Implementing order functions where missings is the smallest value

README.md

@@ -28,6 +28,8 @@ This package provides additional functionality for working with `missing` values
 - `Missings.replace` to wrap a collection in a (possibly indexable) iterator replacing `missing` with another value
 - `Missings.fail` to wrap a collection in a (possibly indexable) iterator throwing an error if `missing` is encountered
 - `skipmissings` to loop through a collection of iterators excluding indices where any iterators are `missing`
+- `missingsmallest(f)` to create a partial order function that treats `missing` as the smallest value and otherwise behaves like `f`
+- `missingsmallest`: the standard `isless` function modified to treat `missing` as the smallest value rather than the largest one
 
 ## Contributing and Questions
 

src/Missings.jl

@@ -2,7 +2,7 @@ module Missings
 
 export allowmissing, disallowmissing, ismissing, missing, missings,
        Missing, MissingException, levels, coalesce, passmissing, nonmissingtype,
-       skipmissings, emptymissing
+       skipmissings, emptymissing, missingsmallest
 
 using Base: ismissing, missing, Missing, MissingException
 
@@ -514,4 +514,84 @@ julia> emptymissing(first)([1], 2)
 """
 emptymissing(f) = (x, args...; kwargs...) -> isempty(x) ? missing : f(x, args...; kwargs...)
 
-end # module
+# Only for internal use. Allows dispatch over anonymous functions.
+struct MissingSmallest{T}
+    lt::T
+end
+
+"""
+    missingsmallest(f)
+
+Return a function of two arguments `x` and `y` that tests whether `x` is less
+than `y` such that `missing` is always less than the other argument. In other 
+words, return a modified version of the partial order function `f` such that
+`missing` is the smallest possible value, and all other non-`missing` values are
+compared according to `f`.
+
+The behavior of the standard `isless` function modified to treat `missing` as
+the smallest value can be obtained by calling the 2-argument `missingsmallest(x,
+y)` function. This is equivalent to `missingsmallest(isless)(x, y)`.
+
+# Examples
+```
+julia> isshorter = missingsmallest((s1, s2) -> isless(length(s1), length(s2)));
+
+julia> isshorter("short", "longstring")
+true
+
+julia> isshorter("longstring", "short")
+false
+
+julia> isshorter("", missing)
+false
+```
+"""
+missingsmallest(f) = MissingSmallest(f)
+
+"""
+    missingsmallest(x, y)
+
+The standard partial order `isless` modified so that `missing` is always the
+smallest possible value:
+- If neither argument is `missing`, the function behaves exactly as `isless`.
+- If `y` is `missing` the result will be `false` regardless of the value of `x`.
+- If `x` is `missing` the result will be `true` unless `y` is `missing`.
+
+See also the 1-argument method which takes a partial ordering function (like
+`isless`) and modifies it to treat `missing` as explained above. These functions
+can be used together with sorting functions so that missing values are sorted
+first. This is useful in particular so that when sorting in reverse order
+missing values appear at the end.
+
+# Examples
+```jldoctest
+julia> sort(v, lt=missingsmallest)
+5-element Vector{Union{Missing, Int64}}:
+   missing
+   missing
+  1
+  2
+ 10
+
+julia> sort(v, lt=missingsmallest, rev=true)
+5-element Vector{Union{Missing, Int64}}:
+ 10
+  2
+  1
+   missing
+   missing
+
+julia> missingsmallest(missing, Inf)
+true
+
+julia> missingsmallest(-Inf, missing)
+false
+
+julia> missingsmallest(missing, missing)
+false
+"""
+missingsmallest(x, y) = missingsmallest(isless)(x, y)
+
+(ms::MissingSmallest)(x, y) = ismissing(y) ? false : ismissing(x) ? true : ms.lt(x, y)
+
+end # module

test/runtests.jl

@@ -158,7 +158,7 @@ struct CubeRooter end
     @test disallowmissing(Any[:a]) == [:a]
     @test disallowmissing(Any[:a]) isa AbstractVector{Any}
     @test_throws MethodError disallowmissing([1, missing])
-    @test_throws MethodError disallowmissing([missing])
+    @test_throws Union{MethodError, ArgumentError} disallowmissing([missing])
 
     @test disallowmissing(Union{Int, Missing}[1 1]) == [1 1]
     @test disallowmissing(Union{Int, Missing}[1 1]) isa AbstractArray{Int, 2}
@@ -167,7 +167,7 @@ struct CubeRooter end
     @test disallowmissing([:a 1]) == [:a 1]
     @test disallowmissing([:a 1]) isa AbstractArray{Any, 2}
     @test_throws MethodError disallowmissing([1 missing])
-    @test_throws MethodError disallowmissing([missing missing])
+    @test_throws Union{MethodError, ArgumentError} disallowmissing([missing missing])
 
     # Lifting
     ## functor
@@ -257,4 +257,30 @@ struct CubeRooter end
     @test emptymissing(fun)(3, 1, c=2) == (1, 2)
 end
 
+@testset "missingsmallest" begin
+    @test missingsmallest(missing, Inf) == true
+    @test missingsmallest(-Inf, missing) == false
+    @test missingsmallest(missing, missing) == false
+    @test missingsmallest(3, 4) == true
+    @test missingsmallest(-Inf, Inf) == true 
+
+    @test missingsmallest("a", "b") == true
+    @test missingsmallest("short", missing) == false
+    @test missingsmallest(missing, "") == true
+
+    @test missingsmallest((1, 2), (3, 4)) == true
+    @test missingsmallest((3, 4), (1, 2)) == false
+    @test missingsmallest(missing, (1e3, 1e4)) == true
+
+    # Compare strings by length, not lexicographically
+    isshorter = missingsmallest((s1, s2) -> isless(length(s1), length(s2)))
+    @test isshorter("short", "longstring") == true
+    @test isshorter("longstring", "short") == false
+    @test isshorter(missing, "short") == true
+    @test isshorter("", missing) == false
+
+    @test_throws MethodError missingsmallest(isless)(isless)
+    @test missingsmallest !== missingsmallest(isless)
+end
+
 end