PReFScript:

Partial Recursive Functions for Scripting

Author: Jose Luis Balcazar, ORCID 0000-0003-4248-4528

Project started: mid Germinal 2003.

Copyleft: MIT License (https://en.wikipedia.org/wiki/MIT_License)

A Python-based environment to explore and experiment with partial recursive functions; naturally doubles as a (purely functional) programming language, but it is not intended to be used much as such.

Current version: 2.0.5, late Fructidor 2026. Previous version 1.2 of mid Messidor 2026 is incompatible.

Scripts

In PReFScript, a script is a sequence of functions defined in terms of each other and of a few basic functions via the partial recursion rules of composition and minimization. All functions are from the natural numbers into the natural numbers and may be undefined for some inputs.

In order to handle tuples or sequences of natural numbers, a Cantor-like encoding is used; see https://github.com/balqui/cantorpairs/blob/main/README.md.

Specifically, the always available basic functions include: k_1, the constant 1 function; id, the identity function; addition and multiplication, add and mul respectively, that interpret the single number received as the Cantor encoding of a pair <x.y> and compute the corresponding operation on x and y; modified difference diff that receives likewise a Cantor-encoded pair <x.y> and computes max(0, x - y) so that we always stay within the natural numbers; and two functions related to projections of Cantor-encoded sequences.

Installation and ways to use PReFScript functions

The usual pip-based process should work. Differently from previous versions, all functionality in 2.0.* is fully compatible with a pipx installation. You may need to specify --upgrade flags, depending on your previous installation. LLMs say that uv should work as well.

The current version installs a stand-alone interpreter. See doc.md.

The following applied to the previous version 1.2: Scripts were maintained in objects of the class PReFScript, that could be imported into your own Python program. Thus, you had available two main ways of programming in PReFScript. All this does not apply anymore to versions 2.0.*.