The IsalProgram Programming Language

TL;DR

IsalProgram is a novel assembly-like language that is regular, syntactically flexible, and memory-address independent, with potential applications in neural program synthesis and formal analysis.

Contribution

The paper formally defines IsalProgram, proves its regularity, and explores its expressive power and potential advantages for program synthesis.

Findings

Programs are accepted by a finite automaton.

Every finite string over the instruction set is valid.

It operates without explicit memory addresses or variable names.

Abstract

We introduce IsalProgram (Instruction Set and Language for Programming), a novel assembly-like programming language with three distinctive theoretical properties: (1) it is a regular language in the sense of formal language theory, meaning its programs are accepted by a finite automaton; (2) every finite string over the instruction alphabet is a syntactically valid program; and (3) it makes no explicit use of memory addresses or variable names, absolute or relative. Programs are finite sequences of tokens drawn from a fixed instruction set, and are executed on a virtual machine whose sole data structure is a circular doubly linked list (CDLL) navigated by three data pointers, with control flow governed by two code pointers. We give a complete formal definition of the language and its virtual machine, prove its regularity, and demonstrate its expressive power. We further discuss IsalProgram's potential advantages as a target language for neural program synthesis, the amenability of its program space to metric-based exploration via the Levenshtein edit distance, and directions for analyzing computability and complexity within this framework.