Sound.SC3.Lang.Pattern.ID

sclang pattern library functions. See http://rd.slavepianos.org/?t=hsc3-texts for tutorial.

P type and instances

data M

Pattern continuation mode

Constructors

Stop

Continue

Instances

Eq M

Show M

data P a

Pattern data type (opaque)

Constructors

P

Fields

unP :: [a]

stP :: M

Instances

Monad P

Functor P

Applicative P

Foldable P

Traversable P

Eq a => Eq (P a)

(Num (P a), Fractional a) => Fractional (P a)

Num a => Num (P a)

Show a => Show (P a)

Monoid (P a)

Audible (P Event)

OrdE a => OrdE (P a)

Audible (String, P Event)

Audible (Synthdef, P Event)

pappend' :: P a -> P a -> P a

A variant of pappend that preserves the continuation mode but is strict in the right argument.

pappend :: P a -> P a -> P a

mappend variant to sequence two patterns.

Note that in order for mappend to be productive in mconcat on an infinite list it cannot store the right-hand stop/continue mode, see pappend'

 toP [1,2] `pappend` toP [2,3] == toP [1,2,2,3]
 ptake 3 (prepeat 3 `pappend` prepeat 4) == toP' [3,3,3]
 ptake 3 (pconcat (cycle [prepeat 3])) == toP' [3,3,3]
 pempty `pappend` pempty == pempty

(>>=*) :: P a -> (a -> P b) -> P b

A >>= variant using the continuation maintaining pappend' function.

inf :: Int

Pseudo-infinite value for use at repeat counts.

nan :: (Monad m, Floating a) => m a

Constant NaN (not a number) value for use as a rest indicator at a frequency model input (not at a rest key).

Extension

stP_join :: [M] -> M

Join a set of M values, if any are Stop then Stop else Continue.

pextension :: [P a] -> [()]

Extension of a set of patterns. If any patterns are stopping, the longest such pattern, else the longest of the continuing patterns.

 pextension [toP [1,2],toP [3,4,5]] == [(),(),()]
 pextension [toP' [1,2],toP [3,4,5]] == [(),()]

pextend :: [P a] -> [P a]

Extend a set of patterns following pextension rule.

 pextend [toP [1,2],toP [3,4,5]] == [toP' [1,2,1],toP' [3,4,5]]

 pextend [toP' [1,2],toP [3,4,5]] == [toP' [1,2],toP' [3,4]]

ptranspose :: [P a] -> P [a]

Variant of transpose.

 ptranspose [toP [1,2],toP [3,4,5]] == toP [[1,3],[2,4],[5]]

pflop' :: [P a] -> P [a]

Variant of pflop.

 pflop' [toP [1,2],toP [3,4,5]] == toP' [[1,3],[2,4],[1,5]]

pflop :: [P a] -> P (P a)

Variant of ptranspose transforming the input patterns by pextension.

 pflop [toP [1,2],toP [3,4,5]] == toP' (map toP [[1,3],[2,4],[1,5]])

pflopJoin :: [P a] -> P a

Composition of pjoin and pflop.

P lifting

liftP :: ([a] -> [b]) -> P a -> P b

Lift unary list function to P.

liftP2 :: ([a] -> [b] -> [c]) -> P a -> P b -> P c

Lift binary list function to P.

liftP3 :: ([a] -> [b] -> [c] -> [d]) -> P a -> P b -> P c -> P d

Lift ternary list function to P.

liftP4 :: ([a] -> [b] -> [c] -> [d] -> [e]) -> P a -> P b -> P c -> P d -> P e

Lift quaternary list function to P.

P functions

pnull :: P a -> Bool

Variant of null.

stp :: Int -> M

Select M according to repeat count, see inf.

stopping :: P a -> P a

Set pattern mode to Stop.

stoppingN :: Int -> P a -> P a

Set pattern mode according to repeat count, see inf.

continuing :: P a -> P a

Set pattern mode to Continue.

fromList :: [a] -> P a

The basic list to pattern function. The pattern is continuing.

 continuing (pseq [1,2,3] 1) == toP [1,2,3]

toP :: [a] -> P a

Alias for fromList.

fromList' :: [a] -> P a

A variant from fromList to make stopping patterns.

 pseq [1,2,3] 1 == toP' [1,2,3]

toP' :: [a] -> P a

Alias for fromList'.

prepeat :: a -> P a

Pattern variant of repeat. See also pure and pcycle.

 ptake 5 (prepeat 3) == toP' [3,3,3,3,3]
 ptake 5 (Control.Applicative.pure 3) == toP' [3]
 take 5 (Control.Applicative.pure 3) == [3]

pzipWith :: (a -> b -> c) -> P a -> P b -> P c

Pattern variant of zipWith. Note that zipWith is truncating, whereas the numerical instances are extending.

 zipWith (*) [1,2,3] [5,6] == [5,12]
 pzipWith (*) (toP [1,2,3]) (toP [5,6]) == toP [5,12,15]
 toP [1,2,3] * toP [5,6] == toP [5,12,15]

Note that the list instance of applicative is combinatorial (ie. Monadic).

 (pure (*) <*> [1,2,3] <*> [5,6]) == [5,6,10,12,15,18]
 (pure (*) <*> toP [1,2] <*> toP [5]) == toP [5,10]

pzipWith3 :: (a -> b -> c -> d) -> P a -> P b -> P c -> P d

Pattern variant of zipWith3.

pzipWith4 :: (a -> b -> c -> d -> e) -> P a -> P b -> P c -> P d -> P e

Pattern variant of zipWith4.

pzip :: P a -> P b -> P (a, b)

Pattern variant of zip.

 ptake 2 (pzip (prepeat 3) (prepeat 4)) == toP' [(3,4),(3,4)]

Note that haskell zip is truncating wheras pzip is extending.

 zip [1 .. 2] [0] == [(1,0)]
 pzip (toP [1..2]) (toP [0]) == toP [(1,0),(2,0)]

pzip3 :: P a -> P b -> P c -> P (a, b, c)

Pattern variant of zip3.

pzip4 :: P a -> P b -> P c -> P d -> P (a, b, c, d)

Tupling variant of pzipWith4.

punzip :: P (a, b) -> (P a, P b)

Pattern variant on unzip.

SC3 patterns

padd :: Key -> P Value -> P Event -> P Event

Add a value to an existing key, or set the key if it doesn't exist.

 Padd(\freq,801,Pbind(\freq,100)).asStream.next(())
 padd "freq" 801 (pbind [("freq",100)]) == pbind [("freq",901)]

pbind' :: [Type] -> [Maybe Int] -> [Maybe Instrument] -> [(Key, P Value)] -> P Event

A primitive form of the SC3 pbind pattern, with explicit type and identifier inputs.

pbind :: [(Key, P Value)] -> P Event

SC3 pattern to assign keys to a set of value patterns making an Event pattern. A finite binding stops the Event pattern.

 Pbind(\x,Pseq([1,2,3]),
       \y,Prand([100,300,200],inf)).asStream.nextN(3,())

 pkey "x" (pbind [("x",prand 'α' [100,300,200] inf)
                 ,("y",pseq [1,2,3] 1)]) == toP' [200,200,300]

pbrown' :: (Enum e, Random n, Num n, Ord n) => e -> P n -> P n -> P n -> Int -> P n

A variant of pbrown where the l, r and s inputs are patterns.

 pbrown' 'α' 1 700 (pseq [1,20] inf) 4 == toP' [415,419,420,428]

pbrown :: (Enum e, Random n, Num n, Ord n) => e -> n -> n -> n -> Int -> P n

SC3 pattern to generate psuedo-brownian motion.

 pbrown 'α' 0 9 1 5 == toP' [4,4,5,4,3]

pclutch :: P a -> P Bool -> P a

SC3 sample and hold pattern. For true values in the control pattern, step the value pattern, else hold the previous value.

 Pclutch(Pser([1,2,3,4,5],8),
         Pseq([1,0,1,0,0,0,1,1],inf)).asStream.all

 let {c = pbool (pseq [1,0,1,0,0,1,1] 1)
     ;r = toP' [1,1,2,2,2,3,4,5,5,1,1,1,2,3]}
 in pclutch (pser [1,2,3,4,5] 8) c == r

Note the initialization behavior, nothing is generated until the first true value.

 let {p = pseq [1,2,3,4,5] 1
     ;q = pbool (pseq [0,0,0,0,0,0,1,0,0,1,0,1] 1)}
 in pclutch p q

pcollect :: (a -> b) -> P a -> P b

SC3 name for fmap, ie. patterns are functors.

 Pcollect({arg i;i * 3},Pseq(#[1,2,3],inf)).asStream.nextN(9)
 pcollect (* 3) (toP [1,2,3]) == toP [3,6,9]

 Pseq(#[1,2,3],3).collect({arg i;i * 3}).asStream.nextN(9)
 fmap (* 3) (toP [1,2,3]) == toP [3,6,9]

pconst :: (Ord a, Num a) => a -> P a -> a -> P a

SC3 pattern to constrain the sum of a numerical pattern. Is equal to p until the accumulated sum is within t of n. At that point, the difference between the specified sum and the accumulated sum concludes the pattern.

 Pconst(10,Prand([1,2,0.5,0.1],inf),0.001).asStream.nextN(15,())

 let p = pconst 10 (prand 'α' [1,2,0.5,0.1] inf) 0.001
 in (p,Data.Foldable.sum p)

pdegreeToKey :: RealFrac a => P a -> P [a] -> P a -> P a

SC3 pattern to derive notes from an index into a scale.

 let {p = pseq [0,1,2,3,4,3,2,1,0,2,4,7,4,2] 2
     ;q = return [0,2,4,5,7,9,11]
     ;r = [0,2,4,5,7,5,4,2,0,4,7,12,7,4,0,2,4,5,7,5,4,2,0,4,7,12,7,4]}
 in pdegreeToKey p q (return 12) == toP' r

 let {p = pseq [0,1,2,3,4,3,2,1,0,2,4,7,4,2] 2
     ;q = pseq (map return [[0,2,4,5,7,9,11],[0,2,3,5,7,8,11]]) 1
     ;r = [0,2,4,5,7,5,4,2,0,4,7,12,7,4,0,2,3,5,7,5,3,2,0,3,7,12,7,3]}
 in pdegreeToKey p (pstutter 14 q) (return 12) == toP' r

This is the pattern variant of degree_to_key.

 let s = [0,2,4,5,7,9,11]
 in map (P.degree_to_key s 12) [0,2,4,7,4,2,0] == [0,4,7,12,7,4,0]

pdiff :: Num n => P n -> P n

SC3 pattern to calculate adjacent element difference.

 pdiff (toP [0,2,3,5,6,8,9]) == toP [-2,-1,-2,-1,-2,-1,7]

pdurStutter :: Fractional a => P Int -> P a -> P a

SC3 pattern to partition a value into n equal subdivisions. Subdivides each duration by each stutter and yields that value stutter times. A stutter of 0 will skip the duration value, a stutter of 1 yields the duration value unaffected.

 s = Pseq(#[1,1,1,1,1,2,2,2,2,2,0,1,3,4,0],inf);
 d = Pseq(#[0.5,1,2,0.25,0.25],inf);
 PdurStutter(s,d).asStream.nextN(24)

 let {s = pseq [1,1,1,1,1,2,2,2,2,2,0,1,3,4,0] inf
     ;d = pseq [0.5,1,2,0.25,0.25] inf}
 in ptake 24 (pdurStutter s d)

pedit :: Key -> (Value -> Value) -> P Event -> P Event

Edit Value at Key in each element of an Event pattern.

pexprand :: (Enum e, Random a, Floating a) => e -> a -> a -> Int -> P a

An SC3 pattern of random values that follow a exponential distribution.

 Pexprand(0.0001,1,10).asStream.all
 pexprand 'α' 0.0001 1 10

pfinval :: Int -> P a -> P a

SC3 pattern to take the first n elements of the pattern. See also ptake.

 Pfinval(5,Pseq(#[1,2,3],inf)).asStream.nextN(5)
 pfinval 5 (pseq [1,2,3] inf) == toP' [1,2,3,1,2]

pfold :: RealFrac n => P n -> n -> n -> P n

SC3 pattern to fold values to lie within range (as opposed to wrap and clip). This is not related to the Foldable pattern instance.

 pfold (toP [10,11,12,-6,-7,-8]) (-7) 11 == toP [10,11,10,-6,-7,-6]

The underlying primitive is the fold_ function.

 let f n = fold_ n (-7) 11
 in map f [10,11,12,-6,-7,-8] == [10,11,10,-6,-7,-6]

pfuncn' :: RandomGen g => g -> (g -> (n, g)) -> Int -> P n

Underlying form of haskell pfuncn pattern.

pfuncn :: Enum e => e -> (StdGen -> (n, StdGen)) -> Int -> P n

A variant of the SC3 pattern that evaluates a closure at each step. The haskell variant function has a StdGen form.

pgeom :: Num a => a -> a -> Int -> P a

SC3 geometric series pattern.

 Pgeom(3,6,5).asStream.nextN(5)
 pgeom 3 6 5 == toP' [3,18,108,648,3888]
 pgeom 1 2 10 == toP' [1,2,4,8,16,32,64,128,256,512]

Real numbers work as well.

 pgeom 1.0 1.1 6

pif :: P Bool -> P a -> P a -> P a

SC3 pattern-based conditional expression.

 var a = Pfunc({0.3.coin});
 var b = Pwhite(0,9,in);
 var c = Pwhite(10,19,inf);
 Pif(a,b,c).asStream.nextN(9)

 let {a = fmap (< 0.3) (pwhite 'α' 0.0 1.0 inf)
     ;b = pwhite 'β' 0 9 inf
     ;c = pwhite 'γ' 10 19 inf}
 in ptake 9 (pif a b c) == toP' [11,3,6,11,11,15,17,4,7]

pinstr :: P Instrument -> P Event -> P Event

Pattern to assign Instruments to Events. An Instrument is either a Synthdef or a String. In the Synthdef case the instrument is asynchronously sent to the server before processing the event, which has timing implications. In general the instrument pattern ought to have a Synthdef for the first occurence of the instrument, and a String for subsequent occurences.

pinstr_s :: P (String, Bool) -> P Event -> P Event

Variant of pinstr which lifts the String pattern to an Instrument pattern.

pinstr_d :: P (Synthdef, Bool) -> P Event -> P Event

Variant of pinstr which lifts the Synthdef pattern to an Instrument pattern.

pkey_m :: Key -> P Event -> P (Maybe Value)

Pattern to extract Values at Key from an Event pattern.

 pkey_m "freq" (pbind [("freq",440)]) == toP' [Just 440]

pkey :: Key -> P Event -> P Value

SC3 pattern to read Value of Key at Event pattern. Note however that in haskell is usually more appropriate to name the pattern using let.

 pkey "freq" (pbind [("freq",440)]) == toP' [440]
 pkey "amp" (pbind [("amp",toP [0,1])]) == toP' [0,1]

place :: [[a]] -> Int -> P a

SC3 interlaced embedding of subarrays.

 Place([0,[1,2],[3,4,5]],3).asStream.all
 place [[0],[1,2],[3,4,5]] 3 == toP' [0,1,3,0,2,4,0,1,5]

 Place(#[1,[2,5],[3,6]],2).asStream.nextN(6)
 place [[1],[2,5],[3,6]] 2 == toP' [1,2,3,1,5,6]
 place [[1],[2,5],[3,6..]] 4 == toP' [1,2,3,1,5,6,1,2,9,1,5,12]

pmono :: Instrument -> Int -> [(Key, P Value)] -> P Event

SC3 pattern that is a variant of pbind for controlling monophonic (persistent) synthesiser nodes.

pmono_d :: Synthdef -> Int -> [(Key, P Value)] -> P Event

Variant of pmono that lifts Synthdef to Instrument.

pmono_s :: String -> Int -> [(Key, P Value)] -> P Event

Variant of pmono that lifts String to Instrument.

pmul :: Key -> P Value -> P Event -> P Event

Idiom to scale Value at Key in an Event pattern.

pmul' :: Key -> P Value -> P Event -> P Event

Variant that does not insert key.

ppatlace :: [P a] -> Int -> P a

SC3 pattern to lace input patterns. Note that the current implementation stops late, it cycles the second series one place.

 ppatlace [1,prand 'α' [2,3] inf] 5 == toP' [1,3,1,2,1,3,1,2,1,2]

pn :: P a -> Int -> P a

SC3 pattern to repeats the enclosed pattern a number of times.

 pn 1 4 == toP' [1,1,1,1]
 pn (toP [1,2,3]) 3 == toP' [1,2,3,1,2,3,1,2,3]

This is related to concat.replicate in standard list processing.

 concat (replicate 4 [1]) == [1,1,1,1]
 concat (replicate 3 [1,2,3]) == [1,2,3,1,2,3,1,2,3]

There is a pconcatReplicate near-alias (reversed argument order).

 pconcatReplicate 4 1 == toP' [1,1,1,1]
 pconcatReplicate 3 (toP [1,2]) == toP' [1,2,1,2,1,2]

This is productive over infinite lists.

 concat (replicate inf [1])
 pconcat (replicate inf 1)
 pconcatReplicate inf 1

pnormalizeSum :: Fractional n => P n -> P n

Pattern variant of normalizeSum.

prand' :: Enum e => e -> [P a] -> Int -> P (P a)

Un-joined variant of prand.

prand :: Enum e => e -> [P a] -> Int -> P a

SC3 pattern to make n random selections from a list of patterns, the resulting pattern is flattened (joined).

 Prand([1,Pseq([10,20,30]),2,3,4,5],6).asStream.all
 prand 'α' [1,toP [10,20],2,3,4,5] 4 == toP' [5,2,10,20,2]

preject :: (a -> Bool) -> P a -> P a

SC3 pattern to rejects values for which the predicate is true. reject f is equal to filter (not . f).

 preject (== 1) (pseq [1,2,3] 2) == toP' [2,3,2,3]
 pfilter (not . (== 1)) (pseq [1,2,3] 2) == toP' [2,3,2,3]

 Pwhite(0,255,20).reject({|x| x.odd}).asStream.all
 preject odd (pwhite 'α' 0 255 10) == toP [32,158,62,216,240,20]

 Pwhite(0,255,20).select({|x| x.odd}).asStream.all
 pselect odd (pwhite 'α' 0 255 10) == toP [241,187,119,127]

prorate' :: Num a => Either a [a] -> a -> P a

Underlying pattern for prorate.

prorate :: Num a => P (Either a [a]) -> P a -> P a

SC3 sub-dividing pattern.

 Prorate(Pseq([0.35,0.5,0.8]),1).asStream.nextN(6)
 prorate (fmap Left (pseq [0.35,0.5,0.8] 1)) 1

 Prorate(Pseq([0.35,0.5,0.8]),Prand([20,1],inf)).asStream.nextN(6)
 prorate (fmap Left (pseq [0.35,0.5,0.8] 1)) (prand 'α' [20,1] 3)

 var l = [[1,2],[5,7],[4,8,9]]).collect(_.normalizeSum);
 Prorate(Pseq(l,1).asStream.nextN(8)

 let l = map (Right . C.normalizeSum) [[1,2],[5,7],[4,8,9]]
 in prorate (toP l) 1

pselect :: (a -> Bool) -> P a -> P a

See pfilter.

 pselect (< 3) (pseq [1,2,3] 2) == toP' [1,2,1,2]

pseq1 :: [P a] -> Int -> P a

Variant of pseq that retrieves only one value from each pattern on each list traversal. Compare to pswitch1.

 pseq [pseq [1,2] 1,pseq [3,4] 1] 2 == toP' [1,2,3,4,1,2,3,4]
 pseq1 [pseq [1,2] 1,pseq [3,4] 1] 2 == toP' [1,3,2,4]
 pseq1 [pseq [1,2] inf,pseq [3,4] inf] 3 == toP' [1,3,2,4,1,3]

pseq :: [P a] -> Int -> P a

SC3 pattern to cycle over a list of patterns. The repeats pattern gives the number of times to repeat the entire list.

 pseq [return 1,return 2,return 3] 2 == toP' [1,2,3,1,2,3]
 pseq [1,2,3] 2 == toP' [1,2,3,1,2,3]
 pseq [1,pn 2 2,3] 2 == toP' [1,2,2,3,1,2,2,3]

There is an inf value for the repeats variable.

 ptake 3 (pdrop 1000000 (pseq [1,2,3] inf)) == toP' [2,3,1]

pseqr :: (Int -> [P a]) -> Int -> P a

A variant of pseq that passes a new seed at each invocation, see also pfuncn.

pseqn :: [Int] -> [P a] -> Int -> P a

A variant of pseq to aid translating a common SC3 idiom where a finite random pattern is included in a Pseq list. In the SC3 case, at each iteration a new computation is run. This idiom does not directly translate to the declarative haskell pattern library.

 Pseq([1,Prand([2,3],1)],5).asStream.all
 pseq [1,prand 'α' [2,3] 1] 5

Although the intended pattern can usually be expressed using an alternate construction:

 Pseq([1,Prand([2,3],1)],5).asStream.all
 ppatlace [1,prand 'α' [2,3] inf] 5 == toP' [1,3,1,2,1,3,1,2,1,2]

the pseqn variant handles many common cases.

 Pseq([Pn(8,2),Pwhite(9,16,1)],5).asStream.all
 pseqn [2,1] [8,pwhite 'α' 9 16 inf] 5

pser1 :: [P a] -> Int -> P a

Variant of pser that consumes sub-patterns one element per iteration.

 pser1 [1,pser [10,20] 3,3] 9 == toP' [1,10,3,1,20,3,1,10,3]

pser :: [P a] -> Int -> P a

SC3 pattern that is like pseq, however the repeats variable gives the number of elements in the sequence, not the number of cycles of the pattern.

 pser [1,2,3] 5 == toP' [1,2,3,1,2]
 pser [1,pser [10,20] 3,3] 9 == toP' [1,10,20,10,3,1,10,20,10]
 pser [1,2,3] 5 * 3 == toP' [3,6,9,3,6]

pseries :: Num a => a -> a -> Int -> P a

SC3 arithmetric series pattern, see also pgeom.

 pseries 0 2 10 == toP' [0,2,4,6,8,10,12,14,16,18]
 pseries 9 (-1) 10 == toP' [9,8 .. 0]
 pseries 1.0 0.2 3 == toP' [1.0,1.2,1.4]

pshuf :: Enum e => e -> [a] -> Int -> P a

SC3 pattern to return n repetitions of a shuffled sequence.

 Pshuf([1,2,3,4],2).asStream.all
 pshuf 'α' [1,2,3,4] 2 == toP' [2,4,3,1,2,4,3,1]

pslide :: [a] -> Int -> Int -> Int -> Int -> Bool -> P a

SC3 pattern to slide over a list of values.

 Pslide([1,2,3,4],inf,3,1,0).asStream.all
 pslide [1,2,3,4] 4 3 1 0 True == toP' [1,2,3,2,3,4,3,4,1,4,1,2]
 pslide [1,2,3,4,5] 3 3 (-1) 0 True == toP' [1,2,3,5,1,2,4,5,1]

psplitAt :: Int -> P a -> (P a, P a)

Pattern variant of splitAt.

psplitPlaces' :: P Int -> P a -> P [a]

Pattern variant of splitPlaces.

psplitPlaces :: P Int -> P a -> P (P a)

A variant of psplitPlaces' that joins the output pattern.

pstretch :: P Value -> P Event -> P Event

SC3 pattern to do time stretching. It is equal to pmul at "stretch".

pstutter :: P Int -> P a -> P a

SC3 pattern to repeat each element of a pattern _n_ times.

 pstutter 2 (toP [1,2,3]) == toP [1,1,2,2,3,3]

The count input may be a pattern.

 let {p = pseq [1,2] inf
     ;q = pseq [1,2,3] 2}
 in pstutter p q == toP' [1,2,2,3,1,1,2,3,3]

 pstutter (toP [1,2,3]) (toP [4,5,6]) == toP [4,5,5,6,6,6]

pswitch :: [P a] -> P Int -> P a

SC3 pattern to select elements from a list of patterns by a pattern of indices.

 switch l i = i >>= (l !!)
 pswitch [pseq [1,2,3] 2,pseq [65,76] 1,800] (toP [2,2,0,1])

pswitch1 :: [P a] -> P Int -> P a

SC3 pattern that uses a pattern of indices to select which pattern to retrieve the next value from. Only one value is selected from each pattern. This is in comparison to pswitch, which embeds the pattern in its entirety.

 Pswitch1([Pseq([1,2,3],inf),
          Pseq([65,76],inf),
          8],
         Pseq([2,2,0,1],6)).asStream.all

 pswitch1 [pseq [1,2,3] inf,pseq [65,76] inf,8] (pseq [2,2,0,1] 6)

ptuple :: [P a] -> Int -> P [a]

SC3 pattern to combine a list of streams to a stream of lists. See also pflop.

 Ptuple([Pseries(7,-1,8),
        Pseq([9,7,7,7,4,4,2,2],1),
        Pseq([4,4,4,2,2,0,0,-3],1)],1).asStream.nextN(8)

 ptuple [pseries 7 (-1) 8
        ,pseq [9,7,7,7,4,4,2,2] 1
        ,pseq [4,4,4,2,2,0,0,-3] 1] 1

pwhite' :: (Enum e, Random n) => e -> P n -> P n -> P n

A variant of pwhite where the range inputs are patterns.

pwhite :: (Random n, Enum e) => e -> n -> n -> Int -> P n

SC3 pattern to generate a uniform linear distribution in given range.

 pwhite 'α' 0 9 5 == toP [3,0,1,6,6]

It is important to note that this structure is not actually indeterminate, so that the below is zero.

 let p = pwhite 'α' 0.0 1.0 3 in p - p == toP [0,0,0]

pwhitei :: (RealFrac n, Random n, Enum e) => e -> n -> n -> Int -> P n

A variant of pwhite that generates integral (rounded) values.

pwrand :: Enum e => e -> [P a] -> [Double] -> Int -> P a

SC3 pattern to embed values randomly chosen from a list. Returns one item from the list at random for each repeat, the probability for each item is determined by a list of weights which should sum to 1.0.

 let w = C.normalizeSum [1,3,5]
 in pwrand 'α' [1,2,3] w 6 == toP [3,1,2,3,3,3]

Pwrand.new([1,2,Pseq([3,4],1)],[1,3,5].normalizeSum,6).asStream.nextN(6)

 let w = C.normalizeSum [1,3,5]
 in pwrand 'α' [1,2,pseq [3,4] 1] w 6 == toP [3,4,1,2,3,4]

pwrap :: (Ord a, Num a) => P a -> a -> a -> P a

SC3 pattern to constrain the range of output values by wrapping. See also pfold.

 Pn(Pwrap(Pgeom(200,1.07,26),200,1000.0),inf).asStream.nextN(26)
 pwrap (pgeom 200 1.07 26) 200 1000

pxrand :: Enum e => e -> [P a] -> Int -> P a

SC3 pattern that is like prand but filters successive duplicates.

 pxrand 'α' [1,toP [2,3],toP [4,5,6]] 15

Monoid aliases

pconcat :: [P a] -> P a

pconcat is mconcat. See also pjoin.

 take 3 (concat (replicate maxBound [1,2])) == [1,2,1]
 ptake 3 (pconcat (cycle [toP [1,2]])) == toP' [1,2,1]
 ptake 3 (pconcat [pseq [1,2] 1,pseq [3,4] 1]) == toP' [1,2,3]

pempty :: P a

Pattern variant for mempty, ie. the empty pattern.

 pempty `pappend` pempty == pempty
 pempty `pappend` 1 == 1 `pappend` pempty

Monad aliases

pjoin :: P (P a) -> P a

join pattern variant. See also pconcat.

 take 3 (Control.Monad.join (replicate maxBound [1,2])) == [1,2,1]
 ptake 3 (pjoin (preplicate inf (toP [1,2]))) == toP' [1,2,1]

pjoin' :: P (P a) -> P a

Variant that maintains the continuing mode of the outer structure.

Data.List functions

pcons :: a -> P a -> P a

Pattern variant of :.

 pcons 'α' (pn (return 'β') 2) == fromList' "αββ"

pcycle :: P a -> P a

Pattern variant of cycle.

 ptake 5 (pcycle (toP [1,2,3])) == toP' [1,2,3,1,2]
 ptake 5 (pseq [1,2,3] inf) == toP' [1,2,3,1,2]

pdrop :: Int -> P a -> P a

Pattern variant of drop.

 Pseries(1,1,20).drop(5).asStream.nextN(15)

 pdrop 5 (pseries 1 1 10) == toP' [6,7,8,9,10]
 pdrop 1 pempty == pempty

pfilter :: (a -> Bool) -> P a -> P a

Pattern variant of filter. Allows values for which the predicate is true. Aliased to pselect. See also preject.

 pfilter (< 3) (pseq [1,2,3] 2) == toP' [1,2,1,2]

preplicate :: Int -> a -> P a

Pattern variant of replicate.

 preplicate 4 1 == toP [1,1,1,1]

Compare to pn:

 pn 1 4 == toP' [1,1,1,1]
 pn (toP [1,2]) 3 == toP' [1,2,1,2,1,2]
 preplicate 4 (toP [1,2]) :: P (P Int)

pscanl :: (a -> b -> a) -> a -> P b -> P a

Pattern variant of scanl. scanl is similar to foldl, but returns a list of successive reduced values from the left.

 Data.Foldable.foldl (\x y -> 2 * x + y) 4 (pseq [1,2,3] 1) == 43
 pscanl (\x y -> 2 * x + y) 4 (pseq [1,2,3] 1) == toP' [4,9,20,43]

ptail :: P a -> P a

Variant of drop, note that tail is partial

 ptail (toP [1,2]) == toP [2]
 ptail pempty == pempty

ptake :: Int -> P a -> P a

Pattern variant of take, see also pfinval.

 ptake 5 (pseq [1,2,3] 2) == toP' [1,2,3,1,2]
 ptake 5 (toP [1,2,3]) == toP' [1,2,3]
 ptake 5 (pseq [1,2,3] inf) == toP' [1,2,3,1,2]
 ptake 5 (pwhite 'α' 0 5 inf) == toP' [5,2,1,2,0]

Note that ptake does not extend the input pattern, unlike pser.

 ptake 5 (toP [1,2,3]) == toP' [1,2,3]
 pser [1,2,3] 5 == toP' [1,2,3,1,2]

Non-SC3 patterns

pbool :: (Ord a, Num a) => P a -> P Bool

Transforms a numerical pattern into a boolean pattern where values greater than zero are True and zero and negative values False.

 pbool (toP [2,1,0,-1]) == toP [True,True,False,False]

pconcatReplicate :: Int -> P a -> P a

pconcat . replicate, stopping after n elements.

pcountpost :: P Bool -> P Int

Count the number of False values following each True value.

 pcountpost (pbool (pseq [1,0,1,0,0,0,1,1] 1)) == toP' [1,3,0,0]

pcountpre :: P Bool -> P Int

Count the number of False values preceding each True value.

 pcountpre (pbool (pseq [0,0,1,0,0,0,1,1] 1)) == toP' [2,3,0]

pinterleave :: P a -> P a -> P a

Interleave elements from two patterns. If one pattern ends the other pattern continues until it also ends.

 let {p = pseq [1,2,3] 2
     ;q = pseq [4,5,6,7] 1}
 in pinterleave p q == toP' [1,4,2,5,3,6,1,7,2,4,3,5]

 ptake 5 (pinterleave (pcycle 1) (pcycle 2)) == toP' [1,2,1,2,1]
 ptake 10 (pinterleave (pwhite 'α' 1 9 inf) (pseries 10 1 5))

prsd :: Eq a => P a -> P a

Pattern to remove successive duplicates.

 prsd (pstutter 2 (toP [1,2,3])) == toP [1,2,3]
 prsd (pseq [1,2,3] 2) == toP' [1,2,3,1,2,3]

ptrigger :: P Bool -> P a -> P (Maybe a)

Pattern where the tr pattern determines the rate at which values are read from the x pattern. For each sucessive true value at tr the output is a `Just e` of each succesive element at x. False values at tr generate Nothing values.

 let {tr = pbool (toP [0,1,0,0,1,1])
     ;r = [Nothing,Just 1,Nothing,Nothing,Just 2,Just 3]}
 in ptrigger tr (toP [1,2,3]) == fromList r

Parallel patterns

ptmerge :: (Time, P Event) -> (Time, P Event) -> P Event

Merge two Event patterns with indicated start Times.

pmerge :: P Event -> P Event -> P Event

Variant of ptmerge with zero start times.

ptpar :: [(Time, P Event)] -> P Event

Merge a set of Event patterns each with indicated start Time.

ppar :: [P Event] -> P Event

Variant of ptpar with zero start times.

Pattern audition

e_send :: Transport m => Time -> Int -> Event -> m ()

Send Event to scsynth at Transport.

e_tplay :: Transport m => Time -> [Int] -> [Event] -> m ()

Function to audition a sequence of Events using the scsynth instance at Transport starting at indicated Time.

e_play :: Transport m => [Int] -> [Event] -> m ()

Variant of e_tplay with current clock time from time as start time. This function is used to implement the pattern instances of Audible.