Am Sonntag, 18. Januar 2009 17:48 schrieb rocon...@theorem.ca: > On Sun, 18 Jan 2009, Ross Paterson wrote: > > Anyone can check out the darcs repos for the libraries, and post > > suggested improvements to the documentation to librar...@haskell.org > > (though you have to subscribe). It doesn't even have to be a patch. > > > > Sure, it could be smoother, but there's hardly a flood of contributions. > > I noticed the Bool datatype isn't well documented. Since Bool is not a > common English word, I figured it could use some haddock to help clarify > it for newcomers.
Thanks. Really helpful. A few minor typos, though. > > -- |The Bool datatype is named after George Boole (1815-1864). > -- The Bool type is the coproduct of the terminal object with itself. > -- As a coproduct, it comes with two maps i : 1 -> 1+1 and j : 1 -> 1+1 > -- such that for any Y and maps u: 1 -> Y and v: 1 -> Y, there is a unique > -- map (u+v): 1+1 -> Y such that (u+v) . i = u, and (u+v) . j = v > -- as shown in the diagram below. > -- > -- 1 -- u --> Y > -- ^ ^^ > -- | / | > -- i u + v v > -- | / | > -- 1+1 - j --> 1 You have the arrows i and j pointing in the wrong direction. > -- > -- In Haskell we call we define 'False' to be i(*) and 'True' to be j(*) Delete "we call". > -- where *:1. > -- Furthermore, if Y is any type, and we are given a:Y and b:Y, then we > -- can define u(*) = a and v(*) = b. > -- From the above there is a unique map (u + v) : 1+1 -> Y, > -- or in other words, (u+v) : Bool -> Y. > -- Haskell has a built in syntax for this map: > -- @if z then a else b@ equals (u+v)(z). > -- > -- From the commuting triangle in the diagram we see that > -- (u+v)(i(*)) = u(*). > -- Translated into Haskell notation, this law reads > -- @if True then a else b = a...@. > -- Similarly from the other commuting triangle we see that > -- (u+v)(j(*)) = v(*), which means > -- @if False then a else b = b@ _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe