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The point is that a lot of tests which are necessary in Ruby/Python are unnecessary in Scala. For example:

    assert(len(f(x)) > 0)

In Scala, you just have `def f(x: X): NonEmptyList[Y]`.

Or a more complicated example that I've run into recently. You have a set of predicates, some of which can be evaluated in the browser, some not - e.g. IsFirefox & EverVisitedUrl(url). You then (server side) evaluate EverVisitedUrl(url), get a partial result IsFirefox & True = IsFirefox, and then push whatever is left to javascript `isBrowserFirefox()`.

In python/ruby/etc, you'd need extensive tests to make sure this translation is properly handled. In Scala, if your function doesn't have type `FreeBool[ArbitraryPredicate] => FreeBool[JavascriptEvaluatablePredicate]`, your code won't compile.

I think a lot of static-language people assume that dynamic-language people write a lot of type-assertion statements in their code and then write a lot of tests to ensure those assertions hold.

Turns out... we don't really do that so much.

> Turns out... we don't really do that so much.

With a suitably enlarged definition of (static) type, a lot of tests become type-assertions.

Eg red black trees have interesting balancing requirements: no t

See eg Red Black Trees are another interesting example. A red black tree is a binary search tree, and all its nodes are coloured either red or black. You can not have two red nodes in a row on any path, but all paths from root to any leave have to have the same number of black nodes.

Testing that these two properties hold after an arbitrary number of inserts sounds like a good candidate for a unit tests, and doesn't sound like a type assertion, does it?

See https://www.reddit.com/r/haskell/comments/ti5il/redblack_tre... for how to encode those properties into the types.

In any case, Haskell has great support for unit tests, too. (Because in general you can't and at any rate don't want to encode everything you care about in the type system.)

Have a look at QuickCheck. There are ports for various other languages, too. QuickCheck is a generalization of the table-driven approach to unit-testing: it's about generating those tables automatically, and automatically simplifying any inputs found that lead to buggy behaviour.

I'm as much a dynamic language person as a static language person - I write as much python as I do Scala. The point is that the guarantees you can get go well beyond simply assert(type(x) == str). See the examples in my previous post - you can guarantee at the type level that a list isn't empty, or that a boolean formula only contains predicates that can be rendered to javascript.

These are things I'd have lots of unit tests for.

Here is another example of using static types to fix a problem I constantly run into in Python (adding vectors from the wrong vector spaces together): https://www.chrisstucchio.com/blog/2014/type_safe_vector_add...

Unit tests almost never prove correctness or completeness. For a non-trivial program, the best you can hope to demonstrate is correctness for the arguments tested in the state determined by the test environment. If you want to prove correctness, you need proofs.

By and large, unit tests exist to quickly find bugs.

As I like to put it: unit tests don't affirm the correctness of code with respect to a specification, they merely affirm that certain implications of the specification hold with the code under test. In that sense, the general tendency to assume correctness in the face of passing test suite is basically an instance affirming the consequent on a huge scale.

Agreed. It's more of a gradual transition towards fewer tests. The more constraints about the system you push into the type system, the less you need to test, hence the dream of dependent types etc etc. You still want to have sanity checks in place in case your constraints make no sense, even if they're being correctly imposed.

Unless you're programming in a dependently typed language and have proven your code correct :P

If you have proven your code correct, it doesn't matter what language it is in or whether it has a type system at all. Proven correct in the absence of a type system is proven correct.

Humans tend to make more mistakes. Convincing, say, Coq's typechecker of your proof is stronger evidence of correctness than convincing yourself.

It is possible to prove program correctness -- by a computer -- that doesn't involve the type system.

Depends on your definition of type system.

Anyway, what methods did you have in mind?

Any of the model checking methods (abstract interpretation etc.). The real life example I like to give is the detection (and correction) a few months ago of the bug in TimSort, possibly the most widely used sorting algorithm in the world (since its inclusion in Java in 2011). It was found using symbolic execution, and I'd like to see a programming language that is able to both express the algorithm in its efficient form (it is only used because of its speed) and prove its correctness using the type system in a way that is any easier than how it was actually verified.

If you stretch the definition of type a bit, any expressible property of your program (such as "this function sorts list") is a type and anything that allows you to automatically prove those properties is a type checker.

OK, actually a lot!

Upon revisiting the article, I am downvoting your comment. Your objection is addressed in the very passage you cite, you merely truncated it misleadingly (and incorrectly - changes made to a quote should be placed in square brackets, and a move from an ellipsis to a period is a change). The truncated portion reads:

"It's interesting to note that the whole TDD movement comes from people who are working in dynamically typed languages... I'm not saying that unit testing is a bad idea with static types; only that it's entirely appropriate to scale it back a little.)"

Your comment is confusing.

What is the difference between "code correctness" and "to show that the result of a function is correct for all input parameters"? In common parlance these are the same thing.

Also, what does it even mean for a piece of code to be sound or complete? Sound with respect to what? Complete with respect to or relative to what?

I think the words that you want are "correct wrt a specification" instead of sound and "total" instead of complete?

Testing cannot prove correctness, period. The proof is a set of unit tests that cover every single input and also a proof that the set of inputs you tested is the entire domain. Basically no in-the-wild unit testing does even the former.

What you mean to say, I think, is, "testing is indispensable when your specification language isn't sufficient for specifying all correctness properties for your code."

Which is about right, but the way that you worded this post was extraordinarily confusing.

The key is "the same kind of exhaustive unit testing". Unit tests can serve many purposes, in terms of raising your confidence that code is correct. In a language with minimal static type checking, a big part of what a good unit test suite will be doing is checking type invariants. In a language where those type invariants are checked for you, you don't need those particular unit tests.