How Samson Abramsky might approach Computer Science
Computer Science, as a discipline, presents a fascinating landscape for investigation. At its heart, it is concerned with the manipulation of information, the execution of procedures, and the very nature of computation. But what is the categorical structure underlying these operations? We must move beyond mere algorithms and finite state machines, which, while useful, often obscure the deeper, compositional principles at play.
Consider the notion of a program. It is not merely a sequence of instructions, but rather a description of a transformation, an object in a category whose morphisms represent the computation itself. This is essentially a matter of compositionality. We can take smaller programs, smaller computations, and compose them to build larger, more complex ones. The meaning of the whole must be a function of the meanings of its parts, and this compositional property is best captured by the language of categories.
We can view the execution of a program as a process unfolding over time, or perhaps across different states. This suggests a perspective rooted in sheaves. Just as a sheaf assigns data to open sets in a topological space, we can assign computational effects to contexts or states. The key insight here is the universal property. What are the universal constructions that define these computational objects and their interactions? Are we talking about algebraic theories, or perhaps monoidal categories that capture the flow of resources?
The challenge, as I see it, is to provide a rigorous denotational semantics for these computational phenomena. Operational semantics, while often intuitive, can be brittle. We need to find the functors that map abstract mathematical structures to concrete computational realities. This is not about reinventing the…
Imagined perspective — an AI synthesis grounded in Samson Abramsky’s recorded ideas and methods, not a quotation or a statement they actually made.