[Haskell-cafe] Composition Operator

Stefan O'Rear stefanor at cox.net
Mon Sep 24 22:01:29 EDT 2007

On Mon, Sep 24, 2007 at 06:47:05PM -0700, Dan Weston wrote:
> Of course I should have proofread this one more time!
>> What is a point? A point in Hask* is a type with only a single value in 
>> it, from which all other values can be constructed. Every value x maps 
>> trivially into a function (const x), and when you apply this function to  
>> the (only) value of a point, you get x back. There is a built-in Haskell 
>> type () whose only value [besides undefined] is also called (), so we 
>> might as well take the type () as our point:
> Actually, a point is any one object, for Hask* it is any one monotype (e.g. 
> (), [Int], (Char,Double)). The magic of an *initial* object (i.e. a type 
> with only one nullary constructor such as () that has only one (defined) 
> value) is that there is a *unique* function mapping it to any other type. 
> But that's being greedy, since we don't need a unique function, just any 
> one function. A forgetful function like const doesn't care which type its 
> second argument is.

() isn't an initial object.

There are no initial objects in Hask-with-⊥, since every object admits
at least four arrows to Bool (const True, const False, const undefined,
and undefined).

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