any() and all() functions broken for empty collections

[dbeach24]

Julia raises an exception when invoking the any() and all() functions with empty collections.

In Julia 0.5.0-RC2, I get:

               _
   _       _ _(_)_     |  A fresh approach to technical computing
  (_)     | (_) (_)    |  Documentation: http:https://docs.julialang.org
   _ _   _| |_  __ _   |  Type "?help" for help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 0.5.0-pre+5606 (2016-07-21 19:23 UTC)
 _/ |\__'_|_|_|\__'_|  |  Commit 5fe9e53* (26 days old master)
|__/                   |  x86_64-apple-darwin13.4.0

julia> any([])
ERROR: ArgumentError: reducing over an empty collection is not allowed
 in _mapreduce(::Base.#identity, ::Base.#or_bool_only, ::Base.LinearFast, ::Array{Any,1}) at ./reduce.jl:148
 in any(::Array{Any,1}) at ./reduce.jl:365
 in eval(::Module, ::Any) at ./boot.jl:234
 in macro expansion at ./REPL.jl:92 [inlined]
 in (::Base.REPL.##3#4{Base.REPL.REPLBackend})() at ./event.jl:46

julia> all([])
ERROR: ArgumentError: reducing over an empty collection is not allowed
 in _mapreduce(::Base.#identity, ::Base.#and_bool_only, ::Base.LinearFast, ::Array{Any,1}) at ./reduce.jl:148
 in all(::Array{Any,1}) at ./reduce.jl:366
 in eval(::Module, ::Any) at ./boot.jl:234
 in macro expansion at ./REPL.jl:92 [inlined]
 in (::Base.REPL.##3#4{Base.REPL.REPLBackend})() at ./event.jl:46

The behavior I would expect:

@assert any([]) == false
@assert all([]) == true

Note that this behavior is generally useful in most logic programming and matches Python:

Python 2.7.10 (default, Sep 22 2015, 12:25:10) 
Type "copyright", "credits" or "license" for more information.

IPython 3.2.0 -- An enhanced Interactive Python.
?         -> Introduction and overview of IPython's features.
%quickref -> Quick reference.
help      -> Python's own help system.
object?   -> Details about 'object', use 'object??' for extra details.

In [1]: any([])
Out[1]: False

In [2]: all([])
Out[2]: True

[dbeach24]

Update:

This is actually an inconsistency between any(iter) and all(iter) and their two argument counterparts that accept a predicate any(pred, iter) and all(pred, iter):

These two argument forms return the expected result in the case of an empty collection:

               _
   _       _ _(_)_     |  A fresh approach to technical computing
  (_)     | (_) (_)    |  Documentation: http:https://docs.julialang.org
   _ _   _| |_  __ _   |  Type "?help" for help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 0.5.0-pre+5606 (2016-07-21 19:23 UTC)
 _/ |\__'_|_|_|\__'_|  |  Commit 5fe9e53* (26 days old master)
|__/                   |  x86_64-apple-darwin13.4.0

julia> any(x -> x > 1, [])
false

julia> all(x -> x > 1, [])
true

[yuyichao]

FWIW

julia> all(Bool[])
true

julia> any(Bool[])
false

[dbeach24]

@yuyichao
Interesting. Perhaps this is only a bug for empty collections where eltype(coll) == Any ?

[TotalVerb]

Similar issue exists for sum and prod... I wonder if they should just return Bool on Any[] arrays. That case is not type stable anyway.

[eschnett]

I guess any and all should call mapreduce with the additional argument specifying the value for empty collections.

[stevengj]

@dbeach24, no, that would destroy type-stability of the sum function. We've had many discussions of sum, see e.g. #8092, #12461, #6994, #6069.

Let's keep this issue focused on the case at hand. any and all always return Bool, so there is no type-stability issue. It is clear that they should return false and true, respectively, for empty arrays of any type. It should be quite a simple PR to fix this.

[dbeach24]

@stevengj Thanks for the background. (Deleting my earlier comment as it is not pertinent to this issue.)