feat: add Monoid algebraic structure - #596
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Add Semigroup interface and concrete implementations (Sum, Product, Str) with full test coverage including associativity law verification. Co-authored-by: Copilot App <223556219+Copilot@users.noreply.github.com>
Implement the Monoid type which extends Semigroup with an identity element (empty). Includes SumMonoid, ProductMonoid, StrMonoid constructors and a generic concatAll function for folding collections. Co-authored-by: Copilot App <223556219+Copilot@users.noreply.github.com>
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Summary
Adds the Monoid algebraic structure, which extends
Semigroupwith an identity element (empty).A Monoid satisfies two additional laws on top of Semigroup's associativity:
a.concat(empty) === aempty.concat(a) === aWhat's included
Monoid<T>interface extendingSemigroup<T>MonoidConstructor<T>type providing theempty()factorySumMonoid— identity isSum(0)ProductMonoid— identity isProduct(1)StrMonoid— identity isStr('')concatAll<T>(monoid, values)— folds an array using the monoid's identity and concat, enabling safe reduction of collections (including empty ones)Why
Having a Monoid enables folding/reducing collections without requiring a non-empty input — the identity element serves as the base case. This is a fundamental building block for many FP patterns.