Data.PropertyList.Algebra

The internal "algebraic" interface for working with property-list-like things. The classes defined here are the basis for a very general system supporting transformations between many property-list representations, including both internal and external formats. The transformations are based on algebra and are very well-behaved mathematically. It is possible to "fuse" operations so that, for example, reading from XML and writing to a text plist can be done without creating any intermediate representations other than those used by the XML parser and the text renderer. Or, expressions using the "smart constructors" can be evaluated to directly synthesize XML-formatted plists, or the view-pattern destructors can be used to directly analyze them.

The interface defined in this module is very heavily influenced by category-theoretical constructions. In particular, F-algebras and F-coalgebras, initiality, and terminality. For those not familiar with these concepts, this will probably be quite incomprehensible. Sorry about that. The basic idea, though, is the use of the PropertyListS type as a sort of a central junction point through which all conversions between property-list-like types and property-list-item types are routed. The classes defined here are chosen to minimize the inderdependence of these types and hence maximize the flexibility of the system as a whole.

More simply stated, these weird math thingies make the design as flexible as possible (in a well-defined and useful sense).

The signature type (PropertyListS)

data PropertyListS a

The signature of the base property list algebra. This algebra is "lifted" in various ways to support several different but similar representations of property lists as well as projections and injections. All the different representations are connected through this signature.

For example, PropertyList is a fixed-point of this signature - that is, a recursive version where a is instantiated as PropertyListS a. That gives the "expected" structure of a basic property list. It is both initial and terminal for this signature in its 'un-lifted' form - which is to say, any other type with an algebra for this signature (such as an XML representation) can be made from a PropertyList, and any type with a coalgebra for this signature (such as a String, an Integer, etc.) can be converted directly to a PropertyList. This also means that any transformation or series of transformations involving the PropertyList type can be fused to "skip" generating intermediate property lists, although there are currently no rewrite rules set up to do so.

Similarly, PartialPropertyList is a fixed point of an arbitrarily- augmented version of this signature (also known as the free monad generated by the signature). Depending on its type parameter, PartialPropertyList can be terminal among many simple extensions to the signature. Thus many types with a coalgebra for an extension of this signature (such as XML given an appropriate tree destructor, or the PropertyList type itself) can be trivially converted to a PartialPropertyList.

Constructors

PLArray [a]

PLData ByteString

PLDate UTCTime

PLDict (Map String a)

PLReal Double

PLInt Integer

PLString String

PLBool Bool

Instances

Functor PropertyListS

Foldable PropertyListS

Traversable PropertyListS

Eq a => Eq (PropertyListS a)

Ord a => Ord (PropertyListS a)

Read a => Read (PropertyListS a)

Show a => Show (PropertyListS a)

foldPropertyListS :: ([a] -> t) -> (ByteString -> t) -> (UTCTime -> t) -> (Map String a -> t) -> (Double -> t) -> (Integer -> t) -> (String -> t) -> (Bool -> t) -> PropertyListS a -> t

Construct a basic non-recursive algebra of property list items. This is equivalent to pattern matching on PropertyListS.

The algebra and coalgebra classes

class Functor f => PListAlgebra f a where

A class for types which can be constructed algebraically from the PropertyListS signature (lifted by f) - in other words, types which you can put property lists into.

The f-lifting is provided to support extending the algebra. The algebra is defined in a class rather than passing around functions because most of the time for any given type there is only one algebra you care about.

Typically a renderer for an output format will be implemented as a type with an instance PListAlgebra Identity. For example, the XML output system is implemented in the instance PListAlgebra Identity Plist.

Methods

plistAlgebra :: f (PropertyListS a) -> a

Build a value of type a from a piece of a property list (using the PropertyListS signature augmented by the "lifting" f).

Instances

PListAlgebra Identity Element

PListAlgebra Identity PropertyList

PListAlgebra Maybe (PartialPropertyList ())

PListAlgebra Identity (BPListRecords Rel)

PListAlgebra Identity (PartialPropertyList a)

PListCoalgebra Identity a => PListAlgebra (Either a) PropertyList

PListAlgebra (Either Element) Element

PListAlgebra (Either UnparsedXmlPlistItem) Element

PListAlgebra (Either a) (PartialPropertyList a)

class (PListAlgebra f a, PListCoalgebra f a) => InitialPList f a | f -> a, a -> f where

An identification of the fact that the type a has an initial plist algebra (under some lifting f). Functional dependencies are in use - for any type, only one of its initial algebras (if multiple apply, which they may because the same type may be initial for multiple distinct liftings) can be chosen, and for any lifting only one type's algebra may be chosen. This is to make types decidable in the not-so-uncommon case where the lifting is encapsulated (eg, any time foldPList is partially applied - for example, see the signature of fromPlist).

For cases where the lifting either needs to be chosen or needs to be transformed to another lifting, fromPlistWith is provided. It is based on the same definition as the default implementation of foldPList but also inserts a chosen transformation of the lifting.

Question for self: Is the PListCoalgebra context reasonable here? Some rough calculations suggest that in the presence of fixed point type operators, it is possible to construct a PListCoalgebra for any InitialPList, which essentially is defined as pattern matching. So, I'm not totally sure but I think this is reasonable - at least, for finitary signatures, which we're using as long as f doesn't go crazy.

Minimal complete definition

Nothing

Methods

foldPList :: (f (PropertyListS t) -> t) -> a -> t

Using some other plist algebra, compute the unique transformation from the type a to that algebra.

The default implementation is:

foldPList f = go
   where
       go = f . fmap (fmap go) . plistCoalgebra

Instances

InitialPList Identity PropertyList

InitialPList (Either a) (PartialPropertyList a)

fromPlist :: (InitialPList f pl, PListAlgebra f t) => pl -> t

Convert from an initial plist to any other plist with the same lifted algebra.

fromPlistWith :: (PListCoalgebra f pl, PListAlgebra g t) => (f (PropertyListS t) -> g (PropertyListS t)) -> pl -> t

class Functor f => PListCoalgebra f a where

A class for types which can be dissected (pattern-matched) into the PropertyListS signature (lifted by f) - in other words, types which you can take property lists out of.

Typically a property list parser will be implemented as a type with a PListCoalgebra instance, where f is either Identity in the case where the parser guarantees to return a fully well-formed property list (assuming it returns anything at all) or Either something when the parser only guarantees that the structure is sound (but that some elements might be defective, in which case a value of type something would be substituted). The XML parser, for example, is based on the latter approach, where something is UnparsedPlistItem.

Methods

plistCoalgebra :: a -> f (PropertyListS a)

Analyze a value of type a by matching it to a constructor in the (lifted by f) PropertyListS signature.

Instances

Applicative f => PListCoalgebra f PropertyList

PListCoalgebra Maybe Element

PListCoalgebra Maybe (BPListRecords Abs)

PListCoalgebra Maybe (PartialPropertyList a)

PListCoalgebra (Either UnparsedXmlPlistItem) Element

PListCoalgebra (Either a) (PartialPropertyList a)

PListCoalgebra (Either UnparsedBPListRecord) (BPListRecords Abs)

class (PListCoalgebra f a, PListAlgebra f a) => TerminalPList f a | f -> a, a -> f where

Chosen terminal coalgebra for the given lifting, and chosen lifting for the given type. See also InitialPList.

Minimal complete definition

Nothing

Methods

unfoldPList :: (t -> f (PropertyListS t)) -> t -> a

Given some coalgebra for the chosen lifted plist signature, compute the unique extraction/unfolding of that coalgebra into the type a.

The default implementation is:

unfoldPList f = go
    where
        go = plistAlgebra . fmap (fmap go) . f

Instances

TerminalPList Identity PropertyList

TerminalPList (Either a) (PartialPropertyList a)

toPlist :: (PListCoalgebra f t, TerminalPList f pl) => t -> pl

Convert from any plist-like thing to a plist which is terminal for a some lifted algebra.

toPlistWith :: (PListCoalgebra f t, PListAlgebra g pl) => (f (PropertyListS t) -> g (PropertyListS t)) -> t -> pl

"Smart" constructors for any PListAlgebra.

plArray :: PListAlgebra Identity a => [a] -> a

plData :: PListAlgebra Identity a => ByteString -> a

plDate :: PListAlgebra Identity a => UTCTime -> a

plDict :: PListAlgebra Identity a => Map String a -> a

plReal :: PListAlgebra Identity a => Double -> a

plInt :: PListAlgebra Identity a => Integer -> a

plString :: PListAlgebra Identity a => String -> a

plBool :: PListAlgebra Identity a => Bool -> a

"View pattern" destructors for any PListCoalgebra.

fromPlArray :: PListCoalgebra Maybe a => a -> Maybe [a]

fromPlData :: PListCoalgebra Maybe a => a -> Maybe ByteString

fromPlDate :: PListCoalgebra Maybe a => a -> Maybe UTCTime

fromPlDict :: PListCoalgebra Maybe a => a -> Maybe (Map String a)

fromPlReal :: PListCoalgebra Maybe a => a -> Maybe Double

fromPlInt :: PListCoalgebra Maybe a => a -> Maybe Integer

fromPlString :: PListCoalgebra Maybe a => a -> Maybe String

fromPlBool :: PListCoalgebra Maybe a => a -> Maybe Bool