Metacomputation is a broad term, so broad as to contain all of the computer activities that deal with knowledge. This paper is a tribute to the legacy of Valentin Turchin, who developed a notation, created programs to manipulate other programs, and demonstrated how to generate compilers.

The author of this paper applies Turchin’s theory to artificial general intelligence (AGI), where the target is to obtain a formal knowledge representation. The specific notation is taken from another seminal work [1], which introduced the concept of a compiler-compiler that applies to formal languages in general. In section 2, the method is shown to conceptually apply to a program that predicts the state of the world given experience and present state. In section 3, the approach is applied to reasoning on states and sharing knowledge between multiple systems. Section 4 is about supercompilation, a quite neglected theory proposed by Turchin, which can be used to transform programs into programs, in order to, for instance, create more efficient programs.

The author concludes that his proposal is a first step toward creating intelligent systems based on metacomputation theory. I agree with this conclusion. The road ahead is still very long. This paper proposes a purely theoretical algebraic formulation, without theorems, metrics, or comparison to the usual formalisms based on mathematical logic.

Another aspect to consider is that the paper by Futamura was written when Algol 60 was the most advanced language. Some of the ideas in that work were applied in generating interpreters and compilers in the 1990s. What is new 20 years later? Why is the most recent cited reference from 1994? It seems that the theory is partially neglected, and I wonder why.