# ~/Blog

## Brandon Rozek

PhD Student @ RPI studying Automated Reasoning in AI and Linux Enthusiast.

# Writing Unit Tests in Lean 4

Published on

When writing Lean code, it’s easier to iterate with unit tests than to prove properties about the function off the bat.

I mean if the unit test doesn’t even pass, why bother with the proof?

Luckily, Lean 4 let’s us do unit tests with a cool command called `#guard`

``````#guard 1 = 1
``````

This checks whether the following expression evaluates to `true`. Note that this does not provide a proof since this check is done using the untrusted evaluator.

What does need to be proven, however, is that the expression given is decidable.

One issue I faced is that I often use the `Except` type for error handling in my code.

``````inductive Except (ε : Type u) (α : Type v) where
/-- A failure value of type `ε` -/
| error : ε → Except ε α
/-- A success value of type `α` -/
| ok    : α → Except ε α
``````

For a simple (somewhat silly) example, look at the following function

``````def gt_0 (n : Nat) : Except String Bool :=
if n = 0 then .error s!"{n} is not greater than zero"
else .ok true
``````

We can evaluate our function on a given input:

``````#eval gt_0 1 -- Except.ok true
``````

However, we can’t guard against it without encountering an error. This is because we haven’t shown that the equality is decidable.

To help with this, I wrote up a function that we can apply generically.

``````def Except.deq [DecidableEq α] [DecidableEq β] : DecidableEq (Except α β) := by
unfold DecidableEq
intro a b
cases a <;> cases b <;>
-- Get rid of obvious cases where .ok != .err
try { apply isFalse ; intro h ; injection h }
case error.error c d =>
match decEq c d with
| isTrue h => apply isTrue (by rw [h])
| isFalse _ => apply isFalse (by intro h; injection h; contradiction)
case ok.ok c d =>
match decEq c d with
| isTrue h => apply isTrue (by rw [h])
| isFalse _ => apply isFalse (by intro h; injection h; contradiction)
``````

We can then show that equality of `Except String Bool` is decidable, since Lean already knows that string and boolean equality is decidable.

``````instance: DecidableEq (Except String Bool) := Except.deq
``````

From here, we can use `#guard`

``````#guard gt_0 1 = (Except.ok true)
``````

When a `#guard` fails, it will throw an error during compilation. This is great for ensuring that our unit tests pass during compilation.