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{Choice of 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{Prototype design}
54 As stated above, we will use the Glasgow Haskell Compiler (\small{GHC}) to
55 implement our prototype compiler. To understand the design of the
56 compiler, we will first dive into the \small{GHC} compiler a bit. It's
57 compilation consists of the following steps (slightly simplified):
59 \startuseMPgraphic{ghc-pipeline}
61 save inp, front, desugar, simpl, back, out;
63 newBox.front(btex Parser etex);
64 newBox.desugar(btex Desugarer etex);
65 newBox.simpl(btex Simplifier etex);
66 newBox.back(btex Backend etex);
69 % Space the boxes evenly
70 inp.c - front.c = front.c - desugar.c = desugar.c - simpl.c
71 = simpl.c - back.c = back.c - out.c = (0, 1.5cm);
74 % Draw lines between the boxes. We make these lines "deferred" and give
75 % them a name, so we can use ObjLabel to draw a label beside them.
76 ncline.inp(inp)(front) "name(haskell)";
77 ncline.front(front)(desugar) "name(ast)";
78 ncline.desugar(desugar)(simpl) "name(core)";
79 ncline.simpl(simpl)(back) "name(simplcore)";
80 ncline.back(back)(out) "name(native)";
81 ObjLabel.inp(btex Haskell source etex) "labpathname(haskell)", "labdir(rt)";
82 ObjLabel.front(btex Haskell AST etex) "labpathname(ast)", "labdir(rt)";
83 ObjLabel.desugar(btex Core etex) "labpathname(core)", "labdir(rt)";
84 ObjLabel.simpl(btex Simplified core etex) "labpathname(simplcore)", "labdir(rt)";
85 ObjLabel.back(btex Native code etex) "labpathname(native)", "labdir(rt)";
87 % Draw the objects (and deferred labels)
88 drawObj (inp, front, desugar, simpl, back, out);
90 \placefigure[right]{GHC compiler pipeline}{\useMPgraphic{ghc-pipeline}}
93 This step takes the Haskell source files and parses them into an
94 abstract syntax tree (\small{AST}). This \small{AST} can express the
95 complete Haskell language and is thus a very complex one (in contrast
96 with the Core \small{AST}, later on). All identifiers in this
97 \small{AST} are resolved by the renamer and all types are checked by the
100 \startdesc{Desugaring}
101 This steps takes the full \small{AST} and translates it to the
102 \emph{Core} language. Core is a very small functional language with lazy
103 semantics, that can still express everything Haskell can express. Its
104 simpleness makes Core very suitable for further simplification and
105 translation. Core is the language we will be working on as well.
107 \startdesc{Simplification}
108 Through a number of simplification steps (such as inlining, common
109 subexpression elimination, etc.) the Core program is simplified to make
110 it faster or easier to process further.
113 This step takes the simplified Core program and generates an actual
114 runnable program for it. This is a big and complicated step we will not
115 discuss it any further, since it is not required for our prototype.
118 In this process, there a number of places where we can start our work.
119 Assuming that we don't want to deal with (or modify) parsing, typechecking
120 and other frontend business and that native code isn't really a useful
121 format anymore, we are left with the choice between the full Haskell
122 \small{AST}, or the smaller (simplified) core representation.
124 The advantage of taking the full \small{AST} is that the exact structure
125 of the source program is preserved. We can see exactly what the hardware
126 descriiption looks like and which syntax constructs were used. However,
127 the full \small{AST} is a very complicated datastructure. If we are to
128 handle everything it offers, we will quickly get a big compiler.
130 Using the core representation gives us a much more compact datastructure
131 (a core expression only uses 9 constructors). Note that this does not mean
132 that the core representation itself is smaller, on the contrary. Since the
133 core language has less constructs, a lot of things will take a larger
134 expression to express.
136 However, the fact that the core language is so much smaller, means it is a
137 lot easier to analyze and translate it into something else. For the same
138 reason, \small{GHC} runs its simplifications and optimizations on the core
139 representation as well.
141 However, we will use the normal core representation, not the simplified
142 core. Reasons for this are detailed below.
144 The final prototype roughly consists of three steps:
146 \startuseMPgraphic{ghc-pipeline}
148 save inp, front, norm, vhdl, out;
149 newEmptyBox.inp(0,0);
150 newBox.front(btex \small{GHC} frontend + desugarer etex);
151 newBox.norm(btex Normalization etex);
152 newBox.vhdl(btex \small{VHDL} generation etex);
153 newEmptyBox.out(0,0);
155 % Space the boxes evenly
156 inp.c - front.c = front.c - norm.c = norm.c - vhdl.c
157 = vhdl.c - out.c = (0, 1.5cm);
160 % Draw lines between the boxes. We make these lines "deferred" and give
161 % them a name, so we can use ObjLabel to draw a label beside them.
162 ncline.inp(inp)(front) "name(haskell)";
163 ncline.front(front)(norm) "name(core)";
164 ncline.norm(norm)(vhdl) "name(normal)";
165 ncline.vhdl(vhdl)(out) "name(vhdl)";
166 ObjLabel.inp(btex Haskell source etex) "labpathname(haskell)", "labdir(rt)";
167 ObjLabel.front(btex Core etex) "labpathname(core)", "labdir(rt)";
168 ObjLabel.norm(btex Normalized core etex) "labpathname(normal)", "labdir(rt)";
169 ObjLabel.vhdl(btex \small{VHDL} description etex) "labpathname(vhdl)", "labdir(rt)";
171 % Draw the objects (and deferred labels)
172 drawObj (inp, front, norm, vhdl, out);
174 \placefigure[right]{GHC compiler pipeline}{\useMPgraphic{ghc-pipeline}}
177 This is exactly the frontend and desugarer from the \small{GHC}
178 pipeline, that translates Haskell sources to a core representation.
180 \startdesc{Normalization}
181 This is a step that transforms the core representation into a normal
182 form. This normal form is still expressed in the core language, but has
183 to adhere to an extra set of constraints. This normal form is less
184 expressive than the full core language (e.g., it can have limited higher
185 order expressions, has a specific structure, etc.), but is also very
186 close to directly describing hardware.
188 \startdesc{\small{VHDL} generation}
189 The last step takes the normal formed core representation and generates
190 \small{VHDL} for it. Since the normal form has a specific, hardware-like
191 structure, this final step is very straightforward.
194 The most interesting step in this process is the normalization step. That
195 is where more complicated functional constructs, which have no direct
196 hardware interpretation, are removed and translated into hardware
197 constructs. This step is described in a lot of detail at
198 \in{chapter}[chap:normalization].
200 \section{The Core language}
201 Most of the prototype deals with handling the program in the Core
202 language. In this section we will show what this language looks like and
205 The Core language is a functional language that describes
206 \emph{expressions}. Every identifier used in Core is called a
207 \emph{binder}, since it is bound to a value somewhere. On the highest
208 level, a Core program is a collection of functions, each of which bind a
209 binder (the function name) to an expression (the function value, which has
212 The Core language itself does not prescribe any program structure, only
213 expression structure. In the \small{GHC} compiler, the Haskell module
214 structure is used for the resulting Core code as well. Since this is not
215 so relevant for understanding the Core language or the Normalization
216 process, we'll only look at the Core expression language here.
218 Each Core expression consists of one of these possible expressions.
220 \startdesc{Variable reference}
224 This is a simple reference to a binder. It's written down as the
225 name of the binder that is being referred to, which should of course be
226 bound in a containing scope (including top level scope, so a reference
227 to a top level function is also a variable reference). Additionally,
228 constructors from algebraic datatypes also become variable references.
230 The value of this expression is the value bound to the given binder.
232 Each binder also carries around its type, but this is usually not shown
233 in the Core expressions. Occasionally, the type of an entire expression
234 or function is shown for clarity, but this is only informational. In
235 practice, the type of an expression is easily determined from the
236 structure of the expression and the types of the binders and occasional
237 cast expressions. This minimize the amount of bookkeeping needed to keep
238 the typing consistent.
244 This is a simple literal. Only primitive types are supported, like
245 chars, strings, ints and doubles. The types of these literals are the
246 \quote{primitive} versions, like \lam{Char\#} and \lam{Word\#}, not the
247 normal Haskell versions (but there are builtin conversion functions).
249 \startdesc{Application}
253 This is simple function application. Each application consists of two
254 parts: The function part and the argument part. Applications are used
255 for normal function \quote{calls}, but also for applying type
256 abstractions and data constructors.
258 The value of an application is the value of the function part, with the
259 first argument binder bound to the argument part.
261 \startdesc{Lambda abstraction}
265 This is the basic lambda abstraction, as it occurs in labmda calculus.
266 It consists of a binder part and a body part. A lambda abstraction
267 creates a function, that can be applied to an argument.
269 Note that the body of a lambda abstraction extends all the way to the
270 end of the expression, or the closing bracket surrounding the lambda. In
271 other words, the lambda abstraction \quote{operator} has the lowest
274 The value of an application is the value of the body part, with the
275 binder bound to the value the entire lambda abstraction is applied to.
277 \startdesc{Non-recursive let expression}
279 let bndr = value in body
281 A let expression allows you to bind a binder to some value, while
282 evaluating to some other value (where that binder is in scope). This
283 allows for sharing of subexpressions (you can use a binder twice) and
284 explicit \quote{naming} of arbitrary expressions. Note that the binder
285 is not in scope in the value bound to it, so it's not possible to make
286 recursive definitions with the normal form of the let expression (see
287 the recursive form below).
289 Even though this let expression is an extension on the basic lambda
290 calculus, it is easily translated to a lambda abstraction. The let
291 expression above would then become:
297 This notion might be useful for verifying certain properties on
298 transformations, since a lot of verification work has been done on
299 lambda calculus already.
301 The value of a let expression is the value of the body part, with the
302 binder bound to the value.
304 \startdesc{Recursive let expression}
314 This is the recursive version of the let expression. In \small{GHC}'s
315 Core implementation, non-recursive and recursive lets are not so
316 distinct as we present them here, but this provides a clearer overview.
318 The main difference with the normal let expression is that each of the
319 binders is in scope in each of the values, in addition to the body. This
320 allows for self-recursive definitions or mutually recursive definitions.
322 It should also be possible to express a recursive let using normal
323 lambda calculus, if we use the \emph{least fixed-point operator},
326 \startdesc{Case expression}
329 DEFAULT -> defaultbody
330 C0 bndr0,0 ... bndr0,m -> body0
332 Cn bndrn,0 ... bndrn,m -> bodyn
337 A case expression is the only way in Core to choose between values. A case
338 expression evaluates its scrutinee, which should have an algebraic
339 datatype, into weak head normal form (\small{WHNF}) and (optionally) binds
340 it to \lam{bndr}. It then chooses a body depending on the constructor of
341 its scrutinee. If none of the constructors match, the \lam{DEFAULT}
342 alternative is chosen.
344 Since we can only match the top level constructor, there can be no overlap
345 in the alternatives and thus order of alternatives is not relevant (though
346 the \lam{DEFAULT} alternative must appear first for implementation
349 Any arguments to the constructor in the scrutinee are bound to each of the
350 binders after the constructor and are in scope only in the corresponding
353 To support strictness, the scrutinee is always evaluated into WHNF, even
354 when there is only a \lam{DEFAULT} alternative. This allows a strict
355 function argument to be written like:
358 function (case argument of arg
362 This seems to be the only use for the extra binder to which the scrutinee
363 is bound. When not using strictness annotations (which is rather pointless
364 in hardware descriptions), \small{GHC} seems to never generate any code
365 making use of this binder. The current prototype does not handle it
366 either, which probably means that code using it would break.
368 Note that these case statements are less powerful than the full Haskell
369 case statements. In particular, they do not support complex patterns like
370 in Haskell. Only the constructor of an expression can be matched, complex
371 patterns are implemented using multiple nested case expressions.
373 Case statements are also used for unpacking of algebraic datatypes, even
374 when there is only a single constructor. For examples, to add the elements
375 of a tuple, the following Core is generated:
378 sum = λtuple.case tuple of
382 Here, there is only a single alternative (but no \lam{DEFAULT}
383 alternative, since the single alternative is already exhaustive). When
384 it's body is evaluated, the arguments to the tuple constructor \lam{(,)}
385 (\eg, the elements of the tuple) are bound to \lam{a} and \lam{b}.
387 \startdesc{Cast expression}
391 A cast expression allows you to change the type of an expression to an
392 equivalent type. Note that this is not meant to do any actual work, like
393 conversion of data from one format to another, or force a complete type
394 change. Instead, it is meant to change between different representations
395 of the same type, \eg switch between types that are provably equal (but
398 In our hardware descriptions, we typically see casts to change between a
399 Haskell newtype and its contained type, since those are effectively
400 different representations of the same type.
402 More complex are types that are proven to be equal by the typechecker,
403 but look different at first glance. To ensure that, once the typechecker
404 has proven equality, this information sticks around, explicit casts are
405 added. In our notation we only write the target type, but in reality a
406 cast expressions carries around a \emph{coercion}, which can be seen as a
407 proof of equality. TODO: Example
409 The value of a cast is the value of its body, unchanged. The type of this
410 value is equal to the target type, not the type of its body.
412 Note that this syntax is also used sometimes to indicate that a particular
413 expression has a particular type, even when no cast expression is
414 involved. This is then purely informational, since the only elements that
415 are explicitely typed in the Core language are the binder references and
416 cast expressions, the types of all other elements are determined at
421 The Core language in \small{GHC} allows adding \emph{notes}, which serve
422 as hints to the inliner or add custom (string) annotations to a core
423 expression. These shouldn't be generated normally, so these are not
424 handled in any way in the prototype.
430 It is possibly to use a Core type as a Core expression. This is done to
431 allow for type abstractions and applications to be handled as normal
432 lambda abstractions and applications above. This means that a type
433 expression in Core can only ever occur in the argument position of an
434 application, and only if the type of the function that is applied to
435 expects a type as the first argument. This happens for all polymorphic
436 functions, for example, the \lam{fst} function:
439 fst :: \forall a. \forall b. (a, b) -> a
440 fst = λtup.case tup of (,) a b -> a
442 fstint :: (Int, Int) -> Int
443 fstint = λa.λb.fst @Int @Int a b
446 The type of \lam{fst} has two universally quantified type variables. When
447 \lam{fst} is applied in \lam{fstint}, it is first applied to two types.
448 (which are substitued for \lam{a} and \lam{b} in the type of \lam{fst}, so
449 the type of \lam{fst} actual type of arguments and result can be found:
450 \lam{fst @Int @Int :: (Int, Int) -> Int}).
453 TODO: Core type system
455 \section[sec:prototype:statetype]{State annotations in Haskell}
456 Ideal: Type synonyms, since there is no additional code overhead for
457 packing and unpacking. Downside: there is no explicit conversion in Core
458 either, so type synonyms tend to get lost in expressions (they can be
459 preserved in binders, but this makes implementation harder, since that
460 statefulness of a value must be manually tracked).
462 Less ideal: Newtype. Requires explicit packing and unpacking of function
463 arguments. If you don't unpack substates, there is no overhead for
464 (un)packing substates. This will result in many nested State constructors
465 in a nested state type. \eg:
468 State (State Bit, State (State Word, Bit), Word)
471 Alternative: Provide different newtypes for input and output state. This
472 makes the code even more explicit, and typechecking can find even more
473 errors. However, this requires defining two type synomyms for each
474 stateful function instead of just one. \eg:
476 type AccumStateIn = StateIn Bit
477 type AccumStateOut = StateOut Bit
479 This also increases the possibility of having different input and output
480 states. Checking for identical input and output state types is also
481 harder, since each element in the state must be unpacked and compared
484 Alternative: Provide a type for the entire result type of a stateful
485 function, not just the state part. \eg:
488 newtype Result state result = Result (state, result)
491 This makes it easy to say "Any stateful function must return a
492 \type{Result} type, without having to sort out result from state. However,
493 this either requires a second type for input state (similar to
494 \type{StateIn} / \type{StateOut} above), or requires the compiler to
495 select the right argument for input state by looking at types (which works
496 for complex states, but when that state has the same type as an argument,
497 things get ambiguous) or by selecting a fixed (\eg, the last) argument,
498 which might be limiting.
500 \subsubsection{Example}
501 As an example of the used approach, a simple averaging circuit, that lets
502 the accumulation of the inputs be done by a subcomponent.
505 newtype State s = State s
507 type AccumState = State Bit
508 accum :: Word -> AccumState -> (AccumState, Word)
509 accum i (State s) = (State (s + i), s + i)
511 type AvgState = (AccumState, Word)
512 avg :: Word -> AvgState -> (AvgState, Word)
513 avg i (State s) = (State s', o)
516 -- Pass our input through the accumulator, which outputs a sum
517 (accums', sum) = accum i accums
518 -- Increment the count (which will be our new state)
520 -- Compute the average
522 s' = (accums', count')
525 And the normalized, core-like versions:
528 accum i spacked = res
530 s = case spacked of (State s) -> s
538 s = case spacked of (State s) -> s
539 accums = case s of (accums, \_) -> accums
540 count = case s of (\_, count) -> count
541 accumres = accum i accums
542 accums' = case accumres of (accums', \_) -> accums'
543 sum = case accumres of (\_, sum) -> sum
546 s' = (accums', count')
553 As noted above, any component of a function's state that is a substate,
554 \eg passed on as the state of another function, should have no influence
555 on the hardware generated for the calling function. Any state-specific
556 \small{VHDL} for this component can be generated entirely within the called
557 function. So,we can completely leave out substates from any function.
559 From this observation, we might think to remove the substates from a
560 function's states alltogether, and leave only the state components which
561 are actual states of the current function. While doing this would not
562 remove any information needed to generate \small{VHDL} from the function, it would
563 cause the function definition to become invalid (since we won't have any
564 substate to pass to the functions anymore). We could solve the syntactic
565 problems by passing \type{undefined} for state variables, but that would
566 still break the code on the semantic level (\ie, the function would no
567 longer be semantically equivalent to the original input).
569 To keep the function definition correct until the very end of the process,
570 we will not deal with (sub)states until we get to the \small{VHDL} generation.
571 Here, we are translating from Core to \small{VHDL}, and we can simply not generate
572 \small{VHDL} for substates, effectively removing the substate components
575 There are a few important points when ignore substates.
577 First, we have to have some definition of "substate". Since any state
578 argument or return value that represents state must be of the \type{State}
579 type, we can simply look at its type. However, we must be careful to
580 ignore only {\em substates}, and not a function's own state.
582 In the example above, this means we should remove \type{accums'} from
583 \type{s'}, but not throw away \type{s'} entirely. We should, however,
584 remove \type{s'} from the output port of the function, since the state
585 will be handled by a \small{VHDL} procedure within the function.
587 When looking at substates, these can appear in two places: As part of an
588 argument and as part of a return value. As noted above, these substates
589 can only be used in very specific ways.
591 \desc{State variables can appear as an argument.} When generating \small{VHDL}, we
592 completely ignore the argument and generate no input port for it.
594 \desc{State variables can be extracted from other state variables.} When
595 extracting a state variable from another state variable, this always means
596 we're extracting a substate, which we can ignore. So, we simply generate no
597 \small{VHDL} for any extraction operation that has a state variable as a result.
599 \desc{State variables can be passed to functions.} When passing a
600 state variable to a function, this always means we're passing a substate
601 to a subcomponent. The entire argument can simply be ingored in the
604 \desc{State variables can be returned from functions.} When returning a
605 state variable from a function (probably as a part of an algebraic
606 datatype), this always mean we're returning a substate from a
607 subcomponent. The entire state variable should be ignored in the resulting
608 port map. The type binder of the binder that the function call is bound
609 to should not include the state type either.
611 \startdesc{State variables can be inserted into other variables.} When inserting
612 a state variable into another variable (usually by constructing that new
613 variable using its constructor), we can identify two cases:
616 \item The state is inserted into another state variable. In this case,
617 the inserted state is a substate, and can be safely left out of the
618 constructed variable.
619 \item The state is inserted into a non-state variable. This happens when
620 building up the return value of a function, where you put state and
621 retsult variables together in an algebraic type (usually a tuple). In
622 this case, we should leave the state variable out as well, since we
623 don't want it to be included as an output port.
626 So, in both cases, we can simply leave out the state variable from the
627 resulting value. In the latter case, however, we should generate a state
628 proc instead, which assigns the state variable to the input state variable
632 \desc{State variables can appear as (part of) a function result.} When
633 generating \small{VHDL}, we can completely ignore any part of a function result
634 that has a state type. If the entire result is a state type, this will
635 mean the entity will not have an output port. Otherwise, the state
636 elements will be removed from the type of the output port.
639 Now, we know how to handle each use of a state variable separately. If we
640 look at the whole, we can conclude the following:
643 \item A state unpack operation should not generate any \small{VHDL}. The binder
644 to which the unpacked state is bound should still be declared, this signal
645 will become the register and will hold the current state.
646 \item A state pack operation should not generate any \small{VHDL}. The binder th
647 which the packed state is bound should not be declared. The binder that is
648 packed is the signal that will hold the new state.
649 \item Any values of a State type should not be translated to \small{VHDL}. In
650 particular, State elements should be removed from tuples (and other
651 datatypes) and arguments with a state type should not generate ports.
652 \item To make the state actually work, a simple \small{VHDL} proc should be
653 generated. This proc updates the state at every clockcycle, by assigning
654 the new state to the current state. This will be recognized by synthesis
655 tools as a register specification.
659 When applying these rules to the example program (in normal form), we will
660 get the following result. All the parts that don't generate any value are
661 crossed out, leaving some very boring assignments here and there.
665 avg i --spacked-- = res
667 s = --case spacked of (State s) -> s--
668 --accums = case s of (accums, \_) -> accums--
669 count = case s of (--\_,-- count) -> count
670 accumres = accum i --accums--
671 --accums' = case accumres of (accums', \_) -> accums'--
672 sum = case accumres of (--\_,-- sum) -> sum
675 s' = (--accums',-- count')
676 --spacked' = State s'--
677 res = (--spacked',-- o)
680 When we would really leave out the crossed out parts, we get a slightly
681 weird program: There is a variable \type{s} which has no value, and there
682 is a variable \type{s'} that is never used. Together, these two will form
683 the state proc of the function. \type{s} contains the "current" state,
684 \type{s'} is assigned the "next" state. So, at the end of each clock
685 cycle, \type{s'} should be assigned to \type{s}.
687 Note that the definition of \type{s'} is not removed, even though one
688 might think it as having a state type. Since the state type has a single
689 argument constructor \type{State}, some type that should be the resulting
690 state should always be explicitly packed with the State constructor,
691 allowing us to remove the packed version, but still generate \small{VHDL} for the
692 unpacked version (of course with any substates removed).
694 As you can see, the definition of \type{s'} is still present, since it
695 does not have a state type (The State constructor. The \type{accums'} substate has been removed,
696 leaving us just with the state of \type{avg} itself.
697 \subsection{Initial state}
698 How to specify the initial state? Cannot be done inside a hardware
699 function, since the initial state is its own state argument for the first
700 call (unless you add an explicit, synchronous reset port).
702 External init state is natural for simulation.
704 External init state works for hardware generation as well.
706 Implementation issues: state splitting, linking input to output state,
707 checking usage constraints on state variables.
709 Implementation issues
710 \subsection[sec:prototype:separate]{Separate compilation}
713 Haskell language coverage / constraints
716 Custom types (Sum types, product types)
717 Function types / higher order expressions