[Haskell-cafe] Re: Why purely in haskell?

[Achim Schneider]

Tillmann Rendel <rendel at rbg.informatik.tu-darmstadt.de> wrote:

> Achim Schneider wrote:
> > [1..] == [1..] 
> > 
> > [some discussion about the nontermination of this expression]
> > 
> > The essence of laziness is to do the least work necessary to cause
> > the desired effect, which is to see that the set of natural numbers
> > equals the set of natural numbers, which, axiomatically, is always
> > computable in O(1) by equality by identity.
> 
> This would make sense if Haskell had inbuild equality and (==) where 
> part of the formal semantics of Haskell, wich it isn't. (==) is a 
> library function like every other library function. How could the 
> language or a system implementing the language decide wether this or
> any other library function returns True without actually running it?
> 
The list instance for Eq might eg. know something about the structure
of the lists and be smart enough not to get caught in the recursion of x
= 1:1:x and y = 1:1:1:y so it could successfully compare x == y to
True in six compares.

> Haskell is a programming language, not a theorem prover.
> 
Yes I know. That's why I wrote axiomatic and operational semantics, not
denotational; I didn't want to start a bar fight.

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