3flatMapn

3flatMapn is a hypothetical higher-order operator described in functional programming discussions as a generalization of the flatMap pattern across three effectful values. It takes three monadic values, typically written as ma: M<A>, mb: M<B>, mc: M<C>, and a function f: (A, B, C) -> D, and produces a monadic value M<D>. In practical terms, it sequences three dependent computations in a single construct.

Semantically, 3flatMapn can be defined as a composition of nested flatMaps and a final map: 3flatMapn(ma, mb, mc, f) = ma.flatMap(a => mb.flatMap(b => mc.map(c => f(a, b, c)))). This structure ensures that the effects represented by ma, mb, and mc occur in order, and that the final result is produced by applying f to the extracted values. If f itself returns a monadic value, the pattern can be adjusted to accommodate that by using additional flatMaps as needed.

Usage and implications: 3flatMapn is primarily a sequencing tool. It is useful when the results of the first two computations must be available before the third begins, or when you want to preserve tight control over the order of effects. It differs from parallel or applicative patterns like mapN, which may allow independent evaluation of the inputs and can be less strict about order. In languages that support concise monadic comprehensions, writers often achieve the same effect with for-bindings or do-notation, but 3flatMapn highlights the explicit chaining of three dependent computations.

Notes: 3flatMapn is not a standard, widely implemented operator in mainstream libraries, but it serves as a conceptual bridge between flatMap chaining and multi-argument composition. Related concepts include flatMap, map, and mapN.