inj (empty) → 1.0

raw patch · 3 files changed

+76/−0 lines, 3 filessetup-changed

Files

• Inj.hs +60/−0
• Setup.hs +2/−0
• inj.cabal +14/−0

@@ -0,0 +1,60 @@+{- |++An injection is a function that never maps distinct elements of the domain to+the same element of the codomain. For example, @(\\x -> x + 1)@ is an injection,+but @(\\x -> min x 0)@ is not.++Injections can be used to construct nested structures from singleton elements.++-}++{-# LANGUAGE NoImplicitPrelude,+             DefaultSignatures,+             MultiParamTypeClasses,+             TypeFamilies #-}++module Inj (Inj(..)) where++-- | Inject @p@ into @a@.+--+-- By convention, the instances of @Inj@ never match on @p@ and always match on+-- @a@. This guarantees that the users will not encounter overlapping instances.+class Inj p a where+  -- | Inject @p@ into @a@.+  inj :: p -> a++  default inj :: (p ~ a) => p -> a+  inj = \x -> x++-- @instance Inj a a@ is tempting to define. Unfortunately, it does not work+-- as well as one might hope. For instance, consider a type like this:+--+-- @+-- data Shape x = Circle | Rectangle | Other x+--   deriving Functor+-- @+--+-- If we want to write @inj Circle@, then we get an ambiguity error:+--+-- @+--    * Could not deduce (Inj (Shape x0) (Shape x))+--        arising from a use of `inj'+-- @+--+-- That is because @Inj a a@ for @Shape x@ is equivalent to+--+-- @instance Inj (Shape x) (Shape x)@+--+-- but for good type inference we want+--+-- @instance (x1 ~ x2) => Inj (Shape x1) (Shape x2)@+--+-- Furthermore, we can take advantage of @Shape@ being a functor and+-- define an even better instance:+--+-- @+-- instance Inj a b => Inj (Shape a) (Shape b) where+--   inj = fmap inj+-- @+--+-- Unfortunately, both of the better instances are overlapping with @Inj a a@.

@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain

@@ -0,0 +1,14 @@+name:                inj+version:             1.0+synopsis:            A class for injective (one-to-one) functions+license:             PublicDomain+author:              Vladislav Zavialov+maintainer:          Vladislav Zavialov <vlad.z.4096@gmail.com>+category:            Data+build-type:          Simple+cabal-version:       >=1.10++library+  exposed-modules:     Inj+  default-language:    Haskell2010+  ghc-options:         -Wall