[Agda] Re: Agda beats Coq

[Nils Anders Danielsson]

On 2008-11-20 12:05, Edsko de Vries wrote:

>> fix-fac-ind : {g : Nat -> D Nat} {n k : Nat}
>>            -> fix-aux g fac-aux n ↓ k
>>            -> fix-aux (fac-aux g) fac-aux (suc n) ↓ suc n * k
>> fix-fac-ind {g} {n} pf with fac-aux g n ⋆
>> fix-fac-ind {g} {n} {k} converge-now | inl .k = converge-now
>> fix-fac-ind (converge-later pf) | inr y = converge-later (fix-fac-ind pf)

> I don't know Agda very well, but there is some magic going on in 
> fix-fac-ind!

The magic is called "magic with" (but is not really magic). See
http://appserv.cs.chalmers.se/users/ulfn/wiki/agda.php?n=Docs.MagicWith
for a quick explanation. Definitions using magic with can be translated
into equivalent definitions which do not use with, see Ulf Norell's
thesis for a detailed story.

-- 
/NAD


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