1 \chapter[chap:prototype]{Prototype}
2 An important step in this research is the creation of a prototype compiler.
3 Having this prototype allows us to apply the ideas from the previous chapter
4 to actual hardware descriptions and evaluate their usefulness. Having a
5 prototype also helps to find new techniques and test possible
8 Obviously the prototype was not created after all research
9 ideas were formed, but its implementation has been interleaved with the
10 research itself. Also, the prototype described here is the final version, it
11 has gone through a number of design iterations which we will not completely
14 \section[sec:prototype:input]{Input language}
15 When implementing this prototype, the first question to ask is:
16 Which (functional) language will be used to describe our hardware?
17 (Note that this does not concern the \emph{implementation language}
18 of the compiler, just the language \emph{translated by} the
21 Initially, we have two choices:
24 \item Create a new functional language from scratch. This has the
25 advantage of having a language that contains exactly those elements that
26 are convenient for describing hardware and can contain special
27 constructs that allows our hardware descriptions to be more powerful or
29 \item Use an existing language and create a new back-end for it. This has
30 the advantage that existing tools can be reused, which will speed up
36 \startframedtext[width=8cm,background=box,frame=no]
37 \startalignment[center]
38 {\tfa No \small{EDSL} or Template Haskell}
42 Note that in this consideration, embedded domain-specific
43 languages (\small{EDSL}) and Template Haskell (\small{TH})
44 approaches have not been included. As we have seen in
45 \in{section}[sec:context:fhdls], these approaches have all kinds
46 of limitations on the description language that we would like to
50 Considering that we required a prototype which should be working quickly,
51 and that implementing parsers, semantic checkers and especially
52 type-checkers is not exactly the core of this research (but it is lots and
53 lots of work, using an existing language is the obvious choice. This
54 also has the advantage that a large set of language features is available
55 to experiment with and it is easy to find which features apply well and
56 which do not. Another important advantage of using an existing language, is
57 that simulation of the code becomes trivial. Since there are existing
58 compilers and interpreters that can run the hardware description directly,
59 it can be simulated without also having to write an interpreter for the
62 A possible second prototype could use a custom language with just the useful
63 features (and possibly extra features that are specific to
64 the domain of hardware description as well).
66 The second choice to be made is which of the many existing languages to use. As
67 mentioned before, the chosen language is Haskell. This choice has not been the
68 result of a thorough comparison of languages, for the simple reason that
69 the requirements on the language were completely unclear at the start of
70 this research. The fact that Haskell is a language with a broad spectrum
71 of features, that it is commonly used in research projects and that the
72 primary compiler, \GHC, provides a high level API to its internals, made
73 Haskell an obvious choice.
75 \section[sec:prototype:output]{Output format}
76 The second important question is: what will be our output format?
77 This output format should at least allow for programming the
78 hardware design into a field-programmable gate array (\small{FPGA}).
79 The choice of output format is thus limited by what hardware
80 synthesis and programming tools can process.
82 Looking at other tools in the industry, the Electronic Design Interchange
83 Format (\small{EDIF}) is commonly used for storing intermediate
84 \emph{netlists} (lists of components and connections between these
85 components) and is commonly the target for \small{VHDL} and Verilog
88 However, \small{EDIF} is not completely tool-independent. It specifies a
89 meta-format, but the hardware components that can be used vary between
90 various tool and hardware vendors, as well as the interpretation of the
91 \small{EDIF} standard. \cite[li89]
93 This means that when working with \small{EDIF}, our prototype would become
94 technology dependent (\eg\ only work with \small{FPGA}s of a specific
95 vendor, or even only with specific chips). This limits the applicability
96 of our prototype. Also, the tools we would like to use for verifying,
97 simulating and draw pretty pictures of our output (like Precision, or
98 QuestaSim) are designed for \small{VHDL} or Verilog input.
100 For these reasons, we will not use \small{EDIF}, but \small{VHDL} as our
101 output language. We choose \VHDL\ over Verilog simply because we are
102 familiar with \small{VHDL} already. The differences between \small{VHDL}
103 and Verilog are on the higher level, while we will be using \small{VHDL}
104 mainly to write low level, netlist-like descriptions anyway.
106 An added advantage of using \VHDL\ is that we can profit from existing
107 optimizations in \VHDL\ synthesizers. A lot of optimizations are done on the
108 \VHDL\ level by existing tools. These tools have been under
109 development for years, so it would not be reasonable to assume we
110 could achieve a similar amount of optimization in our prototype (nor
111 should it be a goal, considering this is just a prototype).
114 \startframedtext[width=8cm,background=box,frame=no]
115 \startalignment[center]
116 {\tfa Translation vs. compilation vs. synthesis}
119 In this thesis the words \emph{translation}, \emph{compilation} and
120 sometimes \emph{synthesis} will be used interchangeably to refer to the
121 process of translating the hardware description from the Haskell
122 language to the \VHDL\ language.
124 Similarly, the prototype created is referred to as both the
125 \emph{translator} as well as the \emph{compiler}.
127 The final part of this process is usually referred to as \emph{\VHDL\
132 Note that we will be using \small{VHDL} as our output language, but will
133 not use its full expressive power. Our output will be limited to using
134 simple, structural descriptions, without any complex behavioral
135 descriptions like arbitrary sequential statements (which might not
136 be supported by all tools). This ensures that any tool that works
137 with \VHDL\ will understand our output. This also leaves open the
138 option to switch to \small{EDIF} in the future, with minimal changes
141 \section{Simulation and synthesis}
142 As mentioned above, by using the Haskell language, we get simulation of
143 our hardware descriptions almost for free. The only thing that is needed
144 is to provide a Haskell implementation of all built-in functions that can
145 be used by the Haskell interpreter to simulate them.
147 The main topic of this thesis is therefore the path from the Haskell
148 hardware descriptions to \small{FPGA} synthesis, focusing of course on the
149 \VHDL\ generation. Since the \VHDL\ generation process preserves the meaning
150 of the Haskell description exactly, any simulation done in Haskell
151 \emph{should} produce identical results as the synthesized hardware.
153 \section[sec:prototype:design]{Prototype design}
154 As suggested above, we will use the Glasgow Haskell Compiler (\small{GHC}) to
155 implement our prototype compiler. To understand the design of the
156 prototype, we will first dive into the \small{GHC} compiler a bit. Its
157 compilatprototype consists of the following steps (slightly simplified):
159 \startuseMPgraphic{ghc-pipeline}
161 save inp, front, desugar, simpl, back, out;
162 newEmptyBox.inp(0,0);
163 newBox.front(btex Frontend etex);
164 newBox.desugar(btex Desugarer etex);
165 newBox.simpl(btex Simplifier etex);
166 newBox.back(btex Backend etex);
167 newEmptyBox.out(0,0);
169 % Space the boxes evenly
170 inp.c - front.c = front.c - desugar.c = desugar.c - simpl.c
171 = simpl.c - back.c = back.c - out.c = (0, 1.5cm);
174 % Draw lines between the boxes. We make these lines "deferred" and give
175 % them a name, so we can use ObjLabel to draw a label beside them.
176 ncline.inp(inp)(front) "name(haskell)";
177 ncline.front(front)(desugar) "name(ast)";
178 ncline.desugar(desugar)(simpl) "name(core)";
179 ncline.simpl(simpl)(back) "name(simplcore)";
180 ncline.back(back)(out) "name(native)";
181 ObjLabel.inp(btex Haskell source etex) "labpathname(haskell)", "labdir(rt)";
182 ObjLabel.front(btex Haskell AST etex) "labpathname(ast)", "labdir(rt)";
183 ObjLabel.desugar(btex Core etex) "labpathname(core)", "labdir(rt)";
184 ObjLabel.simpl(btex Simplified core etex) "labpathname(simplcore)", "labdir(rt)";
185 ObjLabel.back(btex Native code etex) "labpathname(native)", "labdir(rt)";
187 % Draw the objects (and deferred labels)
188 drawObj (inp, front, desugar, simpl, back, out);
190 \placefigure[right]{GHC compiler pipeline}{\startboxed \useMPgraphic{ghc-pipeline}\stopboxed}
193 This step takes the Haskell source files and parses them into an
194 abstract syntax tree (\small{AST}). This \small{AST} can express the
195 complete Haskell language and is thus a very complex one (in contrast
196 with the Core \small{AST}, later on). All identifiers in this
197 \small{AST} are resolved by the renamer and all types are checked by the
200 \startdesc{Desugaring}
201 This step takes the full \small{AST} and translates it to the
202 \emph{Core} language. Core is a very small functional language with lazy
203 semantics, that can still express everything Haskell can express. Its
204 simpleness makes Core very suitable for further simplification and
205 translation. Core is the language we will be working with as well.
207 \startdesc{Simplification}
208 Through a number of simplification steps (such as inlining, common
209 sub-expression elimination, etc.) the Core program is simplified to make
210 it faster or easier to process further.
213 This step takes the simplified Core program and generates an actual
214 runnable program for it. This is a big and complicated step we will not
215 discuss it any further, since it is not relevant to our prototype.
218 In this process, there are a number of places where we can start our work.
219 Assuming that we do not want to deal with (or modify) parsing, type-checking
220 and other front end business and that native code is not really a useful
221 format anymore, we are left with the choice between the full Haskell
222 \small{AST}, or the smaller (simplified) Core representation.
224 The advantage of taking the full \small{AST} is that the exact structure
225 of the source program is preserved. We can see exactly what the hardware
226 description looks like and which syntax constructs were used. However,
227 the full \small{AST} is a very complicated data-structure. If we are to
228 handle everything it offers, we will quickly get a big compiler.
230 Using the Core representation gives us a much more compact data-structure
231 (a Core expression only uses 9 constructors). Note that this does not mean
232 that the Core representation itself is smaller, on the contrary.
233 Since the Core language has less constructs, most Core expressions
234 are larger than the equivalent versions in Haskell.
236 However, the fact that the Core language is so much smaller, means it is a
237 lot easier to analyze and translate it into something else. For the same
238 reason, \small{GHC} runs its simplifications and optimizations on the Core
239 representation as well \cite[jones96].
241 We will use the normal Core representation, not the simplified Core. Even
242 though the simplified Core version is an equivalent, but simpler
243 definition, some problems were encountered with it in practice. The
244 simplifier restructures some (stateful) functions in a way the normalizer
245 and the \VHDL\ generation cannot handle, leading to uncompilable programs
246 (whereas the non-simplified version more closely resembles the original
247 program, allowing the original to be written in a way that can be
248 handled). This problem is further discussed in
249 \in{section}[sec:normalization:stateproblems].
251 \startuseMPgraphic{clash-pipeline}
253 save inp, front, norm, vhdl, out;
254 newEmptyBox.inp(0,0);
255 newBox.front(btex \small{GHC} front-end etex);
256 newBox.norm(btex Normalization etex);
257 newBox.vhdl(btex \small{VHDL} generation etex);
258 newEmptyBox.out(0,0);
260 % Space the boxes evenly
261 inp.c - front.c = front.c - norm.c = norm.c - vhdl.c
262 = vhdl.c - out.c = (0, 1.5cm);
265 % Draw lines between the boxes. We make these lines "deferred" and give
266 % them a name, so we can use ObjLabel to draw a label beside them.
267 ncline.inp(inp)(front) "name(haskell)";
268 ncline.front(front)(norm) "name(core)";
269 ncline.norm(norm)(vhdl) "name(normal)";
270 ncline.vhdl(vhdl)(out) "name(vhdl)";
271 ObjLabel.inp(btex Haskell source etex) "labpathname(haskell)", "labdir(rt)";
272 ObjLabel.front(btex Core etex) "labpathname(core)", "labdir(rt)";
273 ObjLabel.norm(btex Normalized core etex) "labpathname(normal)", "labdir(rt)";
274 ObjLabel.vhdl(btex \small{VHDL} description etex) "labpathname(vhdl)", "labdir(rt)";
276 % Draw the objects (and deferred labels)
277 drawObj (inp, front, norm, vhdl, out);
279 \placefigure[right]{Cλash compiler pipeline}{\startboxed \useMPgraphic{clash-pipeline}\stopboxed}
281 The final prototype roughly consists of three steps:
283 \page[no] % suppress page break here.
285 This is exactly the front-end from the \small{GHC} pipeline, that
286 translates Haskell sources to a typed Core representation.
288 \startdesc{Normalization}
289 This is a step that transforms the Core representation into a normal
290 form. This normal form is still expressed in the Core language, but has
291 to adhere to an additional set of constraints. This normal form is less
292 expressive than the full Core language (e.g., it can have limited
293 higher-order expressions, has a specific structure, etc.), but is
294 also very close to directly describing hardware.
296 \startdesc{\small{VHDL} generation}
297 The last step takes the normal formed Core representation and generates
298 \small{VHDL} for it. Since the normal form has a specific, hardware-like
299 structure, this final step is very straightforward.
302 The most interesting step in this process is the normalization step. That
303 is where more complicated functional constructs, which have no direct
304 hardware interpretation, are removed and translated into hardware
305 constructs. This step is described in a lot of detail at
306 \in{chapter}[chap:normalization].
309 \defref{entry function}Translation of a hardware description always
310 starts at a single function, which is referred to as the \emph{entry
311 function}. \VHDL\ is generated for this function first, followed by
312 any functions used by the entry functions (recursively).
314 \section[sec:prototype:core]{The Core language}
315 \defreftxt{Core}{the Core language}
316 Most of the prototype deals with handling the program in the Core
317 language. In this section we will show what this language looks like and
320 The Core language is a functional language that describes
321 \emph{expressions}. Every identifier used in Core is called a
322 \emph{binder}, since it is bound to a value somewhere. On the highest
323 level, a Core program is a collection of functions, each of which bind a
324 binder (the function name) to an expression (the function value, which has
327 The Core language itself does not prescribe any program structure
328 (like modules, declarations, imports, etc.), only expression
329 structure. In the \small{GHC} compiler, the Haskell module structure
330 is used for the resulting Core code as well. Since this is not so
331 relevant for understanding the Core language or the Normalization
332 process, we will only look at the Core expression language here.
334 Each Core expression consists of one of these possible expressions.
336 \startdesc{Variable reference}
337 \defref{variable reference}
341 This is a reference to a binder. It is written down as the
342 name of the binder that is being referred to along with its type. The
343 binder name should of course be bound in a containing scope
344 (including top level scope, so a reference to a top level function
345 is also a variable reference). Additionally, constructors from
346 algebraic data-types also become variable references (\eg\
349 In our examples, binders will commonly consist of a single
350 characters, but they can have any length.
352 The value of this expression is the value bound to the given
355 Each binder also carries around its type (explicitly shown above), but
356 this is usually not shown in the Core expressions. Only when the type is
357 relevant (when a new binder is introduced, for example) will it be
358 shown. In other cases, the type is either not relevant, or easily
359 derived from the context of the expression. \todo{Ref sidenote on type
368 This is a literal. Only primitive types are supported, like
369 chars, strings, integers and doubles. The types of these literals are the
370 \quote{primitive}, unboxed versions, like \lam{Char\#} and \lam{Word\#}, not the
371 normal Haskell versions (but there are built-in conversion
372 functions). Without going into detail about these types, note that
373 a few conversion functions exist to convert these to the normal
374 (boxed) Haskell equivalents. See
375 \in{section}[sec:normalization:literals] for an example.
378 \startdesc{Application}
383 This is function application. Each application consists of two
384 parts: the function part and the argument part. Applications are used
385 for normal function \quote{calls}, but also for applying type
386 abstractions and data constructors.
388 The value of an application is the value of the function part, with the
389 first argument binder bound to the argument part.
391 In Core, there is no distinction between an operator and a
392 function. This means that, for example the addition of two numbers
393 looks like the following in Core:
399 Where the function \quote{\lam{(+)}} is applied to the numbers 1
400 and 2. However, to increase readability, an application of an
401 operator like \lam{(+)} is sometimes written infix. In this case,
402 the parenthesis are also left out, just like in Haskell. In other
403 words, the following means exactly the same as the addition above:
410 \startdesc{Lambda abstraction}
411 \defref{lambda abstraction}
415 This is the basic lambda abstraction, as it occurs in lambda calculus.
416 It consists of a binder part and a body part. A lambda abstraction
417 creates a function, that can be applied to an argument. The binder is
418 usually a value binder, but it can also be a \emph{type binder} (or
419 \emph{type variable}). The latter case introduces a new polymorphic
420 variable, which can be used in types later on. See
421 \in{section}[sec:prototype:coretypes] for details.
423 The body of a lambda abstraction extends all the way to the end of
424 the expression, or the closing bracket surrounding the lambda. In
425 other words, the lambda abstraction \quote{operator} has the
426 lowest priority of all.
428 The value of an application is the value of the body part, with the
429 binder bound to the value the entire lambda abstraction is applied to.
432 \startdesc{Non-recursive let expression}
433 \defref{let expression}
435 let bndr = value in body
437 A let expression allows you to bind a binder to some value, while
438 evaluating to some other value (for which that binder is in scope). This
439 allows for sharing of sub-expressions (you can use a binder twice) and
440 explicit \quote{naming} of arbitrary expressions. A binder is not
441 in scope in the value bound it is bound to, so it is not possible
442 to make recursive definitions with a non-recursive let expression
443 (see the recursive form below).
445 Even though this let expression is an extension on the basic lambda
446 calculus, it is easily translated to a lambda abstraction. The let
447 expression above would then become:
453 This notion might be useful for verifying certain properties on
454 transformations, since a lot of verification work has been done on
455 lambda calculus already.
457 The value of a let expression is the value of the body part, with the
458 binder bound to the value.
461 \startdesc{Recursive let expression}
470 This is the recursive version of the let expression. In \small{GHC}'s
471 Core implementation, non-recursive and recursive lets are not so
472 distinct as we present them here, but this provides a clearer overview.
474 The main difference with the normal let expression is that it can
475 contain multiple bindings (or even none) and each of the binders
476 is in scope in each of the values, in addition to the body. This
477 allows for self-recursive or mutually recursive definitions.
479 It is also possible to express a recursive let expression using
480 normal lambda calculus, if we use the \emph{least fixed-point
481 operator}, \lam{Y} (but the details are too complicated to help
482 clarify the let expression, so this will not be explored further).
486 \startframedtext[width=8cm,background=box,frame=no]
487 \startalignment[center]
488 {\tfa Weak head normal form (\small{WHNF})}
491 An expression is in weak head normal form if it is either an
492 constructor application or lambda abstraction. \cite[jones87]
494 Without going into detail about the differences with head
495 normal form and normal form, note that evaluating the scrutinee
496 of a case expression to normal form (evaluating any function
497 applications, variable references and case expressions) is
498 sufficient to decide which case alternatives should be chosen.
503 \startdesc{Case expression}
504 \defref{case expression}
506 case scrutinee of bndr
507 DEFAULT -> defaultbody
508 C0 bndr0,0 ... bndr0,m -> body0
510 Cn bndrn,0 ... bndrn,m -> bodyn
513 A case expression is the only way in Core to choose between values. All
514 \hs{if} expressions and pattern matchings from the original Haskell
515 program have been translated to case expressions by the desugarer.
517 A case expression evaluates its scrutinee, which should have an
518 algebraic datatype, into weak head normal form (\small{WHNF}) and
519 (optionally) binds it to \lam{bndr}. If bndr is wild, \refdef{wild
520 binders} it is left out. Every alternative lists a single constructor
521 (\lam{C0 ... Cn}). Based on the actual constructor of the scrutinee, the
522 corresponding alternative is chosen. The binders in the chosen
523 alternative (\lam{bndr0,0 .... bndr0,m} are bound to the actual
524 arguments to the constructor in the scrutinee.
526 This is best illustrated with an example. Assume
527 there is an algebraic datatype declared as follows\footnote{This
528 datatype is not supported by the current Cλash implementation, but
529 serves well to illustrate the case expression}:
532 data D = A Word | B Bit
535 This is an algebraic datatype with two constructors, each getting
536 a single argument. A case expression scrutinizing this datatype
537 could look like the following:
545 What this expression does is check the constructor of the
546 scrutinee \lam{s}. If it is \lam{A}, it always evaluates to
547 \lam{High}. If the constructor is \lam{B}, the binder \lam{bit} is
548 bound to the argument passed to \lam{B} and the case expression
549 evaluates to this bit.
551 If none of the alternatives match, the \lam{DEFAULT} alternative
552 is chosen. A case expression must always be exhaustive, \ie\ it
553 must cover all possible constructors that the scrutinee can have
554 (if all of them are covered explicitly, the \lam{DEFAULT}
555 alternative can be left out).
557 Since we can only match the top level constructor, there can be no overlap
558 in the alternatives and thus order of alternatives is not relevant (though
559 the \lam{DEFAULT} alternative must appear first for implementation
562 To support strictness, the scrutinee is always evaluated into
563 \small{WHNF}, even when there is only a \lam{DEFAULT} alternative. This
564 allows application of the strict function \lam{f} to the argument \lam{a}
568 f (case a of arg DEFAULT -> arg)
571 According to the \GHC\ documentation, this is the only use for the extra
572 binder to which the scrutinee is bound. When not using strictness
573 annotations (which is rather pointless in hardware descriptions),
574 \small{GHC} seems to never generate any code making use of this binder.
575 In fact, \GHC\ has never been observed to generate code using this
576 binder, even when strictness was involved. Nonetheless, the prototype
577 handles this binder as expected.
579 Note that these case expressions are less powerful than the full Haskell
580 case expressions. In particular, they do not support complex patterns like
581 in Haskell. Only the constructor of an expression can be matched,
582 complex patterns are implemented using multiple nested case expressions.
584 Case expressions are also used for unpacking of algebraic data-types, even
585 when there is only a single constructor. For examples, to add the elements
586 of a tuple, the following Core is generated:
589 sum = λtuple.case tuple of
593 Here, there is only a single alternative (but no \lam{DEFAULT}
594 alternative, since the single alternative is already exhaustive). When
595 its body is evaluated, the arguments to the tuple constructor \lam{(,)}
596 (\eg, the elements of the tuple) are bound to \lam{a} and \lam{b}.
599 \startdesc{Cast expression}
600 \defref{cast expression}
604 A cast expression allows you to change the type of an expression to an
605 equivalent type. Note that this is not meant to do any actual work, like
606 conversion of data from one format to another, or force a complete type
607 change. Instead, it is meant to change between different representations
608 of the same type, \eg\ switch between types that are provably equal (but
611 In our hardware descriptions, we typically see casts to change between a
612 Haskell newtype and its contained type, since those are effectively
613 different types (so a cast is needed) with the same representation (but
614 no work is done by the cast).
616 More complex are types that are proven to be equal by the type-checker,
617 but look different at first glance. To ensure that, once the type-checker
618 has proven equality, this information sticks around, explicit casts are
619 added. In our notation we only write the target type, but in reality a
620 cast expressions carries around a \emph{coercion}, which can be seen as a
621 proof of equality. \todo{Example}
623 The value of a cast is the value of its body, unchanged. The type of this
624 value is equal to the target type, not the type of its body.
628 The Core language in \small{GHC} allows adding \emph{notes}, which serve
629 as hints to the inliner or add custom (string) annotations to a Core
630 expression. These should not be generated normally, so these are not
631 handled in any way in the prototype.
635 \defref{type expression}
639 It is possibly to use a Core type as a Core expression. To prevent
640 confusion between types and values, the \lam{@} sign is used to
641 explicitly mark a type that is used in a Core expression.
643 For the actual types supported by Core, see
644 \in{section}[sec:prototype:coretypes]. This \quote{lifting} of a
645 type into the value domain is done to allow for type abstractions
646 and applications to be handled as normal lambda abstractions and
647 applications above. This means that a type expression in Core can
648 only ever occur in the argument position of an application, and
649 only if the type of the function that is applied to expects a type
650 as the first argument. This happens in applications of all
651 polymorphic functions. Consider the \lam{fst} function:
654 fst :: \forall t1. \forall t2. (t1, t2) ->t1
655 fst = λt1.λt2.λ(tup :: (t1, t2)). case tup of (,) a b -> a
657 fstint :: (Int, Int) -> Int
658 fstint = λa.λb.fst @Int @Int a b
661 The type of \lam{fst} has two universally quantified type variables. When
662 \lam{fst} is applied in \lam{fstint}, it is first applied to two types.
663 (which are substituted for \lam{t1} and \lam{t2} in the type of \lam{fst}, so
664 the actual type of arguments and result of \lam{fst} can be found:
665 \lam{fst @Int @Int :: (Int, Int) -> Int}).
668 \subsection[sec:prototype:coretypes]{Core type system}
669 Whereas the expression syntax of Core is very simple, its type system is
670 a bit more complicated. It turns out it is harder to \quote{desugar}
671 Haskell's complex type system into something more simple. Most of the
672 type system is thus very similar to that of Haskell.
674 We will slightly limit our view on Core's type system, since the more
675 complicated parts of it are only meant to support Haskell's (or rather,
676 \GHC's) type extensions, such as existential types, \small{GADT}s, type
677 families and other non-standard Haskell stuff which we do not (plan to)
682 \startframedtext[width=8cm,background=box,frame=no]
683 \startalignment[center]
684 {\tfa The \hs{id} function}
687 A function that is probably present in every functional language, is
688 the \emph{identity} function. This is the function that takes a
689 single argument and simply returns it unmodified. In Haskell this
690 function is called \hs{id} and can take an argument of any type
691 (\ie, it is polymorphic).
693 The \hs{id} function will be used in the examples every now and
697 In Core, every expression is typed. The translation to Core happens
698 after the type-checker, so types in Core are always correct as well
699 (though you could of course construct invalidly typed expressions
700 through the \GHC\ API).
702 Any type in Core is one of the following:
704 \startdesc{A type variable}
709 This is a reference to a type defined elsewhere. This can either be a
710 polymorphic type (like the latter two \lam{t}'s in \lam{id :: \forall t.
711 t -> t}), or a type constructor (like \lam{Bool} in \lam{not :: Bool ->
712 Bool}). Like in Haskell, polymorphic type variables always
713 start with a lowercase letter, while type constructors always start
714 with an uppercase letter.
716 \todo{How to define (new) type constructors?}
718 A special case of a type constructor is the \emph{function type
719 constructor}, \lam{->}. This is a type constructor taking two arguments
720 (using application below). The function type constructor is commonly
721 written inline, so we write \lam{a -> b} when we really mean \lam{-> a
722 b}, the function type constructor applied to \lam{a} and \lam{b}.
724 Polymorphic type variables can only be defined by a lambda
725 abstraction, see the forall type below.
728 \startdesc{A type application}
733 This applies some type to another type. This is particularly used to
734 apply type variables (type constructors) to their arguments.
736 As mentioned above, applications of some type constructors have
737 special notation. In particular, these are applications of the
738 \emph{function type constructor} and \emph{tuple type constructors}:
743 bar' :: (,,) t1 t2 t3
747 \startdesc{The forall type}
749 id :: \forall t. t -> t
751 The forall type introduces polymorphism. It is the only way to
752 introduce new type variables, which are completely unconstrained (Any
753 possible type can be assigned to it). Constraints can be added later
754 using predicate types, see below.
756 A forall type is always (and only) introduced by a type lambda
757 expression. For example, the Core translation of the
763 Here, the type of the binder \lam{x} is \lam{t}, referring to the
764 binder in the topmost lambda.
766 When using a value with a forall type, the actual type
767 used must be applied first. For example Haskell expression \hs{id
768 True} (the function \hs{id} applied to the data-constructor \hs{True})
769 translates to the following Core:
775 Here, id is first applied to the type to work with. Note that the type
776 then changes from \lam{id :: \forall t. t -> t} to \lam{id @Bool ::
777 Bool -> Bool}. Note that the type variable \lam{a} has been
778 substituted with the actual type.
780 In Haskell, forall types are usually not explicitly specified (The use
781 of a lowercase type variable implicitly introduces a forall type for
782 that variable). In fact, in standard Haskell there is no way to
783 explicitly specify forall types. Through a language extension, the
784 \hs{forall} keyword is available, but still optional for normal forall
785 types (it is needed for \emph{existentially quantified types}, which
786 Cλash does not support).
789 \startdesc{Predicate type}
791 show :: \forall t. Show t ⇒ t → String
794 \todo{Sidenote: type classes?}
796 A predicate type introduces a constraint on a type variable introduced
797 by a forall type (or type lambda). In the example above, the type
798 variable \lam{t} can only contain types that are an \emph{instance} of
799 the \emph{type class} \lam{Show}.
801 There are other sorts of predicate types, used for the type families
802 extension, which we will not discuss here.
804 A predicate type is introduced by a lambda abstraction. Unlike with
805 the forall type, this is a value lambda abstraction, that must be
806 applied to a value. We call this value a \emph{dictionary}.
808 Without going into the implementation details, a dictionary can be
809 seen as a lookup table all the methods for a given (single) type class
810 instance. This means that all the dictionaries for the same type class
811 look the same (\eg\ contain methods with the same names). However,
812 dictionaries for different instances of the same class contain
813 different methods, of course.
815 A dictionary is introduced by \small{GHC} whenever it encounters an
816 instance declaration. This dictionary, as well as the binder
817 introduced by a lambda that introduces a dictionary, have the
818 predicate type as their type. These binders are usually named starting
819 with a \lam{\$}. Usually the name of the type concerned is not
820 reflected in the name of the dictionary, but the name of the type
821 class is. The Haskell expression \hs{show True} thus becomes:
824 show @Bool \$dShow True
828 Using this set of types, all types in basic Haskell can be represented.
829 \todo{Overview of polymorphism with more examples (or move examples
832 \section[sec:prototype:statetype]{State annotations in Haskell}
833 As noted in \in{section}[sec:description:stateann], Cλash needs some
834 way to let the programmer explicitly specify which of a function's
835 arguments and which part of a function's result represent the
838 Using the Haskell type systems, there are a few ways we can tackle this.
840 \subsection{Type synonyms}
841 Haskell provides type synonyms as a way to declare a new type that is
842 equal to an existing type (or rather, a new name for an existing type).
843 This allows both the original type and the synonym to be used
844 interchangeably in a Haskell program. This means no explicit conversion
845 is needed. For example, a simple accumulator would become:
848 -- This type synonym would become part of Cλash, it is shown here
852 acc :: Word -> State Word -> (State Word, Word)
853 acc i s = let sum = s + i in (sum, sum)
856 This looks nice in Haskell, but turns out to be hard to implement. There
857 is no explicit conversion in Haskell, but not in Core either. This
858 means the type of a value might be shown as \hs{State Word} in
859 some places, but \hs{Word} in others (and this can even change due
860 to transformations). Since every binder has an explicit type
861 associated with it, the type of every function type will be
862 properly preserved and could be used to track down the
863 statefulness of each value by the compiler. However, this would make
864 the implementation a lot more complicated than when using type
865 renamings as described in the next section.
867 % Use \type instead of \hs here, since the latter breaks inside
869 \subsection{Type renaming (\type{newtype})}
870 Haskell also supports type renamings as a way to declare a new type that
871 has the same (run-time) representation as an existing type (but is in
872 fact a different type to the type-checker). With type renaming,
873 explicit conversion between values of the two types is needed. The
874 accumulator would then become:
877 -- This type renaming would become part of Cλash, it is shown here
879 newtype State s = State s
881 acc :: Word -> State Word -> (State Word, Word)
882 acc i (State s) = let sum = s + i in (State sum, sum)
885 The \hs{newtype} line declares a new type \hs{State} that has one type
886 argument, \hs{s}. This type contains one \quote{constructor} \hs{State}
887 with a single argument of type \hs{s}. It is customary to name the
888 constructor the same as the type, which is allowed (since types can
889 never cause name collisions with values). The difference with the type
890 synonym example is in the explicit conversion between the \hs{State
891 Word} and \hs{Word} types by pattern matching and by using the explicit
892 the \hs{State} constructor.
894 This explicit conversion makes the \VHDL\ generation easier: whenever we
895 remove (unpack) the \hs{State} type, this means we are accessing the
896 current state (\ie, accessing the register output). Whenever we are
897 adding (packing) the \hs{State} type, we are producing a new value for
898 the state (\ie, providing the register input).
900 When dealing with nested states (a stateful function that calls stateful
901 functions, which might call stateful functions, etc.) the state type
902 could quickly grow complex because of all the \hs{State} type constructors
903 needed. For example, consider the following state type (this is just the
904 state type, not the entire function type):
907 State (State Bit, State (State Word, Bit), Word)
910 We cannot leave all these \hs{State} type constructors out, since that
911 would change the type (unlike when using type synonyms). However, when
912 using type synonyms to hide away sub-states (see
913 \in{section}[sec:prototype:substatesynonyms] below), this
914 disadvantage should be limited.
916 \subsubsection{Different input and output types}
917 An alternative could be to use different types for input and output
918 state (\ie\ current and updated state). The accumulator example would
919 then become something like:
922 -- These type renamings would become part of Cλash, it is shown
923 -- here just for clarity.
924 newtype StateIn s = StateIn s
925 newtype StateOut s = StateOut s
927 acc :: Word -> StateIn Word -> (StateIn Word, Word)
928 acc i (StateIn s) = let sum = s + i in (StateIn sum, sum)
931 This could make the implementation easier and the hardware
932 descriptions less error-prone (you can no longer \quote{forget} to
933 unpack and repack a state variable and just return it directly, which
934 can be a problem in the current prototype). However, it also means we
935 need twice as many type synonyms to hide away sub-states, making this
936 approach a bit cumbersome. It also makes it harder to compare input
937 and output state types, possible reducing the type-safety of the
940 \subsection[sec:prototype:substatesynonyms]{Type synonyms for sub-states}
941 As noted above, when using nested (hierarchical) states, the state types
942 of the \quote{upper} functions (those that call other functions, which
943 call other functions, etc.) quickly become complicated. Also, when the
944 state type of one of the \quote{lower} functions changes, the state
945 types of all the upper functions changes as well. If the state type for
946 each function is explicitly and completely specified, this means that a
947 lot of code needs updating whenever a state type changes.
949 To prevent this, it is recommended (but not enforced) to use a type
950 synonym for the state type of every function. Every function calling
951 other functions will then use the state type synonym of the called
952 functions in its own type, requiring no code changes when the state type
953 of a called function changes. This approach is used in
954 \in{example}[ex:AvgState] below. The \hs{AccState} and \hs{AvgState}
955 are examples of such state type synonyms.
957 \subsection{Chosen approach}
958 To keep implementation simple, the current prototype uses the type
959 renaming approach, with a single type for both input and output
960 states. In the future, it might be worthwhile to revisit this
961 approach if more complicated flow analysis is implemented for
962 state variables. This analysis is needed to add proper error
963 checking anyway and might allow the use of type synonyms without
964 losing any expressivity.
966 \subsubsection{Example}
967 As an example of the used approach, a simple averaging circuit
968 is shown in \in{example}[ex:AvgState]. This circuit lets the
969 accumulation of the inputs be done by a sub-component, \hs{acc},
970 but keeps a count of value accumulated in its own
971 state.\footnote{Currently, the prototype is not able to compile
972 this example, since there is no built-in function for division.}
974 \startbuffer[AvgState]
975 -- This type renaming would become part of Cλash, it is shown
976 -- here just for clarity
977 newtype State s = State s
979 -- The accumulator state type
980 type AccState = State Word
982 acc :: Word -> AccState -> (AccState, Word)
983 acc i (State s) = let sum = s + i in (State sum, sum)
985 -- The averaging circuit state type
986 type AvgState = State (AccState, Word)
987 -- The averaging circuit
988 avg :: Word -> AvgState -> (AvgState, Word)
989 avg i (State s) = (State s', o)
992 -- Pass our input through the accumulator, which outputs a sum
993 (accs', sum) = acc i accs
994 -- Increment the count (which will be our new state)
996 -- Compute the average
1001 \placeexample[here][ex:AvgState]{Simple stateful averaging circuit.}
1002 %\startcombination[2*1]
1003 {\typebufferhs{AvgState}}%{Haskell description using function applications.}
1004 % {\boxedgraphic{AvgState}}{The architecture described by the Haskell description.}
1008 \section{\VHDL\ generation for state}
1009 Now its clear how to put state annotations in the Haskell source,
1010 there is the question of how to implement this state translation. As
1011 we have seen in \in{section}[sec:prototype:design], the translation to
1012 \VHDL\ happens as a simple, final step in the compilation process.
1013 This step works on a Core expression in normal form. The specifics
1014 of normal form will be explained in
1015 \in{chapter}[chap:normalization], but the examples given should be
1016 easy to understand using the definition of Core given above. The
1017 conversion to and from the \hs{State} type is done using the cast
1020 \startbuffer[AvgStateNormal]
1023 -- Remove the State newtype
1026 -- Add the State newtype again
1027 spacked' = sum ▶ State Word
1028 res = (spacked', sum)
1034 s = spacked ▶ (AccState, Word)
1035 accs = case s of (a, b) -> a
1036 count = case s of (c, d) -> d
1038 accs' = case accres of (e, f) -> e
1039 sum = case accres of (g, h) -> h
1042 s' = (accs', count')
1043 spacked' = s' ▶ State (AccState, Word)
1049 \placeexample[here][ex:AvgStateNormal]{Normalized version of \in{example}[ex:AvgState]}
1050 {\typebufferlam{AvgStateNormal}}
1052 \subsection[sec:prototype:statelimits]{State in normal form}
1053 Before describing how to translate state from normal form to
1054 \VHDL, we will first see how state handling looks in normal form.
1055 How must their use be limited to guarantee that proper \VHDL\ can
1058 We will formulate a number of rules about what operations are
1059 allowed with state variables. These rules apply to the normalized Core
1060 representation, but will in practice apply to the original Haskell
1061 hardware description as well. Ideally, these rules would become part
1062 of the intended normal form definition \refdef{intended normal form
1063 definition}, but this is not the case right now. This can cause some
1064 problems, which are detailed in
1065 \in{section}[sec:normalization:stateproblems].
1067 In these rules we use the terms \emph{state variable} to refer to any
1068 variable that has a \lam{State} type. A \emph{state-containing
1069 variable} is any variable whose type contains a \lam{State} type,
1070 but is not one itself (like \lam{(AccState, Word)} in the example,
1071 which is a tuple type, but contains \lam{AccState}, which is again
1072 equal to \lam{State Word}).
1074 We also use a distinction between \emph{input} and \emph{output
1075 (state) variables} and \emph{sub-state variables}, which will be
1076 defined in the rules themselves.
1078 These rules describe everything that can be done with state
1079 variables and state-containing variables. Everything else is
1080 invalid. For every rule, the corresponding part of
1081 \in{example}[ex:AvgStateNormal] is shown.
1083 \startdesc{State variables can appear as an argument.}
1085 avg = λi.λspacked. ...
1088 Any lambda that binds a variable with a state type, creates a new
1089 input state variable.
1092 \startdesc{Input state variables can be unpacked.}
1094 s = spacked ▶ (AccState, Word)
1097 An input state variable may be unpacked using a cast operation. This
1098 removes the \lam{State} type renaming and the result has no longer a
1101 If the result of this unpacking does not have a state type and does
1102 not contain state variables, there are no limitations on its
1103 use (this is the function's own state). Otherwise if it does
1104 not have a state type but does contain sub-states, we refer to it
1105 as a \emph{state-containing input variable} and the limitations
1106 below apply. If it has a state type itself, we refer to it as an
1107 \emph{input sub-state variable} and the below limitations apply
1110 It may seem strange to consider a variable that still has a state
1111 type directly after unpacking, but consider the case where a
1112 function does not have any state of its own, but does call a single
1113 stateful function. This means it must have a state argument that
1114 contains just a sub-state. The function signature of such a function
1118 type FooState = State AccState
1121 Which is of course equivalent to \lam{State (State Word)}.
1124 \startdesc{Variables can be extracted from state-containing input variables.}
1126 accs = case s of (a, b) -> a
1129 A state-containing input variable is typically a tuple containing
1130 multiple elements (like the current function's state, sub-states or
1131 more tuples containing sub-states). All of these can be extracted
1132 from an input variable using an extractor case (or possibly
1133 multiple, when the input variable is nested).
1135 If the result has no state type and does not contain any state
1136 variables either, there are no further limitations on its use
1137 (this is the function's own state). If the result has no state
1138 type but does contain state variables we refer to it as a
1139 \emph{state-containing input variable} and this limitation keeps
1140 applying. If the variable has a state type itself, we refer to
1141 it as an \emph{input sub-state variable} and below limitations
1144 \startdesc{Input sub-state variables can be passed to functions.}
1147 accs' = case accres of (e, f) -> e
1150 An input sub-state variable can (only) be passed to a function.
1151 Additionally, every input sub-state variable must be used in exactly
1152 \emph{one} application, no more and no less.
1154 The function result should contain exactly one state variable, which
1155 can be extracted using (multiple) case expressions. The extracted
1156 state variable is referred to the \emph{output sub-state}
1158 The type of this output sub-state must be identical to the type of
1159 the input sub-state passed to the function.
1162 \startdesc{Variables can be inserted into a state-containing output variable.}
1164 s' = (accs', count')
1167 A function's output state is usually a tuple containing its own
1168 updated state variables and all output sub-states. This result is
1169 built up using any single-constructor algebraic datatype
1172 The result of these expressions is referred to as a
1173 \emph{state-containing output variable}, which are subject to these
1177 \startdesc{State containing output variables can be packed.}
1179 spacked' = s' ▶ State (AccState, Word)
1182 As soon as all a functions own update state and output sub-state
1183 variables have been joined together, the resulting
1184 state-containing output variable can be packed into an output
1185 state variable. Packing is done by casting to a state type.
1188 \startdesc{Output state variables can appear as (part of) a function result.}
1197 When the output state is packed, it can be returned as a part
1198 of the function result. Nothing else can be done with this
1199 value (or any value that contains it).
1202 There is one final limitation that is hard to express in the above
1203 itemization. Whenever sub-states are extracted from the input state
1204 to be passed to functions, the corresponding output sub-states
1205 should be inserted into the output state in the same way. In other
1206 words, each pair of corresponding sub-states in the input and
1207 output states should be passed to / returned from the same called
1210 The prototype currently does not check much of the above
1211 conditions. This means that if the conditions are violated,
1212 sometimes a compile error is generated, but in other cases output
1213 can be generated that is not valid \VHDL\ or at the very least does
1214 not correspond to the input.
1216 \subsection{Translating to \VHDL}
1217 As noted above, the basic approach when generating \VHDL\ for stateful
1218 functions is to generate a single register for every stateful function.
1219 We look around the normal form to find the let binding that removes the
1220 \lam{State} type renaming (using a cast). We also find the let binding that
1221 adds a \lam{State} type. These are connected to the output and the input
1222 of the generated let binding respectively. This means that there can
1223 only be one let binding that adds and one that removes the \lam{State}
1224 type. It is easy to violate this constraint. This problem is detailed in
1225 \in{section}[sec:normalization:stateproblems].
1227 This approach seems simple enough, but will this also work for more
1228 complex stateful functions involving sub-states? Observe that any
1229 component of a function's state that is a sub-state, \ie\ passed on as
1230 the state of another function, should have no influence on the
1231 hardware generated for the calling function. Any state-specific
1232 \small{VHDL} for this component can be generated entirely within the
1233 called function. So, we can completely ignore sub-states when
1234 generating \VHDL\ for a function.
1236 From this observation it might seem logical to remove the
1237 sub-states from a function's states altogether and leave only the
1238 state components which are actual states of the current function.
1239 While doing this would not remove any information needed to
1240 generate \small{VHDL} from the function, it would cause the
1241 function definition to become invalid (since we will not have any
1242 sub-state to pass to the functions anymore). We could solve the
1243 syntactic problems by passing \type{undefined} for state
1244 variables, but that would still break the code on the semantic
1245 level (\ie, the function would no longer be semantically
1246 equivalent to the original input).
1248 To keep the function definition correct until the very end of the
1249 process, we will not deal with (sub)states until we get to the
1250 \small{VHDL} generation. Then, we are translating from Core to
1251 \small{VHDL}, and we can simply generate no \VHDL for sub-states,
1252 effectively removing them altogether.
1254 But, how will we know what exactly is a sub-state? Since any state
1255 argument or return value that represents state must be of the
1256 \type{State} type, we can look at the type of a value. However, we
1257 must be careful to ignore only \emph{sub-states}, and not a
1258 function's own state.
1260 For \in{example}[ex:AvgStateNormal] above, we should generate a register
1261 with its output connected to \lam{s} and its input connected
1262 to \lam{s'}. However, \lam{s'} is build up from both \lam{accs'} and
1263 \lam{count'}, while only \lam{count'} should end up in the register.
1264 \lam{accs'} is a sub-state for the \lam{acc} function, for which a
1265 register will be created when generating \VHDL\ for the \lam{acc}
1268 Fortunately, the \lam{accs'} variable (and any other sub-state) has a
1269 property that we can easily check: it has a \lam{State} type. This
1270 means that whenever \VHDL\ is generated for a tuple (or other
1271 algebraic type), we can simply leave out all elements that have a
1272 \lam{State} type. This will leave just the parts of the state that
1273 do not have a \lam{State} type themselves, like \lam{count'},
1274 which is exactly a function's own state. This approach also means
1275 that the state part of the result (\eg\ \lam{s'} in \lam{res}) is
1276 automatically excluded when generating the output port, which is
1279 We can formalize this translation a bit, using the following
1283 \item A state unpack operation should not generate any \small{VHDL}.
1284 The binder to which the unpacked state is bound should still be
1285 declared, this signal will become the register and will hold the
1287 \item A state pack operation should not generate any \small{VHDL}.
1288 The binder to which the packed state is bound should not be
1289 declared. The binder that is packed is the signal that will hold the
1291 \item Any values of a State type should not be translated to
1292 \small{VHDL}. In particular, State elements should be removed from
1293 tuples (and other data-types) and arguments with a state type should
1295 \item To make the state actually work, a simple \small{VHDL}
1296 (sequential) process should be generated. This process updates
1297 the state at every clock cycle, by assigning the new state to the
1298 current state. This will be recognized by synthesis tools as a
1299 register specification.
1302 When applying these rules to the function \lam{avg} from
1303 \in{example}[ex:AvgStateNormal], we be left with the description
1304 below. All the parts that do not generate any \VHDL\ directly are
1305 crossed out, leaving just the actual flow of values in the final
1306 hardware. To illustrate the change of the types of \lam{s} and \lam{s'},
1307 their types are also shown.
1309 \startbuffer[AvgStateRemoved]
1310 avg = iλ.λ--spacked.--
1312 s :: (--AccState,-- Word)
1313 s = --spacked ▶ (AccState, Word)--
1314 --accs = case s of (a, b) -> a--
1315 count = case s of (--c,-- d) -> d
1316 accres = acc i --accs--
1317 --accs' = case accres of (e, f) -> e--
1318 sum = case accres of (--g,-- h) -> h
1321 s' :: (--AccState,-- Word)
1322 s' = (--accs',-- count')
1323 --spacked' = s' ▶ State (AccState, Word)--
1324 res = (--spacked',-- o)
1328 \typebufferlam{AvgStateRemoved}
1330 When we actually leave out the crossed out parts, we get a slightly
1331 weird program: there is a variable \lam{s} which has no value, and there
1332 is a variable \lam{s'} that is never used. But together, these two will form
1333 the state process of the function. \lam{s} contains the "current" state,
1334 \lam{s'} is assigned the "next" state. So, at the end of each clock
1335 cycle, \lam{s'} should be assigned to \lam{s}.
1337 As an illustration of the result of this function,
1338 \in{example}[ex:AccStateVHDL] and \in{example}[ex:AvgStateVHDL] show the the \VHDL\ that is
1339 generated by Cλash from the examples is this section.
1341 \startbuffer[AvgStateVHDL]
1342 entity avgComponent_0 is
1343 port (\izAlE2\ : in \unsigned_31\;
1344 \foozAo1zAo12\ : out \(,)unsigned_31\;
1345 clock : in std_logic;
1346 resetn : in std_logic);
1347 end entity avgComponent_0;
1350 architecture structural of avgComponent_0 is
1351 signal \szAlG2\ : \(,)unsigned_31\;
1352 signal \countzAlW2\ : \unsigned_31\;
1353 signal \dszAm62\ : \(,)unsigned_31\;
1354 signal \sumzAmk3\ : \unsigned_31\;
1355 signal \reszAnCzAnM2\ : \unsigned_31\;
1356 signal \foozAnZzAnZ2\ : \unsigned_31\;
1357 signal \reszAnfzAnj3\ : \unsigned_31\;
1358 signal \s'zAmC2\ : \(,)unsigned_31\;
1360 \countzAlW2\ <= \szAlG2\.A;
1362 \comp_ins_dszAm62\ : entity accComponent_1
1363 port map (\izAob3\ => \izAlE2\,
1364 \foozAoBzAoB2\ => \dszAm62\,
1368 \sumzAmk3\ <= \dszAm62\.A;
1370 \reszAnCzAnM2\ <= to_unsigned(1, 32);
1372 \foozAnZzAnZ2\ <= \countzAlW2\ + \reszAnCzAnM2\;
1374 \reszAnfzAnj3\ <= \sumzAmk3\ * \foozAnZzAnZ2\;
1376 \s'zAmC2\.A <= \foozAnZzAnZ2\;
1378 \foozAo1zAo12\.A <= \reszAnfzAnj3\;
1380 state : process (clock, resetn)
1382 if resetn = '0' then
1383 elseif rising_edge(clock) then
1384 \szAlG2\ <= \s'zAmC2\;
1387 end architecture structural;
1390 \startbuffer[AvgStateTypes]
1392 subtype \unsigned_31\ is unsigned (0 to 31);
1394 type \(,)unsigned_31\ is record
1400 \startbuffer[AccStateVHDL]
1401 entity accComponent_1 is
1402 port (\izAob3\ : in \unsigned_31\;
1403 \foozAoBzAoB2\ : out \(,)unsigned_31\;
1404 clock : in std_logic;
1405 resetn : in std_logic);
1406 end entity accComponent_1;
1408 architecture structural of accComponent_1 is
1409 signal \szAod3\ : \unsigned_31\;
1410 signal \reszAonzAor3\ : \unsigned_31\;
1412 \reszAonzAor3\ <= \szAod3\ + \izAob3\;
1414 \foozAoBzAoB2\.A <= \reszAonzAor3\;
1416 state : process (clock, resetn)
1418 if resetn = '0' then
1419 elseif rising_edge(clock) then
1420 \szAod3\ <= \reszAonzAor3\;
1423 end architecture structural;
1426 \placeexample[][ex:AvgStateTypes]{\VHDL\ types generated for \hs{acc} and \hs{avg} from \in{example}[ex:AvgState]}
1427 {\typebuffervhdl{AvgStateTypes}}
1428 \placeexample[][ex:AccStateVHDL]{\VHDL\ generated for \hs{acc} from \in{example}[ex:AvgState]}
1429 {\typebuffervhdl{AccStateVHDL}}
1430 \placeexample[][ex:AvgStateVHDL]{\VHDL\ generated for \hs{avg} from \in{example}[ex:AvgState]}
1431 {\typebuffervhdl{AvgStateVHDL}}
1432 \section{Prototype implementation}
1433 The prototype has been implemented using Haskell as its
1434 implementation language, just like \GHC. This allows the prototype
1435 do directly use parts of \GHC\ through the \small{API} it exposes
1436 (which essentially taps directly into the internals of \GHC, making
1437 this \small{API} not really a stable interface).
1439 Cλash can be run from a separate library, but has also been
1440 integrated into \type{ghci} \cite[baaij09]. The latter does requires
1441 a custom \GHC\ build, however.
1443 The latest version and all history of the Cλash code can be browsed
1444 on-line or retrieved using the \type{git} program.
1446 http://git.stderr.nl/gitweb?p=matthijs/projects/cλash.git
1448 % \subsection{Initial state}
1449 % How to specify the initial state? Cannot be done inside a hardware
1450 % function, since the initial state is its own state argument for the first
1451 % call (unless you add an explicit, synchronous reset port).
1453 % External init state is natural for simulation.
1455 % External init state works for hardware generation as well.
1457 % Implementation issues: state splitting, linking input to output state,
1458 % checking usage constraints on state variables.
1461 % vim: set sw=2 sts=2 expandtab: