Algorithmic Scientists and the Foundations of Machine Intelligence
Lucius Gregory Meredith — April 2026
Abstract: This paper presents F1R3FLY’s foundational approach to artificial intelligence, grounded in graph-structured lambda theories (GSLTs). GSLTs provide a uniform categorical framework encompassing virtually all known classical models of computation. Within this framework, bisimulation is the finest equivalence any program can learn about its environment; reactive contexts serve as experimental assays; an auto-generated Hennessy–Milner logic provides a canonical language for reasoning; and structural reflection embeds this language back into the calculus. The result is a class of programs—algorithmic scientists—that discover their world through experimentation and formulate hypotheses in a language automatically grounded in bisimulation-based ontology.
Key argument
The paper develops a four-step argument: (1) computation is ontologically isolated—programs can only interact with representations internal to their substrate; (2) bisimulation is the finest distinction a program can draw about its environment; (3) reactive contexts derived from Milner, Leifer, and Sewell’s work provide algorithmic experimental assays; and (4) an auto-generated Hennessy–Milner logic gives programs a canonical language for recording and reasoning about experimental results.
The GSLT framework
A graph-structured lambda theory is a triple ⟨G, E, R⟩ consisting of a grammar of terms, a set of equations forming the smallest equivalence relation erasing irrelevant syntactic differences, and a set of rewrite rules determining term evolution. Lambda calculus, pi-calculus, rho calculus, and ambient calculus are all instances. GSLTs form a category whose morphisms are bisimulation-preserving maps, ensuring all constructions are functorial.
MeTTaIL and the execution engine
MeTTaIL (rholang 1.4), F1R3FLY’s core language technology, provides the execution engine: defining GSLTs as first-class entities, enforcing spatial-behavioral types that enable semantic search over smart contracts, and supporting evolutionary programming over entire causal models.
Why it matters
Rather than treating AI as statistical pattern-matching on large datasets, this framework grounds machine intelligence in a precise mathematical account of computation itself. Programs that behave as scientists—exploring through experimentation, discovering categories through bisimulation, reasoning in automatically generated logic—represent a fundamentally different approach to the aspects of intelligence that computation can capture.