IMA vs tree-ssa

[Joe Buck]

On Mon, 8 Mar 2004, Mark Mitchell wrote:

On Tue, Mar 09, 2004 at 12:48:58AM +0000, Joseph S. Myers wrote:
> > A type system with non-transitive type-equality breaks all the standard 
> > mathematical models for type theory.  (And, yes, I know the C type 
> > system is ugly, but most of it can actually be modeled in pretty 
> > conventional ways.)  The category-theoretician in me is befuddled by 
> > what a non-transitive type-equality model could possibly mean.
> 
> It's not type-equality, it's type-compatibility.  Equality of types also
> exists, and behaves transitively.
> 
> Most of the problem cases involve incomplete types; e.g., int[] is
> compatible with int[3] and int[5] which are not compatible with each
> other.

Such a relationship can still be transitive if there is a direction.
For example, we can have a transitive "is_a" relationship such that

    int[3] is_a int[]
    int[5] is_a int[]

but there is no is_a relationship between int[3] and int[5], or between
int[] and int[3] in the reverse direction.