Lambda the Ultimate

Sage is a project to create a viable free open source alternative to Magma, Maple, Mathematica and Matlab. The lead developer/manager William Stein has recently written Mathematical Software and Me: A Very Personal Recollection, a rather enjoyable story of his experience with mathematical software, especially Magma, and how Sage came to be.

One of the difficulties of writing broadly useful math software is the sheer size and scope of such a project. It is easily outside the abilities of even the most prodigious lone developer. So the focus of Sage, at least up until recently, has been on creating Python-based interfaces to existing mathematical software. For example, for symbolic calculation the Sage distribution includes Maxima (written in Common Lisp), a fork of Macsyma dating back to the early 1980s, and released as open-source software by the US Department of Energy approximately 10 years ago. In addition to Maxima, Sage includes the ability to call out to Magma, Mathematica, and Maple.

There are some interesting PLT-related snippets, for example, Magma's language is frequently criticized, although its algorithms are frequently praised. In conversations with others, OCaml and Haskell were brought up, but William Stein chose Python because he felt that it was more accessible. Also, Axiom, which includes the dependently-typed language Aldor, was rejected in favor of Maxima because Maxima was less esoteric and much more widely used.

Discussion

The use of continuations in a program generally goes together with the use of multiple stacks. That is because several function stack frames can be active at the same time.

This results in obvious memory management issues, such as deciding the location and the size of these stacks. This document explores the idea of a constant size function stack frame, and the conditions in which it allows for a single stack.

I was not sure how to present my ideas in the forum, so I put them in a PDF document.

Does it make sense to think in terms of constant size function stack frame? Is it useful to have a single stack instead of multiple stacks?