Felix has a forward composition operator:
(f \circ g) x = f (g x)
There's no reverse composition operator, because I can't think of
a suitable symbol. Operator dot (.) was used before and leads
to a nice notation:
x . (f . g) = (x . f) . g
but it doesn't work because f. g means application of g to f.
Although this usually works for concrete types, overloading
can get it confused, and polymorphism really screws it up.
I could use
x . (f \cdot g)
[\cdot is a fat centred dot in TeX] although the precedence isn't clear!
Consider also:
f \circ g \cdot h . x
to see: where do the parens go?
Anyhow, i have one more thing to do in the wrapping stuff, actually
lambda lifting:
f \circ g --> fun x => f (g x)
Now the projections work, Felix can finally express properly what C++ can't:
struct Inner { int x; }
struct Outer { Inner y; }
var OI = y of (Outer);
var Ix = x of (Inner);
var Ox = OI \circ Ix;
This is the composition of the projection from Outer to y, and Inner
to x, giving a projection from Outer to x.
In C++, field projections are called pointers to members. they cannot
be composed, showing the type system is incomplete.
In Felix, projections are just functions, so they can be composed if the
domain of the second applied is the codomain of the first. No special
operation is required, it's ordinary function composition.
What's more, since projections work with pointers to a struct (or any
product type). Pointer projections:
var I : Inner;
(&I) . x <- 42;
eliminate the need for idiot lvalue rules. So we have a much nicer
type system which means composing things works much better.
--
john skaller
skal...@users.sourceforge.net
http://felix-lang.org
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