Music.Time.Internal.Transform

The Transformable class

class Transformable a where

Class of values that can be transformed (i.e. scaled and moved) in time.

Law

 transform mempty = id
 transform (s <> t) = transform s . transform t
 transform (s <> negateV s) = id

Law

 onset (delay n a)       = n ^+. onset a
 offset (delay n a)      = n ^+. offset a
 duration (stretch n a)  = n * duration a
 duration (compress n a) = duration a / n

 delay n b ! t    = b ! (t .-^ n)
 undelay n b ! t  = b ! (t .+^ n)

Lemma

 duration a = duration (delay n a)

Methods

transform :: Span -> a -> a

Instances

Transformable Bool

Transformable Char

Transformable Double

Transformable Float

Transformable Int

Transformable Integer

Transformable Ordering

Transformable ()

Transformable Span

Transformable Time

Transformable Duration

Transformable Meta

Transformable Attribute

Transformable DynamicNotation

Transformable ArticulationNotation

Transformable a => Transformable [a]

Transformable a => Transformable (Ratio a)

Transformable a => Transformable (Maybe a)

Transformable a => Transformable (Sum a)

Transformable a => Transformable (Product a)

Transformable a => Transformable (Seq a)

Transformable a => Transformable (Last a)

Transformable a => Transformable (Option a)

Transformable (NoReverse a)

Transformable a => Transformable (Bound a)

Bound transform by transforming the bounded value as well as the bounds.

Transformable a => Transformable (Average a)

Transformable a => Transformable (Ctxt a)

Transformable a => Transformable (AddMeta a)

Transformable (Stretched a)

Transformable (Voice a)

Transformable (Delayed a)

Transformable (Chord a)

Transformable (Track a)

Transformable (Note a)

Transformable (Score a)

Transformable (Behavior a)

Transformable (Segment a)

Segments are invariant under transformation. To transform a timve varying value, use fromSegment.

Transformable (Reactive a)

Transformable a => Transformable (TieT a)

Transformable a => Transformable (SlideT a)

Transformable a => Transformable (TremoloT a)

Transformable a => Transformable (TextT a)

Transformable a => Transformable (HarmonicT a)

Transformable a => Transformable (ColorT a)

(Transformable a, Transformable b) => Transformable (a -> b)

Functions transform by conjugation, i.e. we reverse-transform the argument and transform the result.

Transformable a => Transformable (b, a)

(Ord k, Transformable a) => Transformable (Map k a)

(Monoid b, Transformable a) => Transformable (Couple b a)

Transformable a => Transformable (PartT n a)

Transformable a => Transformable (DynamicT n a)

Transformable a => Transformable (ArticulationT n a)

(Transformable a, Transformable b, Transformable c) => Transformable (a, b, c)

itransform :: Transformable a => Span -> a -> a

Apply the inverse of the given transformation.

 itransform s = transform (negateV s)

transformed :: Transformable a => Span -> Iso' a a

View the given value in the context of the given transformation.

 over (transformed s) = (`whilst` s)

Apply under a transformation

whilst :: (Transformable a, Transformable b) => (a -> b) -> Span -> a -> b

Apply a function under transformation.

Designed to be used infix, as in

 stretch 2 `whilst` delaying 2

whilstM :: (Functor f, Transformable a, Transformable b) => (a -> f b) -> Span -> a -> f b

Apply a morphism under transformation (monadic version).

whilstL :: (Functor f, Transformable a, Transformable b) => LensLike f s t a b -> LensLike f (Span, s) (Span, t) a b

whilstLT :: (Functor f, Transformable a, Transformable b) => LensLike f s t a b -> LensLike f (Time, s) (Time, t) a b

whilstLD :: (Functor f, Transformable a, Transformable b) => LensLike f s t a b -> LensLike f (Duration, s) (Duration, t) a b

whilstStretch :: (Transformable a, Transformable b) => (a -> b) -> Duration -> a -> b

Apply a function under transformation.

whilstDelay :: (Transformable a, Transformable b) => (a -> b) -> Time -> a -> b

Apply a function under transformation.

spanned :: (Transformable a, Transformable b) => Span -> Lens a b a b

Transforms a lens of to a Transformable type to act inside a transformation.

onSpan :: (Transformable a, Functor f) => LensLike' f a b -> Span -> LensLike' f a b

Transforms a lens of to a Transformable type to act inside a transformation.

Designed to be used infix, as in

 l `onSpan` (2 <-> 3)

conjugateS :: Span -> Span -> Span

The conjugate of two spans.

Specific transformations

delay :: Transformable a => Duration -> a -> a

Moves a value forward in time.

undelay :: Transformable a => Duration -> a -> a

Moves a value backward in time. Equnitvalent to stretch . negate.

stretch :: Transformable a => Duration -> a -> a

Stretches (augments) a value by the given factor.

compress :: Transformable a => Duration -> a -> a

Compresses (diminishes) a score. Equnitvalent to stretch . recip.

Applied transformations

delaying :: Duration -> Span

A transformation that moves a value forward in time.

undelaying :: Duration -> Span

A transformation that moves a value backward in time.

stretching :: Duration -> Span

A transformation that stretches (augments) a value by the given factor.

compressing :: Duration -> Span

A transformation that compresses (diminishes) a value by the given factor.

Utility

delayTime :: Transformable a => Time -> a -> a

Delay relative to origin.

Provided for situations when we really want to use startAt, but the type does not have an instance for HasPosition and we can assume that the value is starting at time zero.