Copyright	(C) 2013 Richard Eisenberg
License	BSD-style (see LICENSE)
Maintainer	Richard Eisenberg (eir@cis.upenn.edu)
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Singletons.Decide

Contents

The SDecide class
Supporting definitions

Description

Defines the class SDecide, allowing for decidable equality over singletons.

Synopsis

The SDecide class

class (kparam ~ KProxy) => SDecide kparam where Source

Members of the SDecide "kind" class support decidable equality. Instances of this class are generated alongside singleton definitions for datatypes that derive an Eq instance.

Methods

(%~) :: forall a b. Sing a -> Sing b -> Decision (a :~: b) Source

Compute a proof or disproof of equality, given two singletons.

Instances

SDecide Bool (KProxy Bool)
SDecide Ordering (KProxy Ordering)
SDecide * (KProxy *)
SDecide Nat (KProxy Nat)
SDecide Symbol (KProxy Symbol)
SDecide () (KProxy ())
SDecide a0 (KProxy a0) => SDecide [a] (KProxy [a])
SDecide a0 (KProxy a0) => SDecide (Maybe a) (KProxy (Maybe a))
(SDecide a0 (KProxy a0), SDecide b0 (KProxy b0)) => SDecide (Either a b) (KProxy (Either a b))
(SDecide a0 (KProxy a0), SDecide b0 (KProxy b0)) => SDecide ((,) a b) (KProxy ((,) a b))
(SDecide a0 (KProxy a0), SDecide b0 (KProxy b0), SDecide c0 (KProxy c0)) => SDecide ((,,) a b c) (KProxy ((,,) a b c))
(SDecide a0 (KProxy a0), SDecide b0 (KProxy b0), SDecide c0 (KProxy c0), SDecide d0 (KProxy d0)) => SDecide ((,,,) a b c d) (KProxy ((,,,) a b c d))
(SDecide a0 (KProxy a0), SDecide b0 (KProxy b0), SDecide c0 (KProxy c0), SDecide d0 (KProxy d0), SDecide e0 (KProxy e0)) => SDecide ((,,,,) a b c d e) (KProxy ((,,,,) a b c d e))
(SDecide a0 (KProxy a0), SDecide b0 (KProxy b0), SDecide c0 (KProxy c0), SDecide d0 (KProxy d0), SDecide e0 (KProxy e0), SDecide f0 (KProxy f0)) => SDecide ((,,,,,) a b c d e f) (KProxy ((,,,,,) a b c d e f))
(SDecide a0 (KProxy a0), SDecide b0 (KProxy b0), SDecide c0 (KProxy c0), SDecide d0 (KProxy d0), SDecide e0 (KProxy e0), SDecide f0 (KProxy f0), SDecide g0 (KProxy g0)) => SDecide ((,,,,,,) a b c d e f g) (KProxy ((,,,,,,) a b c d e f g))

Supporting definitions

data a :~: b :: k -> k -> * where infix 4

Propositional equality. If a :~: b is inhabited by some terminating value, then the type a is the same as the type b. To use this equality in practice, pattern-match on the a :~: b to get out the Refl constructor; in the body of the pattern-match, the compiler knows that a ~ b.

Since: 4.7.0.0

Constructors

Refl :: (:~:) k a1 a1

Instances

TestCoercion k ((:~:) k a)
TestEquality k ((:~:) k a)
Typeable (k -> k -> *) ((:~:) k)
(~) k a b => Bounded ((:~:) k a b)
(~) k a b => Enum ((:~:) k a b)
Eq ((:~:) k a b)
((~) * a b, Data a) => Data ((:~:) * a b)
Ord ((:~:) k a b)
(~) k a b => Read ((:~:) k a b)
Show ((:~:) k a b)

data Void Source

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
Typeable * Void
type Rep Void

type Refuted a = a -> Void Source

Because we can never create a value of type Void, a function that type-checks at a -> Void shows that objects of type a can never exist. Thus, we say that a is Refuted

data Decision a Source

A Decision about a type a is either a proof of existence or a proof that a cannot exist.

Constructors

Proved a	Witness for `a`
Disproved (Refuted a)	Proof that no `a` exists