-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/

-- | Abstractions for animation
--   
--   Active abstraction for animated things with finite start and
--   end times.
@package active
@version 0.1.0.9

-- | Inspired by the work of Kevin Matlage and Andy Gill (Every
--   Animation Should Have a Beginning, a Middle, and an End, Trends
--   in Functional Programming, 2010.
--   http://ittc.ku.edu/csdl/fpg/node/46), this module defines a
--   simple abstraction for working with time-varying values. A value of
--   type Active a is either a constant value of type a,
--   or a time-varying value of type a (i.e. a function
--   from time to a) with specific start and end times. Since
--   active values have start and end times, they can be aligned,
--   sequenced, stretched, or reversed.
--   
--   In a sense, this is sort of like a stripped-down version of functional
--   reactive programming (FRP), without the reactivity.
--   
--   The original motivating use for this library is to support making
--   animations with the diagrams framework
--   (http://projects.haskell.org/diagrams), but the hope is that it
--   may find more general utility.
--   
--   There are two basic ways to create an Active value. The first
--   is to use mkActive to create one directly, by specifying a
--   start and end time and a function of time. More indirectly, one can
--   use the Applicative instance together with the unit interval
--   ui, which takes on values from the unit interval from time 0 to
--   time 1, or interval, which creates an active over an arbitrary
--   interval.
--   
--   For example, to create a value of type Active Double which
--   represents one period of a sine wave starting at time 0 and ending at
--   time 1, we could write
--   
--   
--   mkActive 0 1 (\t -> sin (fromTime t * tau))
--   
--   
--   or
--   
--   
--   (sin . (*tau)) <$> ui
--   
--   
--   pure can also be used to create Active values which
--   are constant and have no start or end time. For example,
--   
--   
--   mod <$> (floor <$> interval 0 100) <*> pure 7
--   
--   
--   cycles repeatedly through the numbers 0-6.
--   
--   Note that the "idiom bracket" notation supported by the SHE
--   preprocessor (http://personal.cis.strath.ac.uk/~conor/pub/she/,
--   http://hackage.haskell.org/package/she) can make for somewhat
--   more readable Applicative code. For example, the above example
--   can be rewritten using SHE as
--   
--   
--   {-# OPTIONS_GHC -F -pgmF she #-}
--   
--   ... (| mod (| floor (interval 0 100) |) ~7 |)
--   
--   
--   There are many functions for transforming and composing active values;
--   see the documentation below for more details.
module Data.Active

-- | An abstract type for representing points in time. Note that
--   literal numeric values may be used as Times, thanks to the
--   the Num and Fractional instances. toTime and
--   fromTime are also provided for convenience in converting
--   between Time and other numeric types.
data Time

-- | Convert any value of a Real type (including Int,
--   Integer, Rational, Float, and
--   Double) to a Time.
toTime :: Real a => a -> Time

-- | Convert a Time to a value of any Fractional type (such
--   as Rational, Float, or Double).
fromTime :: Fractional a => Time -> a

-- | An abstract type representing elapsed time between two points
--   in time. Note that durations can be negative. Literal numeric values
--   may be used as Durations thanks to the Num and
--   Fractional instances. toDuration and fromDuration
--   are also provided for convenience in converting between
--   Durations and other numeric types.
data Duration

-- | Convert any value of a Real type (including Int,
--   Integer, Rational, Float, and
--   Double) to a Duration.
toDuration :: Real a => a -> Duration

-- | Convert a Duration to any other Fractional type (such as
--   Rational, Float, or Double).
fromDuration :: Fractional a => Duration -> a

-- | An Era is a concrete span of time, that is, a pair of times
--   representing the start and end of the era. Eras form a
--   semigroup: the combination of two Eras is the smallest
--   Era which contains both. They do not form a Monoid,
--   since there is no Era which acts as the identity with respect
--   to this combining operation.
--   
--   Era is abstract. To construct Era values, use
--   mkEra; to deconstruct, use start and end.
data Era

-- | Create an Era by specifying start and end Times.
mkEra :: Time -> Time -> Era

-- | Get the start Time of an Era.
start :: Era -> Time

-- | Get the end Time of an Era.
end :: Era -> Time

-- | Compute the Duration of an Era.
duration :: Era -> Duration

-- | A Dynamic a can be thought of as an a value that
--   changes over the course of a particular Era. It's envisioned
--   that Dynamic will be mostly an internal implementation detail
--   and that Active will be most commonly used. But you never know
--   what uses people might find for things.
data Dynamic a
Dynamic :: Era -> (Time -> a) -> Dynamic a
era :: Dynamic a -> Era
runDynamic :: Dynamic a -> Time -> a

-- | Create a Dynamic from a start time, an end time, and a
--   time-varying value.
mkDynamic :: Time -> Time -> (Time -> a) -> Dynamic a

-- | Fold for Dynamic.
onDynamic :: (Time -> Time -> (Time -> a) -> b) -> Dynamic a -> b

-- | Shift a Dynamic value by a certain duration.
shiftDynamic :: Duration -> Dynamic a -> Dynamic a

-- | There are two types of Active values:
--   
--   
--   
- An Active can simply be a Dynamic, that is, a
--   time-varying value with start and end times.
--   
- An Active value can also be a constant: a single value,
--   constant across time, with no start and end times.
--   
--   
--   The addition of constant values enable Monoid and
--   Applicative instances for Active.
data Active a

-- | Create a dynamic Active from a start time, an end time, and a
--   time-varying value.
mkActive :: Time -> Time -> (Time -> a) -> Active a

-- | Create an Active value from a Dynamic.
fromDynamic :: Dynamic a -> Active a

-- | Test whether an Active value is constant.
isConstant :: Active a -> Bool

-- | Test whether an Active value is Dynamic.
isDynamic :: Active a -> Bool

-- | Fold for Actives. Process an 'Active a', given a function to
--   apply if it is a pure (constant) value, and a function to apply if it
--   is a Dynamic.
onActive :: (a -> b) -> (Dynamic a -> b) -> Active a -> b

-- | Modify an Active value using a case analysis to see whether it
--   is constant or dynamic.
modActive :: (a -> b) -> (Dynamic a -> Dynamic b) -> Active a -> Active b

-- | Interpret an Active value as a function from time.
runActive :: Active a -> (Time -> a)

-- | Get the Era of an Active value (or Nothing if it
--   is a constant/pure value).
activeEra :: Active a -> Maybe Era

-- | Set the era of an Active value. Note that this will change a
--   constant Active into a dynamic one which happens to have the
--   same value at all times.
setEra :: Era -> Active a -> Active a

-- | atTime t a is an active value with the same behavior as
--   a, shifted so that it starts at time t. If
--   a is constant it is returned unchanged.
atTime :: Time -> Active a -> Active a

-- | Get the value of an Active a at the beginning of its era.
activeStart :: Active a -> a

-- | Get the value of an Active a at the end of its era.
activeEnd :: Active a -> a

-- | ui represents the unit interval, which takes on the
--   value t at time t, and has as its era
--   [0,1]. It is equivalent to interval 0 1, and
--   can be visualized as follows:
--   
--   
--   On the x-axis is time, and the value that ui takes on is on
--   the y-axis. The shaded portion represents the era. Note that the value
--   of ui (as with any active) is still defined outside its era,
--   and this can make a difference when it is combined with other active
--   values with different eras. Applying a function with fmap
--   affects all values, both inside and outside the era. To manipulate
--   values outside the era specifically, see clamp and trim.
--   
--   To alter the values that ui takes on without altering
--   its era, use its Functor and Applicative instances. For
--   example, (*2) <$> ui varies from 0 to
--   2 over the era [0,1]. To alter the era, you can use
--   stretch or shift.
ui :: Fractional a => Active a

-- | interval a b is an active value starting at time a,
--   ending at time b, and taking the value t at time
--   t.
interval :: Fractional a => Time -> Time -> Active a

-- | stretch s act "stretches" the active act so that it
--   takes s times as long (retaining the same start time).
stretch :: Rational -> Active a -> Active a

-- | stretchTo d stretches an Active so it has
--   duration d. Has no effect if (1) d is non-positive,
--   or (2) the Active value is constant, or (3) the Active
--   value has zero duration.
stretchTo :: Duration -> Active a -> Active a

-- | a1 `during` a2 stretches and shifts a1
--   so that it has the same era as a2. Has no effect if either of
--   a1 or a2 are constant.
during :: Active a -> Active a -> Active a

-- | shift d act shifts the start time of act by duration
--   d. Has no effect on constant values.
shift :: Duration -> Active a -> Active a

-- | Reverse an active value so the start of its era gets mapped to the end
--   and vice versa. For example, backwards ui can be
--   visualized as
--   
backwards :: Active a -> Active a

-- | Take a "snapshot" of an active value at a particular time, resulting
--   in a constant value.
snapshot :: Time -> Active a -> Active a

-- | "Clamp" an active value so that it is constant before and after its
--   era. Before the era, clamp a takes on the value of a
--   at the start of the era. Likewise, after the era, clamp a
--   takes on the value of a at the end of the era. clamp
--   has no effect on constant values.
--   
--   For example, clamp ui can be visualized as
--   
--   
--   See also clampBefore and clampAfter, which clamp only
--   before or after the era, respectively.
clamp :: Active a -> Active a

-- | "Clamp" an active value so that it is constant before the start of its
--   era. For example, clampBefore ui can be visualized as
--   
--   
--   See the documentation of clamp for more information.
clampBefore :: Active a -> Active a

-- | "Clamp" an active value so that it is constant after the end of its
--   era. For example, clampBefore ui can be visualized as
--   
--   
--   See the documentation of clamp for more information.
clampAfter :: Active a -> Active a

-- | "Trim" an active value so that it is empty outside its era.
--   trim has no effect on constant values.
--   
--   For example, trim ui can be visualized as
--   
--   
--   Actually, trim ui is not well-typed, since it is not
--   guaranteed that ui's values will be monoidal (and usually
--   they won't be)! But the above image still provides a good intuitive
--   idea of what trim is doing. To make this precise we could
--   consider something like trim (First . Just $ ui).
--   
--   See also trimBefore and trimActive, which trim only
--   before or after the era, respectively.
trim :: Monoid a => Active a -> Active a

-- | "Trim" an active value so that it is empty before the start of
--   its era. For example, trimBefore ui can be visualized
--   as
--   
--   
--   See the documentation of trim for more details.
trimBefore :: Monoid a => Active a -> Active a

-- | "Trim" an active value so that it is empty after the end of its
--   era. For example, trimAfter ui can be visualized as
--   
--   
--   See the documentation of trim for more details.
trimAfter :: Monoid a => Active a -> Active a

-- | a1 `after` a2 produces an active that behaves like
--   a1 but is shifted to start at the end time of a2. If
--   either a1 or a2 are constant, a1 is
--   returned unchanged.
after :: Active a -> Active a -> Active a

-- | Sequence/overlay two Active values: shift the second to start
--   immediately after the first (using after), then compose them
--   (using <>).
(->>) :: Semigroup a => Active a -> Active a -> Active a

-- | "Splice" two Active values together: shift the second to start
--   immediately after the first (using after), and produce the
--   value which acts like the first up to the common end/start point, then
--   like the second after that. If both are constant, return the first.
(|>>) :: Active a -> Active a -> Active a

-- | Splice together a list of active values using |>>. The
--   list must be nonempty.
movie :: [Active a] -> Active a

-- | Create an Active which takes on each value in the given list
--   in turn during the time [0,1], with each value getting an
--   equal amount of time. In other words, discrete creates a
--   "slide show" that starts at time 0 and ends at time 1. The first
--   element is used prior to time 0, and the last element is used after
--   time 1.
--   
--   It is an error to call discrete on the empty list.
discrete :: [a] -> Active a

-- | simulate r act simulates the Active value
--   act, returning a list of "snapshots" taken at regular
--   intervals from the start time to the end time. The interval used is
--   determined by the rate r, which denotes the "frame rate",
--   that is, the number of snapshots per unit time.
--   
--   If the Active value is constant (and thus has no start or end
--   times), a list of length 1 is returned, containing the constant value.
simulate :: Rational -> Active a -> [a]
instance Eq Time
instance Ord Time
instance Show Time
instance Read Time
instance Enum Time
instance Num Time
instance Fractional Time
instance Real Time
instance RealFrac Time
instance AdditiveGroup Time
instance Eq Duration
instance Ord Duration
instance Show Duration
instance Read Duration
instance Enum Duration
instance Num Duration
instance Fractional Duration
instance Real Duration
instance RealFrac Duration
instance AdditiveGroup Duration
instance Semigroup Era
instance Show Era
instance Functor Dynamic
instance Functor Active
instance Apply Active
instance Applicative Active
instance (Monoid a, Semigroup a) => Monoid (Active a)
instance Semigroup a => Semigroup (Active a)
instance Newtype (MaybeApply f a) (Either (f a) a)
instance Newtype (Active a) (MaybeApply Dynamic a)
instance Semigroup a => Semigroup (Dynamic a)
instance Apply Dynamic
instance AffineSpace Time
instance VectorSpace Duration
instance Newtype Duration Rational
instance InnerSpace Time
instance VectorSpace Time
instance Newtype Time Rational
