A dependency-free Clojure library showing that a large body of operations-research algorithms — continuous and discrete optimization, sequential decision making, and validation — are compositions of a small set of higher-order function (HOF) patterns.

It is the companion library to the book Applied Higher Order Functions: A Functional Architecture of Optimization, Decision Making, and Validation (Jiri Knesl). Every code listing in the book runs against this library.

• 254 public functions across 26 namespaces
• Zero dependencies beyond Clojure 1.12
• Three domains: optimization · Markov decision processes / RL · temporal-logic validation

deps.edn (git dependency — replace the sha):

io.github.Flexiana/orhof {:git/sha "<commit-sha>"}

(Clojars coordinates to follow.)

(require '[orhof.optimize :as opt]
         '[orhof.mdp      :as mdp]
         '[orhof.validate :as val])

;; --- Optimization: gradient descent on a paraboloid ---
(opt/gradient-descent (fn [[x y]] (+ (* x x) (* y y))) [5.0 5.0] :lr 0.1 :max-iter 500)
;; => {:x [~0.0 ~0.0] :value ~0.0 :iterations n :converged? true ...}

;; Same problem, Adam — swap one function, same framework
(opt/adam (fn [[x y]] (+ (* x x) (* y y))) [5.0 5.0] :lr 0.1 :max-iter 500)

;; --- Decision making: a multi-armed bandit via Thompson sampling ---
(def bandit (mdp/make-bandit [(fn [] (if (< (rand) 0.3) 1.0 0.0))
                              (fn [] (if (< (rand) 0.7) 1.0 0.0))]))
(mdp/thompson-sampling bandit :n-rounds 2000)   ; => {:alphas ... :betas ... :counts ...}

;; --- Validation: falsify a temporal-logic specification ---
;; see orhof.validate / orhof.val.* and docs/API.md

Full generated reference: docs/API.md. Design notes: ARCHITECTURE.md.

The book's thesis is that these algorithms are not hundreds of unrelated recipes but instances of a few higher-order patterns. Two examples the code makes concrete:

• One descent framework, many optimizers. Gradient descent, steepest descent, conjugate gradient, and Adam are the same template parameterized by a direction function and a step function.
• The Bellman operator is a function transformer mdp -> (V -> V'). Value iteration is just its fixpoint; temporal-logic operators are HOFs on specifications that return continuous robustness values.

clojure -X:test

187 tests. Stochastic algorithms (GA, bandits, PSO, sampling, …) are seeded via a shared fixture, so the suite is deterministic.

MIT — see LICENSE. Copyright © 2026 Jiri Knesl. The companion book is a separate work, licensed CC BY-SA 4.0.