-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Haskell Music Theory Base
--
-- Haskell music theory Base Library
@package hmt-base
@version 0.20
-- | Cell references & indexing.
module Music.Theory.Array.Cell_Ref
-- | A indexed case-insensitive column references. The column
-- following Z is AA.
newtype Column_Ref
Column_Ref :: String -> Column_Ref
[column_ref_string] :: Column_Ref -> String
-- | Inclusive range of column references.
type Column_Range = (Column_Ref, Column_Ref)
-- | 1-indexed row reference.
type Row_Ref = Int
-- | Zero index of Row_Ref.
row_index :: Row_Ref -> Int
-- | Inclusive range of row references.
type Row_Range = (Row_Ref, Row_Ref)
-- | Cell reference, column then row.
type Cell_Ref = (Column_Ref, Row_Ref)
-- | Inclusive range of cell references.
type Cell_Range = (Cell_Ref, Cell_Ref)
-- | Case folding letter to index function. Only valid for ASCII letters.
--
--
-- map letter_index ['A' .. 'Z'] == [0 .. 25]
-- map letter_index ['a','d' .. 'm'] == [0,3 .. 12]
--
letter_index :: Char -> Int
-- | Inverse of letter_index.
--
--
-- map index_letter [0,3 .. 12] == ['A','D' .. 'M']
--
index_letter :: Int -> Char
-- | Translate column reference to 0-index.
--
--
-- :set -XOverloadedStrings
-- map column_index ["A","c","z","ac","XYZ"] == [0,2,25,28,17575]
--
column_index :: Column_Ref -> Int
-- | Column reference to interior index within specified range. Type
-- specialised index.
--
--
-- map (Data.Ix.index ('A','Z')) ['A','C','Z'] == [0,2,25]
-- map (interior_column_index ("A","Z")) ["A","C","Z"] == [0,2,25]
--
--
--
-- map (Data.Ix.index ('B','C')) ['B','C'] == [0,1]
-- map (interior_column_index ("B","C")) ["B","C"] == [0,1]
--
interior_column_index :: Column_Range -> Column_Ref -> Int
-- | Inverse of column_index.
--
--
-- let c = ["A","Z","AA","AZ","BA","BZ","CA"]
-- map column_ref [0,25,26,51,52,77,78] == c
--
--
--
-- column_ref (0+25+1+25+1+25+1) == "CA"
--
column_ref :: Int -> Column_Ref
-- | Type specialised pred.
--
--
-- column_ref_pred "DF" == "DE"
--
column_ref_pred :: Column_Ref -> Column_Ref
-- | Type specialised succ.
--
--
-- column_ref_succ "DE" == "DF"
--
column_ref_succ :: Column_Ref -> Column_Ref
-- | Bimap of column_index.
--
--
-- column_indices ("b","p") == (1,15)
-- column_indices ("B","IT") == (1,253)
--
column_indices :: Column_Range -> (Int, Int)
-- | Type specialised range.
--
--
-- column_range ("L","R") == ["L","M","N","O","P","Q","R"]
-- Data.Ix.range ('L','R') == "LMNOPQR"
--
column_range :: Column_Range -> [Column_Ref]
-- | Type specialised inRange.
--
--
-- map (column_in_range ("L","R")) ["A","N","Z"] == [False,True,False]
-- map (column_in_range ("L","R")) ["L","N","R"] == [True,True,True]
--
--
--
-- map (Data.Ix.inRange ('L','R')) ['A','N','Z'] == [False,True,False]
-- map (Data.Ix.inRange ('L','R')) ['L','N','R'] == [True,True,True]
--
column_in_range :: Column_Range -> Column_Ref -> Bool
-- | Type specialised rangeSize.
--
--
-- map column_range_size [("A","Z"),("AA","ZZ")] == [26,26 * 26]
-- Data.Ix.rangeSize ('A','Z') == 26
--
column_range_size :: Column_Range -> Int
-- | Type specialised range.
row_range :: Row_Range -> [Row_Ref]
-- | The standard uppermost leftmost cell reference, A1.
--
--
-- Just cell_ref_minima == parse_cell_ref "A1"
--
cell_ref_minima :: Cell_Ref
-- | Cell reference parser for standard notation of (column,row).
--
--
-- parse_cell_ref "CC348" == Just ("CC",348)
--
parse_cell_ref :: String -> Maybe Cell_Ref
-- | isJust of parse_cell_ref.
is_cell_ref :: String -> Bool
-- | fromJust of parse_cell_ref
parse_cell_ref_err :: String -> Cell_Ref
-- | Cell reference pretty printer.
--
--
-- cell_ref_pp ("CC",348) == "CC348"
--
cell_ref_pp :: Cell_Ref -> String
-- | Translate cell reference to 0-indexed pair.
--
--
-- cell_index ("CC",348) == (80,347)
-- Data.Ix.index ((Column_Ref "AA",1),(Column_Ref "ZZ",999)) (Column_Ref "CC",348) == 54293
--
cell_index :: Cell_Ref -> (Int, Int)
-- | Inverse of cell_index.
--
--
-- index_to_cell (80,347) == (Column_Ref "CC",348)
-- index_to_cell (4,5) == (Column_Ref "E",6)
--
index_to_cell :: (Int, Int) -> Cell_Ref
-- | cell_index of parse_cell_ref_err
parse_cell_index :: String -> (Int, Int)
-- | Type specialised range, cells are in column-order.
--
--
-- cell_range (("AA",1),("AC",1)) == [("AA",1),("AB",1),("AC",1)]
--
--
--
-- let r = [("AA",1),("AA",2),("AB",1),("AB",2),("AC",1),("AC",2)]
-- cell_range (("AA",1),("AC",2)) == r
--
--
--
-- Data.Ix.range (('A',1),('C',1)) == [('A',1),('B',1),('C',1)]
--
--
--
-- let r = [('A',1),('A',2),('B',1),('B',2),('C',1),('C',2)]
-- Data.Ix.range (('A',1),('C',2)) == r
--
cell_range :: Cell_Range -> [Cell_Ref]
-- | Variant of cell_range in row-order.
--
--
-- let r = [("AA",1),("AB",1),("AC",1),("AA",2),("AB",2),("AC",2)]
-- cell_range_row_order (("AA",1),("AC",2)) == r
--
cell_range_row_order :: Cell_Range -> [Cell_Ref]
instance GHC.Read.Read Music.Theory.Array.Cell_Ref.Column_Ref
instance GHC.Show.Show Music.Theory.Array.Cell_Ref.Column_Ref
instance GHC.Classes.Eq Music.Theory.Array.Cell_Ref.Column_Ref
instance GHC.Classes.Ord Music.Theory.Array.Cell_Ref.Column_Ref
instance GHC.Enum.Enum Music.Theory.Array.Cell_Ref.Column_Ref
instance GHC.Ix.Ix Music.Theory.Array.Cell_Ref.Column_Ref
-- | Bits functions.
module Music.Theory.Bits
-- | True = 1, False = 0
bit_pp :: Bool -> Char
-- | map bit_pp
bits_pp :: [Bool] -> String
-- | Generate n place bit sequence for x.
gen_bitseq :: FiniteBits b => Int -> b -> [Bool]
-- | Given bit sequence (most to least significant) generate Bits
-- value.
--
--
-- :set -XBinaryLiterals
-- pack_bitseq [True,False,True,False] == 0b1010
-- pack_bitseq [True,False,False,True,False,False] == 0b100100
-- 0b100100 == 36
--
pack_bitseq :: Bits i => [Bool] -> i
-- | bits_pp of gen_bitseq.
--
--
-- :set -XBinaryLiterals
-- 0xF0 == 0b11110000
-- gen_bitseq_pp 8 (0xF0::Int) == "11110000"
--
gen_bitseq_pp :: FiniteBits b => Int -> b -> String
-- | Boolean functions.
module Music.Theory.Bool
-- | If-then-else as a function.
--
--
-- ifThenElse True "true" "false" == "true"
--
ifThenElse :: Bool -> a -> a -> a
-- | Case analysis as a function. Find first key that is True else
-- elseValue.
--
--
-- caseElse "z" [(True,"x"),(False,"y")] == "x"
-- caseElse "z" [(False,"x"),(False,"y")] == "z"
--
caseElse :: t -> [(Bool, t)] -> t
-- | Case-of analysis as a function. Find first key that compares equal to
-- selectValue else elseValue.
--
--
-- caseOfElse "z" 'b' [('a',"x"),('b',"y")] == "y"
--
caseOfElse :: Eq k => v -> k -> [(k, v)] -> v
module Music.Theory.Concurrent
-- | Pause current thread for the indicated duration (in seconds), see
-- pauseThreadLimit.
threadDelaySeconds :: RealFrac n => n -> IO ()
-- | The number of seconds that threadDelaySeconds can wait for.
-- Values larger than this require a different thread delay mechanism,
-- see threadSleepForSeconds. The value is the number of
-- microseconds in maxBound::Int. For 64-bit architectures this
-- is not likely to be an issue, however for 32-bit it can be.
--
--
-- round ((2 ** 31) / (60 * 60) / 1e6) == 1 -- hours
-- round ((2 ** 63) / (60 * 60 * 24 * 365 * 100) / 1e6) == 2925 -- years
--
threadDelaySecondsLimit :: Fractional n => n
-- | Sleep current thread for the indicated duration (in seconds). Divides
-- long sleeps into parts smaller than threadSleepForSeconds.
threadSleepForSeconds :: RealFrac n => n -> IO ()
-- | Directory functions using find system utility.
module Music.Theory.Directory.Find
-- | Find files having indicated filename. This runs the system utility
-- find, so is Unix only.
--
--
-- dir_find "DX7-ROM1A.syx" "/home/rohan/sw/hsc3-data/data/yamaha/"
--
dir_find :: FilePath -> FilePath -> IO [FilePath]
-- | Require that exactly one file is located, else error.
--
--
-- dir_find_1 "DX7-ROM1A.syx" "/home/rohan/sw/hsc3-data/data/yamaha/"
--
dir_find_1 :: FilePath -> FilePath -> IO FilePath
-- | Recursively find files having case-insensitive filename extension.
-- This runs the system utility find, so is Unix only.
--
--
-- dir_find_ext ".syx" "/home/rohan/sw/hsc3-data/data/yamaha/"
--
dir_find_ext :: String -> FilePath -> IO [FilePath]
-- | Post-process dir_find_ext to delete starting directory.
--
--
-- dir_find_ext_rel ".syx" "/home/rohan/sw/hsc3-data/data/yamaha/"
--
dir_find_ext_rel :: String -> FilePath -> IO [FilePath]
-- | Scan each directory on path recursively for file. Stop once a file is
-- located. Runs dir_find so is Unix only.
--
--
-- path_scan_recursively ["/home/rohan/sw/hmt-base"] "Directory.hs"
--
path_scan_recursively :: [FilePath] -> FilePath -> IO (Maybe FilePath)
-- | Search each directory on path recursively for file. Runs
-- dir_find so is Unix only.
--
--
-- path_search_recursively ["/home/rohan/sw"] "README.md"
--
path_search_recursively :: [FilePath] -> FilePath -> IO [FilePath]
-- | Either
module Music.Theory.Either
-- | Maybe Left of Either.
from_left :: Either a b -> Maybe a
-- | fromJust of from_left
from_left_err :: Either t e -> t
-- | Maybe Right of Either.
from_right :: Either x t -> Maybe t
-- | fromJust of from_right
from_right_err :: Either e t -> t
-- | Flip from right to left, ie. either Right Left
either_swap :: Either a b -> Either b a
-- | Variant of rights that preserves first Left.
--
--
-- all_right (map Right [1..3]) == Right [1..3]
-- all_right [Right 1,Left 'a',Left 'b'] == Left 'a'
--
all_right :: [Either a b] -> Either a [b]
-- | Lower Either to Maybe by discarding Left.
either_to_maybe :: Either a b -> Maybe b
-- | Data.Either.isLeft, which however hugs doesn't know of.
is_left :: Either a b -> Bool
-- | Data.Either.isRight, which however hugs doesn't know of.
is_right :: Either a b -> Bool
-- | Data.Either.partitionEithers, which however hugs doesn't know of.
partition_eithers :: [Either a b] -> ([a], [b])
-- | Enumeration functions.
module Music.Theory.Enum
-- | Generic variant of fromEnum (p.263).
genericFromEnum :: (Integral i, Enum e) => e -> i
-- | Generic variant of toEnum (p.263).
genericToEnum :: (Integral i, Enum e) => i -> e
-- | Variant of enumFromTo that, if p is after q,
-- cycles from maxBound to minBound.
--
--
-- import Data.Word
-- enum_from_to_cyclic (254 :: Word8) 1 == [254,255,0,1]
--
enum_from_to_cyclic :: (Bounded a, Enum a) => a -> a -> [a]
-- | Variant of enumFromTo that, if p is after q,
-- enumerates from q to p.
--
--
-- enum_from_to_reverse 5 1 == [5,4,3,2,1]
-- enum_from_to_reverse 1 5 == enumFromTo 1 5
--
enum_from_to_reverse :: Enum a => a -> a -> [a]
-- | All elements in sequence.
--
--
-- (enum_univ :: [Data.Word.Word8]) == [0 .. 255]
--
enum_univ :: (Bounded t, Enum t) => [t]
-- | List of Enum values not in sorted input list.
--
--
-- enum_list_gaps "abdh" == "cefg"
--
enum_list_gaps :: (Enum t, Eq t) => [t] -> [t]
-- | enum_list_gaps of sort
enum_set_gaps :: (Enum t, Eq t, Ord t) => [t] -> [t]
-- | Data.Function related functions.
module Music.Theory.Function
-- | Unary operator.
type UOp t = t -> t
-- | Binary operator.
type BinOp t = t -> t -> t
-- | Iterate the function f n times, the inital value is
-- x.
--
--
-- recur_n 5 (* 2) 1 == 32
-- take (5 + 1) (iterate (* 2) 1) == [1,2,4,8,16,32]
--
recur_n :: Integral n => n -> (t -> t) -> t -> t
-- | const of const.
--
--
-- const2 5 undefined undefined == 5
-- const (const 5) undefined undefined == 5
--
const2 :: a -> b -> c -> a
-- | && of predicates, ie. do predicates f and
-- g both hold at x.
predicate_and :: (t -> Bool) -> (t -> Bool) -> t -> Bool
-- | List variant of predicate_and, ie. foldr1
--
--
-- let r = [False,False,True,False,True,False]
-- map (predicate_all [(> 0),(< 5),even]) [0..5] == r
--
predicate_all :: [t -> Bool] -> t -> Bool
-- | || of predicates.
predicate_or :: (t -> Bool) -> (t -> Bool) -> t -> Bool
-- | any of predicates, ie. logical or of list of predicates.
--
--
-- let r = [True,False,True,False,True,True]
-- map (predicate_any [(== 0),(== 5),even]) [0..5] == r
--
predicate_any :: [t -> Bool] -> t -> Bool
-- | == on.
eq_on :: Eq t => (u -> t) -> u -> u -> Bool
-- | fmap . fmap, ie. (t -> c) -> (a -> b
-- -> t) -> a -> b -> c.
fmap2 :: (Functor f, Functor g) => (a -> b) -> f (g a) -> f (g b)
-- | fmap of fmap2, ie. (t -> d) -> (a -> b -> c -> t)
-- -> a -> b -> c -> d.
fmap3 :: (Functor f, Functor g, Functor h) => (a -> b) -> f (g (h a)) -> f (g (h b))
-- | fmap of fmap3.
fmap4 :: (Functor f, Functor g, Functor h, Functor i) => (a -> b) -> f (g (h (i a))) -> f (g (h (i b)))
-- | fmap of fmap4
fmap5 :: (Functor f, Functor g, Functor h, Functor i, Functor j) => (a -> b) -> f (g (h (i (j a)))) -> f (g (h (i (j b))))
-- | fmap of fmap5
fmap6 :: (Functor f, Functor g, Functor h, Functor i, Functor j, Functor k) => (a -> b) -> f (g (h (i (j (k a))))) -> f (g (h (i (j (k b)))))
-- | Operator name for fmap2.
(.:) :: (Functor f, Functor g) => (a -> b) -> f (g a) -> f (g b)
infixr 8 .:
-- | Operator name for fmap3.
(.::) :: (Functor f, Functor g, Functor h) => (a -> b) -> f (g (h a)) -> f (g (h b))
infixr 8 .::
-- | Operator name for fmap4.
(.:::) :: (Functor f, Functor g, Functor h, Functor i) => (a -> b) -> f (g (h (i a))) -> f (g (h (i b)))
infixr 8 .:::
-- | Operator name for fmap5.
(.::::) :: (Functor f, Functor g, Functor h, Functor i, Functor j) => (a -> b) -> f (g (h (i (j a)))) -> f (g (h (i (j b))))
infixr 8 .::::
-- | Operator name for fmap6.
(.:::::) :: (Functor f, Functor g, Functor h, Functor i, Functor j, Functor k) => (a -> b) -> f (g (h (i (j (k a))))) -> f (g (h (i (j (k b)))))
infixr 8 .:::::
-- | Apply f to both sides of p, , ie. bimap f f. This
-- is the generic version of bimap1.
bimap1f :: Bifunctor p => (a -> b) -> p a a -> p b b
-- | Apply f to both elements of a two-tuple. Type-specialised
-- bimap1f.
bimap1 :: (t -> u) -> (t, t) -> (u, u)
-- | System.IO related functions.
module Music.Theory.Io
-- | decodeUtf8 of readFile, implemented via
-- Data.Text.
read_file_utf8_text :: FilePath -> IO Text
-- | Read (strictly) a UTF-8 encoded text file, implemented via
-- Data.Text.
read_file_utf8 :: FilePath -> IO String
-- | read_file_utf8, or a default value if the file doesn't exist.
read_file_utf8_or :: String -> FilePath -> IO String
-- | Write UTF8 string as file, via Data.Text.
write_file_utf8 :: FilePath -> String -> IO ()
-- | readFile variant using Text for ISO 8859-1
-- (Latin 1) encoding.
read_file_iso_8859_1 :: FilePath -> IO String
-- | readFile variant using Text for local encoding.
read_file_locale :: FilePath -> IO String
-- | Interact with files. Like Prelude.interact, but with named files.
interactWithFiles :: FilePath -> FilePath -> (String -> String) -> IO ()
-- | Get line from stdin if there is any input, else Nothing.
getLineFromStdinIfReady :: IO (Maybe String)
-- | Wait for input to be available, and then get lines while input remains
-- available.
getAvailableLinesFromStdin :: IO [String]
-- | Interact with stdin and stdout. Like Prelude.interact, but with pipes.
interactWithStdio :: (String -> String) -> IO ()
-- | List functions.
module Music.Theory.List
-- | slice, ie. starting index (zero-indexed) and number of
-- elements.
--
--
-- slice 4 5 [1..] == [5,6,7,8,9]
--
slice :: Int -> Int -> [a] -> [a]
-- | Variant of slice with start and end indices (zero-indexed).
--
--
-- section 4 8 [1..] == [5,6,7,8,9]
--
section :: Int -> Int -> [a] -> [a]
-- | Bracket sequence with left and right values.
--
--
-- bracket ('<','>') "1,2,3" == "<1,2,3>"
--
bracket :: (a, a) -> [a] -> [a]
-- | Variant where brackets are sequences.
--
--
-- bracket_l ("<:",":>") "1,2,3" == "<:1,2,3:>"
--
bracket_l :: ([a], [a]) -> [a] -> [a]
-- | The first & middle & last elements of a list.
--
--
-- map unbracket_el ["","{12}"] == [(Nothing,"",Nothing),(Just '{',"12",Just '}')]
--
unbracket_el :: [a] -> (Maybe a, [a], Maybe a)
-- | The first & middle & last elements of a list.
--
--
-- map unbracket ["","{12}"] == [Nothing,Just ('{',"12",'}')]
--
unbracket :: [t] -> Maybe (t, [t], t)
-- | Erroring variant.
unbracket_err :: [t] -> (t, [t], t)
-- | Relative of splitOn, but only makes first separation.
--
--
-- splitOn "//" "lhs//rhs//rem" == ["lhs","rhs","rem"]
-- separate_at "//" "lhs//rhs//rem" == Just ("lhs","rhs//rem")
--
separate_at :: Eq a => [a] -> [a] -> Maybe ([a], [a])
-- | Variant of splitWhen that keeps delimiters at left.
--
--
-- split_when_keeping_left (== 'r') "rab rcd re rf r" == ["","rab ","rcd ","re ","rf ","r"]
--
split_when_keeping_left :: (a -> Bool) -> [a] -> [[a]]
-- | Split before the indicated element, keeping it at the left of the
-- sub-sequence it begins. split_when_keeping_left of ==
--
--
-- split_before 'x' "axbcxdefx" == ["a","xbc","xdef","x"]
-- split_before 'x' "xa" == ["","xa"]
--
--
--
-- map (flip split_before "abcde") "ae_" == [["","abcde"],["abcd","e"],["abcde"]]
-- map (flip break "abcde" . (==)) "ae_" == [("","abcde"),("abcd","e"),("abcde","")]
--
--
--
-- split_before 'r' "rab rcd re rf r" == ["","rab ","rcd ","re ","rf ","r"]
--
split_before :: Eq a => a -> [a] -> [[a]]
-- | Split before any of the indicated set of delimiters.
--
--
-- split_before_any ",;" ";a,b,c;d;" == ["",";a",",b",",c",";d",";"]
--
split_before_any :: Eq a => [a] -> [a] -> [[a]]
-- | Singleton variant of splitOn.
--
--
-- split_on_1 ":" "graph:layout" == Just ("graph","layout")
--
split_on_1 :: Eq t => [t] -> [t] -> Maybe ([t], [t])
-- | Erroring variant.
split_on_1_err :: Eq t => [t] -> [t] -> ([t], [t])
-- | Split function that splits only once, ie. a variant of break.
--
--
-- split1 ' ' "three word sentence" == Just ("three","word sentence")
--
split1 :: Eq a => a -> [a] -> Maybe ([a], [a])
-- | Erroring variant.
split1_err :: (Eq a, Show a) => a -> [a] -> ([a], [a])
-- | If length is not even the second "half" is longer.
--
--
-- split_into_halves [] == ([],[])
-- split_into_halves [1] == ([],[1])
-- split_into_halves [1 .. 2] == ([1],[2])
-- split_into_halves [1 .. 8] == ([1,2,3,4],[5,6,7,8])
-- split_into_halves [1 .. 9] == ([1,2,3,4],[5,6,7,8,9])
--
split_into_halves :: [t] -> ([t], [t])
-- | Generic form of rotate_left.
genericRotate_left :: Integral i => i -> [a] -> [a]
-- | Left rotation.
--
--
-- rotate_left 1 [1..3] == [2,3,1]
-- rotate_left 3 [1..5] == [4,5,1,2,3]
--
rotate_left :: Int -> [a] -> [a]
-- | Generic form of rotate_right.
genericRotate_right :: Integral n => n -> [a] -> [a]
-- | Right rotation.
--
--
-- rotate_right 1 [1..3] == [3,1,2]
--
rotate_right :: Int -> [a] -> [a]
-- | Rotate left by n mod #p places. Therefore
-- negative n rotate right.
--
--
-- rotate 1 [1..3] == [2,3,1]
-- rotate 8 [1..5] == [4,5,1,2,3]
-- (rotate (-1) "ABCD",rotate 1 "ABCD") == ("DABC","BCDA")
--
rotate :: Integral n => n -> [a] -> [a]
-- | Rotate right by n places.
--
--
-- rotate_r 8 [1..5] == [3,4,5,1,2]
--
rotate_r :: Integral n => n -> [a] -> [a]
-- | All rotations.
--
--
-- rotations [0,1,3] == [[0,1,3],[1,3,0],[3,0,1]]
--
rotations :: [a] -> [[a]]
-- | Rotate list so that is starts at indicated element.
--
--
-- rotate_starting_from 'c' "abcde" == Just "cdeab"
-- rotate_starting_from '_' "abc" == Nothing
--
rotate_starting_from :: Eq a => a -> [a] -> Maybe [a]
-- | Erroring variant.
rotate_starting_from_err :: Eq a => a -> [a] -> [a]
-- | Sequence of n adjacent elements, moving forward by k
-- places. The last element may have fewer than n places, but will
-- reach the end of the input sequence.
--
--
-- adj 3 2 "adjacent" == ["adj","jac","cen","nt"]
--
adj :: Int -> Int -> [a] -> [[a]]
-- | Variant of adj where the last element has n places but
-- may not reach the end of the input sequence.
--
--
-- adj_trunc 4 1 "adjacent" == ["adja","djac","jace","acen","cent"]
-- adj_trunc 3 2 "adjacent" == ["adj","jac","cen"]
--
adj_trunc :: Int -> Int -> [a] -> [[a]]
-- | adj_trunc of close by n-1.
--
--
-- adj_cyclic_trunc 3 1 "adjacent" == ["adj","dja","jac","ace","cen","ent","nta","tad"]
--
adj_cyclic_trunc :: Int -> Int -> [a] -> [[a]]
-- | Generic form of adj2.
genericAdj2 :: Integral n => n -> [t] -> [(t, t)]
-- | Adjacent elements of list, at indicated distance, as pairs.
--
--
-- adj2 1 [1..5] == [(1,2),(2,3),(3,4),(4,5)]
-- let l = [1..5] in zip l (tail l) == adj2 1 l
-- adj2 2 [1..4] == [(1,2),(3,4)]
-- adj2 3 [1..5] == [(1,2),(4,5)]
--
adj2 :: Int -> [t] -> [(t, t)]
-- | Append first n-elements to end of list.
--
--
-- close 1 [1..3] == [1,2,3,1]
--
close :: Int -> [a] -> [a]
-- | adj2 . close 1.
--
--
-- adj2_cyclic 1 [1..3] == [(1,2),(2,3),(3,1)]
--
adj2_cyclic :: Int -> [t] -> [(t, t)]
-- | Adjacent triples.
--
--
-- adj3 3 [1..6] == [(1,2,3),(4,5,6)]
--
adj3 :: Int -> [t] -> [(t, t, t)]
-- | adj3 . close 2.
--
--
-- adj3_cyclic 1 [1..4] == [(1,2,3),(2,3,4),(3,4,1),(4,1,2)]
--
adj3_cyclic :: Int -> [t] -> [(t, t, t)]
-- | Adjacent quadruples.
--
--
-- adj4 2 [1..8] == [(1,2,3,4),(3,4,5,6),(5,6,7,8)]
-- adj4 4 [1..8] == [(1,2,3,4),(5,6,7,8)]
--
adj4 :: Int -> [t] -> [(t, t, t, t)]
-- | Interleave elements of p and q. If not of equal length
-- elements are discarded.
--
--
-- interleave [1..3] [4..6] == [1,4,2,5,3,6]
-- interleave ".+-" "abc" == ".a+b-c"
-- interleave [1..3] [] == []
--
interleave :: [a] -> [a] -> [a]
-- | Interleave list of lists. Allows lists to be of non-equal lenghts.
--
--
-- interleave_set ["abcd","efgh","ijkl"] == "aeibfjcgkdhl"
-- interleave_set ["abc","defg","hijkl"] == "adhbeicfjgkl"
--
interleave_set :: [[a]] -> [a]
-- | De-interleave n lists.
--
--
-- deinterleave 2 ".a+b-c" == [".+-","abc"]
-- deinterleave 3 "aeibfjcgkdhl" == ["abcd","efgh","ijkl"]
--
deinterleave :: Int -> [a] -> [[a]]
-- | Special case for two-part deinterleaving.
--
--
-- deinterleave2 ".a+b-c" == (".+-","abc")
--
deinterleave2 :: [t] -> ([t], [t])
-- | Variant that continues with the longer input.
--
--
-- interleave_continue ".+-" "abc" == ".a+b-c"
-- interleave_continue [1..3] [] == [1..3]
-- interleave_continue [] [1..3] == [1..3]
--
interleave_continue :: [a] -> [a] -> [a]
-- | interleave of rotate_left by i and j.
--
--
-- interleave_rotations 9 3 [1..13] == [10,4,11,5,12,6,13,7,1,8,2,9,3,10,4,11,5,12,6,13,7,1,8,2,9,3]
--
interleave_rotations :: Int -> Int -> [b] -> [b]
-- | unzip, apply f1 and f2 and zip.
rezip :: ([t] -> [u]) -> ([v] -> [w]) -> [(t, v)] -> [(u, w)]
-- | Generalised histogram, with equality function for grouping and
-- comparison function for sorting.
generic_histogram_by :: Integral i => (a -> a -> Bool) -> Maybe (a -> a -> Ordering) -> [a] -> [(a, i)]
-- | Type specialised generic_histogram_by.
histogram_by :: (a -> a -> Bool) -> Maybe (a -> a -> Ordering) -> [a] -> [(a, Int)]
-- | Count occurences of elements in list, histogram_by of ==
-- and compare.
generic_histogram :: (Ord a, Integral i) => [a] -> [(a, i)]
-- | Type specialised generic_histogram. Elements will be in
-- ascending order.
--
--
-- map histogram ["","hohoh","yxx"] == [[],[('h',3),('o',2)],[('x',2),('y',1)]]
--
histogram :: Ord a => [a] -> [(a, Int)]
-- | Join two histograms, which must be sorted.
--
--
-- histogram_join (zip "ab" [1,1]) (zip "bc" [1,1]) == zip "abc" [1,2,1]
--
histogram_join :: Ord a => [(a, Int)] -> [(a, Int)] -> [(a, Int)]
-- | foldr of histogram_join.
--
--
-- let f x = zip x (repeat 1) in histogram_merge (map f ["ab","bcd","de"]) == zip "abcde" [1,2,1,2,1]
--
histogram_merge :: Ord a => [[(a, Int)]] -> [(a, Int)]
-- | Given (k,#) histogram where k is enumerable generate filled histogram
-- with 0 for empty k.
--
--
-- histogram_fill (histogram "histogram") == zip ['a'..'t'] [1,0,0,0,0,0,1,1,1,0,0,0,1,0,1,0,0,1,1,1]
--
histogram_fill :: (Ord a, Enum a) => [(a, Int)] -> [(a, Int)]
-- | Given two histograms p & q (sorted by key) make composite
-- histogram giving for all keys the counts for (p,q).
--
--
-- r = zip "ABCDE" (zip [4,3,2,1,0] [2,3,4,0,5])
-- histogram_composite (zip "ABCD" [4,3,2,1]) (zip "ABCE" [2,3,4,5]) == r
--
histogram_composite :: Ord a => [(a, Int)] -> [(a, Int)] -> [(a, (Int, Int))]
-- | Apply - at count of histogram_composite, ie. 0 indicates
-- equal number at p and q, negative indicates more elements at p than q
-- and positive more elements at q than p.
--
--
-- histogram_diff (zip "ABCD" [4,3,2,1]) (zip "ABCE" [2,3,4,5]) == zip "ABCDE" [-2,0,2,-1,5]
--
histogram_diff :: Ord a => [(a, Int)] -> [(a, Int)] -> [(a, Int)]
-- | Elements that appear more than once in the input given equality
-- predicate.
duplicates_by :: Ord a => (a -> a -> Bool) -> [a] -> [a]
-- | duplicates_by of ==.
--
--
-- map duplicates ["duplicates","redundant"] == ["","dn"]
--
duplicates :: Ord a => [a] -> [a]
-- | List segments of length i at distance j.
--
--
-- segments 2 1 [1..5] == [[1,2],[2,3],[3,4],[4,5]]
-- segments 2 2 [1..5] == [[1,2],[3,4]]
--
segments :: Int -> Int -> [a] -> [[a]]
-- | foldl1 intersect.
--
--
-- intersect_l [[1,2],[1,2,3],[1,2,3,4]] == [1,2]
--
intersect_l :: Eq a => [[a]] -> [a]
-- | foldl1 union.
--
--
-- sort (union_l [[1,3],[2,3],[3]]) == [1,2,3]
--
union_l :: Eq a => [[a]] -> [a]
-- | Intersection of adjacent elements of list at distance n.
--
--
-- adj_intersect 1 [[1,2],[1,2,3],[1,2,3,4]] == [[1,2],[1,2,3]]
--
adj_intersect :: Eq a => Int -> [[a]] -> [[a]]
-- | List of cycles at distance n.
--
--
-- cycles 2 [1..6] == [[1,3,5],[2,4,6]]
-- cycles 3 [1..9] == [[1,4,7],[2,5,8],[3,6,9]]
-- cycles 4 [1..8] == [[1,5],[2,6],[3,7],[4,8]]
--
cycles :: Int -> [a] -> [[a]]
-- | Variant of filter that has a predicate to halt processing, ie.
-- filter of takeWhile.
--
--
-- filter_halt (even . fst) ((< 5) . snd) (zip [1..] [0..])
--
filter_halt :: (a -> Bool) -> (a -> Bool) -> [a] -> [a]
-- | Variant of filter that retains Nothing as a placeholder
-- for removed elements.
--
--
-- filter_maybe even [1..4] == [Nothing,Just 2,Nothing,Just 4]
--
filter_maybe :: (a -> Bool) -> [a] -> [Maybe a]
-- | Select only the elements from the list that lie in the indicated
-- range, which is (inclusive, exclusive).
--
--
-- filterInRange (3, 5) [1, 1.5 .. 9] == [3.0,3.5,4.0,4.5]
--
filterInRange :: Ord a => (a, a) -> [a] -> [a]
-- | Replace all p with q in s.
--
--
-- replace "_x_" "-X-" "an _x_ string" == "an -X- string"
-- replace "ab" "cd" "ab ab cd ab" == "cd cd cd cd"
--
replace :: Eq a => [a] -> [a] -> [a] -> [a]
-- | Replace the ith value at ns with x.
--
--
-- replace_at "test" 2 'n' == "tent"
--
replace_at :: Integral i => [a] -> i -> a -> [a]
-- | Data.List.stripPrefix, which however hugs doesn't know of.
strip_prefix :: Eq a => [a] -> [a] -> Maybe [a]
-- | error of stripPrefix
strip_prefix_err :: Eq t => [t] -> [t] -> [t]
-- | Equivalent to groupBy eq on f.
--
--
-- group_by_on (==) snd (zip [0..] "abbc") == [[(0,'a')],[(1,'b'),(2,'b')],[(3,'c')]]
--
group_by_on :: (x -> x -> Bool) -> (t -> x) -> [t] -> [[t]]
-- | group_by_on of ==.
--
--
-- r = [[(1,'a'),(1,'b')],[(2,'c')],[(3,'d'),(3,'e')],[(4,'f')]]
-- group_on fst (zip [1,1,2,3,3,4] "abcdef") == r
--
group_on :: Eq x => (a -> x) -> [a] -> [[a]]
-- | Given an equality predicate and accesors for key and
-- value collate adjacent values.
collate_by_on_adjacent :: (k -> k -> Bool) -> (a -> k) -> (a -> v) -> [a] -> [(k, [v])]
-- | collate_by_on_adjacent of ==
collate_on_adjacent :: Eq k => (a -> k) -> (a -> v) -> [a] -> [(k, [v])]
-- | collate_on_adjacent of fst and snd.
--
--
-- collate_adjacent (zip "TDD" "xyz") == [('T',"x"),('D',"yz")]
--
collate_adjacent :: Eq a => [(a, b)] -> [(a, [b])]
-- | Data.List.sortOn, which however hugs doesn't know of.
sort_on :: Ord b => (a -> b) -> [a] -> [a]
-- | sortOn prior to collate_on_adjacent.
--
--
-- r = [('A',"a"),('B',"bd"),('C',"ce"),('D',"f")]
-- collate_on fst snd (zip "ABCBCD" "abcdef") == r
--
collate_on :: Ord k => (a -> k) -> (a -> v) -> [a] -> [(k, [v])]
-- | collate_on of fst and snd.
--
--
-- collate (zip "TDD" "xyz") == [('D',"yz"),('T',"x")]
-- collate (zip [1,2,1] "abc") == [(1,"ac"),(2,"b")]
--
collate :: Ord a => [(a, b)] -> [(a, [b])]
-- | Reverse of collate, inverse if order is not considered.
--
--
-- uncollate [(1,"ac"),(2,"b")] == zip [1,1,2] "acb"
--
uncollate :: [(k, [v])] -> [(k, v)]
-- | Make assoc list with given key.
--
--
-- with_key 'a' [1..3] == [('a',1),('a',2),('a',3)]
--
with_key :: k -> [v] -> [(k, v)]
-- | Left biased merge of association lists p and q.
--
--
-- assoc_merge [(5,"a"),(3,"b")] [(5,"A"),(7,"C")] == [(5,"a"),(3,"b"),(7,"C")]
--
assoc_merge :: Eq k => [(k, v)] -> [(k, v)] -> [(k, v)]
-- | Keys are in ascending order, the entry retrieved is the rightmose with
-- a key less than or equal to the key requested. If the key requested is
-- less than the initial key, or the list is empty, returns
-- Nothing.
--
--
-- let m = [(1,'a'),(4,'x'),(4,'b'),(5,'c')]
-- mapMaybe (ord_map_locate m) [1 .. 6] == [(1,'a'),(1,'a'),(1,'a'),(4,'b'),(5,'c'),(5,'c')]
-- ord_map_locate m 0 == Nothing
--
ord_map_locate :: Ord k => [(k, v)] -> k -> Maybe (k, v)
-- | Intervals to values, zero is n.
--
--
-- dx_d 5 [1,2,3] == [5,6,8,11]
--
dx_d :: Num a => a -> [a] -> [a]
-- | Variant that takes initial value and separates final value. This is an
-- appropriate function for mapAccumL.
--
--
-- dx_d' 5 [1,2,3] == (11,[5,6,8])
-- dx_d' 0 [1,1,1] == (3,[0,1,2])
--
dx_d' :: Num t => t -> [t] -> (t, [t])
-- | Integration with f, ie. apply flip of f between elements
-- of l.
--
--
-- d_dx_by (,) "abcd" == [('b','a'),('c','b'),('d','c')]
-- d_dx_by (-) [0,2,4,1,0] == [2,2,-3,-1]
-- d_dx_by (-) [2,3,0,4,1] == [1,-3,4,-3]
--
d_dx_by :: (t -> t -> u) -> [t] -> [u]
-- | Integrate, d_dx_by -, ie. pitch class segment to
-- interval sequence.
--
--
-- d_dx [5,6,8,11] == [1,2,3]
-- d_dx [] == []
--
d_dx :: Num a => [a] -> [a]
-- | Elements of p not in q.
--
--
-- [1,2,3] `difference` [1,2] == [3]
--
difference :: Eq a => [a] -> [a] -> [a]
-- | Is p a subset of q, ie. is intersect of p
-- and q == p.
--
--
-- map (is_subset [1,2]) [[1],[1,2],[1,2,3]] == [False,True,True]
--
is_subset :: Eq a => [a] -> [a] -> Bool
-- | Is p a proper subset of q, is_subset and
-- not equal.
--
--
-- map (is_proper_subset [1,2]) [[1],[1,2],[1,2,3]] == [False,False,True]
--
is_proper_subset :: Eq a => [a] -> [a] -> Bool
-- | Is p a superset of q, ie. flip is_subset.
--
--
-- is_superset [1,2,3] [1,2] == True
--
is_superset :: Eq a => [a] -> [a] -> Bool
-- | Is p a subsequence of q, ie. synonym for
-- isInfixOf.
--
--
-- subsequence [1,2] [1,2,3] == True
--
subsequence :: Eq a => [a] -> [a] -> Bool
-- | Erroring variant of findIndex.
findIndex_err :: (a -> Bool) -> [a] -> Int
-- | Erroring variant of elemIndex.
elemIndex_err :: Eq a => a -> [a] -> Int
-- | Variant of elemIndices that requires e to be unique in
-- p.
--
--
-- elem_index_unique 'a' "abcda" == undefined
--
elem_index_unique :: Eq a => a -> [a] -> Int
-- | Lookup that errors and prints message and key.
lookup_err_msg :: (Eq k, Show k) => String -> k -> [(k, v)] -> v
-- | Error variant.
lookup_err :: Eq k => k -> [(k, v)] -> v
-- | lookup variant with default value.
lookup_def :: Eq k => k -> v -> [(k, v)] -> v
-- | If l is empty Nothing, else Just l.
non_empty :: [t] -> Maybe [t]
-- | Variant on filter that selects all matches.
--
--
-- lookup_set 1 (zip [1,2,3,4,1] "abcde") == Just "ae"
--
lookup_set :: Eq k => k -> [(k, v)] -> Maybe [v]
-- | Erroring variant.
lookup_set_err :: Eq k => k -> [(k, v)] -> [v]
-- | Reverse lookup.
--
--
-- reverse_lookup 'c' [] == Nothing
-- reverse_lookup 'b' (zip [1..] ['a'..]) == Just 2
-- lookup 2 (zip [1..] ['a'..]) == Just 'b'
--
reverse_lookup :: Eq v => v -> [(k, v)] -> Maybe k
-- | Erroring variant.
reverse_lookup_err :: Eq v => v -> [(k, v)] -> k
-- | Erroring variant of find.
find_err :: (t -> Bool) -> [t] -> t
-- | Basis of find_bounds_scl, indicates if x is to the left
-- or right of the list, and if to the right whether equal or not.
-- Right values will be correct if the list is not ascending,
-- however Left values only make sense for ascending ranges.
--
--
-- map (find_bounds_cmp compare [(0,1),(1,2)]) [-1,0,1,2,3]
--
find_bounds_cmp :: (t -> s -> Ordering) -> [(t, t)] -> s -> Either ((t, t), Ordering) (t, t)
-- | Decide if value is nearer the left or right value of a range, return
-- fst or snd.
decide_nearest_f :: Ord o => Bool -> (p -> o) -> (p, p) -> (x, x) -> x
-- | decide_nearest_f with abs of - as measure.
--
--
-- (decide_nearest True 2 (1,3)) ("left","right") == "left"
--
decide_nearest :: (Num o, Ord o) => Bool -> o -> (o, o) -> (x, x) -> x
-- | sel_f gets comparison key from t.
find_nearest_by :: (Ord n, Num n) => (t -> n) -> Bool -> [t] -> n -> t
-- | Find the number that is nearest the requested value in an ascending
-- list of numbers.
--
--
-- map (find_nearest_err True [0,3.5,4,7]) [-1,1,3,5,7,9] == [0,0,3.5,4,7,7]
--
find_nearest_err :: (Num n, Ord n) => Bool -> [n] -> n -> n
-- | find_nearest_err allowing null input list (which returns
-- Nothing)
find_nearest :: (Num n, Ord n) => Bool -> [n] -> n -> Maybe n
-- | Basis of find_bounds. There is an option to consider the last
-- element specially, and if equal to the last span is given.
--
-- scl=special-case-last
find_bounds_scl :: Bool -> (t -> s -> Ordering) -> [(t, t)] -> s -> Maybe (t, t)
-- | Find adjacent elements of list that bound element under given
-- comparator.
--
--
-- let {f = find_bounds True compare [1..5]
-- ;r = [Nothing,Just (1,2),Just (3,4),Just (4,5)]}
-- in map f [0,1,3.5,5] == r
--
find_bounds :: Bool -> (t -> s -> Ordering) -> [t] -> s -> Maybe (t, t)
-- | Special case of dropRight.
--
--
-- map drop_last ["","?","remove"] == ["","","remov"]
--
drop_last :: [t] -> [t]
-- | Variant of drop from right of list.
--
--
-- dropRight 1 [1..9] == [1..8]
--
dropRight :: Int -> [a] -> [a]
-- | Variant of dropWhile from right of list.
--
--
-- dropWhileRight Data.Char.isDigit "A440" == "A"
--
dropWhileRight :: (a -> Bool) -> [a] -> [a]
-- | Data.List.dropWhileEnd, which however hugs doesn't know of.
drop_while_end :: (a -> Bool) -> [a] -> [a]
-- | foldr form of dropWhileRight.
--
--
-- drop_while_right Data.Char.isDigit "A440" == "A"
--
drop_while_right :: (a -> Bool) -> [a] -> [a]
-- | take from right.
--
--
-- take_right 3 "taking" == "ing"
--
take_right :: Int -> [a] -> [a]
-- | takeWhile from right.
--
--
-- takeWhileRight Data.Char.isDigit "A440" == "440"
--
takeWhileRight :: (a -> Bool) -> [a] -> [a]
-- | foldr form of takeWhileRight.
--
--
-- take_while_right Data.Char.isDigit "A440" == "440"
--
take_while_right :: (a -> Bool) -> [a] -> [a]
-- | Variant of take that allows Nothing to indicate the
-- complete list.
--
--
-- maybe_take (Just 5) [1 .. ] == [1 .. 5]
-- maybe_take Nothing [1 .. 9] == [1 .. 9]
--
maybe_take :: Maybe Int -> [a] -> [a]
-- | Take until f is true. This is not the same as not at
-- takeWhile because it keeps the last element. It is an error if
-- the predicate never succeeds.
--
--
-- take_until (== 'd') "tender" == "tend"
-- takeWhile (not . (== 'd')) "tend" == "ten"
-- take_until (== 'd') "seven" == undefined
--
take_until :: (a -> Bool) -> [a] -> [a]
-- | Apply f at first element, and g at all other elements.
--
--
-- at_head negate id [1..5] == [-1,2,3,4,5]
--
at_head :: (a -> b) -> (a -> b) -> [a] -> [b]
-- | Apply f at all but last element, and g at last element.
--
--
-- at_last (* 2) negate [1..4] == [2,4,6,-4]
--
at_last :: (a -> b) -> (a -> b) -> [a] -> [b]
-- | Separate list into an initial list and perhaps the last element tuple.
--
--
-- separate_last' [] == ([],Nothing)
--
separate_last' :: [a] -> ([a], Maybe a)
-- | Error on null input.
--
--
-- separate_last [1..5] == ([1..4],5)
--
separate_last :: [a] -> ([a], a)
-- | Replace directly repeated elements with Nothing.
--
--
-- indicate_repetitions "abba" == [Just 'a',Just 'b',Nothing,Just 'a']
--
indicate_repetitions :: Eq a => [a] -> [Maybe a]
-- | zipWith of list and it's own tail.
--
--
-- zip_with_adj (,) "abcde" == [('a','b'),('b','c'),('c','d'),('d','e')]
--
zip_with_adj :: (a -> a -> b) -> [a] -> [b]
-- | Type-specialised zip_with_adj.
compare_adjacent_by :: (a -> a -> Ordering) -> [a] -> [Ordering]
-- | compare_adjacent_by of compare.
--
--
-- compare_adjacent [0,1,3,2] == [LT,LT,GT]
--
compare_adjacent :: Ord a => [a] -> [Ordering]
-- | Head and tail of list. Useful to avoid "incomplete-uni-patterns"
-- warnings. It's an error if the list is empty.
headTail :: [a] -> (a, [a])
-- | First and second elements of list. Useful to avoid
-- "incomplete-uni-patterns" warnings. It's an error if the list has less
-- than two elements.
firstSecond :: [t] -> (t, t)
-- | groupBy does not make adjacent comparisons, it compares each
-- new element to the start of the group. This function is the adjacent
-- variant.
--
--
-- groupBy (<) [1,2,3,2,4,1,5,9] == [[1,2,3,2,4],[1,5,9]]
-- adjacent_groupBy (<) [1,2,3,2,4,1,5,9] == [[1,2,3],[2,4],[1,5,9]]
--
adjacent_groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
-- | Reduce sequences of consecutive values to ranges.
--
--
-- group_ranges [-1,0,3,4,5,8,9,12] == [(-1,0),(3,5),(8,9),(12,12)]
-- group_ranges [3,2,3,4,3] == [(3,3),(2,4),(3,3)]
--
group_ranges :: (Num t, Eq t) => [t] -> [(t, t)]
-- | groupBy on structure of Maybe, ie. all
-- Just compare equal.
--
--
-- let r = [[Just 1],[Nothing,Nothing],[Just 4,Just 5]]
-- in group_just [Just 1,Nothing,Nothing,Just 4,Just 5] == r
--
group_just :: [Maybe a] -> [[Maybe a]]
-- | Predicate to determine if all elements of the list are ==.
--
--
-- all_equal "aaa" == True
--
all_equal :: Eq a => [a] -> Bool
-- | Variant using nub.
all_eq :: Eq n => [n] -> Bool
-- | nubBy == on f.
--
--
-- nub_on snd (zip "ABCD" "xxyy") == [('A','x'),('C','y')]
--
nub_on :: Eq b => (a -> b) -> [a] -> [a]
-- | group_on of sortOn.
--
--
-- let r = [[('1','a'),('1','c')],[('2','d')],[('3','b'),('3','e')]]
-- in sort_group_on fst (zip "13123" "abcde") == r
--
sort_group_on :: Ord b => (a -> b) -> [a] -> [[a]]
-- | Maybe cons element onto list.
--
--
-- Nothing `mcons` "something" == "something"
-- Just 's' `mcons` "omething" == "something"
--
mcons :: Maybe a -> [a] -> [a]
-- | Cons onto end of list.
--
--
-- snoc 4 [1,2,3] == [1,2,3,4]
--
snoc :: a -> [a] -> [a]
-- | Comparison function type.
type Compare_F a = a -> a -> Ordering
-- | If f compares EQ, defer to g.
two_stage_compare :: Compare_F a -> Compare_F a -> Compare_F a
-- | compare on of two_stage_compare
two_stage_compare_on :: (Ord i, Ord j) => (t -> i) -> (t -> j) -> t -> t -> Ordering
-- | Sequence of comparison functions, continue comparing until not EQ.
--
--
-- compare (1,0) (0,1) == GT
-- n_stage_compare [compare `on` snd,compare `on` fst] (1,0) (0,1) == LT
--
n_stage_compare :: [Compare_F a] -> Compare_F a
-- | compare on of two_stage_compare
n_stage_compare_on :: Ord i => [t -> i] -> t -> t -> Ordering
-- | Sort sequence a based on ordering of sequence b.
--
--
-- sort_to "abc" [1,3,2] == "acb"
-- sort_to "adbce" [1,4,2,3,5] == "abcde"
--
sort_to :: Ord i => [e] -> [i] -> [e]
-- | flip of sort_to.
--
--
-- sort_to_rev [1,4,2,3,5] "adbce" == "abcde"
--
sort_to_rev :: Ord i => [i] -> [e] -> [e]
-- | sortBy of two_stage_compare.
sort_by_two_stage :: Compare_F a -> Compare_F a -> [a] -> [a]
-- | sortBy of n_stage_compare.
sort_by_n_stage :: [Compare_F a] -> [a] -> [a]
-- | sortBy of two_stage_compare_on.
sort_by_two_stage_on :: (Ord b, Ord c) => (a -> b) -> (a -> c) -> [a] -> [a]
-- | sortBy of n_stage_compare_on.
sort_by_n_stage_on :: Ord b => [a -> b] -> [a] -> [a]
-- | Given a comparison function, merge two ascending lists. Alias for
-- mergeBy
--
--
-- merge_by compare [1,3,5] [2,4] == [1..5]
--
merge_by :: Compare_F a -> [a] -> [a] -> [a]
-- | merge_by compare on.
merge_on :: Ord x => (a -> x) -> [a] -> [a] -> [a]
-- | mergeBy of two_stage_compare.
merge_by_two_stage :: Ord b => (a -> b) -> Compare_F c -> (a -> c) -> [a] -> [a] -> [a]
-- | Alias for merge
merge :: Ord a => [a] -> [a] -> [a]
-- | Merge list of sorted lists given comparison function. Note that this
-- is not equal to mergeAll.
merge_set_by :: (a -> a -> Ordering) -> [[a]] -> [a]
-- | merge_set_by of compare.
--
--
-- merge_set [[1,3,5,7,9],[2,4,6,8],[10]] == [1..10]
--
merge_set :: Ord a => [[a]] -> [a]
-- | merge_by variant that joins (resolves) equal elements.
--
--
-- let {left p _ = p
-- ;right _ q = q
-- ;cmp = compare `on` fst
-- ;p = zip [1,3,5] "abc"
-- ;q = zip [1,2,3] "ABC"
-- ;left_r = [(1,'a'),(2,'B'),(3,'b'),(5,'c')]
-- ;right_r = [(1,'A'),(2,'B'),(3,'C'),(5,'c')]}
-- in merge_by_resolve left cmp p q == left_r &&
-- merge_by_resolve right cmp p q == right_r
--
--
--
-- merge_by_resolve (\x _ -> x) (compare `on` fst) [(0,'A'),(1,'B'),(4,'E')] (zip [1..] "bcd")
--
merge_by_resolve :: (a -> a -> a) -> Compare_F a -> [a] -> [a] -> [a]
-- | Merge two sorted (ascending) sequences. Where elements compare equal,
-- select element from left input.
--
--
-- asc_seq_left_biased_merge_by (compare `on` fst) [(0,'A'),(1,'B'),(4,'E')] (zip [1..] "bcd")
--
asc_seq_left_biased_merge_by :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
-- | Find the first two adjacent elements for which f is True.
--
--
-- find_adj (>) [1,2,3,3,2,1] == Just (3,2)
-- find_adj (>=) [1,2,3,3,2,1] == Just (3,3)
--
find_adj :: (a -> a -> Bool) -> [a] -> Maybe (a, a)
-- | find_adj of >=
--
--
-- filter is_ascending (words "A AA AB ABB ABC ABA") == words "A AB ABC"
--
is_ascending :: Ord a => [a] -> Bool
-- | find_adj of >
--
--
-- filter is_non_descending (words "A AA AB ABB ABC ABA") == ["A","AA","AB","ABB","ABC"]
--
is_non_descending :: Ord a => [a] -> Bool
-- | Variant of elem that operates on a sorted list, halting. This
-- is member.
--
--
-- 16 `elem_ordered` [1,3 ..] == False
-- 16 `elem` [1,3 ..] == undefined
--
elem_ordered :: Ord t => t -> [t] -> Bool
-- | Variant of elemIndex that operates on a sorted list, halting.
--
--
-- 16 `elemIndex_ordered` [1,3 ..] == Nothing
-- 16 `elemIndex_ordered` [0,1,4,9,16,25,36,49,64,81,100] == Just 4
--
elemIndex_ordered :: Ord t => t -> [t] -> Maybe Int
-- | zipWith variant equivalent to mapMaybe (ie.
-- catMaybes of zipWith)
zip_with_maybe :: (a -> b -> Maybe c) -> [a] -> [b] -> [c]
-- | zipWith variant that extends shorter side using given value.
zip_with_ext :: t -> u -> (t -> u -> v) -> [t] -> [u] -> [v]
-- | zip_with_ext of ','
--
--
-- let f = zip_ext 'i' 'j'
-- f "" "" == []
-- f "p" "" == zip "p" "j"
-- f "" "q" == zip "i" "q"
-- f "pp" "q" == zip "pp" "qj"
-- f "p" "qq" == zip "pi" "qq"
--
zip_ext :: t -> u -> [t] -> [u] -> [(t, u)]
-- | Keep right variant of zipWith, where unused rhs values are
-- returned.
--
--
-- zip_with_kr (,) [1..3] ['a'..'e'] == ([(1,'a'),(2,'b'),(3,'c')],"de")
--
zip_with_kr :: (a -> b -> c) -> [a] -> [b] -> ([c], [b])
-- | A zipWith variant that always consumes an element from the left
-- hand side (lhs), but only consumes an element from the right hand side
-- (rhs) if the zip function is Right and not if Left.
-- There's also a secondary function to continue if the rhs ends before
-- the lhs.
zip_with_perhaps_rhs :: (a -> b -> Either c c) -> (a -> c) -> [a] -> [b] -> [c]
-- | Zip a list with a list of lists. Ordinarily the list has at least as
-- many elements as there are elements at the list of lists. There is
-- also a Traversable form of this called
-- adopt_shape_2_zip_stream.
--
--
-- zip_list_with_list_of_list [1 ..] ["a", "list", "of", "strings"]
-- zip_list_with_list_of_list [1 .. 9] ["a", "list", "of", "strings"]
--
zip_list_with_list_of_list :: [p] -> [[q]] -> [[(p, q)]]
-- | Fill gaps in a sorted association list, range is inclusive at both
-- ends.
--
--
-- let r = [(1,'a'),(2,'x'),(3,'x'),(4,'x'),(5,'b'),(6,'x'),(7,'c'),(8,'x'),(9,'x')]
-- in fill_gaps_ascending' 'x' (1,9) (zip [1,5,7] "abc") == r
--
fill_gaps_ascending :: (Enum n, Ord n) => t -> (n, n) -> [(n, t)] -> [(n, t)]
-- | Direct definition.
fill_gaps_ascending' :: (Num n, Enum n, Ord n) => t -> (n, n) -> [(n, t)] -> [(n, t)]
-- | Variant with default value for empty input list case.
minimumBy_or :: t -> (t -> t -> Ordering) -> [t] -> t
-- | minimum and maximum in one pass.
--
--
-- minmax "minmax" == ('a','x')
--
minmax :: Ord t => [t] -> (t, t)
-- | Append k to the right of l until result has n
-- places. Truncates long input lists.
--
--
-- map (pad_right '0' 2 . return) ['0' .. '9']
-- pad_right '0' 12 "1101" == "110100000000"
-- map (pad_right ' '3) ["S","E-L"] == ["S ","E-L"]
-- pad_right '!' 3 "truncate" == "tru"
--
pad_right :: a -> Int -> [a] -> [a]
-- | Variant that errors if the input list has more than n places.
--
--
-- map (pad_right_err '!' 3) ["x","xy","xyz","xyz!"]
--
pad_right_err :: t -> Int -> [t] -> [t]
-- | Variant that will not truncate long inputs.
--
--
-- pad_right_no_truncate '!' 3 "truncate" == "truncate"
--
pad_right_no_truncate :: a -> Int -> [a] -> [a]
-- | Append k to the left of l until result has n
-- places.
--
--
-- map (pad_left '0' 2 . return) ['0' .. '9']
--
pad_left :: a -> Int -> [a] -> [a]
-- | Locate first (leftmost) embedding of q in p. Return
-- partial indices for failure at Left.
--
--
-- embedding ("embedding","ming") == Right [1,6,7,8]
-- embedding ("embedding","mind") == Left [1,6,7]
--
embedding :: Eq t => ([t], [t]) -> Either [Int] [Int]
-- | fromRight of embedding
embedding_err :: Eq t => ([t], [t]) -> [Int]
-- | Does q occur in sequence, though not necessarily adjacently, in
-- p.
--
--
-- is_embedding [1 .. 9] [1,3,7] == True
-- is_embedding "embedding" "ming" == True
-- is_embedding "embedding" "mind" == False
--
is_embedding :: Eq t => [t] -> [t] -> Bool
-- | Unpack one element list.
unlist1 :: [t] -> Maybe t
-- | Erroring variant.
unlist1_err :: [t] -> t
-- | Given an Ordering predicate where LT opens a group,
-- GT closes a group, and EQ continues current group,
-- construct tree from list.
--
--
-- let l = "a {b {c d} e f} g h i"
-- let t = group_tree ((==) '{',(==) '}') l
-- catMaybes (flatten t) == l
--
--
--
-- let {d = putStrLn . drawTree . fmap show}
-- in d (group_tree ((==) '(',(==) ')') "a(b(cd)ef)ghi")
--
group_tree :: (a -> Bool, a -> Bool) -> [a] -> Tree (Maybe a)
-- | Remove element at index.
--
--
-- map (remove_ix 5) ["remove","removed"] == ["remov","removd"]
-- remove_ix 5 "short" -- error
--
remove_ix :: Int -> [a] -> [a]
-- | Delete element at ix from list (c.f. remove_ix, this has a more
-- specific error if index does not exist).
--
--
-- delete_at 3 "deleted" == "delted"
-- delete_at 8 "deleted" -- error
--
delete_at :: (Eq t, Num t) => t -> [a] -> [a]
-- | Select or remove elements at set of indices.
operate_ixs :: Bool -> [Int] -> [a] -> [a]
-- | Select elements at set of indices.
--
--
-- select_ixs [1,3] "select" == "ee"
--
select_ixs :: [Int] -> [a] -> [a]
-- | Remove elements at set of indices.
--
--
-- remove_ixs [1,3,5] "remove" == "rmv"
--
remove_ixs :: [Int] -> [a] -> [a]
-- | Replace element at i in p by application of f.
--
--
-- replace_ix negate 1 [1..3] == [1,-2,3]
--
replace_ix :: (a -> a) -> Int -> [a] -> [a]
-- | List equality, ignoring indicated indices.
--
--
-- list_eq_ignoring_indices [3,5] "abcdefg" "abc.e.g" == True
--
list_eq_ignoring_indices :: (Eq t, Integral i) => [i] -> [t] -> [t] -> Bool
-- | Edit list to have v at indices k. Replacement assoc-list
-- must be ascending. All replacements must be in range.
--
--
-- list_set_indices [(2,'C'),(4,'E')] "abcdefg" == "abCdEfg"
-- list_set_indices [] "abcdefg" == "abcdefg"
-- list_set_indices [(9,'I')] "abcdefg" == undefined
--
list_set_indices :: (Eq ix, Num ix) => [(ix, t)] -> [t] -> [t]
-- | Variant of list_set_indices with one replacement.
list_set_ix :: (Eq t, Num t) => t -> a -> [a] -> [a]
-- | Cyclic indexing function.
--
--
-- map (at_cyclic "cycle") [0..9] == "cyclecycle"
--
at_cyclic :: [a] -> Int -> a
-- | Index list from the end, assuming the list is longer than n + 1.
--
-- atFromEnd [1 .. 30] 0 == 30 atFromEnd [1..100] 15 == 85
atFromEnd :: [t] -> Int -> t
-- | Graph types.
module Music.Theory.Graph.Type
v_is_normal :: [Int] -> Maybe Int
v_is_normal_err :: [Int] -> Int
-- | Un-directed edge equality.
--
--
-- e_eq_undir (0,1) (1,0) == True
--
e_eq_undir :: Eq t => (t, t) -> (t, t) -> Bool
-- | Sort edge.
--
--
-- map e_sort [(0,1),(1,0)] == [(0,1),(0,1)]
--
e_sort :: Ord t => (t, t) -> (t, t)
-- | (vertices,edges)
type Gr t = ([t], [(t, t)])
-- | Gr is a functor.
gr_map :: (t -> u) -> Gr t -> Gr u
-- | (|V|,|E|)
gr_degree :: Gr t -> (Int, Int)
-- | Re-label graph given table.
gr_relabel :: Eq t => [(t, u)] -> Gr t -> Gr u
-- | If (i,j) and (j,i) are both in E delete (j,i) where i < j.
gr_mk_undir :: Ord t => Gr t -> Gr t
-- | List of E to G, derives V from E.
eset_to_gr :: Ord t => [(t, t)] -> Gr t
-- | Sort v and e.
gr_sort :: Ord t => Gr t -> Gr t
-- | Complete k-graph (un-directed) given list of vertices
--
--
-- gr_complete_graph "xyz" == ("xyz",[('x','y'),('x','z'),('y','z')])
--
gr_complete_graph :: Ord t => [t] -> Gr t
-- | Gr of Int
type G = Gr Int
-- | Simple text representation of G. Requires (and checks) that
-- vertices are (0 .. |v|-1). The first line is the number of vertices,
-- following lines are edges.
g_to_text :: G -> String
-- | Graph to G.
graph_to_g :: Graph -> G
-- | G to Graph
--
--
-- g = ([0,1,2],[(0,1),(0,2),(1,2)])
-- g == gr_sort (graph_to_g (g_to_graph g))
--
g_to_graph :: G -> Graph
-- | Unlabel graph, make table.
--
--
-- gr_unlabel ("xyz",[('x','y'),('x','z')]) == (([0,1,2],[(0,1),(0,2)]),[(0,'x'),(1,'y'),(2,'z')])
--
gr_unlabel :: Eq t => Gr t -> (G, [(Int, t)])
-- | fst of gr_unlabel
gr_to_g :: Eq t => Gr t -> G
-- | g_to_graph of gr_unlabel.
--
--
-- gr = ("abc",[('a','b'),('a','c'),('b','c')])
-- (g,tbl) = gr_to_graph gr
--
gr_to_graph :: Eq t => Gr t -> (Graph, [(Int, t)])
-- | Complete k-graph (un-directed).
--
--
-- g_complete_graph 3 == ([0,1,2],[(0,1),(0,2),(1,2)])
--
g_complete_graph :: Int -> G
-- | ((|V|,|E|),[E])
type Edg = ((Int, Int), [(Int, Int)])
-- | Requires (and checks) that vertices are (0 .. |v| - 1).
g_to_edg :: G -> Edg
-- | Requires (but does not check) that vertices of Edg are all in
-- (0,|v| - 1).
edg_to_g :: Edg -> G
-- | Parse Edg as printed by nauty-listg.
edg_parse :: [String] -> Edg
-- | Adjacency list [(left-hand-side,[right-hand-side])]
type Adj t = [(t, [t])]
-- | Adj to edge set.
adj_to_eset :: Ord t => Adj t -> [(t, t)]
-- | Adj to Gr
adj_to_gr :: Ord t => Adj t -> Gr t
-- | Gr to Adj (selection-function)
gr_to_adj :: Ord t => (t -> (t, t) -> Maybe t) -> Gr t -> Adj t
-- | Gr to Adj (directed)
--
--
-- g = ([0,1,2,3],[(0,1),(2,1),(0,3),(3,0)])
-- r = [(0,[1,3]),(2,[1]),(3,[0])]
-- gr_to_adj_dir g == r
--
gr_to_adj_dir :: Ord t => Gr t -> Adj t
-- | Gr to Adj (un-directed)
--
--
-- g = ([0,1,2,3],[(0,1),(2,1),(0,3),(3,0)])
-- gr_to_adj_undir g == [(0,[1,3,3]),(1,[2])]
--
gr_to_adj_undir :: Ord t => Gr t -> Adj t
-- | Adjacency matrix, (|v|,mtx)
type Adj_Mtx t = (Int, [[t]])
-- | Edg to Adj_Mtx for un-directed graph.
--
--
-- e = ((4,3),[(0,3),(1,3),(2,3)])
-- edg_to_adj_mtx_undir (0,1) e == (4,[[0,0,0,1],[0,0,0,1],[0,0,0,1],[1,1,1,0]])
--
--
--
-- e = ((4,4),[(0,1),(0,3),(1,2),(2,3)])
-- edg_to_adj_mtx_undir (0,1) e == (4,[[0,1,0,1],[1,0,1,0],[0,1,0,1],[1,0,1,0]])
--
edg_to_adj_mtx_undir :: (t, t) -> Edg -> Adj_Mtx t
-- | edg_to_adj_mtx_undir of g_to_edg
g_to_adj_mtx_undir :: (t, t) -> G -> Adj_Mtx t
-- | Lookup Adj_Mtx to find connected vertices.
adj_mtx_con :: Eq t => (t, t) -> Adj_Mtx t -> Int -> [Int]
-- | Labelled graph, distinct vertex and edge labels.
type Lbl_Gr v v_lbl e_lbl = ([(v, v_lbl)], [((v, v), e_lbl)])
-- | Lbl_Gr of Int
type Lbl v e = Lbl_Gr Int v e
-- | Lbl with () edge labels.
type Lbl_ v = Lbl v ()
-- | Number of vertices and edges.
lbl_degree :: Lbl v e -> (Int, Int)
-- | Apply v at vertex labels and e at edge labels.
lbl_bimap :: (v -> v') -> (e -> e') -> Lbl v e -> Lbl v' e'
-- | Merge two Lbl graphs, do not share vertices, vertex indices at
-- g1 are stable.
lbl_merge :: Lbl v e -> Lbl v e -> Lbl v e
-- | foldl1 of lbl_merge
lbl_merge_seq :: [Lbl v e] -> Lbl v e
-- | Re-write graph so vertex indices are (0 .. n-1) and vertex labels are
-- unique.
lbl_canonical :: (Eq v, Ord v) => Lbl v e -> Lbl v e
-- | Re-write edges so that vertex indices are ascending.
lbl_undir :: Lbl v e -> Lbl v e
-- | Lbl path graph.
lbl_path_graph :: [x] -> Lbl_ x
-- | Lbl complete graph (undirected, no self-edges)
lbl_complete_graph :: [x] -> Lbl_ x
-- | Lookup vertex label with default value.
v_label :: v -> Lbl v e -> Int -> v
-- | v_label with error as default.
v_label_err :: Lbl v e -> Int -> v
-- | Lookup edge label with default value.
e_label :: e -> Lbl v e -> (Int, Int) -> e
-- | e_label with error as default.
e_label_err :: Lbl v e -> (Int, Int) -> e
-- | Convert from Lbl_Gr to Lbl
lbl_gr_to_lbl :: Eq v => Lbl_Gr v v_lbl e_lbl -> Lbl v_lbl e_lbl
-- | Convert from Gr to Lbl.
--
--
-- gr_to_lbl ("ab",[('a','b')]) == ([(0,'a'),(1,'b')],[((0,1),('a','b'))])
--
gr_to_lbl :: Eq t => Gr t -> Lbl t (t, t)
-- | Delete edge labels from Lbl, replacing with ()
lbl_delete_edge_labels :: Lbl v e -> Lbl_ v
-- | lbl_delete_edge_labels of gr_to_lbl
gr_to_lbl_ :: Eq t => Gr t -> Lbl_ t
-- | Construct Lbl from set of E, derives V from E.
eset_to_lbl :: Ord t => [(t, t)] -> Lbl_ t
-- | Unlabel Lbl graph.
lbl_to_g :: Lbl v e -> G
-- | Lcf (LederbergCoxeterFrucht) notation
--
-- The notation only applies to Hamiltonian graphs, since it achieves its
-- symmetry and conciseness by placing a Hamiltonian cycle in a circular
-- embedding and then connecting specified pairs of nodes with edges.
-- (EW)
module Music.Theory.Graph.Lcf
-- | Lcf notation (l,k). ([3,-3],4) is the cubical graph.
type Lcf = ([Int], Int)
-- | Real, alias for Double
type R = Double
-- | Sequence, ie. l k times.
lcf_seq :: Lcf -> [Int]
-- | Length of lcf_seq, ie. |l|k
lcf_degree :: Lcf -> Int
-- | Lcf to Edg (an edge list)
lcf_to_edg :: Lcf -> Edg
-- | Lcf edge-list to graph labeled with circular co-ordinates.
edg_circ_gr :: R -> Edg -> Lbl (R, R) ()
-- | Lcf graph set given at
-- http://mathworld.wolfram.com/LcfNotation.html
--
--
-- length lcf_mw_set == 57
-- length (nub (map snd lcf_mw_set)) == 57 -- IE. UNIQ
--
lcf_mw_set :: [(String, Lcf)]
-- | http://www.tcs.hut.fi/Software/bliss/fileformat.shtml
module Music.Theory.Graph.Bliss
-- | Problem is (n-vertices,n-edges)
bliss_parse_problem :: String -> (Int, Int)
-- | Vertex colour is (vertex,colour)
bliss_parse_vertex_colour :: String -> (Int, Int)
-- | Edge is (vertex,vertex)
bliss_parse_edge :: String -> (Int, Int)
-- | (problem,vertex-colours,edges) Bliss data is one-indexed.
type Bliss = ((Int, Int), [(Int, Int)], [(Int, Int)])
-- | Parse Bliss
bliss_parse :: String -> Bliss
-- | bliss_parse of readFile
bliss_load :: FilePath -> IO Bliss
-- | Bliss (one-indexed) to G (zero-indexed)
bliss_to_g :: Bliss -> G
-- | graph6 graph encoding
--
-- http://users.cecs.anu.edu.au/~bdm/nauty/
-- https://users.cecs.anu.edu.au/~bdm/data/formats.html
module Music.Theory.Graph.G6
-- | Load Graph6 file, discard optional header if present.
g6_load :: FilePath -> IO [String]
-- | Load G6 file variant where each line is "DescriptiontG6"
g6_dsc_load :: FilePath -> IO [(String, String)]
-- | Call nauty-listg to transform a sequence of G6. (debian = nauty)
g6_to_edg :: [String] -> IO [Edg]
-- | edg_to_g of g6_to_edg
g6_to_g :: [String] -> IO [G]
-- | g6_to_edg of g6_dsc_load.
g6_dsc_load_edg :: FilePath -> IO [(String, Edg)]
-- | edg_to_g of g6_dsc_load_edg
g6_dsc_load_gr :: FilePath -> IO [(String, G)]
-- | Generate the text format read by nauty-amtog.
--
--
-- e = ((4,3),[(0,3),(1,3),(2,3)])
-- m = T.edg_to_adj_mtx_undir (0,1) e
-- putStrLn (adj_mtx_to_am m)
--
adj_mtx_to_am :: Adj_Mtx Int -> String
-- | Call nauty-amtog to transform a sequence of Adj_Mtx to G6.
--
--
-- adj_mtx_to_g6 [m,m]
--
adj_mtx_to_g6 :: [Adj_Mtx Int] -> IO [String]
-- | adj_mtx_to_g6 of g_to_adj_mtx_undir
g_to_g6 :: [G] -> IO [String]
-- | writeFile of g_to_g6
g_store_g6 :: FilePath -> [G] -> IO ()
-- | Call nauty-labelg to canonise a set of graphs.
g6_labelg :: [String] -> IO [String]
-- | g6_to_g of g6_labelg of g_to_g6
--
--
-- g1 = ([0,1,2,3],[(0,3),(3,1),(3,2),(1,2)])
-- g2 = ([0,1,2,3],[(1,0),(0,3),(0,2),(2,3)])
-- [g3,g4] <- g_labelg [g1,g2]
-- (g1 == g2,g3 == g4)
--
g_labelg :: [G] -> IO [G]
-- | https://users.cecs.anu.edu.au/~bdm/plantri/plantri-guide.txt
module Music.Theory.Graph.Planar
-- | The 15-character header text indicating a Planar-Code file.
plc_header_txt :: String
-- | Read Plc header
plc_header :: ByteString -> String
-- | Read Plc data as list of Int
plc_data :: ByteString -> [Int]
-- | Calculate length of Plc data given (n-vertices,n-edges).
plc_length :: (Int, Int) -> Int
-- | Scan Plc data and segment after k zeros.
plc_scanner :: Int -> [Int] -> ([Int], [Int])
-- | (n-vertices,clockwise-edge-sequences)
type Plc = (Int, [[Int]])
plc_n_vertices :: Plc -> Int
-- | Group Plc data into Plc structure.
plc_group :: Int -> [Int] -> Plc
-- | Segment input data into sequence of Plc.
plc_segment :: [Int] -> [Plc]
plc_parse :: ByteString -> [Plc]
-- | Load sequence of Plc from binary Planar-Code file.
plc_load :: FilePath -> IO [Plc]
-- | All edges (one-indexed) at Plc
plc_edge_set :: Plc -> [(Int, Int)]
-- | Element in x after i, the element after the last is the
-- first.
--
--
-- map (plc_next_elem "abcd") "abcd" == "bcda"
--
plc_next_elem :: Eq t => [t] -> t -> t
-- | The next edge in Plc following e.
plc_next_edge :: Plc -> (Int, Int) -> (Int, Int)
-- | The face of Plc starting at e (one-indexed edges).
plc_face_from :: Plc -> (Int, Int) -> [(Int, Int)]
-- | The set of all faces at Plc (one-indexed edges).
plc_face_set :: Plc -> [[(Int, Int)]]
-- | Translate Plc into un-directed G. Plc is one-indexed, G
-- is zero-indexed.
plc_to_g :: Plc -> G
plc_stat :: FilePath -> IO (Int, [(Int, Int, Int)])
plc_stat_txt :: FilePath -> (Int, [(Int, Int, Int)]) -> [String]
-- | Run "nauty-planarg" to convert (if possible) a set of G6 graphs to
-- Planar-Code.
g6_planarg :: [String] -> IO ByteString
-- | plc_parse of g6_planarg of g_to_g6
g_to_plc :: [G] -> IO [Plc]
-- | Run "nauty-planarg" to translate named G6 file to named PL file.
g6_to_pl_wr :: FilePath -> FilePath -> IO ()
-- | Array & table functions
module Music.Theory.Array
-- | minmax of k.
larray_bounds :: Ord k => [(k, v)] -> (k, k)
-- | array of association list.
larray :: Ix k => [(k, v)] -> Array k v
-- | Plain list representation of a two-dimensional table of a in
-- row-order. Tables are regular, ie. all rows have equal numbers of
-- columns.
type Table a = [[a]]
-- | Table row count.
tbl_rows :: Table t -> Int
-- | Table column count, assumes table is regular.
tbl_columns :: Table t -> Int
-- | Determine is table is regular, ie. all rows have the same number of
-- columns.
--
--
-- tbl_is_regular [[0..3],[4..7],[8..11]] == True
--
tbl_is_regular :: Table t -> Bool
-- | Map f at table, padding short rows with k.
tbl_make_regular :: (t -> u, u) -> Table t -> Table u
-- | Append a sequence of nil (or default) values to each row of
-- tbl so to make it regular (ie. all rows of equal length).
tbl_make_regular_nil :: t -> Table t -> Table t
-- | Matrix dimensions are written (rows,columns).
type Dimensions i = (i, i)
-- | Matrix indices are written (row,column) & are here _zero_ indexed.
type Ix i = (i, i)
-- | Translate Ix by row and column delta.
--
--
-- ix_translate (1,2) (3,4) == (4,6)
--
ix_translate :: Num t => (t, t) -> Ix t -> Ix t
-- | Modulo Ix by Dimensions.
--
--
-- ix_modulo (4,4) (3,7) == (3,3)
--
ix_modulo :: Integral t => Dimensions t -> Ix t -> Ix t
-- | Given number of columns and row index, list row indices.
--
--
-- row_indices 3 1 == [(1,0),(1,1),(1,2)]
--
row_indices :: (Enum t, Num t) => t -> t -> [Ix t]
-- | Given number of rows and column index, list column indices.
--
--
-- column_indices_at 3 1 == [(0,1),(1,1),(2,1)]
--
column_indices_at :: (Enum t, Num t) => t -> t -> [Ix t]
-- | All zero-indexed matrix indices, in row order. This is the order given
-- by sort.
--
--
-- matrix_indices (2,3) == [(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)]
-- sort (matrix_indices (2,3)) == matrix_indices (2,3)
--
matrix_indices :: (Enum t, Num t) => Dimensions t -> [Ix t]
-- | Corner indices of given Dimensions, in row order.
--
--
-- matrix_corner_indices (2,3) == [(0,0),(0,2),(1,0),(1,2)]
--
matrix_corner_indices :: Num t => Dimensions t -> [Ix t]
-- | Parallelogram corner indices, given as rectangular Dimensions
-- with an offset for the lower indices.
--
--
-- parallelogram_corner_indices ((2,3),2) == [(0,0),(0,2),(1,2),(1,4)]
--
parallelogram_corner_indices :: Num t => (Dimensions t, t) -> [Ix t]
-- | Apply ix_modulo and ix_translate for all
-- matrix_indices, ie. all translations of a shape in row
-- order. The resulting Ix sets are not sorted and may have
-- duplicates.
--
--
-- concat (all_ix_translations (2,3) [(0,0)]) == matrix_indices (2,3)
--
all_ix_translations :: Integral t => Dimensions t -> [Ix t] -> [[Ix t]]
-- | Sort sets into row order and remove duplicates.
all_ix_translations_uniq :: Integral t => Dimensions t -> [Ix t] -> [[Ix t]]
-- | Map functions.
module Music.Theory.Map
-- | Erroring lookup.
map_lookup_err :: Ord k => k -> Map k c -> c
-- | flip of lookup.
map_ix :: Ord k => Map k c -> k -> Maybe c
-- | flip of map_lookup_err.
map_ix_err :: Ord k => Map k c -> k -> c
-- | IEE754 constants (c.f. Numeric.MathFunctions.Constants)
module Music.Theory.Math.Constant
-- | The smallest Double n such that 1 + n /= 1.
epsilonValue :: Double
-- | Largest representable finite value.
largestFiniteValue :: Double
-- | The smallest representable positive normalized value.
smallestNormalizedValue :: Double
-- | Specialised type conversions, see mk/mk-convert.hs
--
--
-- map int_to_word8 [-1,0,255,256] == [255,0,255,0]
-- map int_to_word8_maybe [-1,0,255,256] == [Nothing,Just 0,Just 255,Nothing]
--
--
--
-- map integer_to_int64_maybe [-2 ^ 63 - 1,2 ^ 63] == [Nothing,Nothing]
-- map integer_to_word64_maybe [2 ^ 64 - 1,2 ^ 64] == [Just 18446744073709551615,Nothing]
--
--
--
-- map int16_to_float [-1,0,1] == [-1,0,1]
--
module Music.Theory.Math.Convert
-- | Type specialised realToFrac
real_to_float :: Real t => t -> Float
-- | Type specialised realToFrac
--
--
-- let n = sqrt (-1) in (n,real_to_double n)
--
real_to_double :: Real t => t -> Double
-- | Type specialised realToFrac
double_to_float :: Double -> Float
-- | Type specialised realToFrac
float_to_double :: Float -> Double
double_to_word8 :: (Double -> Word8) -> Double -> Word8
-- | Type-specialise f, ie. round, ceiling, truncate
--
--
-- map (double_to_int round) [0, 0.25 .. 1] == [0, 0, 0, 1, 1]
-- map (double_to_int ceiling) [0, 0.25 .. 1] == [0, 1, 1, 1, 1]
-- map (double_to_int floor) [0, 0.25 .. 1] == [0, 0, 0, 0, 1]
-- map (double_to_int truncate) [0, 0.25 .. 1] == [0, 0, 0, 0, 1]
--
double_to_int :: (Double -> Int) -> Double -> Int
-- | Type specialised fromIntegral
int_to_rational :: Int -> Rational
-- | Type specialised fromIntegral
word8_to_word16 :: Word8 -> Word16
-- | Type specialised fromIntegral
word8_to_word32 :: Word8 -> Word32
-- | Type specialised fromIntegral
word8_to_word64 :: Word8 -> Word64
-- | Type specialised fromIntegral
word8_to_int8 :: Word8 -> Int8
-- | Type specialised fromIntegral
word8_to_int16 :: Word8 -> Int16
-- | Type specialised fromIntegral
word8_to_int32 :: Word8 -> Int32
-- | Type specialised fromIntegral
word8_to_int64 :: Word8 -> Int64
-- | Type specialised fromIntegral
word8_to_int :: Word8 -> Int
-- | Type specialised fromIntegral
word8_to_integer :: Word8 -> Integer
-- | Type specialised fromIntegral
word8_to_float :: Word8 -> Float
-- | Type specialised fromIntegral
word8_to_double :: Word8 -> Double
-- | Type specialised fromIntegral
word16_to_word8 :: Word16 -> Word8
-- | Type specialised fromIntegral
word16_to_word32 :: Word16 -> Word32
-- | Type specialised fromIntegral
word16_to_word64 :: Word16 -> Word64
-- | Type specialised fromIntegral
word16_to_int8 :: Word16 -> Int8
-- | Type specialised fromIntegral
word16_to_int16 :: Word16 -> Int16
-- | Type specialised fromIntegral
word16_to_int32 :: Word16 -> Int32
-- | Type specialised fromIntegral
word16_to_int64 :: Word16 -> Int64
-- | Type specialised fromIntegral
word16_to_int :: Word16 -> Int
-- | Type specialised fromIntegral
word16_to_integer :: Word16 -> Integer
-- | Type specialised fromIntegral
word16_to_float :: Word16 -> Float
-- | Type specialised fromIntegral
word16_to_double :: Word16 -> Double
-- | Type specialised fromIntegral
word32_to_word8 :: Word32 -> Word8
-- | Type specialised fromIntegral
word32_to_word16 :: Word32 -> Word16
-- | Type specialised fromIntegral
word32_to_word64 :: Word32 -> Word64
-- | Type specialised fromIntegral
word32_to_int8 :: Word32 -> Int8
-- | Type specialised fromIntegral
word32_to_int16 :: Word32 -> Int16
-- | Type specialised fromIntegral
word32_to_int32 :: Word32 -> Int32
-- | Type specialised fromIntegral
word32_to_int64 :: Word32 -> Int64
-- | Type specialised fromIntegral
word32_to_int :: Word32 -> Int
-- | Type specialised fromIntegral
word32_to_integer :: Word32 -> Integer
-- | Type specialised fromIntegral
word32_to_float :: Word32 -> Float
-- | Type specialised fromIntegral
word32_to_double :: Word32 -> Double
-- | Type specialised fromIntegral
word64_to_word8 :: Word64 -> Word8
-- | Type specialised fromIntegral
word64_to_word16 :: Word64 -> Word16
-- | Type specialised fromIntegral
word64_to_word32 :: Word64 -> Word32
-- | Type specialised fromIntegral
word64_to_int8 :: Word64 -> Int8
-- | Type specialised fromIntegral
word64_to_int16 :: Word64 -> Int16
-- | Type specialised fromIntegral
word64_to_int32 :: Word64 -> Int32
-- | Type specialised fromIntegral
word64_to_int64 :: Word64 -> Int64
-- | Type specialised fromIntegral
word64_to_int :: Word64 -> Int
-- | Type specialised fromIntegral
word64_to_integer :: Word64 -> Integer
-- | Type specialised fromIntegral
word64_to_float :: Word64 -> Float
-- | Type specialised fromIntegral
word64_to_double :: Word64 -> Double
-- | Type specialised fromIntegral
int8_to_word8 :: Int8 -> Word8
-- | Type specialised fromIntegral
int8_to_word16 :: Int8 -> Word16
-- | Type specialised fromIntegral
int8_to_word32 :: Int8 -> Word32
-- | Type specialised fromIntegral
int8_to_word64 :: Int8 -> Word64
-- | Type specialised fromIntegral
int8_to_int16 :: Int8 -> Int16
-- | Type specialised fromIntegral
int8_to_int32 :: Int8 -> Int32
-- | Type specialised fromIntegral
int8_to_int64 :: Int8 -> Int64
-- | Type specialised fromIntegral
int8_to_int :: Int8 -> Int
-- | Type specialised fromIntegral
int8_to_integer :: Int8 -> Integer
-- | Type specialised fromIntegral
int8_to_float :: Int8 -> Float
-- | Type specialised fromIntegral
int8_to_double :: Int8 -> Double
-- | Type specialised fromIntegral
int16_to_word8 :: Int16 -> Word8
-- | Type specialised fromIntegral
int16_to_word16 :: Int16 -> Word16
-- | Type specialised fromIntegral
int16_to_word32 :: Int16 -> Word32
-- | Type specialised fromIntegral
int16_to_word64 :: Int16 -> Word64
-- | Type specialised fromIntegral
int16_to_int8 :: Int16 -> Int8
-- | Type specialised fromIntegral
int16_to_int32 :: Int16 -> Int32
-- | Type specialised fromIntegral
int16_to_int64 :: Int16 -> Int64
-- | Type specialised fromIntegral
int16_to_int :: Int16 -> Int
-- | Type specialised fromIntegral
int16_to_integer :: Int16 -> Integer
-- | Type specialised fromIntegral
int16_to_float :: Int16 -> Float
-- | Type specialised fromIntegral
int16_to_double :: Int16 -> Double
-- | Type specialised fromIntegral
int32_to_word8 :: Int32 -> Word8
-- | Type specialised fromIntegral
int32_to_word16 :: Int32 -> Word16
-- | Type specialised fromIntegral
int32_to_word32 :: Int32 -> Word32
-- | Type specialised fromIntegral
int32_to_word64 :: Int32 -> Word64
-- | Type specialised fromIntegral
int32_to_int8 :: Int32 -> Int8
-- | Type specialised fromIntegral
int32_to_int16 :: Int32 -> Int16
-- | Type specialised fromIntegral
int32_to_int64 :: Int32 -> Int64
-- | Type specialised fromIntegral
int32_to_int :: Int32 -> Int
-- | Type specialised fromIntegral
int32_to_integer :: Int32 -> Integer
-- | Type specialised fromIntegral
int32_to_float :: Int32 -> Float
-- | Type specialised fromIntegral
int32_to_double :: Int32 -> Double
-- | Type specialised fromIntegral
int64_to_word8 :: Int64 -> Word8
-- | Type specialised fromIntegral
int64_to_word16 :: Int64 -> Word16
-- | Type specialised fromIntegral
int64_to_word32 :: Int64 -> Word32
-- | Type specialised fromIntegral
int64_to_word64 :: Int64 -> Word64
-- | Type specialised fromIntegral
int64_to_int8 :: Int64 -> Int8
-- | Type specialised fromIntegral
int64_to_int16 :: Int64 -> Int16
-- | Type specialised fromIntegral
int64_to_int32 :: Int64 -> Int32
-- | Type specialised fromIntegral
int64_to_int :: Int64 -> Int
-- | Type specialised fromIntegral
int64_to_integer :: Int64 -> Integer
-- | Type specialised fromIntegral
int64_to_float :: Int64 -> Float
-- | Type specialised fromIntegral
int64_to_double :: Int64 -> Double
-- | Type specialised fromIntegral
int_to_integral :: Integral i => Int -> i
-- | Type specialised fromIntegral
int_to_word8 :: Int -> Word8
-- | Type specialised fromIntegral
int_to_word16 :: Int -> Word16
-- | Type specialised fromIntegral
int_to_word32 :: Int -> Word32
-- | Type specialised fromIntegral
int_to_word64 :: Int -> Word64
-- | Type specialised fromIntegral
int_to_int8 :: Int -> Int8
-- | Type specialised fromIntegral
int_to_int16 :: Int -> Int16
-- | Type specialised fromIntegral
int_to_int32 :: Int -> Int32
-- | Type specialised fromIntegral
int_to_int64 :: Int -> Int64
-- | Type specialised fromIntegral
int_to_integer :: Int -> Integer
-- | Type specialised fromIntegral
int_to_float :: Int -> Float
-- | Type specialised fromIntegral
int_to_double :: Int -> Double
-- | Type specialised fromIntegral
integer_to_word8 :: Integer -> Word8
-- | Type specialised fromIntegral
integer_to_word16 :: Integer -> Word16
-- | Type specialised fromIntegral
integer_to_word32 :: Integer -> Word32
-- | Type specialised fromIntegral
integer_to_word64 :: Integer -> Word64
-- | Type specialised fromIntegral
integer_to_int8 :: Integer -> Int8
-- | Type specialised fromIntegral
integer_to_int16 :: Integer -> Int16
-- | Type specialised fromIntegral
integer_to_int32 :: Integer -> Int32
-- | Type specialised fromIntegral
integer_to_int64 :: Integer -> Int64
-- | Type specialised fromIntegral
integer_to_int :: Integer -> Int
-- | Type specialised fromIntegral
integer_to_float :: Integer -> Float
-- | Type specialised fromIntegral
integer_to_double :: Integer -> Double
-- | Type specialised fromIntegral
word8_to_word16_maybe :: Word8 -> Maybe Word16
-- | Type specialised fromIntegral
word8_to_word32_maybe :: Word8 -> Maybe Word32
-- | Type specialised fromIntegral
word8_to_word64_maybe :: Word8 -> Maybe Word64
-- | Type specialised fromIntegral
word8_to_int8_maybe :: Word8 -> Maybe Int8
-- | Type specialised fromIntegral
word8_to_int16_maybe :: Word8 -> Maybe Int16
-- | Type specialised fromIntegral
word8_to_int32_maybe :: Word8 -> Maybe Int32
-- | Type specialised fromIntegral
word8_to_int64_maybe :: Word8 -> Maybe Int64
-- | Type specialised fromIntegral
word8_to_int_maybe :: Word8 -> Maybe Int
-- | Type specialised fromIntegral
word16_to_word8_maybe :: Word16 -> Maybe Word8
-- | Type specialised fromIntegral
word16_to_word32_maybe :: Word16 -> Maybe Word32
-- | Type specialised fromIntegral
word16_to_word64_maybe :: Word16 -> Maybe Word64
-- | Type specialised fromIntegral
word16_to_int8_maybe :: Word16 -> Maybe Int8
-- | Type specialised fromIntegral
word16_to_int16_maybe :: Word16 -> Maybe Int16
-- | Type specialised fromIntegral
word16_to_int32_maybe :: Word16 -> Maybe Int32
-- | Type specialised fromIntegral
word16_to_int64_maybe :: Word16 -> Maybe Int64
-- | Type specialised fromIntegral
word16_to_int_maybe :: Word16 -> Maybe Int
-- | Type specialised fromIntegral
word32_to_word8_maybe :: Word32 -> Maybe Word8
-- | Type specialised fromIntegral
word32_to_word16_maybe :: Word32 -> Maybe Word16
-- | Type specialised fromIntegral
word32_to_word64_maybe :: Word32 -> Maybe Word64
-- | Type specialised fromIntegral
word32_to_int8_maybe :: Word32 -> Maybe Int8
-- | Type specialised fromIntegral
word32_to_int16_maybe :: Word32 -> Maybe Int16
-- | Type specialised fromIntegral
word32_to_int32_maybe :: Word32 -> Maybe Int32
-- | Type specialised fromIntegral
word32_to_int64_maybe :: Word32 -> Maybe Int64
-- | Type specialised fromIntegral
word32_to_int_maybe :: Word32 -> Maybe Int
-- | Type specialised fromIntegral
word64_to_word8_maybe :: Word64 -> Maybe Word8
-- | Type specialised fromIntegral
word64_to_word16_maybe :: Word64 -> Maybe Word16
-- | Type specialised fromIntegral
word64_to_word32_maybe :: Word64 -> Maybe Word32
-- | Type specialised fromIntegral
word64_to_int8_maybe :: Word64 -> Maybe Int8
-- | Type specialised fromIntegral
word64_to_int16_maybe :: Word64 -> Maybe Int16
-- | Type specialised fromIntegral
word64_to_int32_maybe :: Word64 -> Maybe Int32
-- | Type specialised fromIntegral
word64_to_int64_maybe :: Word64 -> Maybe Int64
-- | Type specialised fromIntegral
word64_to_int_maybe :: Word64 -> Maybe Int
-- | Type specialised fromIntegral
int8_to_word8_maybe :: Int8 -> Maybe Word8
-- | Type specialised fromIntegral
int8_to_word16_maybe :: Int8 -> Maybe Word16
-- | Type specialised fromIntegral
int8_to_word32_maybe :: Int8 -> Maybe Word32
-- | Type specialised fromIntegral
int8_to_word64_maybe :: Int8 -> Maybe Word64
-- | Type specialised fromIntegral
int8_to_int16_maybe :: Int8 -> Maybe Int16
-- | Type specialised fromIntegral
int8_to_int32_maybe :: Int8 -> Maybe Int32
-- | Type specialised fromIntegral
int8_to_int64_maybe :: Int8 -> Maybe Int64
-- | Type specialised fromIntegral
int8_to_int_maybe :: Int8 -> Maybe Int
-- | Type specialised fromIntegral
int16_to_word8_maybe :: Int16 -> Maybe Word8
-- | Type specialised fromIntegral
int16_to_word16_maybe :: Int16 -> Maybe Word16
-- | Type specialised fromIntegral
int16_to_word32_maybe :: Int16 -> Maybe Word32
-- | Type specialised fromIntegral
int16_to_word64_maybe :: Int16 -> Maybe Word64
-- | Type specialised fromIntegral
int16_to_int8_maybe :: Int16 -> Maybe Int8
-- | Type specialised fromIntegral
int16_to_int32_maybe :: Int16 -> Maybe Int32
-- | Type specialised fromIntegral
int16_to_int64_maybe :: Int16 -> Maybe Int64
-- | Type specialised fromIntegral
int16_to_int_maybe :: Int16 -> Maybe Int
-- | Type specialised fromIntegral
int32_to_word8_maybe :: Int32 -> Maybe Word8
-- | Type specialised fromIntegral
int32_to_word16_maybe :: Int32 -> Maybe Word16
-- | Type specialised fromIntegral
int32_to_word32_maybe :: Int32 -> Maybe Word32
-- | Type specialised fromIntegral
int32_to_word64_maybe :: Int32 -> Maybe Word64
-- | Type specialised fromIntegral
int32_to_int8_maybe :: Int32 -> Maybe Int8
-- | Type specialised fromIntegral
int32_to_int16_maybe :: Int32 -> Maybe Int16
-- | Type specialised fromIntegral
int32_to_int64_maybe :: Int32 -> Maybe Int64
-- | Type specialised fromIntegral
int32_to_int_maybe :: Int32 -> Maybe Int
-- | Type specialised fromIntegral
int64_to_word8_maybe :: Int64 -> Maybe Word8
-- | Type specialised fromIntegral
int64_to_word16_maybe :: Int64 -> Maybe Word16
-- | Type specialised fromIntegral
int64_to_word32_maybe :: Int64 -> Maybe Word32
-- | Type specialised fromIntegral
int64_to_word64_maybe :: Int64 -> Maybe Word64
-- | Type specialised fromIntegral
int64_to_int8_maybe :: Int64 -> Maybe Int8
-- | Type specialised fromIntegral
int64_to_int16_maybe :: Int64 -> Maybe Int16
-- | Type specialised fromIntegral
int64_to_int32_maybe :: Int64 -> Maybe Int32
-- | Type specialised fromIntegral
int64_to_int_maybe :: Int64 -> Maybe Int
-- | Type specialised fromIntegral
int_to_word8_maybe :: Int -> Maybe Word8
-- | Type specialised fromIntegral
int_to_word16_maybe :: Int -> Maybe Word16
-- | Type specialised fromIntegral
int_to_word32_maybe :: Int -> Maybe Word32
-- | Type specialised fromIntegral
int_to_word64_maybe :: Int -> Maybe Word64
-- | Type specialised fromIntegral
int_to_int8_maybe :: Int -> Maybe Int8
-- | Type specialised fromIntegral
int_to_int16_maybe :: Int -> Maybe Int16
-- | Type specialised fromIntegral
int_to_int32_maybe :: Int -> Maybe Int32
-- | Type specialised fromIntegral
int_to_int64_maybe :: Int -> Maybe Int64
-- | Type specialised fromIntegral
integer_to_word8_maybe :: Integer -> Maybe Word8
-- | Type specialised fromIntegral
integer_to_word16_maybe :: Integer -> Maybe Word16
-- | Type specialised fromIntegral
integer_to_word32_maybe :: Integer -> Maybe Word32
-- | Type specialised fromIntegral
integer_to_word64_maybe :: Integer -> Maybe Word64
-- | Type specialised fromIntegral
integer_to_int8_maybe :: Integer -> Maybe Int8
-- | Type specialised fromIntegral
integer_to_int16_maybe :: Integer -> Maybe Int16
-- | Type specialised fromIntegral
integer_to_int32_maybe :: Integer -> Maybe Int32
-- | Type specialised fromIntegral
integer_to_int64_maybe :: Integer -> Maybe Int64
-- | Type specialised fromIntegral
integer_to_int_maybe :: Integer -> Maybe Int
-- | Math functions.
module Music.Theory.Math
-- | mod 5.
mod5 :: Integral i => i -> i
-- | mod 7.
mod7 :: Integral i => i -> i
-- | mod 12.
mod12 :: Integral i => i -> i
-- | mod 16.
mod16 :: Integral i => i -> i
-- |
-- http://reference.wolfram.com/mathematica/ref/FractionalPart.html
-- i.e. properFraction
--
--
-- integral_and_fractional_parts 1.5 == (1,0.5)
--
integral_and_fractional_parts :: (Integral i, RealFrac t) => t -> (i, t)
-- | Type specialised.
integer_and_fractional_parts :: RealFrac t => t -> (Integer, t)
-- |
-- http://reference.wolfram.com/mathematica/ref/FractionalPart.html
--
--
-- import Sound.SC3.Plot {- hsc3-plot -}
-- plot_p1_ln [map fractional_part [-2.0,-1.99 .. 2.0]]
--
fractional_part :: RealFrac a => a -> a
-- | floor of real_to_double.
real_floor :: (Real r, Integral i) => r -> i
-- | Type specialised real_floor.
real_floor_int :: Real r => r -> Int
-- | round of real_to_double.
real_round :: (Real r, Integral i) => r -> i
-- | Type specialised real_round.
real_round_int :: Real r => r -> Int
-- | Type specialised round
round_int :: RealFrac t => t -> Int
-- | Type-specialised fromIntegral
from_integral_to_int :: Integral i => i -> Int
-- | Type-specialised id
int_id :: Int -> Int
-- | Is r zero to k decimal places.
--
--
-- map (flip zero_to_precision 0.00009) [4,5] == [True,False]
-- map (zero_to_precision 4) [0.00009,1.00009] == [True,False]
--
zero_to_precision :: Real r => Int -> r -> Bool
-- | Is r whole to k decimal places.
--
--
-- map (flip whole_to_precision 1.00009) [4,5] == [True,False]
--
whole_to_precision :: Real r => Int -> r -> Bool
-- | http://reference.wolfram.com/mathematica/ref/SawtoothWave.html
--
--
-- plot_p1_ln [map sawtooth_wave [-2.0,-1.99 .. 2.0]]
--
sawtooth_wave :: RealFrac a => a -> a
-- | Predicate that is true if n/d can be simplified, ie. where
-- gcd of n and d is not 1.
--
--
-- map rational_simplifies [(2,3),(4,6),(5,7)] == [False,True,False]
--
rational_simplifies :: Integral a => (a, a) -> Bool
-- | numerator and denominator of rational.
rational_nd :: Integral t => Ratio t -> (t, t)
-- | Rational as a whole number, or Nothing.
rational_whole :: Integral a => Ratio a -> Maybe a
-- | Erroring variant.
rational_whole_err :: Integral a => Ratio a -> a
-- | Sum of numerator & denominator.
ratio_nd_sum :: Integral t => Ratio t -> t
-- | Is n a whole (integral) value.
--
--
-- map real_is_whole [-1.0,-0.5,0.0,0.5,1.0] == [True,False,True,False,True]
--
real_is_whole :: Real n => n -> Bool
-- | fromInteger . floor.
floor_f :: (RealFrac a, Num b) => a -> b
-- | Round b to nearest multiple of a.
--
--
-- map (round_to 0.25) [0,0.1 .. 1] == [0.0,0.0,0.25,0.25,0.5,0.5,0.5,0.75,0.75,1.0,1.0]
-- map (round_to 25) [0,10 .. 100] == [0,0,25,25,50,50,50,75,75,100,100]
--
round_to :: RealFrac n => n -> n -> n
-- | Variant of recip that checks input for zero.
--
--
-- map recip [1,1/2,0,-1]
-- map recip_m [1,1/2,0,-1] == [Just 1,Just 2,Nothing,Just (-1)]
--
recip_m :: (Eq a, Fractional a) => a -> Maybe a
-- | One-indexed mod function.
--
--
-- map (`oi_mod` 5) [1..10] == [1,2,3,4,5,1,2,3,4,5]
--
oi_mod :: Integral a => a -> a -> a
-- | One-indexed divMod function.
--
--
-- map (`oi_divMod` 5) [1,3 .. 9] == [(0,1),(0,3),(0,5),(1,2),(1,4)]
--
oi_divMod :: Integral t => t -> t -> (t, t)
-- | Integral square root (sqrt) function.
--
--
-- map i_square_root [0,1,4,9,16,25,36,49,64,81,100] == [0 .. 10]
-- map i_square_root [4 .. 16] == [2,2,2,2,2,3,3,3,3,3,3,3,4]
--
i_square_root :: Integral t => t -> t
-- | (0,1) = {x | 0 < x < 1}
in_open_interval :: Ord a => (a, a) -> a -> Bool
-- |
-- - 0,1 = {x | 0 ≤ x ≤ 1}
--
in_closed_interval :: Ord a => (a, a) -> a -> Bool
-- | (p,q] (0,1] = {x | 0 < x ≤ 1}
in_left_half_open_interval :: Ord a => (a, a) -> a -> Bool
-- | [p,q) [0,1) = {x | 0 ≤ x < 1}
in_right_half_open_interval :: Ord a => (a, a) -> a -> Bool
-- | Calculate nth root of x.
--
--
-- 12 `nth_root` 2 == 1.0594630943592953
--
nth_root :: (Floating a, Eq a) => a -> a -> a
-- | Arithmetic mean (average) of a list.
--
--
-- map arithmetic_mean [[-3..3],[0..5],[1..5],[3,5,7],[7,7],[3,9,10,11,12]] == [0,2.5,3,5,7,9]
--
arithmetic_mean :: Fractional a => [a] -> a
-- | Numerically stable mean
--
--
-- map ns_mean [[-3..3],[0..5],[1..5],[3,5,7],[7,7],[3,9,10,11,12]] == [0,2.5,3,5,7,9]
--
ns_mean :: Floating a => [a] -> a
-- | Square of n.
--
--
-- square 5 == 25
--
square :: Num a => a -> a
-- | The totient function phi(n), also called Euler's totient function.
--
--
-- import Sound.SC3.Plot {- hsc3-plot -}
-- plot_p1_stp [map totient [1::Int .. 100]]
--
totient :: Integral i => i -> i
-- | The n-th order Farey sequence.
--
--
-- farey 1 == [0, 1]
-- farey 2 == [0, 1/2, 1]
-- farey 3 == [0, 1/3, 1/2, 2/3, 1]
-- farey 4 == [0, 1/4, 1/3, 1/2, 2/3, 3/4, 1]
-- farey 5 == [0, 1/5,1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4,4/5, 1]
-- farey 6 == [0, 1/6,1/5,1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4,4/5,5/6, 1]
-- farey 7 == [0, 1/7,1/6,1/5,1/4,2/7,1/3, 2/5,3/7,1/2,4/7,3/5, 2/3,5/7,3/4,4/5,5/6,6/7, 1]
-- farey 8 == [0,1/8,1/7,1/6,1/5,1/4,2/7,1/3,3/8,2/5,3/7,1/2,4/7,3/5,5/8,2/3,5/7,3/4,4/5,5/6,6/7,7/8,1]
--
farey :: Integral i => i -> [Ratio i]
-- | The length of the n-th order Farey sequence.
--
--
-- map farey_length [1 .. 12] == [2,3,5,7,11,13,19,23,29,33,43,47]
-- map (length . farey) [1 .. 12] == map farey_length [1 .. 12]
--
farey_length :: Integral i => i -> i
-- | Function to generate the Stern-Brocot tree from an initial row.
-- % normalises so 1/0 cannot be written as a Rational,
-- hence (n,d).
stern_brocot_tree_f :: Num n => [(n, n)] -> [[(n, n)]]
-- | The Stern-Brocot tree from (01,10).
--
--
-- let t = stern_brocot_tree
-- t !! 0 == [(0,1),(1,0)]
-- t !! 1 == [(0,1),(1,1),(1,0)]
-- t !! 2 == [(0,1),(1,2),(1,1),(2,1),(1,0)]
-- t !! 3 == [(0,1),(1,3),(1,2),(2,3),(1,1),(3,2),(2,1),(3,1),(1,0)]
--
--
--
-- map length (take 12 stern_brocot_tree) == [2,3,5,9,17,33,65,129,257,513,1025,2049] -- A000051
--
stern_brocot_tree :: Num n => [[(n, n)]]
-- | Left-hand (rational) side of the the Stern-Brocot tree, ie, from
-- (01,11).
stern_brocot_tree_lhs :: Num n => [[(n, n)]]
-- | stern_brocot_tree_f as Ratios, for finite subsets.
--
--
-- let t = stern_brocot_tree_f_r [0,1]
-- t !! 1 == [0,1/2,1]
-- t !! 2 == [0,1/3,1/2,2/3,1]
-- t !! 3 == [0,1/4,1/3,2/5,1/2,3/5,2/3,3/4,1]
-- t !! 4 == [0,1/5,1/4,2/7,1/3,3/8,2/5,3/7,1/2,4/7,3/5,5/8,2/3,5/7,3/4,4/5,1]
--
stern_brocot_tree_f_r :: Integral n => [Ratio n] -> [[Ratio n]]
-- | Outer product of vectors represented as lists, c.f. liftM2
--
--
-- outer_product (*) [2..5] [2..5] == [[4,6,8,10],[6,9,12,15],[8,12,16,20],[10,15,20,25]]
-- liftM2 (*) [2..5] [2..5] == [4,6,8,10,6,9,12,15,8,12,16,20,10,15,20,25]
--
outer_product :: (a -> b -> c) -> [a] -> [b] -> [[c]]
-- | c.f. Statistics.Sample.Histogram (this is much slower but doesn't
-- require any libraries)
module Music.Theory.Math.Histogram
-- | Calculate histogram on numBins places. Returns the range of each bin
-- and the number of elements in each.
--
--
-- map (snd . bHistogram 10) [[1 .. 10],[1,1,1,2,2,3,10]] == [[1,1,1,1,1,1,1,1,1,1],[3,2,1,0,0,0,0,0,0,1]]
--
bHistogram :: Int -> [Double] -> ([(Double, Double)], [Int])
-- | Calculate range.
--
--
-- bHistogramRange 10 (replicate 10 1) == (0.9, 1.1)
-- bHistogramRange 10 (replicate 10 0) == (-1, 1)
-- bHistogramRange 10 [1 .. 10] == (0.5, 10.5)
-- bHistogramRange 25 [1 .. 10] == (0.8125,10.1875)
--
bHistogramRange :: Int -> [Double] -> (Double, Double)
-- | Extensions to Data.Maybe.
module Music.Theory.Maybe
-- | Variant with error text.
from_just :: String -> Maybe a -> a
-- | Variant of unzip.
--
--
-- let r = ([Just 1,Nothing,Just 3],[Just 'a',Nothing,Just 'c'])
-- in maybe_unzip [Just (1,'a'),Nothing,Just (3,'c')] == r
--
maybe_unzip :: [Maybe (a, b)] -> ([Maybe a], [Maybe b])
-- | Replace Nothing elements with last Just value. This does
-- not alter the length of the list.
--
--
-- maybe_latch 1 [Nothing,Just 2,Nothing,Just 4] == [1,2,2,4]
--
maybe_latch :: a -> [Maybe a] -> [a]
-- | Variant requiring initial value is not Nothing.
--
--
-- maybe_latch1 [Just 1,Nothing,Nothing,Just 4] == [1,1,1,4]
--
maybe_latch1 :: [Maybe a] -> [a]
-- | map of fmap.
--
--
-- maybe_map negate [Nothing,Just 2] == [Nothing,Just (-2)]
--
maybe_map :: (a -> b) -> [Maybe a] -> [Maybe b]
-- | If either is Nothing then False, else eq of
-- values.
maybe_eq_by :: (t -> u -> Bool) -> Maybe t -> Maybe u -> Bool
-- | Join two values, either of which may be missing.
maybe_join' :: (s -> t) -> (s -> s -> t) -> Maybe s -> Maybe s -> Maybe t
-- | maybe_join' of id
maybe_join :: (t -> t -> t) -> Maybe t -> Maybe t -> Maybe t
-- | Apply predicate inside Maybe.
--
--
-- maybe_predicate even (Just 3) == Nothing
--
maybe_predicate :: (a -> Bool) -> Maybe a -> Maybe a
-- | map of maybe_predicate.
--
--
-- let r = [Nothing,Nothing,Nothing,Just 4]
-- in maybe_filter even [Just 1,Nothing,Nothing,Just 4] == r
--
maybe_filter :: (a -> Bool) -> [Maybe a] -> [Maybe a]
-- | Variant of catMaybes. If all elements of the list are Just
-- a, then gives Just [a] else gives Nothing.
--
--
-- all_just (map Just [1..3]) == Just [1..3]
-- all_just [Just 1,Nothing,Just 3] == Nothing
--
all_just :: [Maybe a] -> Maybe [a]
-- | Monad functions.
module Music.Theory.Monad
-- | sequence_ of repeat.
repeatM_ :: Monad m => m a -> m ()
-- | Monadic variant of iterate.
iterateM_ :: Monad m => (st -> m st) -> st -> m ()
-- | fmap of concat of mapM
concatMapM :: (Functor m, Monad m) => (t -> m [u]) -> [t] -> m [u]
-- | If i then j else k.
m_if :: Monad m => (m Bool, m t, m t) -> m t
-- | Directory functions.
module Music.Theory.Directory
-- | takeDirectory gives different answers depending on whether
-- there is a trailing separator.
--
--
-- x = ["x/y","x/y/","x","/"]
-- map parent_dir x == ["x","x",".","/"]
-- map takeDirectory x == ["x","x/y",".","/"]
--
parent_dir :: FilePath -> FilePath
-- | Colon separated path list.
path_split :: String -> [FilePath]
-- | Read environment variable and split path. Error if enviroment variable
-- not set.
--
--
-- path_from_env "PATH"
-- path_from_env "NONPATH" -- error
--
path_from_env :: String -> IO [FilePath]
-- | Expand a path to include all subdirectories recursively.
--
--
-- p = ["/home/rohan/sw/hmt-base/Music", "/home/rohan/sw/hmt/Music"]
-- r <- path_recursive p
-- length r == 44
--
path_recursive :: [FilePath] -> IO [FilePath]
-- | Scan a list of directories until a file is located, or not. Stop once
-- a file is located, do not traverse any sub-directory structure.
--
--
-- mapM (path_scan ["/sbin","/usr/bin"]) ["fsck","ghc"]
--
path_scan :: [FilePath] -> FilePath -> IO (Maybe FilePath)
-- | Erroring variant.
path_scan_err :: [FilePath] -> FilePath -> IO FilePath
-- | Scan a list of directories and return all located files. Do not
-- traverse any sub-directory structure. Since 1.2.1.0 there is also
-- findFiles.
--
--
-- let path = ["/home/rohan/sw/hmt-base","/home/rohan/sw/hmt"]
-- path_search path "README.md"
-- findFiles path "README.md"
--
path_search :: [FilePath] -> FilePath -> IO [FilePath]
-- | Get sorted list of files at dir with ext, ie. ls
-- dir/*.ext
--
--
-- dir_list_ext "/home/rohan/rd/j/" ".hs"
--
dir_list_ext :: FilePath -> String -> IO [FilePath]
-- | Post-process dir_list_ext to gives file-names with dir
-- prefix.
--
--
-- dir_list_ext_path "/home/rohan/rd/j/" ".hs"
--
dir_list_ext_path :: FilePath -> String -> IO [FilePath]
-- | Subset of files in dir with an extension in ext.
-- Extensions include the leading dot and are case-sensitive. Results are
-- relative to dir.
dir_subset_rel :: [String] -> FilePath -> IO [FilePath]
-- | Variant of dir_subset_rel where results have dir/ prefix.
--
--
-- dir_subset [".hs"] "/home/rohan/sw/hmt/cmd"
--
dir_subset :: [String] -> FilePath -> IO [FilePath]
-- | Subdirectories (relative) of dir.
dir_subdirs_rel :: FilePath -> IO [FilePath]
-- | Subdirectories of dir.
dir_subdirs :: FilePath -> IO [FilePath]
-- | Recursive form of dir_subdirs.
--
--
-- dir_subdirs_recursively "/home/rohan/sw/hmt-base/Music"
--
dir_subdirs_recursively :: FilePath -> IO [FilePath]
-- | If path is not absolute, prepend current working directory.
--
--
-- to_absolute_cwd "x"
--
to_absolute_cwd :: FilePath -> IO FilePath
-- | If i is an existing file then j else k.
if_file_exists :: (FilePath, IO t, IO t) -> IO t
-- | createDirectoryIfMissing (including parents) and then
-- writeFile
writeFile_mkdir :: FilePath -> String -> IO ()
-- | writeFile_mkdir only if file does not exist.
writeFile_mkdir_x :: FilePath -> String -> IO ()
-- | Ordering functions
module Music.Theory.Ord
-- | Minimum by f.
min_by :: Ord a => (t -> a) -> t -> t -> t
-- | Specialised fromEnum.
ord_to_int :: Ordering -> Int
-- | Specialised toEnum.
int_to_ord :: Int -> Ordering
-- | Invert Ordering.
--
--
-- map ord_invert [LT,EQ,GT] == [GT,EQ,LT]
--
ord_invert :: Ordering -> Ordering
-- | Given Ordering, re-order pair,
order_pair :: Ordering -> (t, t) -> (t, t)
-- | Sort a pair of equal type values using given comparison function.
--
--
-- sort_pair compare ('b','a') == ('a','b')
--
sort_pair :: (t -> t -> Ordering) -> (t, t) -> (t, t)
-- | Variant where the comparison function may not compute a value.
sort_pair_m :: (t -> t -> Maybe Ordering) -> (t, t) -> Maybe (t, t)
-- | Permutation functions.
module Music.Theory.Permutations
-- | Factorial function.
--
--
-- (factorial 20,maxBound::Int)
--
factorial :: Integral n => n -> n
-- | Number of k element permutations of a set of n elements.
--
--
-- let f = nk_permutations in (f 3 2,f 3 3,f 4 3,f 4 4,f 13 3,f 12 12) == (6,6,24,24,1716,479001600)
--
nk_permutations :: Integral a => a -> a -> a
-- | Number of nk permutations where n == k.
--
--
-- map n_permutations [1..8] == [1,2,6,24,120,720,5040,40320]
-- n_permutations 12 == 479001600
-- n_permutations 16 `div` 1000000 == 20922789
--
n_permutations :: Integral a => a -> a
-- | Permutation given as a zero-indexed list of destination indices.
type Permutation = [Int]
-- | Generate the permutation from p to q, ie. the
-- permutation that, when applied to p, gives q.
--
--
-- p = permutation "abc" "bac"
-- p == [1,0,2]
-- apply_permutation p "abc" == "bac"
--
permutation :: Eq t => [t] -> [t] -> Permutation
-- | Permutation to list of swaps, ie. zip [0..]
--
--
-- permutation_to_swaps [0,2,1,3] == [(0,0),(1,2),(2,1),(3,3)]
--
permutation_to_swaps :: Permutation -> [(Int, Int)]
-- | Inverse of permutation_to_swaps, ie. map snd
-- . sort
swaps_to_permutation :: [(Int, Int)] -> Permutation
-- | List of cycles to list of swaps.
--
--
-- cycles_to_swaps [[0,2],[1],[3,4]] == [(0,2),(1,1),(2,0),(3,4),(4,3)]
--
cycles_to_swaps :: [[Int]] -> [(Int, Int)]
swaps_to_cycles :: [(Int, Int)] -> [[Int]]
-- | Apply permutation f to p.
--
--
-- let p = permutation [1..4] [4,3,2,1]
-- p == [3,2,1,0]
-- apply_permutation p [1..4] == [4,3,2,1]
--
apply_permutation :: Permutation -> [t] -> [t]
-- | Composition of apply_permutation and
-- from_cycles_zero_indexed.
--
--
-- apply_permutation_c_zero_indexed [[0,3],[1,2]] [1..4] == [4,3,2,1]
-- apply_permutation_c_zero_indexed [[0,2],[1],[3,4]] [1..5] == [3,2,1,5,4]
-- apply_permutation_c_zero_indexed [[0,1,4],[2,3]] [1..5] == [2,5,4,3,1]
-- apply_permutation_c_zero_indexed [[0,1,3],[2,4]] [1..5] == [2,4,5,1,3]
--
apply_permutation_c_zero_indexed :: [[Int]] -> [a] -> [a]
p_inverse :: Permutation -> Permutation
p_cycles :: Permutation -> [[Int]]
-- | True if the inverse of p is p.
--
--
-- non_invertible [1,0,2] == True
-- non_invertible [2,7,4,9,8,3,5,0,6,1] == False
--
--
--
-- let p = permutation [1..4] [4,3,2,1]
-- non_invertible p == True && p_cycles p == [[0,3],[1,2]]
--
non_invertible :: Permutation -> Bool
-- | Generate a permutation from the cycles c (zero-indexed)
--
--
-- apply_permutation (from_cycles_zero_indexed [[0,1,2,3]]) [1..4] == [2,3,4,1]
--
from_cycles_zero_indexed :: [[Int]] -> Permutation
from_cycles_one_indexed :: [[Int]] -> Permutation
-- | Generate all permutations of size n (naive)
--
--
-- let r = [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
-- map one_line (permutations_n 3) == r
--
permutations_n :: Int -> [Permutation]
p_size :: Permutation -> Int
-- | Composition of q then p.
--
--
-- let p = from_cycles_zero_indexed [[0,2],[1],[3,4]]
-- let q = from_cycles_zero_indexed [[0,1,4],[2,3]]
-- let r = p `compose` q
-- apply_permutation r [1,2,3,4,5] == [2,4,5,1,3]
--
compose :: Permutation -> Permutation -> Permutation
-- | One-indexed p_cycles
cycles_one_indexed :: Permutation -> [[Int]]
-- | flip of compose
--
--
-- cycles_one_indexed (from_cycles_one_indexed [[1,5],[2,3,6],[4]] `permutation_mul` from_cycles_one_indexed [[1,6,4],[2],[3,5]])
--
permutation_mul :: Permutation -> Permutation -> Permutation
-- | Two line notation of p.
--
--
-- two_line (permutation [0,1,3] [1,0,3]) == ([1,2,3],[2,1,3])
--
two_line :: Permutation -> ([Int], [Int])
-- | One line notation of p.
--
--
-- one_line (permutation [0,1,3] [1,0,3]) == [2,1,3]
--
--
--
-- let r = [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
-- map one_line (permutations_n 3) == r
--
one_line :: Permutation -> [Int]
-- | Variant of one_line that produces a compact string.
--
--
-- one_line_compact (permutation [0,1,3] [1,0,3]) == "213"
--
--
--
-- let p = permutations_n 3
-- unwords (map one_line_compact p) == "123 132 213 231 312 321"
--
one_line_compact :: Permutation -> String
-- | Multiplication table of symmetric group n.
--
--
-- unlines (map (unwords . map one_line_compact) (multiplication_table 3))
--
--
--
-- ==> 123 132 213 231 312 321
-- 132 123 312 321 213 231
-- 213 231 123 132 321 312
-- 231 213 321 312 123 132
-- 312 321 132 123 231 213
-- 321 312 231 213 132 123
--
multiplication_table :: Int -> [[Permutation]]
-- | Combination functions.
module Music.Theory.Combinations
-- | Number of k element combinations of a set of n elements.
--
--
-- map (uncurry nk_combinations) [(4,2),(5,3),(6,3),(13,3)] == [6,10,20,286]
--
nk_combinations :: Integral a => a -> a -> a
-- | k element subsets of s.
--
--
-- combinations 3 [1..4] == [[1,2,3],[1,2,4],[1,3,4],[2,3,4]]
-- length (combinations 3 [1..5]) == nk_combinations 5 3
-- combinations 3 "xyzw" == ["xyz","xyw","xzw","yzw"]
--
combinations :: Int -> [a] -> [[a]]
-- | http://www.acta.sapientia.ro/acta-info/C1-1/info1-9.pdf (P.110)
--
--
-- dyck_words_lex 3 == [[0,0,0,1,1,1],[0,0,1,0,1,1],[0,0,1,1,0,1],[0,1,0,0,1,1],[0,1,0,1,0,1]]
--
dyck_words_lex :: (Num t, Ord t) => t -> [[t]]
-- | Translate 01 to [].
--
--
-- unwords (map dyck_word_to_str (dyck_words_lex 3)) == "[[[]]] [[][]] [[]][] [][[]] [][][]"
--
dyck_word_to_str :: Integral n => [n] -> [Char]
-- | Translate [] to 01
dyck_word_from_str :: Integral n => [Char] -> [n]
-- | Is x a segment of a lattice word.
is_lattice_segment :: Integral n => [n] -> Bool
-- | Is x a lattice word.
--
-- is_lattice_word [1,1,1,2,2,1,2,1] == True
is_lattice_word :: Integral n => [n] -> Bool
-- | is_lattice_word of reverse.
is_yamanouchi_word :: Integral n => [n] -> Bool
-- | is_lattice_word of dyck_word_from_str
--
--
-- is_dyck_word "[][[][[[][]]]]" == True
--
is_dyck_word :: String -> Bool
-- | Read functions.
module Music.Theory.Read
-- | Transform ReadS function into precise Read function.
-- Requires using all the input to produce a single token. The only
-- exception is a singular trailing white space character.
reads_to_read_precise :: ReadS t -> String -> Maybe t
-- | Error variant of reads_to_read_precise.
reads_to_read_precise_err :: String -> ReadS t -> String -> t
-- | reads_to_read_precise of reads.
--
--
-- read_maybe "1.0" :: Maybe Int
-- read_maybe "1.0" :: Maybe Float
--
read_maybe :: Read a => String -> Maybe a
-- | Variant of read_maybe with default value.
--
--
-- map (read_def 0) ["2","2:","2\n"] == [2,0,2]
--
read_def :: Read a => a -> String -> a
-- | Variant of read_maybe that errors on Nothing, printing
-- message.
read_err_msg :: Read a => String -> String -> a
-- | Default message.
read_err :: Read a => String -> a
-- | Variant of reads requiring exact match, no trailing white
-- space.
--
--
-- map reads_exact ["1.5","2,5"] == [Just 1.5,Nothing]
--
reads_exact :: Read a => String -> Maybe a
-- | Variant of reads_exact that errors on failure.
reads_exact_err :: Read a => String -> String -> a
-- | Allow commas as thousand separators.
--
--
-- let r = [Just 123456,Just 123456,Nothing,Just 123456789]
-- map read_integral_allow_commas_maybe ["123456","123,456","1234,56","123,456,789"] == r
--
read_integral_allow_commas_maybe :: Read i => String -> Maybe i
read_integral_allow_commas_err :: (Integral i, Read i) => String -> i
-- | Type specialised.
--
--
-- map read_int_allow_commas ["123456","123,456","123,456,789"] == [123456,123456,123456789]
--
read_int_allow_commas :: String -> Int
-- | Read a ratio where the division is given by / instead of
-- % and the integers allow commas.
--
--
-- map read_ratio_with_div_err ["123,456/7","123,456,789"] == [123456/7,123456789]
--
read_ratio_with_div_err :: (Integral i, Read i) => String -> Ratio i
-- | Read Ratio, allow commas for thousand separators.
--
--
-- read_ratio_allow_commas_err "327,680" "177,147" == 327680 / 177147
--
read_ratio_allow_commas_err :: (Integral i, Read i) => String -> String -> Ratio i
-- | Delete trailing ., read fails for 700..
delete_trailing_point :: String -> String
-- | read_err disallows trailing decimal points.
--
--
-- map read_fractional_allow_trailing_point_err ["123.","123.4"] == [123.0,123.4]
--
read_fractional_allow_trailing_point_err :: Read n => String -> n
-- | Type specialised read_maybe.
--
--
-- map read_maybe_int ["2","2:","2\n","x"] == [Just 2,Nothing,Just 2,Nothing]
--
read_maybe_int :: String -> Maybe Int
-- | Type specialised read_err.
read_int :: String -> Int
-- | Type specialised read_maybe.
read_maybe_double :: String -> Maybe Double
-- | Type specialised read_err.
read_double :: String -> Double
-- | Type specialised read_maybe.
--
--
-- map read_maybe_rational ["1","1%2","1/2"] == [Nothing,Just (1/2),Nothing]
--
read_maybe_rational :: String -> Maybe Rational
-- | Type specialised read_err.
--
--
-- read_rational "1%4"
--
read_rational :: String -> Rational
-- | Read binary integer.
--
--
-- mapMaybe read_bin (words "000 001 010 011 100 101 110 111") == [0 .. 7]
--
read_bin :: Integral a => String -> Maybe a
-- | Erroring variant.
read_bin_err :: Integral a => String -> a
-- | Error variant of readHex.
--
--
-- read_hex_err "F0B0" == 61616
--
read_hex_err :: (Eq n, Integral n) => String -> n
-- | Read hex value from string of at most k places.
read_hex_sz :: (Eq n, Integral n) => Int -> String -> n
-- | Read hexadecimal representation of 32-bit unsigned word.
--
--
-- map read_hex_word32 ["00000000","12345678","FFFFFFFF"] == [minBound,305419896,maxBound]
--
read_hex_word32 :: String -> Word32
-- | Parser for rational_pp.
--
--
-- map rational_parse ["1","3/2","5/4","2"] == [1,3/2,5/4,2]
-- rational_parse "" == undefined
--
rational_parse :: (Read t, Integral t) => String -> Ratio t
-- | Very simple command line interface option parser.
--
-- Only allows options of the form --key=value, with the form --key equal
-- to --key=True.
--
-- A list of OptUsr describes the options and provides default values.
--
-- get_opt_arg merges user and default values into a table with
-- values for all options.
--
-- To fetch options use opt_get and opt_read.
module Music.Theory.Opt
-- | (Key,Value)
--
-- Key does not include leading '--'.
type Opt = (String, String)
-- | (Key,Default-Value,Type,Note)
type OptUsr = (String, String, String, String)
-- | Re-write default values at OptUsr.
opt_usr_rw_def :: [Opt] -> [OptUsr] -> [OptUsr]
-- | OptUsr to Opt.
opt_plain :: OptUsr -> Opt
-- | OptUsr to help string, indent is two spaces.
opt_usr_help :: OptUsr -> String
-- | unlines of opt_usr_help
opt_help :: [OptUsr] -> String
-- | Lookup Key in Opt, error if non-existing.
opt_get :: [Opt] -> String -> String
-- | Variant that returns Nothing if the result is the empty string, else
-- Just the result.
opt_get_nil :: [Opt] -> String -> Maybe String
-- | read of get_opt
opt_read :: Read t => [Opt] -> String -> t
-- | Parse k or k=v string, else error.
opt_param_parse :: String -> Opt
-- | Parse option string of form "--opt" or "--key=value".
--
--
-- opt_parse "--opt" == Just ("opt","True")
-- opt_parse "--key=value" == Just ("key","value")
--
opt_parse :: String -> Maybe Opt
-- | Parse option sequence, collating options and non-options.
--
--
-- opt_set_parse (words "--a --b=c d") == ([("a","True"),("b","c")],["d"])
--
opt_set_parse :: [String] -> ([Opt], [String])
-- | Left-biased Opt merge.
opt_merge :: [Opt] -> [Opt] -> [Opt]
-- | Process argument list.
opt_proc :: [OptUsr] -> [String] -> ([Opt], [String])
-- | Usage text
type OptHelp = [String]
-- | Format usage pre-amble and opt_help.
opt_help_pp :: OptHelp -> [OptUsr] -> String
-- | Print help and exit.
opt_usage :: OptHelp -> [OptUsr] -> IO ()
-- | Print help and error.
opt_error :: OptHelp -> [OptUsr] -> t
-- | Verify that all Opt have keys that are in OptUsr
opt_verify :: OptHelp -> [OptUsr] -> [Opt] -> IO ()
-- | opt_set_parse and maybe opt_verify and opt_merge
-- of getArgs. If arguments include -h or --help run
-- opt_usage
opt_get_arg :: Bool -> OptHelp -> [OptUsr] -> IO ([Opt], [String])
-- | Parse param set, one parameter per line.
--
--
-- opt_param_set_parse "a\nb=c" == [("a","True"),("b","c")]
--
opt_param_set_parse :: String -> [Opt]
-- | Simple scanner over argument list.
opt_scan :: [String] -> String -> Maybe String
-- | Scanner with default value.
opt_scan_def :: [String] -> (String, String) -> String
-- | Reading scanner with default value.
opt_scan_read :: Read t => [String] -> (String, t) -> t
-- | Byte functions.
module Music.Theory.Byte
-- | toEnum of word8_to_int
word8_to_enum :: Enum e => Word8 -> e
-- | int_to_word8_maybe of fromEnum
enum_to_word8 :: Enum e => e -> Maybe Word8
-- | Type-specialised word8_to_enum
--
--
-- map word8_to_char [60,62] == "<>"
--
word8_to_char :: Word8 -> Char
-- | int_to_word8 of fromEnum
char_to_word8 :: Char -> Word8
-- | int_to_word8 of digitToInt
digit_to_word8 :: Char -> Word8
-- | intToDigit of word8_to_int
word8_to_digit :: Word8 -> Char
-- | at of word8_to_int
word8_at :: [t] -> Word8 -> t
-- | Given n in (0,255) make two character hex string.
--
--
-- mapMaybe byte_hex_pp [0x0F,0xF0,0xF0F] == ["0F","F0"]
--
byte_hex_pp :: (Integral i, Show i) => i -> Maybe String
-- | Erroring variant.
byte_hex_pp_err :: (Integral i, Show i) => i -> String
-- | byte_hex_pp_err either plain (ws = False) or with spaces (ws =
-- True). Plain is the same format written by xxd -p and read by xxd -r
-- -p.
--
--
-- byte_seq_hex_pp True [0x0F,0xF0] == "0F F0"
--
byte_seq_hex_pp :: (Integral i, Show i) => Bool -> [i] -> String
-- | Read two character hexadecimal string.
--
--
-- mapMaybe read_hex_byte (Split.chunksOf 2 "0FF0F") == [0x0F,0xF0]
--
read_hex_byte :: (Eq t, Integral t) => String -> Maybe t
-- | Erroring variant.
read_hex_byte_err :: (Eq t, Integral t) => String -> t
-- | Sequence of read_hex_byte_err
--
--
-- read_hex_byte_seq "000FF0FF" == [0x00,0x0F,0xF0,0xFF]
--
read_hex_byte_seq :: (Eq t, Integral t) => String -> [t]
-- | Variant that filters white space.
--
--
-- read_hex_byte_seq_ws "00 0F F0 FF" == [0x00,0x0F,0xF0,0xFF]
--
read_hex_byte_seq_ws :: (Eq t, Integral t) => String -> [t]
-- | Load binary U8 sequence from file.
load_byte_seq :: Integral i => FilePath -> IO [i]
-- | Store binary U8 sequence to file.
store_byte_seq :: Integral i => FilePath -> [i] -> IO ()
-- | Load hexadecimal text U8 sequences from file.
load_hex_byte_seq :: Integral i => FilePath -> IO [[i]]
-- | Store U8 sequences as hexadecimal text, one sequence per
-- line.
store_hex_byte_seq :: (Integral i, Show i) => FilePath -> [[i]] -> IO ()
castFloatToWord32 :: Float -> Word32
castWord32ToFloat :: Word32 -> Float
castDoubleToWord64 :: Double -> Word64
castWord64ToDouble :: Word64 -> Double
-- | Show functions.
module Music.Theory.Show
-- | Show positive and negative values always with sign, maybe show zero,
-- maybe right justify.
--
--
-- map (num_diff_str_opt (True,2)) [-2,-1,0,1,2] == ["-2","-1"," 0","+1","+2"]
--
num_diff_str_opt :: (Ord a, Num a, Show a) => (Bool, Int) -> a -> String
-- | Show only positive and negative values, always with sign.
--
--
-- map num_diff_str [-2,-1,0,1,2] == ["-2","-1","","+1","+2"]
-- map show [-2,-1,0,1,2] == ["-2","-1","0","1","2"]
--
num_diff_str :: (Num a, Ord a, Show a) => a -> String
-- | Pretty printer for Rational using / and eliding
-- denominators of 1.
--
--
-- map rational_pp [1,3/2,5/4,2] == ["1","3/2","5/4","2"]
--
rational_pp :: (Show a, Integral a) => Ratio a -> String
-- | Pretty print ratio as : separated integers, if nil is
-- True elide unit denominator.
--
--
-- map (ratio_pp_opt True) [1,3/2,2] == ["1","3:2","2"]
--
ratio_pp_opt :: Bool -> Rational -> String
-- | Pretty print ratio as : separated integers.
--
--
-- map ratio_pp [1,3/2,2] == ["1:1","3:2","2:1"]
--
ratio_pp :: Rational -> String
-- | Show rational to n decimal places.
--
--
-- let r = approxRational pi 1e-100
-- r == 884279719003555 / 281474976710656
-- show_rational_decimal 12 r == "3.141592653590"
-- show_rational_decimal 3 (-100) == "-100.000"
--
show_rational_decimal :: Int -> Rational -> String
-- | Show r as float to k places.
--
--
-- real_pp 4 (1/3 :: Rational) == "0.3333"
-- map (real_pp 4) [1,1.1,1.12,1.123,1.1234,1/0,sqrt (-1)]
--
real_pp :: Real t => Int -> t -> String
-- | Variant that writes ∞ for Infinity.
--
--
-- putStrLn $ unwords $ map (real_pp_unicode 4) [1/0,-1/0]
--
real_pp_unicode :: Real t => Int -> t -> [Char]
-- | Prints n as integral or to at most k decimal places.
-- Does not print -0.
--
--
-- real_pp_trunc 4 (1/3 :: Rational) == "0.3333"
-- map (real_pp_trunc 4) [1,1.1,1.12,1.123,1.1234] == ["1","1.1","1.12","1.123","1.1234"]
-- map (real_pp_trunc 4) [1.00009,1.00001] == ["1.0001","1"]
-- map (real_pp_trunc 2) [59.999,60.001,-0.00,-0.001]
--
real_pp_trunc :: Real t => Int -> t -> String
-- | Variant of showFFloat. The Show instance for floats
-- resorts to exponential notation very readily.
--
--
-- [show 0.01,realfloat_pp 2 0.01] == ["1.0e-2","0.01"]
-- map (realfloat_pp 4) [1,1.1,1.12,1.123,1.1234,1/0,sqrt (-1)]
--
realfloat_pp :: RealFloat a => Int -> a -> String
-- | Type specialised realfloat_pp.
float_pp :: Int -> Float -> String
-- | Type specialised realfloat_pp.
--
--
-- double_pp 4 0
--
double_pp :: Int -> Double -> String
-- | Read binary integer.
--
--
-- unwords (map (show_bin Nothing) [0 .. 7]) == "0 1 10 11 100 101 110 111"
-- unwords (map (show_bin (Just 3)) [0 .. 7]) == "000 001 010 011 100 101 110 111"
--
show_bin :: (Integral i, Show i) => Maybe Int -> i -> String
-- | String functions.
module Music.Theory.String
-- | Case-insensitive ==.
--
--
-- map (str_eq_ci "ci") (words "CI ci Ci cI")
--
str_eq_ci :: String -> String -> Bool
-- | Remove r.
filter_cr :: String -> String
-- | Delete trailing Char where isSpace holds.
--
--
-- delete_trailing_whitespace " str " == " str"
-- delete_trailing_whitespace "\t\n \t\n" == ""
--
delete_trailing_whitespace :: String -> String
-- | Variant of unwords that does not write spaces for NIL elements.
--
--
-- unwords_nil [] == ""
-- unwords_nil ["a"] == "a"
-- unwords_nil ["a",""] == "a"
-- unwords_nil ["a","b"] == "a b"
-- unwords_nil ["a","","b"] == "a b"
-- unwords_nil ["a","","","b"] == "a b"
-- unwords_nil ["a","b",""] == "a b"
-- unwords_nil ["a","b","",""] == "a b"
-- unwords_nil ["","a","b"] == "a b"
-- unwords_nil ["","","a","b"] == "a b"
--
unwords_nil :: [String] -> String
-- | Variant of unlines that does not write empty lines for NIL
-- elements.
unlines_nil :: [String] -> String
-- | unlines without a trailing newline.
--
--
-- unlines (words "a b c") == "a\nb\nc\n"
-- unlinesNoTrailingNewline (words "a b c") == "a\nb\nc"
--
unlinesNoTrailingNewline :: [String] -> String
-- | Capitalise first character of word.
--
--
-- capitalise "freqShift" == "FreqShift"
--
capitalise :: String -> String
-- | Downcase first character of word.
--
--
-- unCapitalise "FreqShift" == "freqShift"
--
unCapitalise :: String -> String
-- | Apply function at each line of string.
--
--
-- on_lines reverse "ab\ncde\nfg" == "ba\nedc\ngf\n"
--
on_lines :: (String -> String) -> String -> String
-- | Regular array data as plain text tables.
module Music.Theory.Array.Text
-- | Tabular text.
type Text_Table = [[String]]
-- | Split table at indicated places.
--
--
-- let tbl = [["1","2","3","4"],["A","B","E","F"],["C","D","G","H"]]
-- table_split [2,2] tbl
--
table_split :: [Int] -> Text_Table -> [Text_Table]
-- | Join tables left to right.
--
--
-- table_concat [[["1","2"],["A","B"],["C","D"]],[["3","4"],["E","F"],["G","H"]]]
--
table_concat :: [Text_Table] -> Text_Table
-- | Add a row number column at the front of the table.
--
--
-- table_number_rows 0 tbl
--
table_number_rows :: Int -> Text_Table -> Text_Table
-- | (HEADER,PAD-LEFT,EQ-WIDTH,COL-SEP,TBL-DELIM).
--
-- Options are: has header pad text with space to left instead of right,
-- make all columns equal width, column separator string, print table
-- delimiters
type Text_Table_Opt = (Bool, Bool, Bool, String, Bool)
-- | Options for plain layout.
table_opt_plain :: Text_Table_Opt
-- | Options for simple layout.
table_opt_simple :: Text_Table_Opt
-- | Options for pipe layout.
table_opt_pipe :: Text_Table_Opt
-- | Pretty-print table. Table is in row order.
--
--
-- let tbl = [["1","2","3","4"],["a","bc","def"],["ghij","klm","no","p"]]
-- putStrLn$unlines$"": table_pp (True,True,True," ",True) tbl
-- putStrLn$unlines$"": table_pp (False,False,True," ",False) tbl
--
table_pp :: Text_Table_Opt -> Text_Table -> [String]
-- | Variant relying on Show instances.
--
--
-- table_pp_show table_opt_simple [[1..4],[5..8],[9..12]]
--
table_pp_show :: Show t => Text_Table_Opt -> Table t -> [String]
-- | Variant in column order (ie. transpose).
--
--
-- table_pp_column_order table_opt_simple [["a","bc","def"],["ghij","klm","no"]]
--
table_pp_column_order :: Text_Table_Opt -> Text_Table -> [String]
-- | Matrix form, ie. header in both first row and first column, in each
-- case displaced by one location which is empty.
--
--
-- let h = (map return "abc",map return "efgh")
-- let t = table_matrix h (map (map show) [[1,2,3,4],[2,3,4,1],[3,4,1,2]])
--
--
--
-- >>> putStrLn $ unlines $ table_pp table_opt_simple t
-- - - - - -
-- e f g h
-- a 1 2 3 4
-- b 2 3 4 1
-- c 3 4 1 2
-- - - - - -
--
table_matrix :: ([String], [String]) -> Text_Table -> Text_Table
-- | Variant that takes a show function and a header
-- decoration function.
--
--
-- table_matrix_opt show id ([1,2,3],[4,5,6]) [[7,8,9],[10,11,12],[13,14,15]]
--
table_matrix_opt :: (a -> String) -> (String -> String) -> ([a], [a]) -> Table a -> Text_Table
-- | Ordinary timing durations, in H:M:S:m
-- (Hours:Minutes:Seconds:milliseconds)
module Music.Theory.Time.Duration
-- | Duration stored as hours, minutes, seconds and
-- milliseconds.
data Duration
Duration :: Int -> Int -> Int -> Int -> Duration
[hours] :: Duration -> Int
[minutes] :: Duration -> Int
[seconds] :: Duration -> Int
[milliseconds] :: Duration -> Int
-- | Convert fractional seconds to integral
-- (seconds,milliseconds).
--
--
-- s_sms 1.75 == (1,750)
--
s_sms :: (RealFrac n, Integral i) => n -> (i, i)
-- | Inverse of s_sms.
--
--
-- sms_s (1,750) == 1.75
--
sms_s :: Integral i => (i, i) -> Double
-- | Read function for Duration tuple. The notation writes
-- seconds fractionally, and allows hours and minutes to be elided if
-- zero.
read_duration_tuple :: String -> (Int, Int, Int, Int)
-- | Read function for Duration. Allows either
-- H:M:S.MS or M:S.MS or S.MS.
--
--
-- read_duration "01:35:05.250" == Duration 1 35 5 250
-- read_duration "35:05.250" == Duration 0 35 5 250
-- read_duration "05.250" == Duration 0 0 5 250
--
read_duration :: String -> Duration
-- | Show function for Duration. Inverse of read_duration.
-- Hours and minutes are always shown, even if zero.
--
--
-- show_duration (Duration 1 35 5 250) == "01:35:05.250"
-- show (Duration 1 15 0 000) == "01:15:00.000"
-- show (Duration 0 0 3 500) == "00:00:03.500"
--
show_duration :: Duration -> String
-- | If minutes is not in (0,59) then edit hours.
normalise_minutes :: Duration -> Duration
-- | If seconds is not in (0,59) then edit minutes.
normalise_seconds :: Duration -> Duration
-- | If milliseconds is not in (0,999) then edit seconds.
normalise_milliseconds :: Duration -> Duration
-- | Normalise duration so that all parts are in normal ranges.
normalise_duration :: Duration -> Duration
-- | Extract Duration tuple applying filter function at each element
--
--
-- duration_to_tuple id (Duration 1 35 5 250) == (1,35,5,250)
--
duration_to_tuple :: (Int -> a) -> Duration -> (a, a, a, a)
-- | Inverse of duration_to_tuple.
tuple_to_duration :: (a -> Int) -> (a, a, a, a) -> Duration
-- | Duration as fractional hours.
--
--
-- duration_to_hours (read "01:35:05.250") == 1.5847916666666668
--
duration_to_hours :: Fractional n => Duration -> n
-- | Duration as fractional minutes.
--
--
-- duration_to_minutes (read "01:35:05.250") == 95.0875
--
duration_to_minutes :: Fractional n => Duration -> n
-- | Duration as fractional seconds.
--
--
-- duration_to_seconds (read "01:35:05.250") == 5705.25
--
duration_to_seconds :: Fractional n => Duration -> n
-- | Inverse of duration_to_hours.
--
--
-- hours_to_duration 1.5847916 == Duration 1 35 5 250
--
hours_to_duration :: RealFrac a => a -> Duration
-- | Inverse of duration_to_minutes.
minutes_to_duration :: RealFrac a => a -> Duration
-- | Inverse of duration_to_seconds.
seconds_to_duration :: RealFrac a => a -> Duration
-- | Empty (zero) duration.
nil_duration :: Duration
-- | Negate the leftmost non-zero element of Duration.
negate_duration :: Duration -> Duration
-- | Difference between two durations as a duration. Implemented by
-- translation to and from Rational fractional hours.
--
--
-- duration_diff (Duration 1 35 5 250) (Duration 0 25 1 125) == Duration 1 10 4 125
-- duration_diff (Duration 0 25 1 125) (Duration 1 35 5 250) == Duration (-1) 10 4 125
-- duration_diff (Duration 0 25 1 125) (Duration 0 25 1 250) == Duration 0 0 0 (-125)
--
duration_diff :: Duration -> Duration -> Duration
instance GHC.Classes.Eq Music.Theory.Time.Duration.Duration
instance GHC.Read.Read Music.Theory.Time.Duration.Duration
instance GHC.Show.Show Music.Theory.Time.Duration.Duration
-- | Ordinary time and duration notations. In terms of Weeks, Days, Hours,
-- Minutes, Second and Centiseconds. c.f.
-- Music.Theory.Time.Duration.
module Music.Theory.Time.Notation
-- | Week, one-indexed, ie. 1-52
type Week = Int
-- | Week, one-indexed, ie. 1-31
type Day = Int
-- | Hour, zero-indexed, ie. 0-23
type Hour = Int
-- | Minute, zero-indexed, ie. 0-59
type Min = Int
-- | Second, zero-indexed, ie. 0-59
type Sec = Int
-- | Centi-seconds, zero-indexed, ie. 0-99
type Csec = Int
-- | Minutes, seconds as (min,sec)
type MinSec = (Min, Sec)
-- | Generic MinSec
type GMinSec n = (n, n)
-- | Minutes, seconds, centi-seconds as (min,sec,csec)
type MinCsec = (Min, Sec, Csec)
-- | Generic MinCsec
type GMinCsec n = (n, n, n)
-- | (Hours,Minutes,Seconds)
type Hms = (Hour, Min, Sec)
-- | (Days,Hours,Minutes,Seconds)
type Dhms = (Day, Hour, Min, Sec)
-- | Fractional days.
type FDay = Double
-- | Fractional hour, ie. 1.50 is one and a half hours, ie. 1 hour and 30
-- minutes.
type FHour = Double
-- | Fractional minute, ie. 1.50 is one and a half minutes, ie. 1 minute
-- and 30 seconds, cf. FMinSec
type FMin = Double
-- | Fractional seconds.
type FSec = Double
-- | Fractional minutes and seconds (mm.ss, ie. 01.45 is 1 minute and 45
-- seconds).
type FMinSec = Double
-- | parseTimeOrError with defaultTimeLocale.
parse_time_str :: ParseTime t => String -> String -> t
format_time_str :: FormatTime t => String -> t -> String
-- | Parse date in ISO-8601 extended (YYYY-MM-DD) or basic
-- (YYYYMMDD) form.
--
--
-- Time.toGregorian (Time.utctDay (parse_iso8601_date "2011-10-09")) == (2011,10,09)
-- Time.toGregorian (Time.utctDay (parse_iso8601_date "20190803")) == (2019,08,03)
--
parse_iso8601_date :: String -> UTCTime
-- | Format date in ISO-8601 form.
--
--
-- format_iso8601_date True (parse_iso8601_date "2011-10-09") == "2011-10-09"
-- format_iso8601_date False (parse_iso8601_date "20190803") == "20190803"
--
format_iso8601_date :: FormatTime t => Bool -> t -> String
-- | Format date in ISO-8601 (YYYY-WWW) form.
--
--
-- r = ["2016-W52","2011-W40"]
-- map (format_iso8601_week . parse_iso8601_date) ["2017-01-01","2011-10-09"] == r
--
format_iso8601_week :: FormatTime t => t -> String
-- | Parse ISO-8601 time is extended (HH:MM:SS) or basic
-- (HHMMSS) form.
--
--
-- format_iso8601_time True (parse_iso8601_time "21:44:00") == "21:44:00"
-- format_iso8601_time False (parse_iso8601_time "172511") == "172511"
--
parse_iso8601_time :: String -> UTCTime
-- | Format time in ISO-8601 form.
--
--
-- format_iso8601_time True (parse_iso8601_date_time "2011-10-09T21:44:00") == "21:44:00"
-- format_iso8601_time False (parse_iso8601_date_time "20190803T172511") == "172511"
--
format_iso8601_time :: FormatTime t => Bool -> t -> String
-- | Parse date and time in extended or basic forms.
--
--
-- Time.utctDayTime (parse_iso8601_date_time "2011-10-09T21:44:00") == Time.secondsToDiffTime 78240
-- Time.utctDayTime (parse_iso8601_date_time "20190803T172511") == Time.secondsToDiffTime 62711
--
parse_iso8601_date_time :: String -> UTCTime
-- | Format date in YYYY-MM-DD and time in HH:MM:SS
-- forms.
--
--
-- t = parse_iso8601_date_time "2011-10-09T21:44:00"
-- format_iso8601_date_time True t == "2011-10-09T21:44:00"
-- format_iso8601_date_time False t == "20111009T214400"
--
format_iso8601_date_time :: FormatTime t => Bool -> t -> String
-- | fsec_to_minsec . * 60
--
--
-- fmin_to_minsec 6.48 == (6,29)
--
fmin_to_minsec :: FMin -> MinSec
-- | Translate fractional seconds to picoseconds.
--
--
-- fsec_to_picoseconds 78240.05
--
fsec_to_picoseconds :: FSec -> Integer
fsec_to_difftime :: FSec -> DiffTime
-- | Translate fractional minutes.seconds to picoseconds.
--
--
-- map fminsec_to_fsec [0.45,15.355] == [45,935.5]
--
fminsec_to_fsec :: FMinSec -> FSec
fminsec_to_sec_generic :: (RealFrac f, Integral i) => f -> i
-- | Fractional minutes are mm.ss, so that 15.35 is 15 minutes and 35
-- seconds.
--
--
-- map fminsec_to_sec [0.45,15.35] == [45,935]
--
fminsec_to_sec :: FMinSec -> Sec
fsec_to_fminsec :: FSec -> FMinSec
sec_to_fminsec :: Sec -> FMinSec
fminsec_add :: BinOp FMinSec
fminsec_sub :: BinOp FMinSec
fminsec_mul :: BinOp FMinSec
-- | Type specialised fromInteger of floor.
ffloor :: Double -> Double
-- | Fractional hour to (hours,minutes,seconds).
--
--
-- fhour_to_hms 21.75 == (21,45,0)
--
fhour_to_hms :: FHour -> Hms
-- | Hms to fractional hours.
--
--
-- hms_to_fhour (21,45,0) == 21.75
--
hms_to_fhour :: Hms -> FHour
-- | Fractional hour to seconds.
--
--
-- fhour_to_fsec 21.75 == 78300.0
--
fhour_to_fsec :: FHour -> FSec
fhour_to_difftime :: FHour -> DiffTime
-- | Time in fractional days.
--
--
-- round (utctime_to_fday (parse_iso8601_date_time "2011-10-09T09:00:00")) == 55843
-- round (utctime_to_fday (parse_iso8601_date_time "2011-10-09T21:00:00")) == 55844
--
utctime_to_fday :: UTCTime -> FDay
-- | DiffTime in fractional seconds.
--
--
-- difftime_to_fsec (hms_to_difftime (21,44,30)) == 78270
--
difftime_to_fsec :: DiffTime -> FSec
-- | DiffTime in fractional minutes.
--
--
-- difftime_to_fmin (hms_to_difftime (21,44,30)) == 1304.5
--
difftime_to_fmin :: DiffTime -> Double
-- | DiffTime in fractional hours.
--
--
-- difftime_to_fhour (hms_to_difftime (21,45,00)) == 21.75
--
difftime_to_fhour :: DiffTime -> FHour
hms_to_difftime :: Hms -> DiffTime
hms_to_sec :: Hms -> Sec
-- | Seconds to (hours,minutes,seconds).
--
--
-- map sec_to_hms [60-1,60+1,60*60-1,60*60+1] == [(0,0,59),(0,1,1),(0,59,59),(1,0,1)]
--
sec_to_hms :: Sec -> Hms
-- | Hms pretty printer.
--
--
-- map (hms_pp True) [(0,1,2),(1,2,3)] == ["01:02","01:02:03"]
--
hms_pp :: Bool -> Hms -> String
hms_parse :: String -> Hms
-- | divMod by 60.
--
--
-- sec_to_minsec 123 == (2,3)
--
sec_to_minsec :: Integral n => n -> GMinSec n
-- | Inverse of sec_minsec.
--
--
-- minsec_to_sec (2,3) == 123
--
minsec_to_sec :: Num n => GMinSec n -> n
-- | Convert p and q to seconds, apply f, and convert
-- back to MinSec.
minsec_binop :: Integral t => (t -> t -> t) -> GMinSec t -> GMinSec t -> GMinSec t
-- | minsec_binop -, assumes q precedes p.
--
--
-- minsec_sub (2,35) (1,59) == (0,36)
--
minsec_sub :: Integral n => GMinSec n -> GMinSec n -> GMinSec n
-- | minsec_binop subtract, assumes p precedes
-- q.
--
--
-- minsec_diff (1,59) (2,35) == (0,36)
--
minsec_diff :: Integral n => GMinSec n -> GMinSec n -> GMinSec n
-- | minsec_binop +.
--
--
-- minsec_add (1,59) (2,35) == (4,34)
--
minsec_add :: Integral n => GMinSec n -> GMinSec n -> GMinSec n
-- | foldl of minsec_add
--
--
-- minsec_sum [(1,59),(2,35),(4,34)] == (9,08)
--
minsec_sum :: Integral n => [GMinSec n] -> GMinSec n
-- | round fractional seconds to (min,sec).
--
--
-- map fsec_to_minsec [59.49,60,60.51] == [(0,59),(1,0),(1,1)]
--
fsec_to_minsec :: FSec -> MinSec
-- | MinSec pretty printer.
--
--
-- map (minsec_pp . fsec_to_minsec) [59,61] == ["00:59","01:01"]
--
minsec_pp :: MinSec -> String
minsec_parse :: (Num n, Read n) => String -> GMinSec n
-- | Fractional seconds to (min,sec,csec), csec value is
-- rounded.
--
--
-- map fsec_to_mincsec [1,1.5,4/3] == [(0,1,0),(0,1,50),(0,1,33)]
--
fsec_to_mincsec :: FSec -> MinCsec
-- | Inverse of fsec_mincsec.
mincsec_to_fsec :: Real n => GMinCsec n -> FSec
mincsec_to_csec :: Num n => GMinCsec n -> n
-- | Centi-seconds to MinCsec.
--
--
-- map csec_to_mincsec [123,12345] == [(0,1,23),(2,3,45)]
--
csec_to_mincsec :: Integral n => n -> GMinCsec n
-- | MinCsec pretty printer, concise mode omits centiseconds when
-- zero.
--
--
-- map (mincsec_pp_opt True . fsec_to_mincsec) [1,60.5] == ["00:01","01:00.50"]
--
mincsec_pp_opt :: Bool -> MinCsec -> String
-- | MinCsec pretty printer.
--
--
-- let r = ["00:01.00","00:06.67","02:03.45"]
-- map (mincsec_pp . fsec_to_mincsec) [1,6+2/3,123.45] == r
--
mincsec_pp :: MinCsec -> String
mincsec_binop :: Integral t => (t -> t -> t) -> GMinCsec t -> GMinCsec t -> GMinCsec t
-- | Convert seconds into (days,hours,minutes,seconds).
sec_to_dhms_generic :: Integral n => n -> (n, n, n, n)
-- | Type specialised sec_to_dhms_generic.
--
--
-- sec_to_dhms 1475469 == (17,1,51,9)
--
sec_to_dhms :: Sec -> Dhms
-- | Inverse of seconds_to_dhms.
--
--
-- dhms_to_sec (17,1,51,9) == 1475469
--
dhms_to_sec :: Num n => (n, n, n, n) -> n
-- | Generic form of parse_dhms.
parse_dhms_generic :: (Integral n, Read n) => String -> (n, n, n, n)
-- | Parse DHms text. All parts are optional, order is not significant,
-- multiple entries are allowed.
--
--
-- parse_dhms "17d1h51m9s" == (17,1,51,9)
-- parse_dhms "1s3d" == (3,0,0,1)
-- parse_dhms "1h1h" == (0,2,0,0)
--
parse_dhms :: String -> Dhms
-- | Week that t lies in.
--
--
-- map (time_to_week . parse_iso8601_date) ["2017-01-01","2011-10-09"] == [52,40]
--
time_to_week :: UTCTime -> Week
-- | Given printer, pretty print time span.
span_pp :: (t -> String) -> (t, t) -> String
-- | Traversable functions.
module Music.Theory.Traversable
-- | Replace elements at Traversable with result of joining with
-- elements from list.
--
--
-- let t = Tree.Node 0 [Tree.Node 1 [Tree.Node 2 [],Tree.Node 3 []],Tree.Node 4 []]
-- putStrLn $ Tree.drawTree (fmap show t)
-- let (_,u) = adopt_shape (\_ x -> x) "abcde" t
-- putStrLn $ Tree.drawTree (fmap return u)
--
adopt_shape :: Traversable t => (a -> b -> c) -> [b] -> t a -> ([b], t c)
-- | Two-level variant of adopt_shape.
--
--
-- adopt_shape_2 (,) [0..4] (words "a bc d") == ([4],[[('a',0)],[('b',1),('c',2)],[('d',3)]])
--
adopt_shape_2 :: (Traversable t, Traversable u) => (a -> b -> c) -> [b] -> t (u a) -> ([b], t (u c))
-- | Adopt stream to shape of traversable and zip elements.
--
--
-- adopt_shape_2_zip_stream [1..] ["a", "list", "of", "strings"]
--
adopt_shape_2_zip_stream :: (Traversable t, Traversable u) => [c] -> t (u a) -> t (u (c, a))
-- | Two-level variant of zip [1..]
--
--
-- list_number_2 ["number","list","two"] == [[(1,'n'),(2,'u'),(3,'m'),(4,'b'),(5,'e'),(6,'r')],[(7,'l'),(8,'i'),(9,'s'),(10,'t')],[(11,'t'),(12,'w'),(13,'o')]]
--
list_number_2 :: [[x]] -> [[(Int, x)]]
-- | Variant of adopt_shape that considers only Just elements
-- at Traversable.
--
--
-- let s = "a(b(cd)ef)ghi"
-- let t = group_tree (begin_end_cmp_eq '(' ')') s
-- adopt_shape_m (,) [1..13] t
--
adopt_shape_m :: Traversable t => (a -> b -> c) -> [b] -> t (Maybe a) -> ([b], t (Maybe c))
-- | Tree functions
module Music.Theory.Tree
-- | Print forest as markdown list.
mdForest :: Forest String -> String
-- | Print tree as markdown list with indicated starting indent level.
mdTree :: Int -> Tree String -> [String]
-- | Tuple functions.
--
-- Uniform tuples have types T2, T3 etc. and functions
-- names are prefixed t2_ etc.
--
-- Heterogenous tuples (products) are prefixed p2_ etc.
module Music.Theory.Tuple
p2_from_list :: (t -> t1, t -> t2) -> [t] -> (t1, t2)
-- | Swap elements of P2
--
--
-- p2_swap (1,2) == (2,1)
--
p2_swap :: (s, t) -> (t, s)
-- | Uniform two-tuple.
type T2 a = (a, a)
t2_from_list :: [t] -> T2 t
t2_to_list :: T2 a -> [a]
t2_swap :: T2 t -> T2 t
t2_map :: (p -> q) -> T2 p -> T2 q
t2_zipWith :: (p -> q -> r) -> T2 p -> T2 q -> T2 r
t2_infix :: (a -> a -> b) -> T2 a -> b
-- | t2_infix mappend.
--
--
-- t2_join ([1,2],[3,4]) == [1,2,3,4]
--
t2_join :: Monoid m => T2 m -> m
-- | t2_map mconcat of unzip
--
--
-- t2_concat [("ab","cd"),("ef","gh")] == ("abef","cdgh")
--
t2_concat :: Monoid m => [T2 m] -> T2 m
-- | sort
--
--
-- t2_sort (2,1) == (1,2)
--
t2_sort :: Ord t => (t, t) -> (t, t)
-- | sum
t2_sum :: Num n => (n, n) -> n
-- | mapM
t2_mapM :: Monad m => (t -> m u) -> (t, t) -> m (u, u)
-- | mapM_
t2_mapM_ :: Monad m => (t -> m u) -> (t, t) -> m ()
-- | Left rotation.
--
--
-- p3_rotate_left (1,2,3) == (2,3,1)
--
p3_rotate_left :: (s, t, u) -> (t, u, s)
p3_fst :: (a, b, c) -> a
p3_snd :: (a, b, c) -> b
p3_third :: (a, b, c) -> c
type T3 a = (a, a, a)
t3_from_list :: [t] -> T3 t
t3_to_list :: T3 a -> [a]
t3_rotate_left :: T3 t -> T3 t
t3_fst :: T3 t -> t
t3_snd :: T3 t -> t
t3_third :: T3 t -> t
t3_map :: (p -> q) -> T3 p -> T3 q
t3_zipWith :: (p -> q -> r) -> T3 p -> T3 q -> T3 r
t3_infix :: (a -> a -> a) -> T3 a -> a
t3_join :: T3 [a] -> [a]
t3_sort :: Ord t => (t, t, t) -> (t, t, t)
p4_fst :: (a, b, c, d) -> a
p4_snd :: (a, b, c, d) -> b
p4_third :: (a, b, c, d) -> c
p4_fourth :: (a, b, c, d) -> d
p4_zip :: (a, b, c, d) -> (e, f, g, h) -> ((a, e), (b, f), (c, g), (d, h))
type T4 a = (a, a, a, a)
t4_from_list :: [t] -> T4 t
t4_to_list :: T4 t -> [t]
t4_fst :: T4 t -> t
t4_snd :: T4 t -> t
t4_third :: T4 t -> t
t4_fourth :: T4 t -> t
t4_map :: (p -> q) -> T4 p -> T4 q
t4_zipWith :: (p -> q -> r) -> T4 p -> T4 q -> T4 r
t4_infix :: (a -> a -> a) -> T4 a -> a
t4_join :: T4 [a] -> [a]
p5_fst :: (a, b, c, d, e) -> a
p5_snd :: (a, b, c, d, e) -> b
p5_third :: (a, b, c, d, e) -> c
p5_fourth :: (a, b, c, d, e) -> d
p5_fifth :: (a, b, c, d, e) -> e
p5_from_list :: (t -> t1, t -> t2, t -> t3, t -> t4, t -> t5) -> [t] -> (t1, t2, t3, t4, t5)
p5_to_list :: (t1 -> t, t2 -> t, t3 -> t, t4 -> t, t5 -> t) -> (t1, t2, t3, t4, t5) -> [t]
type T5 a = (a, a, a, a, a)
t5_from_list :: [t] -> T5 t
t5_to_list :: T5 t -> [t]
t5_map :: (p -> q) -> T5 p -> T5 q
t5_fst :: T5 t -> t
t5_snd :: T5 t -> t
t5_fourth :: T5 t -> t
t5_fifth :: T5 t -> t
t5_infix :: (a -> a -> a) -> T5 a -> a
t5_join :: T5 [a] -> [a]
p6_fst :: (a, b, c, d, e, f) -> a
p6_snd :: (a, b, c, d, e, f) -> b
p6_third :: (a, b, c, d, e, f) -> c
p6_fourth :: (a, b, c, d, e, f) -> d
p6_fifth :: (a, b, c, d, e, f) -> e
p6_sixth :: (a, b, c, d, e, f) -> f
type T6 a = (a, a, a, a, a, a)
t6_from_list :: [t] -> T6 t
t6_to_list :: T6 t -> [t]
t6_map :: (p -> q) -> T6 p -> T6 q
t6_sum :: Num t => T6 t -> t
type T7 a = (a, a, a, a, a, a, a)
t7_to_list :: T7 t -> [t]
t7_map :: (p -> q) -> T7 p -> T7 q
type T8 a = (a, a, a, a, a, a, a, a)
t8_to_list :: T8 t -> [t]
t8_map :: (p -> q) -> T8 p -> T8 q
p8_third :: (a, b, c, d, e, f, g, h) -> c
type T9 a = (a, a, a, a, a, a, a, a, a)
t9_to_list :: T9 t -> [t]
t9_from_list :: [t] -> T9 t
t9_map :: (p -> q) -> T9 p -> T9 q
type T10 a = (a, a, a, a, a, a, a, a, a, a)
t10_to_list :: T10 t -> [t]
t10_map :: (p -> q) -> T10 p -> T10 q
type T11 a = (a, a, a, a, a, a, a, a, a, a, a)
t11_to_list :: T11 t -> [t]
t11_map :: (p -> q) -> T11 p -> T11 q
type T12 t = (t, t, t, t, t, t, t, t, t, t, t, t)
t12_to_list :: T12 t -> [t]
t12_from_list :: [t] -> T12 t
-- | foldr1 of t12_to_list.
--
--
-- t12_foldr1 (+) (1,2,3,4,5,6,7,8,9,10,11,12) == 78
--
t12_foldr1 :: (t -> t -> t) -> T12 t -> t
-- | sum of t12_to_list.
--
--
-- t12_sum (1,2,3,4,5,6,7,8,9,10,11,12) == 78
--
t12_sum :: Num n => T12 n -> n
uncurry3 :: (a -> b -> c -> z) -> (a, b, c) -> z
uncurry4 :: (a -> b -> c -> d -> z) -> (a, b, c, d) -> z
uncurry5 :: (a -> b -> c -> d -> e -> z) -> (a, b, c, d, e) -> z
uncurry6 :: (a -> b -> c -> d -> e -> f -> z) -> (a, b, c, d, e, f) -> z
uncurry7 :: (a -> b -> c -> d -> e -> f -> g -> z) -> (a, b, c, d, e, f, g) -> z
uncurry8 :: (a -> b -> c -> d -> e -> f -> g -> h -> z) -> (a, b, c, d, e, f, g, h) -> z
uncurry9 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> z) -> (a, b, c, d, e, f, g, h, i) -> z
uncurry10 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> z) -> (a, b, c, d, e, f, g, h, i, j) -> z
uncurry11 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> z) -> (a, b, c, d, e, f, g, h, i, j, k) -> z
uncurry12 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> z) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> z
uncurry13 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> z) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> z
uncurry14 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> n -> z) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> z
uncurry15 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> n -> o -> z) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> z
uncurry16 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> n -> o -> p -> z) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) -> z
uncurry17 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> n -> o -> p -> q -> z) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q) -> z
uncurry18 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> n -> o -> p -> q -> r -> z) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r) -> z
uncurry19 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> n -> o -> p -> q -> r -> s -> z) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s) -> z
uncurry20 :: (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> n -> o -> p -> q -> r -> s -> t -> z) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> z
-- | LGL = Large Graph Layout (NCOL, LGL)
--
-- http://lgl.sourceforge.net/#FileFormat
module Music.Theory.Graph.Lgl
-- | (edge,weight)
type Ncol_Ent t = ((t, t), Maybe Double)
-- |
type Ncol t = [Ncol_Ent t]
-- | Parse Ncol_Ent from String
ncol_parse :: Read t => String -> Ncol_Ent t
-- | Load Ncol from .ncol file.
ncol_load :: Read t => FilePath -> IO (Ncol t)
-- | Type-specialised.
ncol_load_int :: FilePath -> IO (Ncol Int)
-- | Format Ncol_Ent.
--
--
-- ncol_ent_format 4 ((0,1),Nothing) == "0 1"
-- ncol_ent_format 4 ((0,1),Just 2.0) == "0 1 2.0000"
--
ncol_ent_format :: Show t => Int -> Ncol_Ent t -> String
-- | Store Ncol of Int to .ncol file
ncol_store :: Show t => Int -> FilePath -> Ncol t -> IO ()
-- | Type-specialised.
ncol_store_int :: Int -> FilePath -> Ncol Int -> IO ()
-- | Ncol data must be un-directed and have no self-arcs. This function
-- sorts edges (i,j) so that i <= j and deletes edges where i == j.
ncol_rewrite_eset :: Ord t => [(t, t)] -> [(t, t)]
-- | eset (edge-set) to Ncol (runs ncol_rewrite_eset)
eset_to_ncol :: Ord t => [(t, t)] -> Ncol t
-- | Inverse of eset_to_ncol, error if Ncol is
-- weighted
ncol_to_eset :: Ncol t -> [(t, t)]
-- | ncol_store of eset_to_ncol
ncol_store_eset :: (Ord t, Show t) => FilePath -> [(t, t)] -> IO ()
-- | Lgl is an adjaceny set with optional weights.
type Lgl t = [(t, [(t, Maybe Double)])]
-- | Format Lgl, k is floating point precision for optional weights.
lgl_format :: Show t => Int -> Lgl t -> String
-- | writeFile of lgl_format
lgl_store :: Show t => Int -> FilePath -> Lgl t -> IO ()
-- | adj (adjaceny-set) to Lgl.
adj_to_lgl :: Adj t -> Lgl t
-- | Inverse of adj_to_lgl, error if Lgl is weighted
lgl_to_adj :: Lgl t -> Adj t
-- | lgl_store of adj_to_lgl
lgl_store_adj :: Show t => FilePath -> Adj t -> IO ()
-- | Regular matrix array data, Csv, column & row indexing.
module Music.Theory.Array.Csv
-- | Quoting is required is the string has a double-quote, comma newline or
-- carriage-return.
csv_requires_quote :: String -> Bool
-- | Quoting places double-quotes at the start and end and escapes
-- double-quotes.
csv_quote :: String -> String
-- | Quote field if required.
csv_quote_if_req :: String -> String
-- | When reading a CSV file is the first row a header?
type Csv_Has_Header = Bool
-- | Alias for Char, allow characters other than , as
-- delimiter.
type Csv_Delimiter = Char
-- | Alias for Bool, allow linebreaks in fields.
type Csv_Allow_Linebreaks = Bool
-- | When writing a CSV file should the delimiters be aligned, ie. should
-- columns be padded with spaces, and if so at which side of the data?
data Csv_Align_Columns
Csv_No_Align :: Csv_Align_Columns
Csv_Align_Left :: Csv_Align_Columns
Csv_Align_Right :: Csv_Align_Columns
-- | CSV options.
type Csv_Opt = (Csv_Has_Header, Csv_Delimiter, Csv_Allow_Linebreaks, Csv_Align_Columns)
-- | Default CSV options, no header, comma delimiter, no linebreaks, no
-- alignment.
def_csv_opt :: Csv_Opt
-- | CSV table, ie. a Table with Maybe a header.
type Csv_Table a = (Maybe [String], Table a)
-- | Read Csv_Table from CSV file.
csv_table_read :: Csv_Opt -> (String -> a) -> FilePath -> IO (Csv_Table a)
-- | Read Table only with def_csv_opt.
csv_table_read_def :: (String -> a) -> FilePath -> IO (Table a)
-- | Read plain CSV Table.
csv_table_read_plain :: FilePath -> IO (Table String)
-- | Read and process CSV Csv_Table.
csv_table_with :: Csv_Opt -> (String -> a) -> FilePath -> (Csv_Table a -> b) -> IO b
-- | Align table according to Csv_Align_Columns.
--
--
-- csv_table_align Csv_No_Align [["a","row","and"],["then","another","one"]]
--
csv_table_align :: Csv_Align_Columns -> Table String -> Table String
-- | Pretty-print Csv_Table.
csv_table_pp :: (a -> String) -> Csv_Opt -> Csv_Table a -> String
-- | write_file_utf8 of csv_table_pp.
csv_table_write :: (a -> String) -> Csv_Opt -> FilePath -> Csv_Table a -> IO ()
-- | Write Table only (no header) with def_csv_opt.
csv_table_write_def :: (a -> String) -> FilePath -> Table a -> IO ()
-- | Write plain CSV Table.
csv_table_write_plain :: FilePath -> Table String -> IO ()
-- | 0-indexed (row,column) cell lookup.
table_lookup :: Table a -> (Int, Int) -> a
-- | Row data.
table_row :: Table a -> Row_Ref -> [a]
-- | Column data.
table_column :: Table a -> Column_Ref -> [a]
-- | Lookup value across columns.
table_column_lookup :: Eq a => Table a -> (Column_Ref, Column_Ref) -> a -> Maybe a
-- | Table cell lookup.
table_cell :: Table a -> Cell_Ref -> a
-- | 0-indexed (row,column) cell lookup over column range.
table_lookup_row_segment :: Table a -> (Int, (Int, Int)) -> [a]
-- | Range of cells from row.
table_row_segment :: Table a -> (Row_Ref, Column_Range) -> [a]
-- | Translate Table to Array. It is assumed that the
-- Table is regular, ie. all rows have an equal number of
-- columns.
--
--
-- let a = table_to_array [[0,1,3],[2,4,5]]
-- in (bounds a,indices a,elems a)
--
--
--
-- > (((A,1),(C,2))
-- > ,[(A,1),(A,2),(B,1),(B,2),(C,1),(C,2)]
-- > ,[0,2,1,4,3,5])
--
table_to_array :: Table a -> Array Cell_Ref a
-- | table_to_array of csv_table_read.
csv_array_read :: Csv_Opt -> (String -> a) -> FilePath -> IO (Array Cell_Ref a)
csv_field_str :: CSVField -> String
csv_error_recover :: CSVError -> CSVRow
csv_row_recover :: Either [CSVError] CSVRow -> CSVRow
-- | Read irregular CSV file, ie. rows may have any number of
-- columns, including no columns.
csv_load_irregular :: (String -> a) -> FilePath -> IO [[a]]
csv_write_irregular :: (a -> String) -> Csv_Opt -> FilePath -> Csv_Table a -> IO ()
csv_write_irregular_def :: (a -> String) -> FilePath -> Table a -> IO ()
type P2_Parser t1 t2 = (String -> t1, String -> t2)
csv_table_read_p2 :: P2_Parser t1 t2 -> Csv_Opt -> FilePath -> IO (Maybe (String, String), [(t1, t2)])
type P5_Parser t1 t2 t3 t4 t5 = (String -> t1, String -> t2, String -> t3, String -> t4, String -> t5)
type P5_Writer t1 t2 t3 t4 t5 = (t1 -> String, t2 -> String, t3 -> String, t4 -> String, t5 -> String)
csv_table_read_p5 :: P5_Parser t1 t2 t3 t4 t5 -> Csv_Opt -> FilePath -> IO (Maybe [String], [(t1, t2, t3, t4, t5)])
csv_table_write_p5 :: P5_Writer t1 t2 t3 t4 t5 -> Csv_Opt -> FilePath -> (Maybe [String], [(t1, t2, t3, t4, t5)]) -> IO ()
csv_table_read_t9 :: (String -> t) -> Csv_Opt -> FilePath -> IO (Maybe [String], [T9 t])
-- | http://www.unicode.org/charts/PDF/U1D100.pdf
--
-- These symbols are in http://www.gnu.org/software/freefont/,
-- debian=ttf-freefont.
module Music.Theory.Unicode
-- | Unicode non breaking hypen character.
--
--
-- non_breaking_hypen == '‑'
--
non_breaking_hypen :: Char
-- | Unicode non breaking space character.
--
--
-- non_breaking_space == ' '
--
non_breaking_space :: Char
-- | Unicode interpunct.
--
--
-- middle_dot == '·'
--
middle_dot :: Char
-- | The superscript variants of the digits 0-9
superscript_digits :: [Char]
-- | Map show of Int to superscript_digits.
--
--
-- unwords (map int_show_superscript [0,12,345,6789]) == "⁰ ¹² ³⁴⁵ ⁶⁷⁸⁹"
--
int_show_superscript :: Int -> String
-- | The subscript variants of the digits 0-9
subscript_digits :: [Char]
-- | The combining over line character.
--
--
-- ['1',combining_overline] == "1̅"
-- ['A',combining_overline] == "A̅"
--
combining_overline :: Char
-- | Add combining_overline to each Char.
--
--
-- overline "1234" == "1̅2̅3̅4̅"
--
overline :: String -> String
-- | The combining under line character.
--
--
-- ['1',combining_underline] == "1̲"
--
combining_underline :: Char
-- | Add combining_underline to each Char.
--
--
-- underline "1234" == "1̲2̲3̲4̲"
--
underline :: String -> String
type Unicode_Index = Int
type Unicode_Name = String
type Unicode_Range = (Unicode_Index, Unicode_Index)
type Unicode_Point = (Unicode_Index, Unicode_Name)
type Unicode_Table = [Unicode_Point]
-- | http://unicode.org/Public/11.0.0/ucd/UnicodeData.txt
--
--
-- let fn = "/home/rohan/data/unicode.org/Public/11.0.0/ucd/UnicodeData.txt"
-- tbl <- unicode_data_table_read fn
-- length tbl == 32292
-- T.reverse_lookup_err "MIDDLE DOT" tbl == 0x00B7
-- putStrLn $ unwords $ map (\(n,x) -> toEnum n : x) $ filter (\(_,x) -> "EMPTY SET" `isInfixOf` x) tbl
-- T.lookup_err 0x22C5 tbl == "DOT OPERATOR"
--
unicode_data_table_read :: FilePath -> IO Unicode_Table
unicode_table_block :: (Unicode_Index, Unicode_Index) -> Unicode_Table -> Unicode_Table
unicode_point_hs :: Unicode_Point -> String
unicode_table_hs :: Unicode_Table -> String
music_tbl :: [Unicode_Table]
accidentals_rng_set :: [Unicode_Range]
barlines_rng :: Unicode_Range
-- | UNICODE barline symbols.
--
--
-- let r = "𝄀𝄁𝄂𝄃𝄄𝄅" in map (toEnum . fst) barlines_tbl == r
--
barlines_tbl :: Unicode_Table
-- | UNICODE accidental symbols.
--
--
-- let r = "♭♮♯𝄪𝄫𝄬𝄭𝄮𝄯𝄰𝄱𝄲𝄳" in map (toEnum . fst) accidentals_tbl == r
--
accidentals_tbl :: Unicode_Table
notes_rng :: Unicode_Range
-- | UNICODE note duration symbols.
--
--
-- let r = "𝅜𝅝𝅗𝅥𝅘𝅥𝅘𝅥𝅮𝅘𝅥𝅯𝅘𝅥𝅰𝅘𝅥𝅱𝅘𝅥𝅲" in map (toEnum . fst) notes_tbl == r
--
notes_tbl :: Unicode_Table
rests_rng :: Unicode_Range
-- | UNICODE rest symbols.
--
--
-- let r = "𝄻𝄼𝄽𝄾𝄿𝅀𝅁𝅂" in map (toEnum . fst) rests_tbl == r
--
rests_tbl :: Unicode_Table
-- | Augmentation dot.
--
--
-- map toEnum [0x1D15E,0x1D16D,0x1D16D] == "𝅗𝅥𝅭𝅭"
--
augmentation_dot :: Unicode_Point
clefs_rng :: Unicode_Range
-- | UNICODE clef symbols.
--
--
-- let r = "𝄞𝄟𝄠𝄡𝄢𝄣𝄤𝄥𝄦" in map (toEnum . fst) clefs_tbl == r
--
clefs_tbl :: Unicode_Table
noteheads_rng :: Unicode_Range
-- | UNICODE notehead symbols.
--
--
-- let r = "𝅃𝅄𝅅𝅆𝅇𝅈𝅉𝅊𝅋𝅌𝅍𝅎𝅏𝅐𝅑𝅒𝅓𝅔𝅕𝅖𝅗𝅘𝅙𝅚𝅛" in map (toEnum . fst) noteheads_tbl == r
--
noteheads_tbl :: Unicode_Table
stem :: Unicode_Point
dynamics_rng :: Unicode_Range
dynamics_tbl :: Unicode_Table
articulations_rng :: Unicode_Range
articulations_tbl :: Unicode_Table
ix_set_to_tbl :: Unicode_Table -> [Unicode_Index] -> Unicode_Table
-- | Unicode dot-operator.
--
--
-- dot_operator == '⋅'
--
dot_operator :: Char
-- | Math symbols outside of the math blocks.
--
--
-- putStrLn (unicode_table_hs (ix_set_to_tbl tbl math_plain_ix))
--
math_plain_ix :: [Unicode_Index]
math_plain_tbl :: Unicode_Table
type Unicode_Block = (Unicode_Range, String)
unicode_blocks :: [Unicode_Block]
-- | Bagua tri-grams.
--
--
-- putStrLn $ unicode_table_hs (unicode_table_block (fst bagua) tbl)
--
bagua :: Unicode_Block
-- | Table of eight tri-grams.
--
-- HEAVEN,乾,Qián,☰,111 LAKE,兌,Duì,☱,110 FIRE,離,Lí,☲,101
-- THUNDER,震,Zhèn,☳,100 WIND,巽,Xùn,☴,011 WATER,坎,Kǎn,☵,010
-- MOUNTAIN,艮,Gèn,☶,001 EARTH,坤,Kūn,☷,000
bagua_tbl :: Unicode_Table
-- | Yijing hexagrams in King Wen sequence.
--
--
-- putStrLn $ unicode_table_hs (unicode_table_block (fst yijing) tbl)
--
yijing :: Unicode_Block
-- | Yijing hexagrams in King Wen sequence.
--
-- ䷀,乾,qián,111,111 ䷁,坤,kūn,000,000 ䷂,屯,chún,100,010 ䷃,蒙,méng,010,001
-- ䷄,需,xū,111,010 ䷅,訟,sòng,010,111 ䷆,師,shī,010,000 ䷇,比,bǐ,000,010
-- ䷈,小畜,xiǎo chù,111,011 ䷉,履,lǚ,110,111 ䷊,泰,tài,111,000 ䷋,否,pǐ,000,111
-- ䷌,同人,tóng rén,101,111 ䷍,大有,dà yǒu,111,101 ䷎,謙,qiān,001,000
-- ䷏,豫,yù,000,100 ䷐,隨,suí,100,110 ䷑,蠱,gŭ,011,001 ䷒,臨,lín,110,000
-- ䷓,觀,guān,000,011 ䷔,噬嗑,shì kè,100,101 ䷕,賁,bì,101,001 ䷖,剝,bō,000,001
-- ䷗,復,fù,100,000 ䷘,無妄,wú wàng,100,111 ䷙,大畜,dà chù,111,001 ䷚,頤,yí,100,001
-- ䷛,大過,dà guò,011,110 ䷜,坎,kǎn,010,010 ䷝,離,lí,101,101 ䷞,咸,xián,001,110
-- ䷟,恆,héng,011,100 ䷠,遯,dùn,001,111 ䷡,大壯,dà zhuàng,111,100
-- ䷢,晉,jìn,000,101 ䷣,明夷,míng yí,101,000 ䷤,家人,jiā rén,101,011
-- ䷥,睽,kuí,110,101 ䷦,蹇,jiǎn,001,010 ䷧,解,xiè,010,100 ䷨,損,sǔn,110,001
-- ䷩,益,yì,100,011 ䷪,夬,guài,111,110 ䷫,姤,gòu,011,111 ䷬,萃,cuì,000,110
-- ䷭,升,shēng,011,000 ䷮,困,kùn,010,110 ䷯,井,jǐng,011,010 ䷰,革,gé,101,110
-- ䷱,鼎,dǐng,011,101 ䷲,震,zhèn,100,100 ䷳,艮,gèn,001,001 ䷴,漸,jiàn,001,011
-- ䷵,歸妹,guī mèi,110,100 ䷶,豐,fēng,101,100 ䷷,旅,lǚ,001,101 ䷸,巽,xùn,011,011
-- ䷹,兌,duì,110,110 ䷺,渙,huàn,010,011 ䷻,節,jié,110,010 ䷼,中孚,zhōng fú,110,011
-- ䷽,小過,xiǎo guò,001,110 ䷾,既濟,jì jì,101,010 ䷿,未濟,wèi jì,010,101
yijing_tbl :: Unicode_Table