Re: how to write a simple cat

At 20:08 +0200 1999/06/03, Mariano Suarez-Alvarez wrote: >A ``category with + and ^ '' is called cartesian closed aditive >category, cf MacLane, Category Theory for the Working Mathematician Is this a suggestion or a theorem? Hans Aberg * Email: Hans Aberg

Re: Church numerals in Haskell

Jerzy Karczmarczuk wrote: > 6. Subtraction. Largo. >According to some folklore Church himself thought for some time >that it is not possible to define the subtraction using pure >lambdas. >In fact it is possible to subtract Church numerals (but never >getting negative number

Re: how to write a simple cat

On Wed, 2 Jun 1999, Hans Aberg wrote: > But it can be a spin-off for thoughts: A category is essentially an object > with I and *, and a functor is a map preserving those. So what about the > two other operations, + and ^ ?. A ``category with + and ^ '' is called cartesian closed aditive categor

Re: how to write a simple cat

Hello, Friedrich. On Tue, Jun 01, 1999 at 04:04:42PM +0200, Friedrich Dominicus wrote: > [...] > > longerThan :: String {- filename -} -> Int {- length limit -} -> IO () > > longerThan fn lenlim = do > > content <- readFile fn > > let li = lines content > > fl = filter (\l -> len

Re: Church numerals in Haskell

At 15:37 +0100 1999/06/03, Peter Hancock wrote: >By the way, I'm not wild about Hans's term "constant variables". In >Church's lambda-I calculus, you aren't allowed abstractions where the >bound variable doesn't occur in the body. It would be better to >distinguish linear (exactly once), affine

Re: Church numerals in Haskell

At 13:46 +0100 1999/06/03, Peter Hancock wrote: >Just regard log_x ... as alternative >notation for \ x -> ... > >log_x (a * b) = log_x a + log_x b >log_x 1 = 0 >log_x x = 1 > >log_x (a ^ b) = (log_x a) * b , x not free in b . These are interesting relations in some sense, even thou

Re: Church numerals in Haskell

> "Hans" == Hans Aberg <[EMAIL PROTECTED]> writes: > In real life though, it is very difficult to translate an arbitrarily given > lambda expression into a combination of the given primitive set. I cannot resist illustrating Hans's point. This is the sort of thing that comes up...

Re: Church numerals in Haskell

At 13:39 +0100 1999/06/03, Jerzy Karczmarczuk wrote: >... I don't understand >the Hans remark about making from +, * etc. the primitive basis >for the set theory. What's so primitive about them? A set of lambda expressions is called primitive if all other lambda expressions can be generated from

Church numerals in Haskell

> "Jerzy" == Jerzy Karczmarczuk <[EMAIL PROTECTED]> writes: > Somebody tried to suggest that lambda provides a kind of logarithm... In defense of it I can offer the following laws, which follow from the eta-rule of lambda calculus. Just regard log_x ... as alternative notation for \ x -

Church numerals in Haskell

Laszlo Nemeth wrote: > I somehow managed to delete Hans's earlier post in which he gives the > definitions for + and ^. So I wanted to fetch them from the > archive...which was last updated on the 28 May. Is the archive broken > or just rarely updated? > > Thanks, > Laszlo Nemeth Somebody trie