On Sun, 30 Dec 2007 19:13:47 +0200, Jonathan Cast wrote:

On 30 Dec 2007, at 11:10 AM, Cristian Baboi wrote:

...

In section 4.3.3., chapter 4: Structured types and the semantics of pattern-matching, by S.Peyton Jones and Philip Wadler, there is this equation:

Eval[[\(s p1 p2 ... pt).E]] (s a1 a2 ...at) = Eval[[\p1 ... \pt.E]] a1 ... at

The text say: "To apply \(s p1 ... pt).E to an argument A we first evaluate A to find out what sort of object it is." "Finally, if A was built with the same constructor as the patern, then the first rule applies."

What I don't get it :

(s a1 a2 ... at) must be the value of A in the semantic domain. Let call that value a. Then how can one know if a was built with (s a1 a2 ... at) and not with (egg b1 b2) ?

I suspect that s and egg are constructors, in which case their images are (by definition) mutually exclusive.

I have not seen that definition in the book.

Thank you. The thing is that when talking about the semantic of Prolog, one can choose any set as the semantic domain to start, and then a reason is given for choosing the Herbrand universe. On Sun, 30 Dec 2007 19:23:00 +0200, Benja Fallenstein wrote:

Hi Cristian,

On Dec 30, 2007 6:10 PM, Cristian Baboi wrote:

...

What I don't get it :

(s a1 a2 ... at) must be the value of A in the semantic domain. Let call that value a. Then how can one know if a was built with (s a1 a2 ... at) and not with (egg b1 b2) ?

Because the semantic domain is chosen so that (s a1 a2 ... at) and (egg b1 b2) are distinct objects.

More precisely, the domain corresponding to (for example) the type

data T = C1 T11 T12 | C2 T21 T22

should be isomorphic to the domain

[[T]] = lift (([[T11]] * [[T12]]) + ([[T21]] * [[T22]]))

where * is cartesian product, + is disjoint sum (e.g., X+Y = {(1,x) | x in X} union {(2,y) | y in Y}, and 'lift' adds the bottom element to the domain.

So here, C1 and C2 correspond to the two sides of the disjoint sum, meaning you can tell them apart.

Hope that helps?

- Benja