NetOptics

This is a prototype optics library for .NET in F# based on an approach that does not require (an encoding of) higher-kinded polymorphism or ad-hoc polymorphism and can also be implemented and used in C# (in which the initial work was done) and other languages with similar features (first-class functions, rank-1 polymorphism, mutable objects, ability to create a default value of any type).

NOTE: I have no plans to productize this as a proper library.

Overview

Please study the NetOptics.Optic.fsi signature.

Features:

• Simple polymorphic types
• Optics are just functions and can be composed with the standard function composition operator <<
• Isomorphisms (or adapters) are invertible
• Lenses
• Prisms
• Folds
• Traversals
• Ability to remove focuses of an optic

Not supported:

• Applicative traverse over focuses of an optic

On type safety

The approach in this prototype is mostly type-safe. However, the number of focuses or the class of an optic is not tracked in the types.

For example, the view operation requires the given optic to have at least one focus on the target data structure. If there are no focuses, view will raise an exception. Likewise, the invertI combinator and the review operation require an (explicitly constructed) isomorphism or composition thereof. If the given optic is not an explicitly constructed isomorphism, invertI and review will raise an exception.

NOTE: I have not explored a design that would use phantom types to track all the details required to avoid exceptions in the course of prototyping this library, but based on previous experience I'm confident that it can be done.

On performance

This approach admits an implementation that does not perform large numbers of allocations when an optic is used. This means that performance should be good. However, limited inlining in .NET and F# will put a cap on performance.

On the implementation

Here I will describe the internal implementation briefly for the interest of people who might want to implement this approach in their language. This description is just a hint. Read the code for full details.

The signature of this library reveals that the optic type t<'S, 'F, 'G, 'T> is a function type, but does not expose the implementation of the Pipe<'S, 'T> type:

type Pipe<'S, 'T>

type t<'S, 'F, 'G, 'T> = Pipe<'F, 'G> -> Pipe<'S, 'T>

Here is how the Pipe<'S, 'T> type is defined internally:

type [<Struct>] Context =
  val mutable Hit: bool
  val mutable Over: bool
  val mutable Index: int
  val mutable View: obj

type D<'S, 'T> = delegate of byref<Context> * 'S -> 'T

type Pipe<'S, 'T> = P of D<'S, 'T> * inverted: bool

Now we can see that an optic is a function that takes a mapping function with a mutable context to a another mapping function with a mutable context.

NOTE: The D<'S, 'T> type is an explicit delegate type and is required in .NET to use byref<_> arguments. The use of byref<_> is an optimization to avoid a heap allocation for the context. In other languages (and also in .NET) you could also just use a function type taking a mutable context object (with the cost of an extra allocation in .NET).

The inverted flag of the Pipe<'S, 'T> type is used to track whether an isomorphism is being inverted by use of review. Isomorphisms propagate the flag during construction, but other optics set it to false. This allows review to check that inversion works and allows an isomorphism to avoid performing potentially illegal operations on invalid data. During an inverse operation the input data given to the pipe is undefined (an Unchecked.defaultof<_>).

The mutable context is used by operations on optics, like view and over, to communicate with the optic being operated upon and to determine the result of the operation. The context is created just before the optic is used and does not escape the use. This means that outside of the internal mechanism one cannot observe the use of mutation and operations can be referentially transparent. In fact, the use of a mutable context is merely an optimization. If we would instead define Pipe<'S, 'T> essentially as

type Pipe<'S, 'T> = Context * 'S -> Context * 'T

we could implement optics with same behaviour without using any mutation even in a pure language like Haskell. Purity is an extensional property.

The fields of the context are used roughly as follows:

• Over specifies whether or not an over or a view style operation is being performed. An over style operation must construct a return value, while a view style operation can avoid the construction and return anything that fits the type (like an Unchecked.defaultof<_>).

• Hit is used differently depending on Over:

  • A view style operation is stopped after Hit is set to true. No value can be returned when a view style operation ends with Hit = false.

  • During an over style operation, focuses that are Hit are removed. No value can be returned when an over style operation ends with Hit = true.

• View is an untyped placeholder for the result of simple view operations and is an optimization to avoid an allocation.

• Index is used by some of the operations and is an optimization to avoid an allocation.