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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
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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,
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451 % math in the abstract anyway.
458 % For peer review papers, you can put extra information on the cover
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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 tool.
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 $a * b + c$:
554 mac a b c = add (mul a b) c
558 \centerline{\includegraphics{mac}}
559 \caption{Combinatorial Multiply-Accumulate}
563 The result of using a complex input type can be seen in
564 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
565 input tuple for the |a|, |b|, and |c| arguments:
568 mac (a, b, c) = add (mul a b) c
572 \centerline{\includegraphics{mac-nocurry}}
573 \caption{Combinatorial Multiply-Accumulate (complex input)}
574 \label{img:mac-comb-nocurry}
578 In Haskell, choice can be achieved by a large set of language constructs,
579 consisting of: \hs{case} constructs, \hs{if-then-else} constructs,
580 pattern matching, and guards. The easiest of these are the \hs{case}
581 constructs (and \hs{if} expressions, which can be very directly translated
582 to \hs{case} expressions). A \hs{case} expression can in turn simply be
583 translated to a conditional assignment in \VHDL, where the conditions use
584 equality comparisons against the constructors in the \hs{case}
585 expressions. We can see two versions of a contrived example, the first
586 using a \hs{case} construct and the other using a \hs{if-then-else}
587 constructs, in the code below. The example sums two values when they are
588 equal or non-equal (depending on the predicate given) and returns 0
592 sumif pred a b = case pred of
596 Neq -> case a != b of
604 if a == b then a + b else 0
606 if a != b then a + b else 0
609 Both versions of the example correspond to the same netlist, which is
610 depicted in \Cref{img:choice}
613 \centerline{\includegraphics{choice-case}}
614 \caption{Choice - sumif}
618 A slightly more complex (but very powerful) form of choice is pattern
619 matching. A function can be defined in multiple clauses, where each clause
620 specifies a pattern. When the arguments match the pattern, the
621 corresponding clause will be used. Expressions can also contain guards,
622 where the expression is only executed if the guard evaluates to true. A
623 pattern match (with optional guards) can be to a conditional assignments
624 in \VHDL, where the conditions are an equality test of the argument and
625 one of the patterns (combined with the guard if was present). A third
626 version of the earlier example, using both pattern matching and guards,
630 sumif Eq a b | a == b = a + b
631 sumif Neq a b | a != b = a + b
635 The version using pattern matching and guards has the same netlist
636 representation (\Cref{img:choice}) as the earlier two versions of the
640 % \centerline{\includegraphics{choice-ifthenelse}}
641 % \caption{Choice - \emph{if-then-else}}
646 Translation of two most basic functional concepts has been
647 discussed: function application and choice. Before looking further
648 into less obvious concepts like higher-order expressions and
649 polymorphism, the possible types that can be used in hardware
650 descriptions will be discussed.
652 Some way is needed to translate every value used to its hardware
653 equivalents. In particular, this means a hardware equivalent for
654 every \emph{type} used in a hardware description is needed.
656 The following types are \emph{built-in}, meaning that their hardware
657 translation is fixed into the \CLaSH\ compiler. A designer can also
658 define his own types, which will be translated into hardware types
659 using translation rules that are discussed later on.
661 \subsection{Built-in types}
664 This is the most basic type available. It can have two values:
665 \hs{Low} and \hs{High}. It is mapped directly onto the
666 \texttt{std\_logic} \VHDL\ type.
668 This is a basic logic type. It can have two values: \hs{True}
669 and \hs{False}. It is translated to \texttt{std\_logic} exactly
670 like the \hs{Bit} type (where a value of \hs{True} corresponds
671 to a value of \hs{High}). Supporting the Bool type is
672 particularly useful to support \hs{if ... then ... else ...}
673 expressions, which always have a \hs{Bool} value for the
675 \item[\hs{SizedWord}, \hs{SizedInt}]
676 These are types to represent integers. A \hs{SizedWord} is unsigned,
677 while a \hs{SizedInt} is signed. These types are parametrized by a
678 length type, so you can define an unsigned word of 32 bits wide as
682 type Word32 = SizedWord D32
685 Here, a type synonym \hs{Word32} is defined that is equal to the
686 \hs{SizedWord} type constructor applied to the type \hs{D32}. \hs{D32}
687 is the \emph{type level representation} of the decimal number 32,
688 making the \hs{Word32} type a 32-bit unsigned word. These types are
689 translated to the \VHDL\ \texttt{unsigned} and \texttt{signed}
692 This is a vector type, that can contain elements of any other type and
693 has a fixed length. The \hs{Vector} type constructor takes two type
694 arguments: the length of the vector and the type of the elements
695 contained in it. The state type of an 8 element register bank would
699 type RegisterState = Vector D8 Word32
702 Here, a type synonym \hs{RegisterState} is defined that is equal to
703 the \hs{Vector} type constructor applied to the types \hs{D8} (The
704 type level representation of the decimal number 8) and \hs{Word32}
705 (The 32 bit word type as defined above). In other words, the
706 \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
707 vector is translated to a \VHDL\ array type.
708 \item[\hs{RangedWord}]
709 This is another type to describe integers, but unlike the previous
710 two it has no specific bit-width, but an upper bound. This means that
711 its range is not limited to powers of two, but can be any number.
712 A \hs{RangedWord} only has an upper bound, its lower bound is
713 implicitly zero. The main purpose of the \hs{RangedWord} type is to be
714 used as an index to a \hs{Vector}.
716 \comment{TODO: Perhaps remove this example?} To define an index for
717 the 8 element vector above, we would do:
720 type RegisterIndex = RangedWord D7
723 Here, a type synonym \hs{RegisterIndex} is defined that is equal to
724 the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
725 other words, this defines an unsigned word with values from
726 0 to 7 (inclusive). This word can be be used to index the
727 8 element vector \hs{RegisterState} above. This type is translated to
728 the \texttt{unsigned} \VHDL type.
731 \subsection{User-defined types}
732 There are three ways to define new types in Haskell: algebraic
733 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
734 keyword and type renamings with the \hs{newtype} keyword. \GHC\
735 offers a few more advanced ways to introduce types (type families,
736 existential typing, {\small{GADT}}s, etc.) which are not standard
737 Haskell. These are not currently supported.
739 Only an algebraic datatype declaration actually introduces a
740 completely new type, for which we provide the \VHDL\ translation
741 below. Type synonyms and renamings only define new names for
742 existing types (where synonyms are completely interchangeable and
743 renamings need explicit conversion). Therefore, these do not need
744 any particular \VHDL\ translation, a synonym or renamed type will
745 just use the same representation as the original type. The
746 distinction between a renaming and a synonym does no longer matter
747 in hardware and can be disregarded in the generated \VHDL.
749 For algebraic types, we can make the following distinction:
752 \item[\bf{Single constructor}]
753 Algebraic datatypes with a single constructor with one or more
754 fields, are essentially a way to pack a few values together in a
755 record-like structure. An example of such a type is the following pair
759 data IntPair = IntPair Int Int
762 Haskell's builtin tuple types are also defined as single
763 constructor algebraic types and are translated according to this
764 rule by the \CLaSH\ compiler. These types are translated to \VHDL\
765 record types, with one field for every field in the constructor.
766 \item[\bf{No fields}]
767 Algebraic datatypes with multiple constructors, but without any
768 fields are essentially a way to get an enumeration-like type
769 containing alternatives. Note that Haskell's \hs{Bool} type is also
770 defined as an enumeration type, but we have a fixed translation for
771 that. These types are translated to \VHDL\ enumerations, with one
772 value for each constructor. This allows references to these
773 constructors to be translated to the corresponding enumeration value.
774 \item[\bf{Multiple constructors with fields}]
775 Algebraic datatypes with multiple constructors, where at least
776 one of these constructors has one or more fields are not
780 \subsection{Polymorphic functions}
781 A powerful construct in most functional language is polymorphism.
782 This means the arguments of a function (and consequentially, values
783 within the function as well) do not need to have a fixed type.
784 Haskell supports \emph{parametric polymorphism}, meaning a
785 function's type can be parameterized with another type.
787 As an example of a polymorphic function, consider the following
788 \hs{append} function's type:
790 TODO: Use vectors instead of lists?
793 append :: [a] -> a -> [a]
796 This type is parameterized by \hs{a}, which can contain any type at
797 all. This means that append can append an element to a list,
798 regardless of the type of the elements in the list (but the element
799 added must match the elements in the list, since there is only one
802 This kind of polymorphism is extremely useful in hardware designs to
803 make operations work on a vector without knowing exactly what elements
804 are inside, routing signals without knowing exactly what kinds of
805 signals these are, or working with a vector without knowing exactly
806 how long it is. Polymorphism also plays an important role in most
807 higher order functions, as we will see in the next section.
809 The previous example showed unconstrained polymorphism (TODO: How is
810 this really called?): \hs{a} can have \emph{any} type. Furthermore,
811 Haskell supports limiting the types of a type parameter to specific
812 class of types. An example of such a type class is the \hs{Num}
813 class, which contains all of Haskell's numerical types.
815 Now, take the addition operator, which has the following type:
818 (+) :: Num a => a -> a -> a
821 This type is again parameterized by \hs{a}, but it can only contain
822 types that are \emph{instances} of the \emph{type class} \hs{Num}.
823 Our numerical built-in types are also instances of the \hs{Num}
824 class, so we can use the addition operator on \hs{SizedWords} as
825 well as on {SizedInts}.
827 In \CLaSH, unconstrained polymorphism is completely supported. Any
828 function defined can have any number of unconstrained type
829 parameters. The \CLaSH\ compiler will infer the type of every such
830 argument depending on how the function is applied. There is one
831 exception to this: The top level function that is translated, can
832 not have any polymorphic arguments (since it is never applied, so
833 there is no way to find out the actual types for the type
836 \CLaSH\ does not support user-defined type classes, but does use some
837 of the builtin ones for its builtin functions (like \hs{Num} and
840 \subsection{Higher order}
841 Another powerful abstraction mechanism in functional languages, is
842 the concept of \emph{higher order functions}, or \emph{functions as
843 a first class value}. This allows a function to be treated as a
844 value and be passed around, even as the argument of another
845 function. Let's clarify that with an example:
848 notList xs = map not xs
851 This defines a function \hs{notList}, with a single list of booleans
852 \hs{xs} as an argument, which simply negates all of the booleans in
853 the list. To do this, it uses the function \hs{map}, which takes
854 \emph{another function} as its first argument and applies that other
855 function to each element in the list, returning again a list of the
858 As you can see, the \hs{map} function is a higher order function,
859 since it takes another function as an argument. Also note that
860 \hs{map} is again a polymorphic function: It does not pose any
861 constraints on the type of elements in the list passed, other than
862 that it must be the same as the type of the argument the passed
863 function accepts. The type of elements in the resulting list is of
864 course equal to the return type of the function passed (which need
865 not be the same as the type of elements in the input list). Both of
866 these can be readily seen from the type of \hs{map}:
869 map :: (a -> b) -> [a] -> [b]
872 As an example from a common hardware design, let's look at the
873 equation of a FIR filter.
876 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
879 A FIR filter multiplies fixed constants ($h$) with the current and
880 a few previous input samples ($x$). Each of these multiplications
881 are summed, to produce the result at time $t$.
883 This is easily and directly implemented using higher order
884 functions. Consider that the vector \hs{hs} contains the FIR
885 coefficients and the vector \hs{xs} contains the current input sample
886 in front and older samples behind. How \hs{xs} gets its value will be
887 show in the next section about state.
890 fir ... = foldl1 (+) (zipwith (*) xs hs)
893 Here, the \hs{zipwith} function is very similar to the \hs{map}
894 function: It takes a function two lists and then applies the
895 function to each of the elements of the two lists pairwise
896 (\emph{e.g.}, \hs{zipwith (+) [1, 2] [3, 4]} becomes
899 The \hs{foldl1} function takes a function and a single list and applies the
900 function to the first two elements of the list. It then applies to
901 function to the result of the first application and the next element
902 from the list. This continues until the end of the list is reached.
903 The result of the \hs{foldl1} function is the result of the last
906 As you can see, the \hs{zipwith (*)} function is just pairwise
907 multiplication and the \hs{foldl1 (+)} function is just summation.
909 To make the correspondence between the code and the equation even
910 more obvious, we turn the list of input samples in the equation
911 around. So, instead of having the the input sample received at time
912 $t$ in $x_t$, $x_0$ now always stores the current sample, and $x_i$
913 stores the $ith$ previous sample. This changes the equation to the
914 following (Note that this is completely equivalent to the original
915 equation, just with a different definition of $x$ that better suits
916 the \hs{x} from the code):
919 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
922 So far, only functions have been used as higher order values. In
923 Haskell, there are two more ways to obtain a function-typed value:
924 partial application and lambda abstraction. Partial application
925 means that a function that takes multiple arguments can be applied
926 to a single argument, and the result will again be a function (but
927 that takes one argument less). As an example, consider the following
928 expression, that adds one to every element of a vector:
934 Here, the expression \hs{(+) 1} is the partial application of the
935 plus operator to the value \hs{1}, which is again a function that
936 adds one to its argument.
938 A labmda expression allows one to introduce an anonymous function
939 in any expression. Consider the following expression, which again
940 adds one to every element of a list:
946 Finally, higher order arguments are not limited to just builtin
947 functions, but any function defined in \CLaSH\ can have function
948 arguments. This allows the hardware designer to use a powerful
949 abstraction mechanism in his designs and have an optimal amount of
952 TODO: Describe ALU example (no code)
955 A very important concept in hardware it the concept of state. In a
956 stateful design, the outputs depend on the history of the inputs, or the
957 state. State is usually stored in registers, which retain their value
958 during a clock cycle. As we want to describe more than simple
959 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
961 An important property in Haskell, and in most other functional languages,
962 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
965 \item given the same arguments twice, it should return the same value in
967 \item when the function is called, it should not have observable
970 This purity property is important for functional languages, since it
971 enables all kinds of mathematical reasoning that could not be guaranteed
972 correct for impure functions. Pure functions are as such a perfect match
973 for a combinatorial circuit, where the output solely depends on the
974 inputs. When a circuit has state however, it can no longer be simply
975 described by a pure function. Simply removing the purity property is not a
976 valid option, as the language would then lose many of it mathematical
977 properties. In an effort to include the concept of state in pure
978 functions, the current value of the state is made an argument of the
979 function; the updated state becomes part of the result.
981 A simple example is the description of an accumulator circuit:
983 acc :: Word -> State Word -> (State Word, Word)
984 acc inp (State s) = (State s', outp)
989 This approach makes the state of a function very explicit: which variables
990 are part of the state is completely determined by the type signature. This
991 approach to state is well suited to be used in combination with the
992 existing code and language features, such as all the choice constructs, as
993 state values are just normal values.
994 \section{\CLaSH\ prototype}
998 \section{Related work}
999 Many functional hardware description languages have been developed over the
1000 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1001 extension of Backus' \acro{FP} language to synchronous streams, designed
1002 particularly for describing and reasoning about regular circuits. The
1003 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1004 circuits, and has a particular focus on layout. \acro{HML}~\cite{HML2} is a
1005 hardware modeling language based on the strict functional language
1006 \acro{ML}, and has support for polymorphic types and higher-order functions.
1007 Published work suggests that there is no direct simulation support for
1008 \acro{HML}, and that the translation to \VHDL\ is only partial.
1010 Like this work, many functional hardware description languages have some sort
1011 of foundation in the functional programming language Haskell.
1012 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1013 specifications used to model the behavior of superscalar microprocessors. Hawk
1014 specifications can be simulated, but there seems to be no support for
1015 automated circuit synthesis. The ForSyDe~\cite{ForSyDe2} system uses Haskell
1016 to specify abstract system models, which can (manually) be transformed into an
1017 implementation model using semantic preserving transformations. ForSyDe has
1018 several simulation and synthesis backends, though synthesis is restricted to
1019 the synchronous subset of the ForSyDe language.
1021 Lava~\cite{Lava} is a hardware description language that focuses on the
1022 structural representation of hardware. Besides support for simulation and
1023 circuit synthesis, Lava descriptions can be interfaced with formal method
1024 tools for formal verification. Lava descriptions are actually circuit
1025 generators when viewed from a synthesis viewpoint, in that the language
1026 elements of Haskell, such as choice, can be used to guide the circuit
1027 generation. If a developer wants to insert a choice element inside an actual
1028 circuit he will have to specify this explicitly as a component. In this
1029 respect \CLaSH\ differs from Lava, in that all the choice elements, such as
1030 case-statements and pattern matching, are synthesized to choice elements in the
1031 eventual circuit. As such, richer control structures can both be specified and
1032 synthesized in \CLaSH\ compared to any of the languages mentioned in this
1035 The merits of polymorphic typing, combined with higher-order functions, are
1036 now also recognized in the `main-stream' hardware description languages,
1037 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 has
1038 support to specify types as generics, thus allowing a developer to describe
1039 polymorphic components. Note that those types still require an explicit
1040 generic map, whereas type-inference and type-specialization are implicit in
1043 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1045 % A functional language designed specifically for hardware design is
1046 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1047 % language called \acro{FL}~\cite{FL} to la
1049 % An example of a floating figure using the graphicx package.
1050 % Note that \label must occur AFTER (or within) \caption.
1051 % For figures, \caption should occur after the \includegraphics.
1052 % Note that IEEEtran v1.7 and later has special internal code that
1053 % is designed to preserve the operation of \label within \caption
1054 % even when the captionsoff option is in effect. However, because
1055 % of issues like this, it may be the safest practice to put all your
1056 % \label just after \caption rather than within \caption{}.
1058 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1059 % option should be used if it is desired that the figures are to be
1060 % displayed while in draft mode.
1064 %\includegraphics[width=2.5in]{myfigure}
1065 % where an .eps filename suffix will be assumed under latex,
1066 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1067 % via \DeclareGraphicsExtensions.
1068 %\caption{Simulation Results}
1072 % Note that IEEE typically puts floats only at the top, even when this
1073 % results in a large percentage of a column being occupied by floats.
1076 % An example of a double column floating figure using two subfigures.
1077 % (The subfig.sty package must be loaded for this to work.)
1078 % The subfigure \label commands are set within each subfloat command, the
1079 % \label for the overall figure must come after \caption.
1080 % \hfil must be used as a separator to get equal spacing.
1081 % The subfigure.sty package works much the same way, except \subfigure is
1082 % used instead of \subfloat.
1084 %\begin{figure*}[!t]
1085 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1086 %\label{fig_first_case}}
1088 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1089 %\label{fig_second_case}}}
1090 %\caption{Simulation results}
1094 % Note that often IEEE papers with subfigures do not employ subfigure
1095 % captions (using the optional argument to \subfloat), but instead will
1096 % reference/describe all of them (a), (b), etc., within the main caption.
1099 % An example of a floating table. Note that, for IEEE style tables, the
1100 % \caption command should come BEFORE the table. Table text will default to
1101 % \footnotesize as IEEE normally uses this smaller font for tables.
1102 % The \label must come after \caption as always.
1105 %% increase table row spacing, adjust to taste
1106 %\renewcommand{\arraystretch}{1.3}
1107 % if using array.sty, it might be a good idea to tweak the value of
1108 % \extrarowheight as needed to properly center the text within the cells
1109 %\caption{An Example of a Table}
1110 %\label{table_example}
1112 %% Some packages, such as MDW tools, offer better commands for making tables
1113 %% than the plain LaTeX2e tabular which is used here.
1114 %\begin{tabular}{|c||c|}
1124 % Note that IEEE does not put floats in the very first column - or typically
1125 % anywhere on the first page for that matter. Also, in-text middle ("here")
1126 % positioning is not used. Most IEEE journals/conferences use top floats
1127 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1128 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1129 % command of the stfloats package.
1133 \section{Conclusion}
1134 The conclusion goes here.
1139 % conference papers do not normally have an appendix
1142 % use section* for acknowledgement
1143 \section*{Acknowledgment}
1146 The authors would like to thank...
1152 % trigger a \newpage just before the given reference
1153 % number - used to balance the columns on the last page
1154 % adjust value as needed - may need to be readjusted if
1155 % the document is modified later
1156 %\IEEEtriggeratref{8}
1157 % The "triggered" command can be changed if desired:
1158 %\IEEEtriggercmd{\enlargethispage{-5in}}
1160 % references section
1162 % can use a bibliography generated by BibTeX as a .bbl file
1163 % BibTeX documentation can be easily obtained at:
1164 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1165 % The IEEEtran BibTeX style support page is at:
1166 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1167 \bibliographystyle{IEEEtran}
1168 % argument is your BibTeX string definitions and bibliography database(s)
1169 \bibliography{IEEEabrv,clash.bib}
1171 % <OR> manually copy in the resultant .bbl file
1172 % set second argument of \begin to the number of references
1173 % (used to reserve space for the reference number labels box)
1174 % \begin{thebibliography}{1}
1176 % \bibitem{IEEEhowto:kopka}
1177 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1178 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1180 % \end{thebibliography}
1188 % vim: set ai sw=2 sts=2 expandtab: