[Agda] pattern matching order

[Thorsten Altenkirch]

Hi,

I tried to define the following function by pattern matching

codeDouble : ∀{n : ℕ} → Bool × Fin n → Fin (double n)
codeDouble {zero} (b , ())
codeDouble {suc n} (false , zero) = zero
codeDouble {suc n} (true , zero) = suc zero
codeDouble {suc n} (b , suc x) = suc (suc (codeDouble (b , x)) )

But to my confusion the term "codeDouble {suc n} (b , suc x) “ didn’t reduce. This can be fixed by changing the order

codeDouble : ∀{n : ℕ} → Bool × Fin n → Fin (double n)
codeDouble {zero} (b , ())
codeDouble {suc n} (b , suc x) = suc (suc (codeDouble (b , x)) )
codeDouble {suc n} (false , zero) = zero
codeDouble {suc n} (true , zero) = suc zero

I guess I can answer this myself: since I first match on the boolean agda decides also to do case analysis first on the boolean and then on the Fin which duplicates my last line and has the effect that the defining equality doesn’t hold definitionally (this is always a bit agda). In this case agda could have matched my definition by changing the order. Is this too much to ask for?

Cheers,
Thorsten




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