Behavioural Theory of Reflective Algorithms I: Reflective Sequential Algorithms

TL;DR

This paper introduces a behavioral theory for reflective sequential algorithms that can modify their own behavior, providing a formal model and proof that captures all such algorithms through an extended abstract state machine framework.

Contribution

It develops a formal, language-independent theory and model for reflective sequential algorithms, extending existing models with self-representation and modification capabilities.

Findings

All RSAs are captured by the rsASM model.

States include a representation of the algorithm enabling reflection.

Bounded exploration is maintained through term values.

Abstract

We develop a behavioural theory of reflective sequential algorithms (RSAs), i.e. sequential algorithms that can modify their own behaviour. The theory comprises a set of language-independent postulates defining the class of RSAs, an abstract machine model, and the proof that all RSAs are captured by this machine model. As in Gurevich's behavioural theory for sequential algorithms RSAs are sequential-time, bounded parallel algorithms, where the bound depends on the algorithm only and not on the input. Different from the class of sequential algorithms every state of an RSA includes a representation of the algorithm in that state, thus enabling linguistic reflection. Bounded exploration is preserved using terms as values. The model of reflective sequential abstract state machines (rsASMs) extends sequential ASMs using extended states that include an updatable representation of the main ASM rule to be executed by the machine in that state. Updates to the representation of ASM signatures and rules are realised by means of a sophisticated tree algebra.