Sets
Type signatures are provisional and may contain errors.
Data jetted sets of nouns. Sets are represented as a law where the row has no duplicate elements and all elements are stored in ascending order, with the form:
(0 1 2 row)Set Functions
isSet
(isSet x)> x : a> BoolChecks if a value is a valid set.
isSet %[] == 1isSet %[1 2 3] == 1isSet (0 1 2 []) == 1isSet (0 2 2 []) == 0 ; Invalid set representationisSet [1 2 3] == 0 ; Not a set, just a rowemptySet
(emptySet)> Set aReturns an empty set.
emptySet == %[]emptySet == setFromRow []emptySet == setDel 1 %[1]setIsEmpty
(setIsEmpty xs)> xs : Set a> BoolChecks if a set is empty.
setIsEmpty emptySet == 1setIsEmpty %[1] == 0setIsEmpty %[1 2 3] == 0setSing
(setSing e)> e : a> Set aCreates a singleton set containing one element.
setSing 3 == %[3]setSing {a} == %[a]setSing 0 == %[0]setFromRow
(setFromRow xs)> xs : Row a> Set aCreates a set from a row, removing duplicates and sorting.
setFromRow [3 1 2 1] == %[1 2 3]setFromRow [{a} {b} {a}] == %[a b]setFromRow [5 4 3 2 1] == %[1 2 3 4 5]setFromRowAsc
(setFromRowAsc xs)> xs : Row a> Set aCreates a set from a row that is already in ascending order with no duplicates.
setFromRowAsc [1 2 3] == %[1 2 3]setFromRowAsc [{a} {b} {c}] == %[a b c]setFromRowAsc [0] == %[0]setToRow
(setToRow xs)> xs : Set a> Row aConverts a set to a row.
setToRow %[1 2 3] == [1 2 3]setToRow %[a b c] == [a b c]setToRow %[] == []setLen
(setLen xs)> xs : Set a> NatReturns the number of elements in a set.
setLen %[] == 0setLen %[1 2 3] == 3setLen %[a] == 1setToList
(setToList xs)> xs : Set a> List aConverts a set to a list.
setToList %[1 2 3] == [1 [2 [3 0]]]setToList %[a b] == [%a [%b 0]]setToList %[] == 0 ; NILsetFoldl
(setFoldl f z xs)> f : (b > a > b)> z : b> xs : Set a> bLeft-associative fold over a set.
setFoldl add 0 %[1 2 3] == 6setFoldl mul 1 %[1 2 3 4] == 24setFoldl (flip CONS) NIL %[1 2 3] == [3 [2 [1 0]]]setFoldr
(setFoldr f z xs)> f : (a > b > b)> z : b> xs : Set a> bRight-associative fold over a set.
setFoldr (flip CONS) NIL %[1 2 3] == [[[0 3] 2] 1]setFoldr sub 0 %[1 2 3] == 1setFoldr strWeld {} %[{a} {b} {c}] == %abcsetIns
(setIns e xs)> e : a> xs : Set a> Set aInserts an element into a set.
setIns 3 %[1 2] == %[1 2 3]setIns 2 %[1 2] == %[1 2] ; No change if element already existssetIns {a} %[b c] == %[a b c]setDel
(setDel e xs)> e : a> xs : Set a> Set aRemoves an element from a set.
setDel 2 %[1 2 3] == %[1 3]setDel 4 %[1 2 3] == %[1 2 3] ; No change if element doesn't existsetDel {b} %[a b c] == %[a c]setHas
(setHas e xs)> e : a> xs : Set a> BoolChecks if an element is in a set.
setHas 2 %[1 2 3] == 1setHas 4 %[1 2 3] == 0setHas {b} %[a b c] == 1setWeld
(setWeld xs ys)> xs : Set a> ys : Set a> Set aCombines two sets.
setWeld %[1 2] %[2 3] == %[1 2 3]setWeld %[a b] %[c d] == %[a b c d]setWeld %[] %[1 2 3] == %[1 2 3]setUnion
(setUnion xs ys)> xs : Set a> ys : Set a> Set aAlias for setWeld. Combines two sets.
setUnion %[1 2] %[2 3] == %[1 2 3]setUnion %[a b] %[c d] == %[a b c d]setUnion %[] %[1 2 3] == %[1 2 3]setCatRow
(setCatRow xs)> xs : Row (Set a)> Set aCombines a row of sets into a single set.
setCatRow [%[1 2] %[2 3] %[3 4]] == %[1 2 3 4]setCatRow [%[a b] %[c] %[d e]] == %[a b c d e]setCatRow [%[] %[1] %[]] == %[1]setCatList
(setCatList xs)> xs : List (Set a)> Set aCombines a list of sets into a single set.
setCatList [%[1 2] [%[3 4] [%[2 3] 0]]] == %[1 2 3 4]setCatList [%[a b] [%[c] [%[d e] 0]]] == %[a b c d e]setCatList [%[] [%[1] [%[] 0]]] == %[1]setCatRowAsc
(setCatRowAsc x)> xs : Row (Set a)> Set aCombines a row of sets that are already in ascending order.
setCatRowAsc [%[1 2] %[3 4] %[5 6]] == %[1 2 3 4 5 6]setCatRowAsc [%[a b] %[c d] %[e f]] == %[a b c d e f]setCatRowAsc [%[] %[1] %[2 3]] == %[1 2 3]setMin
(setMin xs)> xs : Set a> aReturns the minimum element in a set.
setMin %[1 2 3] == 1setMin %[c b a] == asetMin %[5] == 5setMax
(setMax xs)> xs : Set a> aReturns the maximum element in a set.
setMax %[1 2 3] == 3setMax %[c b a] == csetMax %[5] == 5setPop
(setPop xs)> xs : Set a> (a, Set a)Removes and returns the minimum element from a set.
setPop %[1 2 3 4] == [1 %[2 3 4]]setPop %[a b c] == [%a %[b c]]setPop %[5] == [5 %[]]setDrop
(setDrop n xs)> n : Nat> xs : Set a> Set aRemoves the first n elements from a set.
setDrop 2 %[1 2 3 4] == %[3 4]setDrop 1 %[a b c] == %[b c]setDrop 0 %[1 2 3] == %[1 2 3]setTake
(setTake n xs)> n : Nat> xs : Set a> Set aKeeps the first n elements of a set.
setTake 2 %[1 2 3 4] == %[1 2]setTake 3 %[a b c d] == %[a b c]setTake 0 %[1 2 3] == %[]setSplitAt
(setSplitAt i xs)> i : Nat> xs : Set a> (Set a, Set a)Splits a set at a given index.
setSplitAt 2 %[1 2 3 4] == [%[1 2] %[3 4]]setSplitAt 1 %[a b c] == [%[a] %[b c]]setSplitAt 0 %[1 2 3] == [%[] %[1 2 3]]setSplitLT
(setSplitLT n xs)> n : a> xs : Set a> (Set a, Set a)Splits a set into elements less than a given value and the rest.
setSplitLT 3 %[1 2 3 4 5] == [%[1 2] %[3 4 5]]setSplitLT {c} %[a b c d e] == [%[a b] %[c d e]]setSplitLT 0 %[1 2 3] == [%[] %[1 2 3]]setIntersect
(setIntersect xs ys)> xs : Set a> ys : Set a> Set aReturns the intersection of two sets.
setIntersect %[1 2 3] %[2 3 4] == %[2 3]setIntersect %[a b c] %[b c d] == %[b c]setIntersect %[1 2 3] %[4 5 6] == %[]setSub
(setSub xs ys)> xs : Set a> ys : Set a> Set aSubtracts one set from another.
setSub %[1 2 3] %[2 3] == %[1]setSub %[a b c d] %[b d] == %[a c]setSub %[1 2 3] %[4 5 6] == %[1 2 3]setElem
(setElem n xs)> n : Nat> xs : Set a> aReturns the nth element of a set.
setElem 1 %[1 2 3] == 2setElem 0 %[a b c] == %asetElem 2 %[x y z] == %zsetDifference
Alias for setSub.
setInsert
Alias for setIns.
setSubtract
Alias for setSub.
setIntersection
Alias for setIntersect.