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Free monad

As explained in Functional Programming in Scala, Second Edition

A free monad is a monad generated from an underlying set of operations, representing computations as composable syntax whose interpretation is supplied separately.

A free monad turns primitive operations from an algebra into a composable value representing a program. The program can be stored, passed to functions, or created dynamically; a separate interpreter later gives it meaning. section 13.10 section 13.0

Free[F, A] is a recursive structure containing a value of type A beneath zero or more layers of F. Return and FlatMap generate the monad, while flatMap adds further layers and F defines the permitted interaction protocol. section 13.4.1

Use the structure in several related ways:

  • Sequence primitive operations from an algebra into a program value. section 13.10
  • Interpret a completed program into a target monad, including a specialized trampolined interpreter for Free[Function0, A]. section 13.4.1
  • Combine free monads from different algebras into a unioned algebra, such as file and console operations. section 13.10
enum Free[F[_], A]:
  ...
 
  def run(using F: Monad[F]): F[A] = ???
 
  @annotation.tailrec
  final def step: Free[F, A] = ???

Inspect the Free definition’s generic run method and tail-recursive step operation. section 13.4.1

How Functional Programming in Scala, Second Edition covers it

How deep it goes
Defines recursive structure, monadic construction, trampolined execution, and generic interpretation without detailing a complete implementation.
Examples
Uses Free[F, A], Return and FlatMap, runTrampoline, generic run, and combined Files and Console algebras.
What it assumes
Assumes monads and algebraic data types while teaching how their constructors generate Free and constrain interactions through F.
What you can do after
Builds Free monad operations and interpreters, including a specialized tail-recursive interpreter and a generic interpreter given Monad[F].
How it connects
Connects monads, algebraic data types, trampolining, interpreters, IO, embedded domain-specific languages, and capability traits.

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This explainer was generated by Manning's knowledge graph from the text of Functional Programming in Scala, Second Edition. The section links point to the parts of the book it draws on.