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Planet Haskell

An exploration of the monus algebraic structure and its application to heap-based algorithms in Haskell. A monus is an ordered monoid supporting partial subtraction, useful for representing heap weights as differences rather than absolute values. The post covers pairing heap implementation using monuses, derives an efficient Phases applicative transformer ordered by arbitrary keys, addresses stability issues via a Key monus combining ordering with positional offsets, and discusses a monadic heap variant. The key insight is that storing weight differences instead of absolute weights enables O(1) global weight updates and enables type-safe heap invariants.

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