singletons 0.9.0
This is the README file for the singletons library. This file contains all the
documentation for the definitions and functions in the library.
The singletons library was written by Richard Eisenberg, eir@cis.upenn.edu.
See also Dependently typed programming with singletons, available
here.
Purpose of the singletons library
The library contains a definition of singleton types, which allow
programmers to use dependently typed techniques to enforce rich constraints
among the types in their programs. See the paper cited above for a
more thorough introduction.
Compatibility
The singletons library requires GHC version 7.6.3 or greater.
Any code that uses the singleton generation primitives will also need
to enable a long list of GHC extensions. This list includes, but
is not necessarily limited to, the following:
ScopedTypeVariables
(absolutely required)
TemplateHaskell
TypeFamilies
GADTs
KindSignatures
DataKinds
PolyKinds
TypeOperators
FlexibleContexts
RankNTypes
UndecidableInstances
FlexibleInstances
EmptyCase
(for GHC 7.8)
Functions to generate singletons
The toplevel functions used to generate singletons are documented in the
Data.Singletons.TH
module. The most common case is just calling singletons
,
which I'll describe here:
singletons :: Q [Dec] > Q [Dec]
Generates singletons from the definitions given. Because singleton generation
requires promotion, this also promotes all of the definitions given to the
type level.
To use:
$(singletons [d
data Nat = Zero  Succ Nat
pred :: Nat > Nat
pred Zero = Zero
pred (Succ n) = n
])
Definitions used to support singletons
Please refer to the paper cited above for a more indepth explanation of these
definitions. Many of the definitions were developed in tandem with Iavor Diatchki.
data family Sing (a :: k)
The data family of singleton types. A new instance of this data family is
generated for every new singleton type.
class SingI (a :: k) where
sing :: Sing a
A class used to pass singleton values implicitly. The sing
method produces
an explicit singleton value.
data SomeSing (kproxy :: KProxy k) where
SomeSing :: Sing (a :: k) > SomeSing ('KProxy :: KProxy k)
The SomeSing
type wraps up an existentiallyquantified singleton. Note that
the type parameter a
does not appear in the SomeSing
type. Thus, this type
can be used when you have a singleton, but you don't know at compile time what
it will be. SomeSing ('KProxy :: KProxy Thing)
is isomorphic to Thing
.
class (kparam ~ 'KProxy) => SingKind (kparam :: KProxy k) where
type DemoteRep kparam :: *
fromSing :: Sing (a :: k) > DemoteRep kparam
toSing :: DemoteRep kparam > SomeSing kparam
This class is used to convert a singleton value back to a value in the
original, unrefined ADT. The fromSing
method converts, say, a
singleton Nat
back to an ordinary Nat
. The toSing
method produces
an existentiallyquantified singleton, wrapped up in a SomeSing
.
The DemoteRep
associated
kindindexed type family maps a proxy of the kind Nat
back to the type Nat
.
data SingInstance (a :: k) where
SingInstance :: SingI a => SingInstance a
singInstance :: Sing a > SingInstance a
Sometimes you have an explicit singleton (a Sing
) where you need an implicit
one (a dictionary for SingI
). The SingInstance
type simply wraps a SingI
dictionary, and the singInstance
function produces this dictionary from an
explicit singleton. The singInstance
function runs in constant time, using
a little magic.
Equality classes
There are two different notions of equality applicable to singletons: Boolean
equality and propositional equality.

Boolean equality is implemented in the type family (:==)
(which is actually
a synonym for the type family (==)
from Data.Type.Equality
) and the class
SEq
. See the Data.Singletons.Eq
module for more information.

Propositional equality is implemented through the constraint (~)
, the type
(:~:)
, and the class SDecide
. See modules Data.Type.Equality
and
Data.Singletons.Decide
for more information.
Which one do you need? That depends on your application. Boolean equality has
the advantage that your program can take action when two types do not equal,
while propositional equality has the advantage that GHC can use the equality
of types during type inference.
Instances of both SEq
and SDecide
are generated when singletons
is called
on a datatype that has deriving Eq
. You can also generate these instances
directly through functions exported from Data.Singletons.TH
.
Predefined singletons
The singletons library defines a number of singleton types and functions
by default:
Bool
Maybe
Either
Ordering
()
 tuples up to length 7
 lists
These are all available through Data.Singletons.Prelude
. Functions that
operate on these singletons are available from modules such as Data.Singletons.Bool
and Data.Singletons.Maybe
.
On names
The singletons library has to produce new names for the new constructs it
generates. Here are some examples showing how this is done:
original datatype: Nat
promoted kind: Nat
singleton type: SNat
(which is really a synonym for Sing
)
original datatype: :/\:
promoted kind: :/\:
singleton type: :%/\:
original constructor: Zero
promoted type: 'Zero
(you can use Zero
when unambiguous)
singleton constructor: SZero
original constructor: :+:
promoted type: ':+:
singleton constructor: :%+:
original value: pred
promoted type: Pred
singleton value: sPred
original value: +
promoted type: :+
singleton value: %:+
Special names
There are some special cases:
original datatype: []
singleton type: SList
original constructor: []
singleton constructor: SNil
original constructor: :
singleton constructor: SCons
original datatype: (,)
singleton type: STuple2
original constructor: (,)
singleton constructor: STuple2
All tuples (including the 0tuple, unit) are treated similarly.
original value: undefined
promoted type: Any
singleton value: undefined
Supported Haskell constructs
The following constructs are fully supported:
 variables
 tuples
 constructors
 if statements
 infix expressions
 !, ~, and _ patterns
 aliased patterns (except at toplevel)
 lists
 (+) sections
 (x +) sections
 undefined
 error
 deriving Eq
 class constraints
 literals (for
Nat
and Symbol
)
The following constructs will be coming soon:
 unboxed tuples
 records
 scoped type variables
 overlapping patterns
 pattern guards
 (+ x) sections
 case
 let
 list comprehensions
 lambda expressions
 do
 arithmetic sequences
As described briefly in the paper, the singletons generation mechanism does not
currently work for higherorder datatypes (though higherorder functions are
just peachy). So, if you have a declaration such as
data Foo = Bar (Bool > Maybe Bool)
its singleton will not work correctly. It turns out that getting this to work
requires fairly thorough changes to the whole singleton generation scheme.
Please shout (to eir@cis.upenn.edu) if you have a compelling use case for this
and I can take a look at it. No promises, though.
Support for *
The builtin Haskell promotion mechanism does not yet have a full story around
the kind *
(the kind of types that have values). Ideally, promoting some form
of TypeRep
would yield *
, but the implementation of TypeRep would have to be
updated for this to really work out. In the meantime, users who wish to
experiment with this feature have two options:

The module Data.Singletons.TypeRepStar
has all the definitions possible for
making *
the promoted version of TypeRep
, as TypeRep
is currently implemented.
The singleton associated with TypeRep
has one constructor:
data instance Sing (a :: *) where
STypeRep :: Typeable a => Sing a
Thus, an implicit TypeRep
is stored in the singleton constructor. However,
any datatypes that store TypeRep
s will not generally work as expected; the
builtin promotion mechanism will not promote TypeRep
to *
.
 The module
Data.Singletons.CustomStar
allows the programmer to define a subset
of types with which to work. See the Haddock documentation for the function
singletonStar
for more info.
Changes from earlier versions
singletons 0.9 contains a bit of an API change from previous versions. Here is
a summary:

There are no more "smart" constructors. Those were necessary because each
singleton used to carry both explicit and implicit versions of any children
nodes. However, this leads to exponential overhead! Now, the magic (i.e., a
use of unsafeCoerce
) in singInstance
gets rid of the need for storing
implicit singletons. The smart constructors did some of the work of managing
the stored implicits, so they are no longer needed.

SingE
and SingRep
are gone. If you need to carry an implicit singleton,
use SingI
. Otherwise, you probably want SingKind
.

The Template Haskell functions are now exported from Data.Singletons.TH
.

The Prelude singletons are now exported from Data.Singletons.Prelude
.