[Haskell-cafe] Type Theory? Relations

[haskell at alias.spaceandtime.org]

Hello,

I have a question that may pertain to type theory.

According to Enderton, one of the ways to define an ordered pair (a,b)
is {{a},{a,b}}.  A relation is defined as a set of ordered-pairs.  A
map, of course, is a single-valued relation.

Given all that, suppose I have a "FiniteMap Int String" in Haskell. 
This is, according to the definitions above, a "Set (Int,String)".    An
element of that has type (Int,String), which contains {Int,String}.  But
that can't exist because a Set contains only elements of one type.

What I'm getting at is that it seems that a Relation should be defined

type Relation a = Set (a,a)

rather than 

type Relation a b = Set (a,b)

so that we don't have this problem.

Thanks.