Idris - First Steps

Writing my first dependently typed function in Idris.

Posted by Iain Hull on October 20, 2015

I hate debugging code, so I try really hard to produce correct code in the first place. As a result one of my main interests is automatic program verification. Initially for me this meant unit testing, then design by contract, later exploring how the type system can improve correctness. I was luck enough to attend an introduction to Idris with Edwin Brady at Functional Kats Conf in September. Idris is a dependently typed language, this means that types are first class citizens, they can interact with and depend on values. This enables you to to improve (and even prove) correctness on a whole new level. For example a Vect in Idris is a generic list whose length is part of its type, therefore a Vect of three chars has a different type to a list of four chars. This means if a function parameter requires a Vect of a certain size the compiler guarantees the function is only called with a Vect of that size. No more checking the size at runtime and no more illegal argument exceptions. With one parameter type the compiler prevents a whole class of bugs.

I was really impressed by Idris, and have spent the past few weeks trying to learn it. I started with the book, Type-Driven Development with Idris available on Manning's early access program. Next I needed an exercise to practice, so chose the Bank OCR Kata. This involves parsing lines of text and recognising numbers. The requirements state: "Each entry is 4 lines long, and each line has 27 characters", this is a perfect application of dependent types. Therefore the first function I wrote was maybeVect, this takes a size and a list and returns a Maybe containing a Vect of the specified size. If the list is the correct size it returns a Just and if the size is wrong it returns Nothing.

Here is the code

maybeVect : (n: Nat) -> List a -> Maybe (Vect n a)
maybeVect Z [] = Just []
maybeVect n [] = Nothing
maybeVect Z xs = Nothing
maybeVect n (x :: xs) = let S(k) = n in
                             map (\ xs' => x :: xs') (maybeVect xs k)

The function has four cases: * the required size is zero and list is empty return an empty Vect wrapped in a Just. * the required size is not zero and the list is empty, the size is incorrect so return Nothing. * the required size is zero and the list is not empty, again the size is incorrect so return Nothing. * finally the size is not zero and the list is not empty, here we split the list into its head and tail and use recursion to process the tail, then if the tail is valid we add the head back on.

The key in this final case is letting the compiler track the size of the list in the recursive call. This is done by assigning the number previous to n into the value k, then using this in the recursive call to maybeVect. Now when the head is added to the Vect the compiler knows the size of the returned Vect will be n. The map function adds the head to the tail, inside the Maybe if it's a Just or does nothing if its Nothing.

Lets test it out in the repl:

maybeVect> maybeVect 0 (the (List Char) [])
Just [] : Maybe (Vect 0 Char)

maybeVect> maybeVect 0 ['a']
Nothing : Maybe (Vect 0 Char)

maybeVect> maybeVect 1 (the (List Char) [])
Nothing : Maybe (Vect 1 Char)

maybeVect> maybeVect 1 ['a']
Just ['a'] : Maybe (Vect 1 Char)

maybeVect> maybeVect 2 ['a', 'b']
Just ['a', 'b'] : Maybe (Vect 2 Char)

maybeVect> maybeVect 3 ['a', 'b']
Nothing : Maybe (Vect 3 Char)

This is my first Idris function and of course it wasn't plain sailing. Type-driven development, means specifying your types first and letting the compiler guide your implementation. Or as I found, specify your types and let compile error thwart my implementation, so below is how I reached the function above.

The first three cases were easy however I struggled with the last one. I knew I could use the map function, but struggled with compile errors so I wrote my own function to prepend an item on to the head of a Vect inside a Maybe.

maybePrepend : a -> Maybe (Vect n a) -> Maybe (Vect (S n) a)
maybePrepend x Nothing = Nothing
maybePrepend x (Just xs) = Just (x :: xs)

This function although not required simplified my remaining type errors. My first attempt was to use S(n) in the pattern matching the size

maybeVect S(k) (x :: xs) = maybePrepend x (maybeVect xs k)

I am not sure why this didn't work (I still have lots to learn), but here is the error.

When checking left hand side of maybeVect2:
Type mismatch between
        Maybe (Vect n a) (Type of maybeVect n _)
and
        argTy -> retTy (Is maybeVect n
                                    _ applied to too many arguments?)

Specifically:
        Type mismatch between
                Maybe
        and
                \uv => argTy -> uv

Then I read some Idris code and part of the implementation of Vect and came up with the following

maybeVect { n = S(k) } (x :: xs) =  maybePrepend x (maybeVect xs k)

Which results in this error

MaybeVect.idr:15:12:When checking left hand side of maybeVect:
n is not an implicit argument of maybeVect.maybeVect
Holes: maybeVect.maybeVect

Ok so that was a wild guess and once I saw the error I realised I was going in the wrong direction. I looked for other examples of S(n) in the Vect source code and found the let syntax. This resulted in the following line.

maybeVect n (x :: xs) = let S(k) = n in
                            maybePrepend x (maybeVect k xs)

This worked and from here applying map was easy. I am still not sure why my first attempt did not work, but I learned the importance of reducing the moving parts when debugging type-errors in dependently typed languages. Once I defined maybePrepend the compiler did guide me in the right direction, I just have to get better at reading that guide.

If you find any of this interesting I encourage you to try Idris yourself. I will continue with my Bank OCR example and let you know how I get on.

The code is available in this gist.