Lambda the Ultimate

Shape Theory
started 11/5/2003; 8:21:50 PM - last post 11/6/2003; 7:00:56 PM

11/5/2003; 8:21:50 PM (reads: 6753, responses: 2)

Shape Theory

A theory with some languages dangling from it, and then for Frank, more theory:

Novel type systems designed to support shape-based programming can be found in the various programming languages described below. For example, Functorial ML supports a class of functors used to support new forms of polymorphism, which go by the name of functorial or shape polymorphism, or polytypy. Also, FISh is an Algol-like language that supports data types of arrays, by having a distinct class of shape types.

The semantics of programming languages typically uses category theory to represent the denotations of programs, so that a program and its output have the same value. However, enriched categories allow for the expression of operational information. For example, order-enriched categories can express rewriting rules.

Ehud I did due diligence with Google, and you asked for it...

Posted to theory by Mark Evans on 11/5/03; 8:24:04 PM

Olivier Lefevre - Re: Shape Theory

11/6/2003; 1:27:14 PM (reads: 275, responses: 0)

FISh is interesting but seems to have completely stalled: I remember seeing the exact same home page more than three years ago. Also, if you must dig into shape theory, do not think it started with or is limited to ML derivatives. The topic has a long history in connection with APL, for instance, and is related to work on skeletons in parallel computation. Look, e.g., at the work of Lenore Mullin and her Psi calculus: http://www.cs.albany.edu/~lenore/, at the book "Arrays, Functional Languages and Parallel Systems" published by Kluwer in 1991: http://www.wkap.nl/prod/b/0-7923-9213-2 or at the SAC (Single Assignment C) project: http://www.sac-home.org/.

Mark Evans - Re: Shape Theory

11/6/2003; 7:00:56 PM (reads: 261, responses: 0)

No such thoughts were expressed or implied, it's just an LtU post. I hope others unacquainted with these topics find them interesting.

Good theory, of course, is timeless.