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: What
16 (functional) language will we use to describe our hardware? (Note that
17 this does not concern the \emph{implementation language} of the compiler,
18 just the language \emph{translated by} the compiler).
20 On the highest level, we have two choices:
23 \item Create a new functional language from scratch. This has the
24 advantage of having a language that contains exactly those elements that
25 are convenient for describing hardware and can contain special
26 constructs that might.
27 \item Use an existing language and create a new backend for it. This has
28 the advantage that existing tools can be reused, which will speed up
32 Considering that we required a prototype which should be working quickly,
33 and that implementing parsers, semantic checkers and especially
34 typcheckers isn't exactly the core of this research (but it is lots and
35 lots of work!), using an existing language is the obvious choice. This
36 also has the advantage that a large set of language features is available
37 to experiment with and it is easy to find which features apply well and
38 which don't. A possible second prototype could use a custom language with
39 just the useful features (and possibly extra features that are specific to
40 the domain of hardware description as well).
42 The second choice is to pick one of the many existing languages. As
43 mentioned before, this language is Haskell. This choice has not been the
44 result of a thorough comparison of languages, for the simple reason that
45 the requirements on the language were completely unclear at the start of
46 this language. The fact that Haskell is a language with a broad spectrum
47 of features, that it is commonly used in research projects and that the
48 primary compiler, GHC, provides a high level API to its internals, made
49 Haskell an obvious choice.
51 TODO: Was Haskell really a good choice? Perhaps say this somewhere else?
53 \section[sec:prototype:output]{Output format}
54 The second important question is: What will be our output format? Since
55 our prototype won't be able to program FPGA's directly, we'll have to have
56 output our hardware in some format that can be later processed and
57 programmed by other tools.
59 Looking at other tools in the industry, the Electronic Design Interchange
60 Format (\small{EDIF}) is commonly used for storing intermediate
61 \emph{netlists} (lists of components and connections between these
62 components) and is commonly the target for \small{VHDL} and Verilog
65 However, \small{EDIF} is not completely tool-independent. It specifies a
66 meta-format, but the hardware components that can be used vary between
67 various tool and hardware vendors, as well as the interpretation of the
68 \small{EDIF} standard (TODO Is this still true? Reference:
69 http://delivery.acm.org/10.1145/80000/74534/p803-li.pdf?key1=74534\&key2=8370537521\&coll=GUIDE\&dl=GUIDE\&CFID=61207158\&CFTOKEN=61908473).
71 This means that when working with EDIF, our prototype would become
72 technology dependent (\eg only work with \small{FPGA}s of a specific
73 vendor, or even only with specific chips). This limits the applicability
74 of our prototype. Also, the tools we'd like to use for verifying,
75 simulating and draw pretty pictures of our output (like Precision, or
76 QuestaSim) work on \small{VHDL} or Verilog input (TODO: Is this really
79 For these reasons, we will use \small{VHDL} as our output language.
80 Verilog is not used simply because we are familiar with \small{VHDL}
81 already. The differences between \small{VHDL} and Verilog are on the
82 higher level, while we will be using \small{VHDL} mainly to write low
83 level, netlist-like descriptions anyway.
85 An added advantage of using VHDL is that we can profit from existing
86 optimizations in VHDL synthesizers. A lot of optimizations are done on the
87 VHDL level by existing tools. These tools have years of experience in this
88 field, so it would not be reasonable to assume we could achieve a similar
89 amount of optimization in our prototype (nor should it be a goal,
90 considering this is just a prototype).
92 Note that we will be using \small{VHDL} as our output language, but will
93 not use its full expressive power. Our output will be limited to using
94 simple, structural descriptions, without any behavioural descriptions
95 (which might not be supported by all tools).
97 \section{Prototype design}
98 As stated above, we will use the Glasgow Haskell Compiler (\small{GHC}) to
99 implement our prototype compiler. To understand the design of the
100 compiler, we will first dive into the \small{GHC} compiler a bit. It's
101 compilation consists of the following steps (slightly simplified):
103 \startuseMPgraphic{ghc-pipeline}
105 save inp, front, desugar, simpl, back, out;
106 newEmptyBox.inp(0,0);
107 newBox.front(btex Parser etex);
108 newBox.desugar(btex Desugarer etex);
109 newBox.simpl(btex Simplifier etex);
110 newBox.back(btex Backend etex);
111 newEmptyBox.out(0,0);
113 % Space the boxes evenly
114 inp.c - front.c = front.c - desugar.c = desugar.c - simpl.c
115 = simpl.c - back.c = back.c - out.c = (0, 1.5cm);
118 % Draw lines between the boxes. We make these lines "deferred" and give
119 % them a name, so we can use ObjLabel to draw a label beside them.
120 ncline.inp(inp)(front) "name(haskell)";
121 ncline.front(front)(desugar) "name(ast)";
122 ncline.desugar(desugar)(simpl) "name(core)";
123 ncline.simpl(simpl)(back) "name(simplcore)";
124 ncline.back(back)(out) "name(native)";
125 ObjLabel.inp(btex Haskell source etex) "labpathname(haskell)", "labdir(rt)";
126 ObjLabel.front(btex Haskell AST etex) "labpathname(ast)", "labdir(rt)";
127 ObjLabel.desugar(btex Core etex) "labpathname(core)", "labdir(rt)";
128 ObjLabel.simpl(btex Simplified core etex) "labpathname(simplcore)", "labdir(rt)";
129 ObjLabel.back(btex Native code etex) "labpathname(native)", "labdir(rt)";
131 % Draw the objects (and deferred labels)
132 drawObj (inp, front, desugar, simpl, back, out);
134 \placefigure[right]{GHC compiler pipeline}{\useMPgraphic{ghc-pipeline}}
137 This step takes the Haskell source files and parses them into an
138 abstract syntax tree (\small{AST}). This \small{AST} can express the
139 complete Haskell language and is thus a very complex one (in contrast
140 with the Core \small{AST}, later on). All identifiers in this
141 \small{AST} are resolved by the renamer and all types are checked by the
144 \startdesc{Desugaring}
145 This steps takes the full \small{AST} and translates it to the
146 \emph{Core} language. Core is a very small functional language with lazy
147 semantics, that can still express everything Haskell can express. Its
148 simpleness makes Core very suitable for further simplification and
149 translation. Core is the language we will be working on as well.
151 \startdesc{Simplification}
152 Through a number of simplification steps (such as inlining, common
153 subexpression elimination, etc.) the Core program is simplified to make
154 it faster or easier to process further.
157 This step takes the simplified Core program and generates an actual
158 runnable program for it. This is a big and complicated step we will not
159 discuss it any further, since it is not required for our prototype.
162 In this process, there a number of places where we can start our work.
163 Assuming that we don't want to deal with (or modify) parsing, typechecking
164 and other frontend business and that native code isn't really a useful
165 format anymore, we are left with the choice between the full Haskell
166 \small{AST}, or the smaller (simplified) core representation.
168 The advantage of taking the full \small{AST} is that the exact structure
169 of the source program is preserved. We can see exactly what the hardware
170 descriiption looks like and which syntax constructs were used. However,
171 the full \small{AST} is a very complicated datastructure. If we are to
172 handle everything it offers, we will quickly get a big compiler.
174 Using the core representation gives us a much more compact datastructure
175 (a core expression only uses 9 constructors). Note that this does not mean
176 that the core representation itself is smaller, on the contrary. Since the
177 core language has less constructs, a lot of things will take a larger
178 expression to express.
180 However, the fact that the core language is so much smaller, means it is a
181 lot easier to analyze and translate it into something else. For the same
182 reason, \small{GHC} runs its simplifications and optimizations on the core
183 representation as well.
185 However, we will use the normal core representation, not the simplified
186 core. Reasons for this are detailed below.
188 The final prototype roughly consists of three steps:
190 \startuseMPgraphic{ghc-pipeline}
192 save inp, front, norm, vhdl, out;
193 newEmptyBox.inp(0,0);
194 newBox.front(btex \small{GHC} frontend + desugarer etex);
195 newBox.norm(btex Normalization etex);
196 newBox.vhdl(btex \small{VHDL} generation etex);
197 newEmptyBox.out(0,0);
199 % Space the boxes evenly
200 inp.c - front.c = front.c - norm.c = norm.c - vhdl.c
201 = vhdl.c - out.c = (0, 1.5cm);
204 % Draw lines between the boxes. We make these lines "deferred" and give
205 % them a name, so we can use ObjLabel to draw a label beside them.
206 ncline.inp(inp)(front) "name(haskell)";
207 ncline.front(front)(norm) "name(core)";
208 ncline.norm(norm)(vhdl) "name(normal)";
209 ncline.vhdl(vhdl)(out) "name(vhdl)";
210 ObjLabel.inp(btex Haskell source etex) "labpathname(haskell)", "labdir(rt)";
211 ObjLabel.front(btex Core etex) "labpathname(core)", "labdir(rt)";
212 ObjLabel.norm(btex Normalized core etex) "labpathname(normal)", "labdir(rt)";
213 ObjLabel.vhdl(btex \small{VHDL} description etex) "labpathname(vhdl)", "labdir(rt)";
215 % Draw the objects (and deferred labels)
216 drawObj (inp, front, norm, vhdl, out);
218 \placefigure[right]{GHC compiler pipeline}{\useMPgraphic{ghc-pipeline}}
221 This is exactly the frontend and desugarer from the \small{GHC}
222 pipeline, that translates Haskell sources to a core representation.
224 \startdesc{Normalization}
225 This is a step that transforms the core representation into a normal
226 form. This normal form is still expressed in the core language, but has
227 to adhere to an extra set of constraints. This normal form is less
228 expressive than the full core language (e.g., it can have limited higher
229 order expressions, has a specific structure, etc.), but is also very
230 close to directly describing hardware.
232 \startdesc{\small{VHDL} generation}
233 The last step takes the normal formed core representation and generates
234 \small{VHDL} for it. Since the normal form has a specific, hardware-like
235 structure, this final step is very straightforward.
238 The most interesting step in this process is the normalization step. That
239 is where more complicated functional constructs, which have no direct
240 hardware interpretation, are removed and translated into hardware
241 constructs. This step is described in a lot of detail at
242 \in{chapter}[chap:normalization].
244 \section{The Core language}
245 Most of the prototype deals with handling the program in the Core
246 language. In this section we will show what this language looks like and
249 The Core language is a functional language that describes
250 \emph{expressions}. Every identifier used in Core is called a
251 \emph{binder}, since it is bound to a value somewhere. On the highest
252 level, a Core program is a collection of functions, each of which bind a
253 binder (the function name) to an expression (the function value, which has
256 The Core language itself does not prescribe any program structure, only
257 expression structure. In the \small{GHC} compiler, the Haskell module
258 structure is used for the resulting Core code as well. Since this is not
259 so relevant for understanding the Core language or the Normalization
260 process, we'll only look at the Core expression language here.
262 Each Core expression consists of one of these possible expressions.
264 \startdesc{Variable reference}
268 This is a simple reference to a binder. It's written down as the
269 name of the binder that is being referred to, which should of course be
270 bound in a containing scope (including top level scope, so a reference
271 to a top level function is also a variable reference). Additionally,
272 constructors from algebraic datatypes also become variable references.
274 The value of this expression is the value bound to the given binder.
276 Each binder also carries around its type, but this is usually not shown
277 in the Core expressions. Occasionally, the type of an entire expression
278 or function is shown for clarity, but this is only informational. In
279 practice, the type of an expression is easily determined from the
280 structure of the expression and the types of the binders and occasional
281 cast expressions. This minimize the amount of bookkeeping needed to keep
282 the typing consistent.
289 This is a simple literal. Only primitive types are supported, like
290 chars, strings, ints and doubles. The types of these literals are the
291 \quote{primitive} versions, like \lam{Char\#} and \lam{Word\#}, not the
292 normal Haskell versions (but there are builtin conversion functions).
295 \startdesc{Application}
299 This is simple function application. Each application consists of two
300 parts: The function part and the argument part. Applications are used
301 for normal function \quote{calls}, but also for applying type
302 abstractions and data constructors.
304 The value of an application is the value of the function part, with the
305 first argument binder bound to the argument part.
308 \startdesc{Lambda abstraction}
312 This is the basic lambda abstraction, as it occurs in labmda calculus.
313 It consists of a binder part and a body part. A lambda abstraction
314 creates a function, that can be applied to an argument.
316 Note that the body of a lambda abstraction extends all the way to the
317 end of the expression, or the closing bracket surrounding the lambda. In
318 other words, the lambda abstraction \quote{operator} has the lowest
321 The value of an application is the value of the body part, with the
322 binder bound to the value the entire lambda abstraction is applied to.
325 \startdesc{Non-recursive let expression}
327 let bndr = value in body
329 A let expression allows you to bind a binder to some value, while
330 evaluating to some other value (where that binder is in scope). This
331 allows for sharing of subexpressions (you can use a binder twice) and
332 explicit \quote{naming} of arbitrary expressions. Note that the binder
333 is not in scope in the value bound to it, so it's not possible to make
334 recursive definitions with the normal form of the let expression (see
335 the recursive form below).
337 Even though this let expression is an extension on the basic lambda
338 calculus, it is easily translated to a lambda abstraction. The let
339 expression above would then become:
345 This notion might be useful for verifying certain properties on
346 transformations, since a lot of verification work has been done on
347 lambda calculus already.
349 The value of a let expression is the value of the body part, with the
350 binder bound to the value.
353 \startdesc{Recursive let expression}
362 This is the recursive version of the let expression. In \small{GHC}'s
363 Core implementation, non-recursive and recursive lets are not so
364 distinct as we present them here, but this provides a clearer overview.
366 The main difference with the normal let expression is that each of the
367 binders is in scope in each of the values, in addition to the body. This
368 allows for self-recursive definitions or mutually recursive definitions.
370 It should also be possible to express a recursive let using normal
371 lambda calculus, if we use the \emph{least fixed-point operator},
375 \startdesc{Case expression}
378 DEFAULT -> defaultbody
379 C0 bndr0,0 ... bndr0,m -> body0
381 Cn bndrn,0 ... bndrn,m -> bodyn
386 A case expression is the only way in Core to choose between values. A case
387 expression evaluates its scrutinee, which should have an algebraic
388 datatype, into weak head normal form (\small{WHNF}) and (optionally) binds
389 it to \lam{bndr}. It then chooses a body depending on the constructor of
390 its scrutinee. If none of the constructors match, the \lam{DEFAULT}
391 alternative is chosen.
393 Since we can only match the top level constructor, there can be no overlap
394 in the alternatives and thus order of alternatives is not relevant (though
395 the \lam{DEFAULT} alternative must appear first for implementation
398 Any arguments to the constructor in the scrutinee are bound to each of the
399 binders after the constructor and are in scope only in the corresponding
402 To support strictness, the scrutinee is always evaluated into WHNF, even
403 when there is only a \lam{DEFAULT} alternative. This allows a strict
404 function argument to be written like:
407 function (case argument of arg
411 This seems to be the only use for the extra binder to which the scrutinee
412 is bound. When not using strictness annotations (which is rather pointless
413 in hardware descriptions), \small{GHC} seems to never generate any code
414 making use of this binder. The current prototype does not handle it
415 either, which probably means that code using it would break.
417 Note that these case statements are less powerful than the full Haskell
418 case statements. In particular, they do not support complex patterns like
419 in Haskell. Only the constructor of an expression can be matched, complex
420 patterns are implemented using multiple nested case expressions.
422 Case statements are also used for unpacking of algebraic datatypes, even
423 when there is only a single constructor. For examples, to add the elements
424 of a tuple, the following Core is generated:
427 sum = λtuple.case tuple of
431 Here, there is only a single alternative (but no \lam{DEFAULT}
432 alternative, since the single alternative is already exhaustive). When
433 it's body is evaluated, the arguments to the tuple constructor \lam{(,)}
434 (\eg, the elements of the tuple) are bound to \lam{a} and \lam{b}.
437 \startdesc{Cast expression}
441 A cast expression allows you to change the type of an expression to an
442 equivalent type. Note that this is not meant to do any actual work, like
443 conversion of data from one format to another, or force a complete type
444 change. Instead, it is meant to change between different representations
445 of the same type, \eg switch between types that are provably equal (but
448 In our hardware descriptions, we typically see casts to change between a
449 Haskell newtype and its contained type, since those are effectively
450 different representations of the same type.
452 More complex are types that are proven to be equal by the typechecker,
453 but look different at first glance. To ensure that, once the typechecker
454 has proven equality, this information sticks around, explicit casts are
455 added. In our notation we only write the target type, but in reality a
456 cast expressions carries around a \emph{coercion}, which can be seen as a
457 proof of equality. TODO: Example
459 The value of a cast is the value of its body, unchanged. The type of this
460 value is equal to the target type, not the type of its body.
462 Note that this syntax is also used sometimes to indicate that a particular
463 expression has a particular type, even when no cast expression is
464 involved. This is then purely informational, since the only elements that
465 are explicitely typed in the Core language are the binder references and
466 cast expressions, the types of all other elements are determined at
472 The Core language in \small{GHC} allows adding \emph{notes}, which serve
473 as hints to the inliner or add custom (string) annotations to a core
474 expression. These shouldn't be generated normally, so these are not
475 handled in any way in the prototype.
482 It is possibly to use a Core type as a Core expression. This is done to
483 allow for type abstractions and applications to be handled as normal
484 lambda abstractions and applications above. This means that a type
485 expression in Core can only ever occur in the argument position of an
486 application, and only if the type of the function that is applied to
487 expects a type as the first argument. This happens for all polymorphic
488 functions, for example, the \lam{fst} function:
491 fst :: \forall a. \forall b. (a, b) -> a
492 fst = λtup.case tup of (,) a b -> a
494 fstint :: (Int, Int) -> Int
495 fstint = λa.λb.fst @Int @Int a b
498 The type of \lam{fst} has two universally quantified type variables. When
499 \lam{fst} is applied in \lam{fstint}, it is first applied to two types.
500 (which are substitued for \lam{a} and \lam{b} in the type of \lam{fst}, so
501 the type of \lam{fst} actual type of arguments and result can be found:
502 \lam{fst @Int @Int :: (Int, Int) -> Int}).
505 TODO: Core type system
507 \section[sec:prototype:statetype]{State annotations in Haskell}
508 Ideal: Type synonyms, since there is no additional code overhead for
509 packing and unpacking. Downside: there is no explicit conversion in Core
510 either, so type synonyms tend to get lost in expressions (they can be
511 preserved in binders, but this makes implementation harder, since that
512 statefulness of a value must be manually tracked).
514 Less ideal: Newtype. Requires explicit packing and unpacking of function
515 arguments. If you don't unpack substates, there is no overhead for
516 (un)packing substates. This will result in many nested State constructors
517 in a nested state type. \eg:
520 State (State Bit, State (State Word, Bit), Word)
523 Alternative: Provide different newtypes for input and output state. This
524 makes the code even more explicit, and typechecking can find even more
525 errors. However, this requires defining two type synomyms for each
526 stateful function instead of just one. \eg:
529 type AccumStateIn = StateIn Bit
530 type AccumStateOut = StateOut Bit
533 This also increases the possibility of having different input and output
534 states. Checking for identical input and output state types is also
535 harder, since each element in the state must be unpacked and compared
538 Alternative: Provide a type for the entire result type of a stateful
539 function, not just the state part. \eg:
542 newtype Result state result = Result (state, result)
545 This makes it easy to say "Any stateful function must return a
546 \type{Result} type, without having to sort out result from state. However,
547 this either requires a second type for input state (similar to
548 \type{StateIn} / \type{StateOut} above), or requires the compiler to
549 select the right argument for input state by looking at types (which works
550 for complex states, but when that state has the same type as an argument,
551 things get ambiguous) or by selecting a fixed (\eg, the last) argument,
552 which might be limiting.
554 \subsubsection{Example}
555 As an example of the used approach, a simple averaging circuit, that lets
556 the accumulation of the inputs be done by a subcomponent.
559 newtype State s = State s
561 type AccumState = State Bit
562 accum :: Word -> AccumState -> (AccumState, Word)
563 accum i (State s) = (State (s + i), s + i)
565 type AvgState = (AccumState, Word)
566 avg :: Word -> AvgState -> (AvgState, Word)
567 avg i (State s) = (State s', o)
570 -- Pass our input through the accumulator, which outputs a sum
571 (accums', sum) = accum i accums
572 -- Increment the count (which will be our new state)
574 -- Compute the average
576 s' = (accums', count')
579 And the normalized, core-like versions:
582 accum i spacked = res
584 s = case spacked of (State s) -> s
592 s = case spacked of (State s) -> s
593 accums = case s of (accums, \_) -> accums
594 count = case s of (\_, count) -> count
595 accumres = accum i accums
596 accums' = case accumres of (accums', \_) -> accums'
597 sum = case accumres of (\_, sum) -> sum
600 s' = (accums', count')
607 As noted above, any component of a function's state that is a substate,
608 \eg passed on as the state of another function, should have no influence
609 on the hardware generated for the calling function. Any state-specific
610 \small{VHDL} for this component can be generated entirely within the called
611 function. So,we can completely leave out substates from any function.
613 From this observation, we might think to remove the substates from a
614 function's states alltogether, and leave only the state components which
615 are actual states of the current function. While doing this would not
616 remove any information needed to generate \small{VHDL} from the function, it would
617 cause the function definition to become invalid (since we won't have any
618 substate to pass to the functions anymore). We could solve the syntactic
619 problems by passing \type{undefined} for state variables, but that would
620 still break the code on the semantic level (\ie, the function would no
621 longer be semantically equivalent to the original input).
623 To keep the function definition correct until the very end of the process,
624 we will not deal with (sub)states until we get to the \small{VHDL} generation.
625 Here, we are translating from Core to \small{VHDL}, and we can simply not generate
626 \small{VHDL} for substates, effectively removing the substate components
629 There are a few important points when ignore substates.
631 First, we have to have some definition of "substate". Since any state
632 argument or return value that represents state must be of the \type{State}
633 type, we can simply look at its type. However, we must be careful to
634 ignore only {\em substates}, and not a function's own state.
636 In the example above, this means we should remove \type{accums'} from
637 \type{s'}, but not throw away \type{s'} entirely. We should, however,
638 remove \type{s'} from the output port of the function, since the state
639 will be handled by a \small{VHDL} procedure within the function.
641 When looking at substates, these can appear in two places: As part of an
642 argument and as part of a return value. As noted above, these substates
643 can only be used in very specific ways.
645 \desc{State variables can appear as an argument.} When generating \small{VHDL}, we
646 completely ignore the argument and generate no input port for it.
648 \desc{State variables can be extracted from other state variables.} When
649 extracting a state variable from another state variable, this always means
650 we're extracting a substate, which we can ignore. So, we simply generate no
651 \small{VHDL} for any extraction operation that has a state variable as a result.
653 \desc{State variables can be passed to functions.} When passing a
654 state variable to a function, this always means we're passing a substate
655 to a subcomponent. The entire argument can simply be ingored in the
658 \desc{State variables can be returned from functions.} When returning a
659 state variable from a function (probably as a part of an algebraic
660 datatype), this always mean we're returning a substate from a
661 subcomponent. The entire state variable should be ignored in the resulting
662 port map. The type binder of the binder that the function call is bound
663 to should not include the state type either.
665 \startdesc{State variables can be inserted into other variables.} When inserting
666 a state variable into another variable (usually by constructing that new
667 variable using its constructor), we can identify two cases:
670 \item The state is inserted into another state variable. In this case,
671 the inserted state is a substate, and can be safely left out of the
672 constructed variable.
673 \item The state is inserted into a non-state variable. This happens when
674 building up the return value of a function, where you put state and
675 retsult variables together in an algebraic type (usually a tuple). In
676 this case, we should leave the state variable out as well, since we
677 don't want it to be included as an output port.
680 So, in both cases, we can simply leave out the state variable from the
681 resulting value. In the latter case, however, we should generate a state
682 proc instead, which assigns the state variable to the input state variable
686 \desc{State variables can appear as (part of) a function result.} When
687 generating \small{VHDL}, we can completely ignore any part of a function result
688 that has a state type. If the entire result is a state type, this will
689 mean the entity will not have an output port. Otherwise, the state
690 elements will be removed from the type of the output port.
693 Now, we know how to handle each use of a state variable separately. If we
694 look at the whole, we can conclude the following:
697 \item A state unpack operation should not generate any \small{VHDL}. The binder
698 to which the unpacked state is bound should still be declared, this signal
699 will become the register and will hold the current state.
700 \item A state pack operation should not generate any \small{VHDL}. The binder th
701 which the packed state is bound should not be declared. The binder that is
702 packed is the signal that will hold the new state.
703 \item Any values of a State type should not be translated to \small{VHDL}. In
704 particular, State elements should be removed from tuples (and other
705 datatypes) and arguments with a state type should not generate ports.
706 \item To make the state actually work, a simple \small{VHDL} proc should be
707 generated. This proc updates the state at every clockcycle, by assigning
708 the new state to the current state. This will be recognized by synthesis
709 tools as a register specification.
713 When applying these rules to the example program (in normal form), we will
714 get the following result. All the parts that don't generate any value are
715 crossed out, leaving some very boring assignments here and there.
719 avg i --spacked-- = res
721 s = --case spacked of (State s) -> s--
722 --accums = case s of (accums, \_) -> accums--
723 count = case s of (--\_,-- count) -> count
724 accumres = accum i --accums--
725 --accums' = case accumres of (accums', \_) -> accums'--
726 sum = case accumres of (--\_,-- sum) -> sum
729 s' = (--accums',-- count')
730 --spacked' = State s'--
731 res = (--spacked',-- o)
734 When we would really leave out the crossed out parts, we get a slightly
735 weird program: There is a variable \type{s} which has no value, and there
736 is a variable \type{s'} that is never used. Together, these two will form
737 the state proc of the function. \type{s} contains the "current" state,
738 \type{s'} is assigned the "next" state. So, at the end of each clock
739 cycle, \type{s'} should be assigned to \type{s}.
741 Note that the definition of \type{s'} is not removed, even though one
742 might think it as having a state type. Since the state type has a single
743 argument constructor \type{State}, some type that should be the resulting
744 state should always be explicitly packed with the State constructor,
745 allowing us to remove the packed version, but still generate \small{VHDL} for the
746 unpacked version (of course with any substates removed).
748 As you can see, the definition of \type{s'} is still present, since it
749 does not have a state type (The State constructor. The \type{accums'} substate has been removed,
750 leaving us just with the state of \type{avg} itself.
751 \subsection{Initial state}
752 How to specify the initial state? Cannot be done inside a hardware
753 function, since the initial state is its own state argument for the first
754 call (unless you add an explicit, synchronous reset port).
756 External init state is natural for simulation.
758 External init state works for hardware generation as well.
760 Implementation issues: state splitting, linking input to output state,
761 checking usage constraints on state variables.
763 TODO: Implementation issues
764 TODO: \subsection[sec:prototype:separate]{Separate compilation}
765 TODO: Simplified core?