Operations research as compositions of a few higher-order functions

Operations research is usually taught as hundreds of named recipes: gradient descent, value iteration, the Hungarian method, particle filters, temporal-logic monitors. orhof, Operations Research in Higher-Order Functions, is a zero-dependency Clojure library built to demonstrate a different claim: most of these are compositions of a small set of higher-order-function patterns.

The shape of the idea

One generic descent framework, parameterised by a direction function and a step rule, yields gradient descent, conjugate gradient and Adam. The Bellman operator is expressed as a function transformer mdp → (V → V′), so value iteration, policy iteration and their variants share one core. Temporal-logic operators — always, eventually, until — become higher-order functions with continuous robustness semantics, which turns falsification into an optimisation problem.

What is in it

• 251 public functions across 30 namespaces, zero third-party dependencies.
• Three domains: continuous and discrete optimisation; Markov decision processes and reinforcement learning; temporal-logic validation.
• 187 deterministic tests under a seeded RNG fixture, so every result reproduces.

It is the executable companion to the book Applied Higher Order Functions; every listing in the book runs against it, and Rainbow uses the same catalogue as its proving curriculum.

Why it matters commercially

When we model a client’s decision, we are not starting from a blank solver. The composition patterns here are the parts we assemble. So a modelling conversation becomes running, testable code in days rather than weeks. That is a claim about our delivery, tested on our own work. A client engagement is where it gets measured against a baseline.