Hello Jared, Tuesday, July 18, 2006, 9:05:09 AM, you wrote:
% defining natural numbers natural(zero). natural(s(X)) :- natural(X).
% translate to integers toInt(zero, 0). toInt(s(X), N) :- toInt(X, Y), N is Y + 1.
Thank you. I can now more precisely state that what I'm trying to figure out is: what is 's', a predicate or a data structure? If it's a predicate, where are its instances? If not, what is the difference between the type language and Prolog such that the type language requires data structures?
it's data structure, to be exact, it's data constructor - just like, for example, "Just" in Haskell. Haskell requires that all data constructors should be explicitly defined before they can be used. you can use "Just" to construct data values only if your program declares "Just" as data constructor with "data" definition like this: data Maybe a = Just a | Nothing Prolog is more liberate language and there you can use any data constructors without their explicit declarations, moreover, there is no such declarations anyway The more important difference is what Prolog is _logic_ programming language and there you can use unification and backtracking in functions' definitions. Haskell is _not_ logic programming language so you can't define functions what use these techniques. The humor, though, is that Haskell's multi-parameter type classes defines logic programming language, but at the _type_ level. Values of this language is _types_ instead of ordinary values. And naturally, instead of data constructors - _type_ constructors are used to construct new type values and in the unification operations. So, you can't use "Just" in this language, but "Maybe" can be used. GHC also supports nullary data definitions which defines just type constructor without data constructors: data Zero data Succ a i once said you about good paper on type-classes level programming. if you want, i can send you my unfinished article on this topic which shows correspondences between logic programming, type classes and GADTs -- Best regards, Bulat mailto:Bulat.Ziganshin@gmail.com