[Haskell] Re: lambda calculus theory

[Marc A. Ziegert]

(this duplicates that inquiry from glasgow-haskell-users@ to haskell@)



Am Sonntag, 6. November 2005 15:53 schrieb Hans N Beck:
> Hi,
> 
> I'm searching for a good mathematical oriented introduction to the  
> theory of lambda calculus or other theoretical foundations of Lisp/ 
> Haskell, i.e. monads or such (of course in the web there are much  
> hints, but what is the best for mathematicans foreign to this field)
> 
> Regards
> 
> Hans
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> Glasgow-haskell-users at haskell.org
> http://www.haskell.org/mailman/listinfo/glasgow-haskell-users
> 
> 



Hi Hans,

i'm searching for such lectures/papers/scripts, too.
well, untill there is a better answer, i send you some links, which i think could be interesting to you.
the first real mathematical definition of "monad", i read, was in the paper "The essence of dataflow programming". i approve to not omit that paper, if you like both, haskell and that theory.
beside that, i attended a german lecture about Algebraic Topology. one chapter was about cathegory theory. it was not that much, but interesting.


lambda:
<http://en.wikipedia.org/wiki/Lambda_calculus>
(<http://de.wikipedia.org/wiki/Lambda-Kalk%C3%BCl>)
very interesting is the "typed lambda calculus", which allows effective bug-prevention, which you do not have in most variants of lisp (or lisp's derivatives) but in haskell.

functor:
<http://haskell.org/hawiki/CategoryTheory_2fFunctor>

monad:
there is a mathematical definition in the paper "The essence of dataflow programming", see 'comonad:' below.

cathegory theory:
<http://haskell.org/hawiki/CategoryTheory>
<http://haskell.org/hawiki/CategoryTheory_2fPapers>
<http://en.wikipedia.org/wiki/List_of_category_theory_topics>
<http://www.eyrie.org/~zednenem/2004/hsce/>

arrow:
<http://www.haskell.org/arrows/>
<http://www.soi.city.ac.uk/~ross/papers/fop.html>

comonad:
<http://comments.gmane.org/gmane.comp.lang.haskell.general/12171>


beside these links, do not abstain from reading parts of the haskell library. (Data.Maybe, Data.Monoid, Control.Monad, Data.FunctorM, Control.Arrow)
<http://www.haskell.org/ghc/docs/latest/html/libraries/>


- marc