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Towards Tactic Metaprogramming in Haskell

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Isn’t it odd that we treat offer code as textual reveal? That is, now we delight in this extremely smartly-structured and strongly-typed object — the summary syntax tree — that exists conceptually in our minds, and finally inner of our compiler, nonetheless for some cause we fake it’s lovely a pile of bytes and edit it byte-by-byte quite than semantically?

Whereas you quit and diagram it, that’s love the stupidest thought ever. We because the authors don’t speak of our code as bytes, nor does our interpreter or compiler. But as a change we shield the semantic belief inner of our heads, serialize it into bytes, and then secure the compiler to parse and rediscover the solutions inner our head. What a wreck of effort.

Instead, you are going to be in a situation to employ the amazing TOTBWF and my original Ways Plugin for the Haskell Language Server, that might well well additionally automatically and intelligently accept as true with holes in your Haskell purposes.

This weblog put up describes what a ways engine is and why you in deciding to delight in one, and is a true introduction to how in the hell we can automatically write your code for you.

Ways

Take into consideration you’re pair programming with a junior engineer. Within the navigator seat, you’ll be guiding your companion through the implementation, guiding them through the excessive-level strokes and permitting them to finally end the coding part. In listing to put in force foldr :: (a -> b -> b) -> b -> [a] -> b, as an instance, the steerage you give your companion might well well be:

  1. Bind the goal arguments
  2. Case split on the [a] parameter
  3. If it’s [], end the glaring ingredient
  4. In every other case call your goal and recurse.

These instructions aren’t a true program by any draw, nonetheless you doubtlessly can call them a “program sketch.” The sharp part of programming (hooked in to what to end) is captured here, nonetheless finally doing it is left as an exercise to the reader.

A ways engine transforms a program sketch love the above into an true program. Ways free us from the tyranny of textual reveal bettering and pedantic important aspects, allowing us to work at a greater semantic level of programming.

Ways correspond to semantic operations over our program. Mighty love how the damaged-down instructions in textual reveal editors (delete to complete of line, insert parentheses, and many others) is also peaceful to refine the textual representation of one program into the textual representation of one other, we can assemble diminutive ways in listing to invent better solutions.

As an illustration, shield into consideration how we can accept as true with in the following hole:

info Id a = Id a

instance Functor Id where
  fmap ::  (a -> b) -> Id a -> Id b
  fmap = _

Rather than writing this goal , we can as a change invent it, one thought at a time. Step one is obviously to bind goal arguments (the intros tactic), which outcomes in the sophisticated expression:

fmap ::  (a -> b) -> Id a -> Id b
fmap = fab ida -> _

We’re left with a original hole, nonetheless this one is “smaller” than the ragged one; we’ve sophisticated the outdated hole, filling in about a of its building. As a end result, the fashion of our original hole is Id b, and now we delight in each and every fab :: a -> b and ida :: Id a in scope. We can simplify the outlet additional by now sample matching on ida (the destruct ida tactic):

fmap ::  (a -> b) -> Id a -> Id b
fmap = fab ida -> case ida of
  Id a -> _

The resulting hole easy has type Id b, nonetheless we’ve now launched a :: a in scope. Our next step is to invent an Id price, which we can end by producing its info constructor (the split tactic):

fmap ::  (a -> b) -> Id a -> Id b
fmap = fab ida -> case ida of
  Id a -> Id _

Again we’ve diminished in size the verbalize — now our hole has type b. At this point we can call the fab goal to operate a b (through the notice fab tactic):

fmap ::  (a -> b) -> Id a -> Id b
fmap = fab ida -> case ida of
  Id a -> Id (fab _)

All that’s left is a hole with type a. Happily, now we delight in a :: a in scope, so we can lovely plop that in to the outlet through the assumption tactic:

fmap ::  (a -> b) -> Id a -> Id b
fmap = fab ida -> case ida of
  Id a -> Id (fab a)

And beautiful love that, we’ve produced an implementation of our desired goal! By thinking by skill of the semantic operations we’d opt to operate at each and every hole (as a change of manipulate the bytes of textual reveal), we’ve changed the level of abstraction at which we take under consideration bettering. The implications of that is per chance now now not accurate now glaring, so let’s explore them collectively.

Let’s list the method steps we took to derive fmap:

intros
destruct ida
split
notice fab
assumption

As a lot as alpha renaming, this composition of how is enough to derive fmap for any sum or product type that doesn’t end anything else “sharp” with its type variable. By working the identical steps, we can put in force fmap for any of the following kinds:

(a, b)
Either a b
Possibly a
Const a b

Let’s persuade ourselves of this by lickety-split working through the derivation for Possibly a. We start up again with fmap and its type:

fmap ::  (a -> b) -> Possibly a -> Possibly b
fmap = _

After working intros:

fmap ::  (a -> b) -> Possibly a -> Possibly b
fmap = fab ma -> _

and then destruct ma

fmap ::  (a -> b) -> Possibly a -> Possibly b
fmap = fab ma -> case ma of
  Nothing -> _
  Best a  -> _

Making employ of split here’s a microscopic bit tricky; technically it’s miles going to force us to examine up on each and every Nothing and Best _ at each and every hole in a odd variety of quantum superposition. Let’s ignore this ingredient for true now, and come support to it accurate now after finishing the derivation. Assuming we acquire the true info cons, after split our program appears to be like love this:

fmap ::  (a -> b) -> Possibly a -> Possibly b
fmap = fab ma -> case ma of
  Nothing -> Nothing
  Best a  -> Best _

Now we bustle notice fab. Because Nothing doesn’t shield any arguments, it didn’t operate any holes, so we desire peek most efficient on the Best case:

fmap ::  (a -> b) -> Possibly a -> Possibly b
fmap = fab ma -> case ma of
  Nothing -> Nothing
  Best a  -> Best (fab _)

and at closing we bustle assumption to accept as true with in the outlet:

fmap ::  (a -> b) -> Possibly a -> Possibly b
fmap = fab ma -> case ma of
  Nothing -> Nothing
  Best a  -> Best (fab a)

Take a look at at that! Even supposing it would require vastly various bettering instructions to write down the syntax of these two functor conditions, they’re each and every descried by the identical composition of how. This is what I imply by “semantic bettering,” we’re challenging the algorithm for producing functor conditions out of our heads and reifying it into something the pc understands. In essence, by writing fmap once, we can declare the pc write it for us in the long bustle.

I mentioned earlier that split provides us some complications here. Reading closely, you’ll query that there might be nothing in our ways in which teach now we should always split the identical info constructor that we lovely destructed. If truth be told there are four various, genuine purposes that might well well also be produced by the above space of how:

fmap = fab ma -> case ma of
  Nothing -> Nothing
  Best a  -> Nothing

fmap = fab ma -> case ma of
  Nothing -> Nothing
  Best a  -> Best (fab a)

fmap = fab ma -> case ma of
  Nothing -> Best (fab a)
  Best a  -> Nothing

fmap = fab ma -> case ma of
  Nothing -> Best (fab a)
  Best a  -> Best (fab a)

Deciding on the “most gripping” implementation of these probabilities is basically a matter of heuristics, which I diagram to listing in a later put up. For now, let’s lovely acquire our ways engine is desirable passable to come support up with the one you had in thoughts.

Clearly, the true predicament here is that nothing forces our destruct and split ways to employ the identical info constructor. We can effect away with this ambiguity by noticing that in fmap, we’re now now not finally making an strive to destruct and then split, nonetheless as a change we’re making an strive to put in force a homomorphism (a building-holding goal.) In listing to withhold building, we’d greater draw an info constructor to itself. In listing a change, let’s employ the homo tactic as a change of destruct and split. Our original ways metaprogram for writing functor conditions is thus:

intros
homo ida
notice fab
assumption

This original model now can now now not generate any of the pathological fmap implementations for Possibly, as they are now not building holding. We’re left most efficient with the true implementation. Let’s end yet every other derivation, this time for Either c a. After intros and homo eca, we’re left with:

fmap ::  (a -> b) -> Either c a -> Either c b
fmap = fab ma -> case eca of
  Left  c -> Left _
  Lovely a -> Lovely _

For the principle time, we’re now left with two holes. The default habits is for a tactic to notice to all holes (although there are combinators for “zipping” holes), meaning that the notice fab tactic will possible be bustle on each and every holes. For the Left case, our hole has type c, nonetheless fab _ has type b, so this tactic fails to notice here. Tactic failure is per-hole, so we can easy notice it to the assorted hole, leading to:

fmap ::  (a -> b) -> Either c a -> Either c b
fmap = fab ma -> case eca of
  Left  c -> Left _
  Lovely a -> Lovely (fab _)

And finally, assumption fills the outlet and not using a matter would typecheck. Within the principle hole that’s c, and in the 2d it’s a as sooner than.

fmap ::  (a -> b) -> Either c a -> Either c b
fmap = fab ma -> case eca of
  Left  c -> Left c
  Lovely a -> Lovely (fab a)

Unparalleled! Three various functor implementations, with various numbers of information constructors, type variables, and cardinalities. By programming on the level of how quite than bytes, we can ignore the superficial differences between these implementations, focusing as a change on the truth that they’re all derived the identical skill.

Hopefully this put up has given you some perception into what ways are and why they’re treasured. Within the next put up we’ll peek at how these items is utilized on the support of the scenes, and the difficulties we’ve had integrating it into the language server. Take care of tuned!



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