Re: [Haskell-cafe] Church Encoding Function
On 3/10/07, Robert Dockins [EMAIL PROTECTED] wrote: I'm pretty sure you can define a catamorphism for any regular algebraic data type. I'm not 100% sure what the story is for non-regular (AKA nested) datatypes. They do exist: Initial Algebra Semantics is Enough! Patricia Johann and Neil Ghani. http://crab.rutgers.edu/~pjohann/tlca07.pdf code: http://www.cs.nott.ac.uk/~nxg/Tlca07.hs Jim ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Church Encoding Function
On Sat, Mar 10, 2007 at 03:43:41PM +0100, Joachim Breitner wrote: Hi, some more ideas following from the last post. I noticed how the function Data.Maybe.maybe converts a Haskell Maybe into a Church encoded Maybe. Also, the if construct, interpreted as a function, converts a Bool into a church encoded Bool. If lists are encoded as forall b. (a - b - b) - b - b, then foldr, with the right order of arguments, converts a haskell [] to a Church encoded List. Is there a name for these functions? ???Characteristic Church Encoding Functions??? maybe? Are there more than these: I usually hear deconstructor. either :: Either a b - (a - r) - (b - r) - r Maybe -- maybe Bool -- ifthenelse List -- foldr (,) -- uncurry Just a short idea while waiting at the airport... Greetings, Joachim -- Joachim nomeata Breitner mail: [EMAIL PROTECTED] | ICQ# 74513189 | GPG-Key: 4743206C JID: [EMAIL PROTECTED] | http://www.joachim-breitner.de/ Debian Developer: [EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Church Encoding Function
On Saturday 10 March 2007 09:43, Joachim Breitner wrote: Hi, some more ideas following from the last post. I noticed how the function Data.Maybe.maybe converts a Haskell Maybe into a Church encoded Maybe. Also, the if construct, interpreted as a function, converts a Bool into a church encoded Bool. If lists are encoded as forall b. (a - b - b) - b - b, then foldr, with the right order of arguments, converts a haskell [] to a Church encoded List. Is there a name for these functions? “Characteristic Church Encoding Functions” maybe? Are there more than these: I believe these are the same as catamorphisms. http://en.wikipedia.org/wiki/Catamorphism Here is the paper where the term (AFAIK) was coined (although I have to admit to having only skimmed it): http://citeseer.ist.psu.edu/meijer91functional.html I'm pretty sure you can define a catamorphism for any regular algebraic data type. I'm not 100% sure what the story is for non-regular (AKA nested) datatypes. Maybe -- maybe Bool -- ifthenelse List -- foldr (,) -- uncurry Just a short idea while waiting at the airport... Greetings, Joachim ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Church Encoding Function
On Sat, Mar 10, 2007 at 03:43:41PM +0100, Joachim Breitner wrote: Hi, some more ideas following from the last post. I noticed how the function Data.Maybe.maybe converts a Haskell Maybe into a Church encoded Maybe. Also, the if construct, interpreted as a function, converts a Bool into a church encoded Bool. If lists are encoded as forall b. (a - b - b) - b - b, then foldr, with the right order of arguments, converts a haskell [] to a Church encoded List. Is there a name for these functions? folds (with the arguments flipped) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Church Encoding Function
On 10/03/07, Joachim Breitner [EMAIL PROTECTED] wrote: Is there a name for these functions? Characteristic Church Encoding Functions maybe? Are there more than these: Catamorphisms is indeed the name I've heard. -- -David House, [EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
