3mapFlatMapn

3mapFlatMapn is a conceptual operator in functional programming that extends the ideas of map and flatMap to three input monadic values. It takes a ternary function and three monadic containers, applying the function to the unwrapped values and flattening the results to a single monad. The name suggests a family of operators with three inputs (the leading 3) and a flattened, monadic result (the flatMap idea), with n indicating generalizability to more inputs in related variants.

Definition and signature

Let M be a common monad. If ma :: M A, mb :: M B, mc :: M C, and f :: A -> B -> C -> M D, then 3mapFlatMapn f ma mb mc is defined as ma.flatMap a => mb.flatMap b => mc.flatMap c => f a b c. In languages with lambda syntax, this is expressed as:

ma.flatMap(a => mb.flatMap(b => mc.flatMap(c => f(a, b, c))))

The operation yields a value of type M D. If any input is empty or fails, the result is empty, consistent with monadic laws.

Examples

Using the List monad, with ma = [1, 2], mb = [10, 20], mc = [100, 200], and f a b c = [a + b + c], 3mapFlatMapn f ma mb mc produces [111, 211, 121, 221, 131, 231, 141, 241].

Relation to similar constructs

3mapFlatMapn is related to monadic comprehensions, for-expressions, and join operations. It provides a structured way to combine three sources while preserving monadic effects, enabling multi-source queries and data processing pipelines in a purely functional style.

See also

map, flatMap, monad, list monad, Maybe/Option, monadic comprehension.

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