Editing CTRex (section)

== Row polymorphism ==

Some extensible record systems, such as CTRex, support '''row polymorphism'''. This concept is best explained by an example, consider the following function (in CTRex):

<haskell> 
f ::    Rec ("x" ::= Double .| "y" ::= Double .| Empty) 
     -> Rec ("x" ::= Double .| "y" ::= Double .| "dist" ::= Double .| Empty)
f r = norm := dist ((r.!x * r.!x) + (r.!y * r.!y)) .| r
</haskell>

Where <hask>(.!)</hask> is the function to get a value from a record. This function takes a record with row <hask>{ x = Double, y = Double }</hask> and add returns the same record with a label <hask>dist</hask> added, which carries the distance of the point <hask>(x,y)</hask> from <hask>(0,0)</hask>. 


Now suppose we want to call this function with record <hask>{ name = "PointA", x = 10, y = 10  }</hask>. This is not possible, because the row <hask>{ name = String, x = Double, y = Double  }</hask> and  <hask>{ x = Double, y = Double  }</hask> are not the same.


For this we need row polymorphism: we want to make the function <hask>f</hask> '''polymorphic''' in the rest of the row as follows: 
<haskell> 
f :: ((r :! "x") ~ Double, (r :! "y") ~ Double) =>
     Rec r -> Rec ("norm" ::= Double :| r)
f r = norm := dist ((r.!x * r.!x) + (r.!y * r.!y)) .| r
</haskell>
Now the type <hask> f </hask> reads as follows: Given some record with row <hask>r</hask>where x and y have type Double, return a record in which x,y and dist have type Double and there are also some other fields described by row <hask>r</hask>. The type that GHC infers is even more general :

<haskell>
f :: (Floating t, (r :! "y") ~ t, (r :! "x") ~ t) =>
     Rec r -> Rec (Extend "norm" (r :! "x") r)
</haskell>