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82 lines
2.4 KiB
Markdown
82 lines
2.4 KiB
Markdown
---
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title: "Writing Unit Tests in Lean 4"
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date: 2024-08-05T20:43:52-07:00
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draft: false
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tags: []
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math: false
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medium_enabled: false
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---
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When writing Lean code, it's easier to iterate with unit tests than to prove properties about the function off the bat.
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I mean if the unit test doesn't even pass, why bother with the proof?
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Luckily, Lean 4 let's us do unit tests with a cool command called `#guard`
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```lean4
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#guard 1 = 1
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```
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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.
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What does need to be proven, however, is that the expression given is decidable.
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One issue I faced is that I often use the `Except` type for error handling in my code.
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```lean4
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inductive Except (ε : Type u) (α : Type v) where
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/-- A failure value of type `ε` -/
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| error : ε → Except ε α
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/-- A success value of type `α` -/
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| ok : α → Except ε α
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```
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For a simple (somewhat silly) example, look at the following function
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```lean4
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def gt_0 (n : Nat) : Except String Bool :=
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if n = 0 then .error s!"{n} is not greater than zero"
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else .ok true
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```
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We can evaluate our function on a given input:
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```lean4
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#eval gt_0 1 -- Except.ok true
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```
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However, we can't guard against it without encountering an error. This is because we haven't shown that the equality is decidable.
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To help with this, I wrote up a function that we can apply generically.
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```lean4
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def Except.deq [DecidableEq α] [DecidableEq β] : DecidableEq (Except α β) := by
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unfold DecidableEq
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intro a b
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cases a <;> cases b <;>
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-- Get rid of obvious cases where .ok != .err
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try { apply isFalse ; intro h ; injection h }
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case error.error c d =>
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match decEq c d with
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| isTrue h => apply isTrue (by rw [h])
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| isFalse _ => apply isFalse (by intro h; injection h; contradiction)
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case ok.ok c d =>
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match decEq c d with
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| isTrue h => apply isTrue (by rw [h])
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| isFalse _ => apply isFalse (by intro h; injection h; contradiction)
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```
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We can then show that equality of `Except String Bool` is decidable, since Lean already knows that string and boolean equality is decidable.
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```lean4
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instance: DecidableEq (Except String Bool) := Except.deq
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```
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From here, we can use `#guard`
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```lean4
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#guard gt_0 1 = (Except.ok true)
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```
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When a `#guard` fails, it will throw an error during compilation. This is great for ensuring that our unit tests pass during compilation.
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