These standard languages are very good at describing
475 detailed hardware properties such as timing behavior, but are generally
476 cumbersome in expressing higher-level abstractions. In an attempt to raise the
477 abstraction level of the descriptions, a great number of approaches based on
478 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
479 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
480 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
481 a time which also saw the birth of the currently popular hardware description
482 languages such as \VHDL. The merit of using a functional language to describe
483 hardware comes from the fact that basic combinatorial circuits are equivalent
484 to mathematical functions and that functional languages are very good at
485 describing and composing mathematical functions.
487 In an attempt to decrease the amount of work involved with creating all the
488 required tooling, such as parsers and type-checkers, many functional hardware
489 description languages are embedded as a domain specific language inside the
490 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This
491 means that a developer is given a library of Haskell~\cite{Haskell} functions
492 and types that together form the language primitives of the domain specific
493 language. As a result of how the signals are modeled and abstracted, the
494 functions used to describe a circuit also build a large domain-specific
495 datatype (hidden from the designer) which can be further processed by an
496 embedded compiler. This compiler actually runs in the same environment as the
497 description; as a result compile-time and run-time become hard to define, as
498 the embedded compiler is usually compiled by the same Haskell compiler as the
499 circuit description itself.
501 The approach taken in this research is not to make another domain specific
502 language embedded in Haskell, but to use (a subset of) the Haskell language
503 itself for the purpose of describing hardware. By taking this approach, we can
504 capture certain language constructs, such as Haskell's choice elements
505 (if-constructs, case-constructs, pattern matching, etc.), which are not
506 available in the functional hardware description languages that are embedded
507 in Haskell as a domain specific languages. As far as the authors know, such
508 extensive support for choice-elements is new in the domain of functional
509 hardware description language. As the hardware descriptions are plain Haskell
510 functions, these descriptions can be compiled for simulation using using the
511 optimizing Haskell compiler \GHC.
513 Where descriptions in a conventional hardware description language have an
514 explicit clock for the purpose state and synchronicity, the clock is implied
515 in this research. The functions describe the behavior of the hardware between
516 clock cycles, as such, only synchronous systems can be described. Many
517 functional hardware description models signals as a stream of all values over
518 time; state is then modeled as a delay on this stream of values. The approach
519 taken in this research is to make the current state of a circuit part of the
520 input of the function and the updated state part of the output.
522 Like the standard hardware description languages, descriptions made in a
523 functional hardware description language must eventually be converted into a
524 netlist. This research also features a prototype translator called \CLaSH\
525 (pronounced: clash), which converts the Haskell code to equivalently behaving
526 synthesizable \VHDL\ code, ready to be converted to an actual netlist format
527 by an optimizing \VHDL\ synthesis tools.
529 \section{Hardware description in Haskell}
531 \subsection{Function application}
532 The basic syntactic elements of a functional program are functions
533 and function application. These have a single obvious translation to a
534 netlist: every function becomes a component, every function argument is an
535 input port and the result value is of a function is an output port. This
536 output port can have a complex type (such as a tuple), so having just a
537 single output port does not create a limitation. Each function application
538 in turn becomes a component instantiation. Here, the result of each
539 argument expression is assigned to a signal, which is mapped to the
540 corresponding input port. The output port of the function is also mapped
541 to a signal, which is used as the result of the application itself.
543 Since every top level function generates its own component, the
544 hierarchy of function calls is reflected in the final netlist aswell,
545 creating a hierarchical description of the hardware. This separation in
546 different components makes the resulting \VHDL\ output easier to read and
549 As an example we can see the netlist of the |mac| function in
550 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
551 function to calculate $a * b + c$:
553 mac a b c = add (mul a b) c
556 \centerline{\includegraphics{mac}}
557 \caption{Combinatorial Multiply-Accumulate}
560 The result of using a complex input type can be seen in
561 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
562 input tuple for the |a|, |b|, and |c| arguments:
564 mac (a, b, c) = add (mul a b) c
567 \centerline{\includegraphics{mac-nocurry}}
568 \caption{Combinatorial Multiply-Accumulate (complex input)}
569 \label{img:mac-comb-nocurry}
573 Although describing components and connections allows describing a
574 lot of hardware designs already, there is an obvious thing missing:
575 choice. We need some way to be able to choose between values based
576 on another value. In Haskell, choice is achieved by \hs{case}
577 expressions, \hs{if} expressions, pattern matching and guards.
579 The easiest of these are of course case expressions (and \hs{if}
580 expressions, which can be very directly translated to \hs{case}
581 expressions). A \hs{case} expression can in turn simply be
582 translated to a conditional assignment in \VHDL, where the
583 conditions use equality comparisons against the constructors in the
584 \hs{case} expressions.
586 A slightly more complex (but very powerful) form of choice is
587 pattern matching. A function can be defined in multiple clauses,
588 where each clause specifies a pattern. When the arguments match the
589 pattern, the corresponding clause will be used.
591 A pattern match (with optional guards) can also be implemented using
592 conditional assignments in \VHDL, where the condition is the logical
593 and of comparison results of each part of the pattern as well as the
596 Contrived example that sums two values when they are equal or
597 non-equal (depending on the predicate given) and returns 0
598 otherwise. This shows three implementations, one using and if
599 expression, one using only case expressions and one using pattern
603 sumif pred a b = if pred == Eq && a == b ||
604 pred == Neq && a != b
608 sumif pred a b = case pred of
612 Neq -> case a != b of
616 sumif Eq a b | a == b = a + b
617 sumif Neq a b | a != b = a + b
622 \centerline{\includegraphics{choice-ifthenelse}}
623 \caption{Choice - \emph{if-then-else}}
628 \centerline{\includegraphics{choice-case}}
629 \caption{Choice - \emph{case-statement / pattern matching}}
634 Translation of two most basic functional concepts has been
635 discussed: function application and choice. Before looking further
636 into less obvious concepts like higher-order expressions and
637 polymorphism, the possible types that can be used in hardware
638 descriptions will be discussed.
640 Some way is needed to translate every value used to its hardware
641 equivalents. In particular, this means a hardware equivalent for
642 every \emph{type} used in a hardware description is needed.
644 The following types are \emph{built-in}, meaning that their hardware
645 translation is fixed into the \CLaSH\ compiler. A designer can also
646 define his own types, which will be translated into hardware types
647 using translation rules that are discussed later on.
649 \subsection{Built-in types}
652 This is the most basic type available. It can have two values:
653 \hs{Low} and \hs{High}. It is mapped directly onto the
654 \texttt{std\_logic} \VHDL\ type.
656 This is a basic logic type. It can have two values: \hs{True}
657 and \hs{False}. It is translated to \texttt{std\_logic} exactly
658 like the \hs{Bit} type (where a value of \hs{True} corresponds
659 to a value of \hs{High}). Supporting the Bool type is
660 particularly useful to support \hs{if ... then ... else ...}
661 expressions, which always have a \hs{Bool} value for the
663 \item[\hs{SizedWord}, \hs{SizedInt}]
664 These are types to represent integers. A \hs{SizedWord} is unsigned,
665 while a \hs{SizedInt} is signed. These types are parametrized by a
666 length type, so you can define an unsigned word of 32 bits wide as
670 type Word32 = SizedWord D32
673 Here, a type synonym \hs{Word32} is defined that is equal to the
674 \hs{SizedWord} type constructor applied to the type \hs{D32}. \hs{D32}
675 is the \emph{type level representation} of the decimal number 32,
676 making the \hs{Word32} type a 32-bit unsigned word. These types are
677 translated to the \VHDL\ \texttt{unsigned} and \texttt{signed}
680 This is a vector type, that can contain elements of any other type and
681 has a fixed length. The \hs{Vector} type constructor takes two type
682 arguments: the length of the vector and the type of the elements
683 contained in it. The state type of an 8 element register bank would
687 type RegisterState = Vector D8 Word32
690 Here, a type synonym \hs{RegisterState} is defined that is equal to
691 the \hs{Vector} type constructor applied to the types \hs{D8} (The
692 type level representation of the decimal number 8) and \hs{Word32}
693 (The 32 bit word type as defined above). In other words, the
694 \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
695 vector is translated to a \VHDL\ array type.
696 \item[\hs{RangedWord}]
697 This is another type to describe integers, but unlike the previous
698 two it has no specific bit-width, but an upper bound. This means that
699 its range is not limited to powers of two, but can be any number.
700 A \hs{RangedWord} only has an upper bound, its lower bound is
701 implicitly zero. The main purpose of the \hs{RangedWord} type is to be
702 used as an index to a \hs{Vector}.
704 \comment{TODO: Perhaps remove this example?} To define an index for
705 the 8 element vector above, we would do:
708 type RegisterIndex = RangedWord D7
711 Here, a type synonym \hs{RegisterIndex} is defined that is equal to
712 the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
713 other words, this defines an unsigned word with values from
714 0 to 7 (inclusive). This word can be be used to index the
715 8 element vector \hs{RegisterState} above. This type is translated to
716 the \texttt{unsigned} \VHDL type.
719 \subsection{User-defined types}
720 There are three ways to define new types in Haskell: algebraic
721 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
722 keyword and type renamings with the \hs{newtype} keyword. \GHC\
723 offers a few more advanced ways to introduce types (type families,
724 existential typing, {\small{GADT}}s, etc.) which are not standard
725 Haskell. These are not currently supported.
727 Only an algebraic datatype declaration actually introduces a
728 completely new type, for which we provide the \VHDL\ translation
729 below. Type synonyms and renamings only define new names for
730 existing types (where synonyms are completely interchangeable and
731 renamings need explicit conversion). Therefore, these do not need
732 any particular \VHDL\ translation, a synonym or renamed type will
733 just use the same representation as the original type. The
734 distinction between a renaming and a synonym does no longer matter
735 in hardware and can be disregarded in the generated \VHDL.
737 For algebraic types, we can make the following distinction:
740 \item[\bf{Single constructor}]
741 Algebraic datatypes with a single constructor with one or more
742 fields, are essentially a way to pack a few values together in a
743 record-like structure. An example of such a type is the following pair
747 data IntPair = IntPair Int Int
750 Haskell's builtin tuple types are also defined as single
751 constructor algebraic types and are translated according to this
752 rule by the \CLaSH\ compiler. These types are translated to \VHDL\
753 record types, with one field for every field in the constructor.
754 \item[\bf{No fields}]
755 Algebraic datatypes with multiple constructors, but without any
756 fields are essentially a way to get an enumeration-like type
757 containing alternatives. Note that Haskell's \hs{Bool} type is also
758 defined as an enumeration type, but we have a fixed translation for
759 that. These types are translated to \VHDL\ enumerations, with one
760 value for each constructor. This allows references to these
761 constructors to be translated to the corresponding enumeration value.
762 \item[\bf{Multiple constructors with fields}]
763 Algebraic datatypes with multiple constructors, where at least
764 one of these constructors has one or more fields are not
768 \subsection{Polymorphic functions}
769 A powerful construct in most functional language is polymorphism.
770 This means the arguments of a function (and consequentially, values
771 within the function as well) do not need to have a fixed type.
772 Haskell supports \emph{parametric polymorphism}, meaning a
773 function's type can be parameterized with another type.
775 As an example of a polymorphic function, consider the following
776 \hs{append} function's type:
778 TODO: Use vectors instead of lists?
781 append :: [a] -> a -> [a]
784 This type is parameterized by \hs{a}, which can contain any type at
785 all. This means that append can append an element to a list,
786 regardless of the type of the elements in the list (but the element
787 added must match the elements in the list, since there is only one
790 This kind of polymorphism is extremely useful in hardware designs to
791 make operations work on a vector without knowing exactly what elements
792 are inside, routing signals without knowing exactly what kinds of
793 signals these are, or working with a vector without knowing exactly
794 how long it is. Polymorphism also plays an important role in most
795 higher order functions, as we will see in the next section.
797 The previous example showed unconstrained polymorphism (TODO: How is
798 this really called?): \hs{a} can have \emph{any} type. Furthermore,
799 Haskell supports limiting the types of a type parameter to specific
800 class of types. An example of such a type class is the \hs{Num}
801 class, which contains all of Haskell's numerical types.
803 Now, take the addition operator, which has the following type:
806 (+) :: Num a => a -> a -> a
809 This type is again parameterized by \hs{a}, but it can only contain
810 types that are \emph{instances} of the \emph{type class} \hs{Num}.
811 Our numerical built-in types are also instances of the \hs{Num}
812 class, so we can use the addition operator on \hs{SizedWords} as
813 well as on {SizedInts}.
815 In \CLaSH, unconstrained polymorphism is completely supported. Any
816 function defined can have any number of unconstrained type
817 parameters. The \CLaSH\ compiler will infer the type of every such
818 argument depending on how the function is applied. There is one
819 exception to this: The top level function that is translated, can
820 not have any polymorphic arguments (since it is never applied, so
821 there is no way to find out the actual types for the type
824 \CLaSH\ does not support user-defined type classes, but does use some
825 of the builtin ones for its builtin functions (like \hs{Num} and
828 \subsection{Higher order}
829 Another powerful abstraction mechanism in functional languages, is
830 the concept of \emph{higher order functions}, or \emph{functions as
831 a first class value}. This allows a function to be treated as a
832 value and be passed around, even as the argument of another
833 function. Let's clarify that with an example:
836 notList xs = map not xs
839 This defines a function \hs{notList}, with a single list of booleans
840 \hs{xs} as an argument, which simply negates all of the booleans in
841 the list. To do this, it uses the function \hs{map}, which takes
842 \emph{another function} as its first argument and applies that other
843 function to each element in the list, returning again a list of the
846 As you can see, the \hs{map} function is a higher order function,
847 since it takes another function as an argument. Also note that
848 \hs{map} is again a polymorphic function: It does not pose any
849 constraints on the type of elements in the list passed, other than
850 that it must be the same as the type of the argument the passed
851 function accepts. The type of elements in the resulting list is of
852 course equal to the return type of the function passed (which need
853 not be the same as the type of elements in the input list). Both of
854 these can be readily seen from the type of \hs{map}:
857 map :: (a -> b) -> [a] -> [b]
860 As an example from a common hardware design, let's look at the
861 equation of a FIR filter.
864 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
867 A FIR filter multiplies fixed constants ($h$) with the current and
868 a few previous input samples ($x$). Each of these multiplications
869 are summed, to produce the result at time $t$.
871 This is easily and directly implemented using higher order
872 functions. Consider that the vector \hs{hs} contains the FIR
873 coefficients and the vector \hs{xs} contains the current input sample
874 in front and older samples behind. How \hs{xs} gets its value will be
875 show in the next section about state.
878 fir ... = foldl1 (+) (zipwith (*) xs hs)
881 Here, the \hs{zipwith} function is very similar to the \hs{map}
882 function: It takes a function two lists and then applies the
883 function to each of the elements of the two lists pairwise
884 (\emph{e.g.}, \hs{zipwith (+) [1, 2] [3, 4]} becomes
887 The \hs{foldl1} function takes a function and a single list and applies the
888 function to the first two elements of the list. It then applies to
889 function to the result of the first application and the next element
890 from the list. This continues until the end of the list is reached.
891 The result of the \hs{foldl1} function is the result of the last
894 As you can see, the \hs{zipwith (*)} function is just pairwise
895 multiplication and the \hs{foldl1 (+)} function is just summation.
897 To make the correspondence between the code and the equation even
898 more obvious, we turn the list of input samples in the equation
899 around. So, instead of having the the input sample received at time
900 $t$ in $x_t$, $x_0$ now always stores the current sample, and $x_i$
901 stores the $ith$ previous sample. This changes the equation to the
902 following (Note that this is completely equivalent to the original
903 equation, just with a different definition of $x$ that better suits
904 the \hs{x} from the code):
907 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
910 So far, only functions have been used as higher order values. In
911 Haskell, there are two more ways to obtain a function-typed value:
912 partial application and lambda abstraction. Partial application
913 means that a function that takes multiple arguments can be applied
914 to a single argument, and the result will again be a function (but
915 that takes one argument less). As an example, consider the following
916 expression, that adds one to every element of a vector:
922 Here, the expression \hs{(+) 1} is the partial application of the
923 plus operator to the value \hs{1}, which is again a function that
924 adds one to its argument.
926 A labmda expression allows one to introduce an anonymous function
927 in any expression. Consider the following expression, which again
928 adds one to every element of a list:
934 Finally, higher order arguments are not limited to just builtin
935 functions, but any function defined in \CLaSH\ can have function
936 arguments. This allows the hardware designer to use a powerful
937 abstraction mechanism in his designs and have an optimal amount of
940 TODO: Describe ALU example (no code)
943 A very important concept in hardware it the concept of state. In a
944 stateful design, the outputs depend on the history of the inputs, or the
945 state. State is usually stored in registers, which retain their value
946 during a clock cycle. As we want to describe more than simple
947 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
949 An important property in Haskell, and in most other functional languages,
950 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
953 \item given the same arguments twice, it should return the same value in
955 \item when the function is called, it should not have observable
958 This purity property is important for functional languages, since it
959 enables all kinds of mathematical reasoning that could not be guaranteed
960 correct for impure functions. Pure functions are as such a perfect match
961 for a combinatorial circuit, where the output solely depends on the
962 inputs. When a circuit has state however, it can no longer be simply
963 described by a pure function. Simply removing the purity property is not a
964 valid option, as the language would then lose many of it mathematical
965 properties. In an effort to include the concept of state in pure
966 functions, the current value of the state is made an argument of the
967 function; the updated state becomes part of the result.
969 A simple example is the description of an accumulator circuit:
971 acc :: Word -> State Word -> (State Word, Word)
972 acc inp (State s) = (State s', outp)
977 This approach makes the state of a function very explicit: which variables
978 are part of the state is completely determined by the type signature. This
979 approach to state is well suited to be used in combination with the
980 existing code and language features, such as all the choice constructs, as
981 state values are just normal values.
982 \section{\CLaSH\ prototype}
986 \section{Related work}
987 Many functional hardware description languages have been developed over the
988 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
989 extension of Backus' \acro{FP} language to synchronous streams, designed
990 particularly for describing and reasoning about regular circuits. The
991 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
992 circuits, and has a particular focus on layout. \acro{HML}~\cite{HML2} is a
993 hardware modeling language based on the strict functional language
994 \acro{ML}, and has support for polymorphic types and higher-order functions.
995 Published work suggests that there is no direct simulation support for
996 \acro{HML}, and that the translation to \VHDL\ is only partial.
998 Like this work, many functional hardware description languages have some sort
999 of foundation in the functional programming language Haskell.
1000 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1001 specifications used to model the behavior of superscalar microprocessors. Hawk
1002 specifications can be simulated, but there seems to be no support for
1003 automated circuit synthesis. The ForSyDe~\cite{ForSyDe2} system uses Haskell
1004 to specify abstract system models, which can (manually) be transformed into an
1005 implementation model using semantic preserving transformations. ForSyDe has
1006 several simulation and synthesis backends, though synthesis is restricted to
1007 the synchronous subset of the ForSyDe language.
1009 Lava~\cite{Lava} is a hardware description language that focuses on the
1010 structural representation of hardware. Besides support for simulation and
1011 circuit synthesis, Lava descriptions can be interfaced with formal method
1012 tools for formal verification. Lava descriptions are actually circuit
1013 generators when viewed from a synthesis viewpoint, in that the language
1014 elements of Haskell, such as choice, can be used to guide the circuit
1015 generation. If a developer wants to insert a choice element inside an actual
1016 circuit he will have to specify this explicitly as a component. In this
1017 respect \CLaSH\ differs from Lava, in that all the choice elements, such as
1018 case-statements and pattern matching, are synthesized to choice elements in the
1019 eventual circuit. As such, richer control structures can both be specified and
1020 synthesized in \CLaSH\ compared to any of the languages mentioned in this
1023 The merits of polymorphic typing, combined with higher-order functions, are
1024 now also recognized in the `main-stream' hardware description languages,
1025 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 has
1026 support to specify types as generics, thus allowing a developer to describe
1027 polymorphic components. Note that those types still require an explicit
1028 generic map, whereas type-inference and type-specialization are implicit in
1031 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1033 % A functional language designed specifically for hardware design is
1034 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1035 % language called \acro{FL}~\cite{FL} to la
1037 % An example of a floating figure using the graphicx package.
1038 % Note that \label must occur AFTER (or within) \caption.
1039 % For figures, \caption should occur after the \includegraphics.
1040 % Note that IEEEtran v1.7 and later has special internal code that
1041 % is designed to preserve the operation of \label within \caption
1042 % even when the captionsoff option is in effect. However, because
1043 % of issues like this, it may be the safest practice to put all your
1044 % \label just after \caption rather than within \caption{}.
1046 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1047 % option should be used if it is desired that the figures are to be
1048 % displayed while in draft mode.
1052 %\includegraphics[width=2.5in]{myfigure}
1053 % where an .eps filename suffix will be assumed under latex,
1054 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1055 % via \DeclareGraphicsExtensions.
1056 %\caption{Simulation Results}
1060 % Note that IEEE typically puts floats only at the top, even when this
1061 % results in a large percentage of a column being occupied by floats.
1064 % An example of a double column floating figure using two subfigures.
1065 % (The subfig.sty package must be loaded for this to work.)
1066 % The subfigure \label commands are set within each subfloat command, the
1067 % \label for the overall figure must come after \caption.
1068 % \hfil must be used as a separator to get equal spacing.
1069 % The subfigure.sty package works much the same way, except \subfigure is
1070 % used instead of \subfloat.
1072 %\begin{figure*}[!t]
1073 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1074 %\label{fig_first_case}}
1076 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1077 %\label{fig_second_case}}}
1078 %\caption{Simulation results}
1082 % Note that often IEEE papers with subfigures do not employ subfigure
1083 % captions (using the optional argument to \subfloat), but instead will
1084 % reference/describe all of them (a), (b), etc., within the main caption.
1087 % An example of a floating table. Note that, for IEEE style tables, the
1088 % \caption command should come BEFORE the table. Table text will default to
1089 % \footnotesize as IEEE normally uses this smaller font for tables.
1090 % The \label must come after \caption as always.
1093 %% increase table row spacing, adjust to taste
1094 %\renewcommand{\arraystretch}{1.3}
1095 % if using array.sty, it might be a good idea to tweak the value of
1096 % \extrarowheight as needed to properly center the text within the cells
1097 %\caption{An Example of a Table}
1098 %\label{table_example}
1100 %% Some packages, such as MDW tools, offer better commands for making tables
1101 %% than the plain LaTeX2e tabular which is used here.
1102 %\begin{tabular}{|c||c|}
1112 % Note that IEEE does not put floats in the very first column - or typically
1113 % anywhere on the first page for that matter. Also, in-text middle ("here")
1114 % positioning is not used. Most IEEE journals/conferences use top floats
1115 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1116 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1117 % command of the stfloats package.
1121 \section{Conclusion}
1122 The conclusion goes here.
1127 % conference papers do not normally have an appendix
1130 % use section* for acknowledgement
1131 \section*{Acknowledgment}
1134 The authors would like to thank...
1140 % trigger a \newpage just before the given reference
1141 % number - used to balance the columns on the last page
1142 % adjust value as needed - may need to be readjusted if
1143 % the document is modified later
1144 %\IEEEtriggeratref{8}
1145 % The "triggered" command can be changed if desired:
1146 %\IEEEtriggercmd{\enlargethispage{-5in}}
1148 % references section
1150 % can use a bibliography generated by BibTeX as a .bbl file
1151 % BibTeX documentation can be easily obtained at:
1152 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1153 % The IEEEtran BibTeX style support page is at:
1154 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1155 \bibliographystyle{IEEEtran}
1156 % argument is your BibTeX string definitions and bibliography database(s)
1157 \bibliography{IEEEabrv,clash.bib}
1159 % <OR> manually copy in the resultant .bbl file
1160 % set second argument of \begin to the number of references
1161 % (used to reserve space for the reference number labels box)
1162 % \begin{thebibliography}{1}
1164 % \bibitem{IEEEhowto:kopka}
1165 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1166 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1168 % \end{thebibliography}
1176 % vim: set ai sw=2 sts=2 expandtab: