Adaptive search (posing queries, observing outcomes, and refining knowledge) is a common pattern in security testing, logical deduction, and preference learning, yet typical implementations are ad-hoc and problem-specific. This talk presents a Haskell framework that expresses adaptive search purely as a recursion scheme, showing how the familiar trio of anamorphism, catamorphism, and their composition as a hylomorphism can express a generic solution to a wide range of adaptive search problems.

Starting from an imperative specification of how queries interact with an unknown target, written in a DSL, we perform symbolic execution to derive logical constraints on search parameters, perform model counting to compute probabilities of search outcomes, and generate search steps by maximizing expected Shannon information gain.

The resulting adaptive strategy is an online hylomorphism: an anamorphism lazily unfolds an optimal search tree while a catamorphism simultaneously drives the concrete interaction with an instantiated search problem, so only the explored path is ever materialized.

We will describe our Haskell implementation for adaptive search synthesis making use of functor algebras, and a few combinators, composed with model counting and information theory, unifying a wide range of problems.

Because we separates strategy synthesis (tree construction) from strategy execution, alternatives for critical components (model counters or information optimization algorithms) can be swapped in and out.

The talk will emphasize lessons for the broader Haskell community: - how recursion-scheme abstractions give a reusable template for search and inference, - how laziness enables demand-driven synthesis, and - how symbolic execution can be expressed functionally.

The work is ongoing: we are experimenting with larger search problem spaces and improved model counting. But the key ideas and approach are ready to share. We hope attendees will leave with a compact, idiomatic pattern for recognizing when a problem can be framed as an adaptive search and easily solved.