Lens.Family.Total

This module lets you exhaustively pattern match on types using Lenses, Traversals, or Prisms.

Here's an example use of this library:

 import Lens.Family.Total
 import Lens.Family.Stock

 total :: Either Char Int -> String       -- Same as:
 total = _case                            -- total = \case
     & on _Left  (\c -> replicate 3  c )  --     Left  c -> replicate 3 c
     & on _Right (\n -> replicate n '!')  --     Right n -> replicate n '!'

Our total function pattern matches exhaustively on the Either type using the _Left and _Right prisms:

>>> total (Left 'X')
"XXX"
>>> total (Right 2)
"!!"

The types ensure that the above function is total. For example, if you omit the _Right branch:

partial :: Either Char Int -> String
partial = _case
    & on _Left  (\c -> replicate 3  c )

... then you will get the following type error:

No instance for (Empty Int) arising from a use of ‘_case’
In the first argument of ‘(&)’, namely ‘_case’
In the expression: _case & on _Left (\ c -> replicate 3 c)
In an equation for ‘partial’:
    partial = _case & on _Left (\ c -> replicate 3 c)

That type error means that you didn't pattern match on the branch with the Int.

You can also implement exhaustive pattern matching for your own data types with Traversals or Prisms. However, this only works if you have one type variable for each branch of your type:

 {-# LANGUAGE DeriveGeneric   #-}
 {-# LANGUAGE TemplateHaskell #-}

 import Control.Lens.TH
 import GHC.Generics (Generic)
 import Lens.Family.Total

 data Example a b c = C1 a | C2 b | C3 c deriving (Generic)

 makePrisms ''Example

 instance (Empty a, Empty b, Empty c) => Empty (Example a b c)

 example :: Example String Char Int -> String  -- Same as:
 example = _case                               -- example = \case
     & on _C1 (\s -> s              )          --     C1 s -> s
     & on _C2 (\c -> replicate 3  c )          --     C2 c -> replicate 3  c
     & on _C3 (\n -> replicate n '!')          --     C3 n -> replicate n '!'

There is no way to prove that the pattern match is exhaustive unless there is a type parameter for every branch. This is because each successive pattern match Voids out that branch's type parameter to prove that the branch no longer needs to be handled. _case just verifies that all type parameters are Void.

You can still write an inexhaustive pattern match so long as you provide a default:

example :: Example Int String Float -> String
example = _default "default"
    & on _C2 (\s -> s)

You can even pattern match using Lenses, too:

example :: (Int, Char) -> String     -- Same as:
example = _case                      -- example = \case
    & on _1 (\n -> replicate n '1')  --     (n, _) -> replicate n '1'

... and of course the identity lens (id) works, too:

example :: (Int, Char) -> String        -- Same as:
example = _case                         -- example = \case
    & on id (\(n, c) -> replicate n c)  --     (n, c) -> replicate n c

Documentation

class Empty a where

A type class for uninhabited types

Minimal complete definition

Nothing

Methods

impossible :: a -> x

Instances

Empty Void

(Empty a, Empty b) => Empty (Either a b)

Empty a => Empty (a, b)

_case :: Empty a => a -> x

Synonym for impossible, used to check if a pattern match is exhaustive

_default :: x -> a -> x

Synonym for const, used to provide a default if a pattern match is inexhaustive

on :: ((a -> Either a Void) -> i -> Either l r) -> (l -> o) -> (r -> o) -> i -> o

Pattern match on a Traversal

(&) :: a -> (a -> b) -> b infixl 1

Operator for post-fix function application

Re-exports

data Void :: *

A logically uninhabited data type.

Instances

Eq Void

Data Void

Ord Void

Read Void

Reading a Void value is always a parse error, considering Void as a data type with no constructors.

Show Void

Ix Void

Generic Void

Exception Void

Hashable Void

Semigroup Void

Empty Void

Typeable * Void

type Rep Void = D1 D1Void (C1 C1_0Void (S1 NoSelector (Rec0 Void)))