🧘‍♂️ @fizzwiz/search

🧮 Exploring Combinatoric Calculus with   Search The   Search   abstraction in   @fizzwiz/search   provides a clean, declarative way to generate and explore   combinatorial structures . You simply   describe   how candidates expand — and let the lazy search engine handle the traversal. 🧠 Concept: Combinatorics as Exploration Most combinatorial problems can be understood as a   space of possible choices : Dispositions   → sequences of fixed length Combinations   → subsets of fixed length Power sets   → all subsets Traditionally, each one requires its own custom algorithm — often recursive, imperative, and hard to generalize. With   Search , you model them all with a single idea: Start from an initial candidate, and expand it into new candidates using a declarative rule. ⚙️ Defining a Search Process Each search consists of three parts: Start   – The initial candidate (e.g., an empty path). Space   – A function des...

⚡ Early vs. Late Restriction in Combinatorial Search One of the core design strengths of   @fizzwiz/fluent   — and by extension   @fizzwiz/search   — is the ability to optimize   combinatorial search   via   early restriction   of the search space. This distinction may look subtle, but its impact on performance can be dramatic. 🚧 The Problem Imagine generating all sorted paths of length   3   from the items   [0, 1] ,   with repetitions . A naive approach would: Generate   all possible paths   of length 3 Filter out the unsorted ones This works — but performs far more work than necessary. With   @fizzwiz/fluent , you can   reject invalid paths immediately ,   before   their descendants are ever constructed. ⚙️ Early vs. Late Restriction Side-by-side comparison: const // Returns a `What` of paths without eagerly building arrays space = Each . each ([ 0 , 1 ], [ 0 , 1 ], [ 0 , 1 ]), // Pred...

🧠 The Search-and-Select Pattern 🔍 Multivalued Functions as Possibility A function that returns   iterables   instead of a single value can be understood in two powerful ways: Uncertainty: The function doesn’t know the answer yet, so it returns several plausible options. Exploration: When input and output share the same type, the function becomes a   map : from one point, it shows all the directions you can go next. That second interpretation unlocks something fundamental: A multivalued function   is   a search space. 🧭 Step by Step Toward a Solution Think about how you actually solve hard problems. You don’t jump straight to the solution. You: make a rough guess, explore variations, discard bad paths, and gradually converge on something that works. The Search class models exactly this process. Each step looks like: Pull the most promising candidate from a queue Push all neighboring possibilities back into the queue Prune the least promising candidates if th...