>> % 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
[deletia]
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
So predicates and data constructors have similar syntax but different
semantics in Prolog? Say, for the sake of argument, if I wanted to do
automatic translation, how would I tell which was which in a Prolog
program?
"Faking it: Simulating dependent types in Haskell" certainly explains
*one* way to simulate dependent types, but I need to justify the
existence of type constructors in an Idealised Haskell, so I must
understand why the implementation in Prolog does not appear to be a
literal translation.
I would love to read your article! (I can give you a [forthcoming?]
citation if I ever get through this part of my thesis. :-/)
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