Result (Either) Monad

Result, as a Monad, provides bind (Result.bind in F#), which enables robust error handling and control flow.

Example in F#

let safeDivide = fun x y -> if y = 0 then Error "div by zero" else Ok (x / y)
let result = Ok 100 |> Result.bind (fun x -> safeDivide x 2) |> Result.bind (fun x -> safeDivide x 0)
// result = Error "div by zero"

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Functor (map) vs Monad (bind): Capabilities and Limitations

• Functor’s map applies a function only if the value is Ok, leaving Error unchanged. It can transform the value inside Ok, but cannot change Ok to Error or vice versa. The success/failure state is preserved, so error propagation or early exit is not possible.
• Monad’s bind allows the function to return Ok or Error, enabling short-circuiting: if any step returns Error, subsequent computations are skipped. This allows for safe error propagation, early exit on failure, and composition of error-prone computations—capabilities not possible with map alone.

This distinction is fundamental: map is for value transformation only, while bind enables control over the computation’s flow and error handling.