librarylibs/Lists/src/Lists.xtl

Lists: list functions -- differences, windows, moving means, run lengths, chunks, shifts, interleaving, binary search, raze. Import it with an alias of your choice: "q:" u_se< "Lists". Put libs/Lists/src on XETAL_PATH ("just path"); the reference is libs/Lists/docs. Names with l: are exported; those under h: are private to this file.

Counts and sizes go on the left, the list on the right, as for the built-ins: 3 q:w_indows v.

source

Differences and windows

ˡd̲eltas : Num a => a -> a

function · line 13

d_eltas v: each item minus the one before (one fewer item).

ˡd̲eltas ← { v → (1 d̲rop v) − -1 d̲rop v }
Used in: ˡr̲unLengths, d

ˡw̲indows : Int -> a -> a

function · line 16

n w_indows v: every run of n consecutive items, one per row.

ˡw̲indows ← { n v →
  n < 1 ? @ p̲anic< "a window holds 1 item or more, not {n}"
  k ← 1 + (t̲ally v) − n
  k < 1 ? (0 c̲at n) r̲eshape v
  ((r̲ange k) '+ t̲able o̲ffsets n) s̲elect v
}
p̲anic< expands to
(⎕P̲ANIC ("a window holds 1 item or more, not " c̲at (f̲ormat (n))))
Used in: ˡm̲ovingMean

ˡm̲ovingMean : Num a => Int -> a -> Float

function · line 24

n m_ovingMean v: the mean of each window of n (a Float each).

ˡm̲ovingMean ← { n v → (f̲loat '+ r̲/₂ n ˡw̲indows v) ÷ f̲loat n }
Used in: libs/Lists/demos/temperatures.xtl:11

Runs

ʰs̲tarts : (Eq a, Num b, Truthy b) => a -> b

function (private) · line 29

Where each run of equal items starts (a 0/1 mask).

ʰs̲tarts ← { v → 0 = t̲ally v ? 0 r̲eshape 1 = 1◆ 1 c̲at (1 d̲rop v) ≠ -1 d̲rop v }
Used in: ˡr̲unValues, ˡr̲unLengths

ˡr̲unValues : Eq a => a -> a

function · line 32

r_unValues v: the item of each run of equal items ("aaabcc" is "abc").

ˡr̲unValues ← { v → (ʰs̲tarts v) r̲eplicate v }
Used in: libs/Lists/demos/temperatures.xtl:15

ˡr̲unLengths : Eq a => a -> Int

function · line 35

r_unLengths v: the length of each run ("aaabcc" is 3 1 2).

ˡr̲unLengths ← { v → ˡd̲eltas (w̲here ʰs̲tarts v) c̲at 1 + t̲ally v }
Used in: libs/Lists/demos/temperatures.xtl:15

Reshaping

ˡc̲hunks : Int -> a -> Box a

function · line 40

n c_hunks v: v cut into pieces of n (the last may be shorter), as a list.

ˡc̲hunks ← { n v →
  n < 1 ? @ p̲anic< "a chunk holds 1 item or more, not {n}"
  (1 + (o̲ffsets t̲ally v) d̲iv n) p̲artition v
}
p̲anic< expands to
(⎕P̲ANIC ("a chunk holds 1 item or more, not " c̲at (f̲ormat (n))))

ˡr̲aze : Box a -> a

function · line 48

r_aze list: the items of a list of lists joined into one list (APL2's enlist of a simple list). An empty list has no items to take a type's fill from: error[no-identity].

ˡr̲aze ← { b →
  0 = t̲ally b ? @ p̲anic< "r_aze needs at least one list: an empty list has no items to join (nor a type to make an empty result of)"
  d̲isclose '{ e̲nclose (d̲isclose ⍺) c̲at d̲isclose ⍵ } r̲/ b
}
p̲anic< expands to
(⎕P̲ANIC ("r_aze needs at least one list: an empty list has no items to join (nor a type to make an empty result of)"))
Used in: ʰr̲ows, ˡr̲ows

ˡs̲hift : Int -> a -> a

function · line 55

n s_hift v: v moved n places toward the front (back for negative n), without wrapping: the places left empty get the fill (0, or a space).

ˡs̲hift ← { n v → t ← t̲ally v◆ n ≥ 0 ? t t̲ake n d̲rop v◆ (n̲eg t) t̲ake n d̲rop v }

ˡi̲nterleave : a -> a -> a

function · line 58

a i_nterleave b: a1 b1 a2 b2 ... (a and b of one length).

ˡi̲nterleave ← { a b → r̲avel₂ (2 c̲at t̲ally a) r̲eshape a c̲at b }

Searching

ʰb̲s : Ord a => a -> a -> Int -> Int -> Int

function (private) · line 63

Binary search in sorted v between lo and hi: how many items are <= x.

ʰb̲s ← { v x lo hi →
  lo ≥ hi ? lo
  m ← (lo + hi + 1) d̲iv 2
  (f̲irst m s̲elect v) ≤ x ? (((v ʰb̲s x)_ m)_ hi)
  ((v ʰb̲s x)_ lo)_ m − 1
}
Used in: ʰb̲s, ˡb̲search