[Agda] Does the order of patterns matter?

[Altenkirch Thorsten]

On 27/09/2012 12:58, "Martin Escardo" <m.escardo at cs.bham.ac.uk> wrote:

>
>
>On 27/09/12 12:06, Altenkirch Thorsten wrote:
>>
>>
>> On 27/09/2012 11:51, "Martin Escardo" <m.escardo at cs.bham.ac.uk> wrote:
>>
>>> Already in definitions by pattern matching on natural
>>> numbers there is a departure from Martin-Lof type theory, because in
>>> MLTT you need an inductive definition to even compute the predecessor
>>> function.
>>
>> I don't understand this remark.
>>
>> Certainly we can define
>>
>> pred : Nat -> Nat
>> pred 0 = 0
>> pred (suc n) = n
>>
>> without any difficulties.
>
>Yes, that's my point. How do you write in MLTT?

What is wrong with

pred : ℕ → ℕ
pred = RecNat (λ _ → ℕ) 0 (λ n x → n)


assuming that we have

RecNat : (P : ℕ → Set) → P 0 → ((n : ℕ) → P n → P (suc n)) → (n : ℕ) → P n
RecNat P z s zero = z
RecNat P z s (suc n) = s n (RecNat P z s n)


?

Thorsten (puzzled)


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