monad: Monad Operators and Generics

In monad: Operators and Generics for Monads

Monad Operators and Generics

Description

Classes implementing methods for these S7 generics are called monads. fmap() should be implemented such that the functor laws hold. bind() or join() should be implemented such that the monad laws hold. ⁠%>>%⁠ is the fmap() pipe operator, and ⁠%>-%⁠ is the bind() pipe operator. Operator usage is in the form m %>>% f(...).

Usage

lhs %>>% rhs

lhs %>-% rhs

fmap(m, f, ...)

bind(m, f, ...)

join(m)

Arguments

m, lhs	A monadic object.
f, rhs	A function. For bind(), it should return a monadic object.
...	Additional arguments passed to f.

Value

A monadic object.

Details

Monads are containers for values. fmap() transforms the contained value with a function. bind() transforms the contained value with a function that returns a monadic object. join() takes a monad whose contained value is another monad, and combines them into a new monadic object. It's used to unwrap a layer of monadic structure. Implementing classes typically embed some form of control flow or state management in bind() or join().

There's a default implementation for join() if you provide bind(), and there's a default implementation for bind() if you provide join() and fmap(). For performance reasons you may wish to implement both regardless.

Operators

The pipe operators expect a monadic object as lhs and a function or a call expression as rhs. A call in rhs is treated as partial application of the function f. The pipe expression is transformed into a call to the corresponding monad generic with any call arguments in rhs passed as additional arguments to f in the generic. For example, m %>>% f(x) is equivalent to fmap(m, f, x) and m %>-% f(x) is equivalent to bind(m, f, x).

Trivia

A class that only implements fmap() is called a functor.

See Also

The monad laws and functor laws that implementations should satisfy.

List and Maybe for examples of implementing classes.

Examples

# We demonstrate by implementing a simple Either monad.
library(S7)

# Start by defining constructors of the Left and Right variants. Conventionally
# a Right variant signifies success and Left an error condition with a context.
left <- function(x) structure(list(value = x), class = c("left", "either"))
right <- function(x) structure(list(value = x), class = c("right", "either"))

# Implement fmap() and bind() methods to gain access to monad operators.
class_either <- new_S3_class("either")

method(fmap, class_either) <- function(m, f, ...) {
  if (inherits(m, "left")) m else right(f(m$value))
}

method(bind, class_either) <- function(m, f, ...) {
  if (inherits(m, "left")) m else f(m$value)
}

# Use with your function that handles errors by returning a monadic value.
mlog <- function(x) {
  if (x > 0) right(log(x)) else left("`x` must be strictly positive.")
}

# fmap() modifies the contained value with a regular function.
mlog(2) %>>% \(x) x + 1
mlog(0) %>>% \(x) x + 1

# bind() modifies the contained value with a function that returns an Either.
mlog(2) %>-% mlog()
mlog(0) %>-% mlog()

monad documentation built on Oct. 28, 2024, 5:07 p.m.