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Function composition and negation, take 2 #17184

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Function composition and negation, take 2 #17184

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dc8e1b5
function negation and composition: !f, f∘g
StefanKarpinski Jun 27, 2016
bda9052
Added docstrings and tests for compositions
Jun 29, 2016
786c579
rst for docs
Jun 29, 2016
21fcc91
Changed to closure approach: no splatting penalty
Jun 29, 2016
e6a69b7
Simplified definition of function negation
Jun 30, 2016
e3d9579
Fixed typo in test
Jun 30, 2016
b95404a
Clarify docstring
andyferris Jul 7, 2016
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74 changes: 68 additions & 6 deletions base/operators.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -339,18 +339,80 @@ Creates a composition of two functions (or functor objects), such that
`(f ∘ g)(x...) == f(g(x...))`. The `∘` symbol can be accessed at the REPL using
`\\circ`.

By default, an anonymous function `(x...) -> f(g(x...))` is returned, but this may
be specialized to create any functionally-equivalent callable object.
By default, a function equivalent to `(x...) -> f(g(x...))` is returned, but
this may be specialized to create any functionally-equivalent, callable object.
"""
∘(f, g) = (x...)->f(g(x...))
function ∘(f, g)
# Avoids splatting penalty. TODO: remove when that is fixed.
# Chose to implement up to length 16 (current setting of MAX_TUPLE_SPLAT)
composed() = f(g())
composed(x1) = f(g(x1))
composed(x1,x2) = f(g(x1,x2))
composed(x1,x2,x3) = f(g(x1,x2,x3))
composed(x1,x2,x3,x4) = f(g(x1,x2,x3,x4))
composed(x1,x2,x3,x4,x5) = f(g(x1,x2,x3,x4,x5))
composed(x1,x2,x3,x4,x5,x6) = f(g(x1,x2,x3,x4,x5,x6))
composed(x1,x2,x3,x4,x5,x6,x7) = f(g(x1,x2,x3,x4,x5,x6,x7))
composed(x1,x2,x3,x4,x5,x6,x7,x8) = f(g(x1,x2,x3,x4,x5,x6,x7,x8))
composed(x1,x2,x3,x4,x5,x6,x7,x8,x9) = f(g(x1,x2,x3,x4,x5,x6,x7,x8,x9))
composed(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10) =
f(g(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10))
composed(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11) =
f(g(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11))
composed(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12) =
f(g(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12))
composed(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13) =
f(g(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13))
composed(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14) =
f(g(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14))
composed(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15) =
f(g(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15))
composed(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16) =
f(g(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16))

composed(xs...) = f(g(xs...))

return composed # This name is remembered and visible at the REPL
end

"""
!(f::Function)

Returns a new function which applies boolean not to the output of `f`, equal to
`(x...) -> !f(x...)`.
Returns a new function which applies boolean not to the output of `f`,
equivalent to `(x...) -> !f(x...)`.
"""
!(f::Function) = (x...)->!f(x...)
function !(f::Function)
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Can't you just define this as ! ∘ f to avoid repeating the same machinery as above?

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I would like to, and I tried that first, but I got some kind of recursion when I tried to compile Julia. I didn't have time to investigate the cause of that yet, so I just used copy-paste.

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@TotalVerb TotalVerb Jun 30, 2016 •
edited
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I'm pretty sure that's because ! ∘ f doesn't parse correctly. We probably need (!) ∘ f. This is a little ugly, which makes me like !f syntax a little more.

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@andyferris andyferris Jun 30, 2016 •
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That worked... thanks!

# Avoids splatting penalty. TODO: remove when that is fixed.
# Chose to implement up to length 16 (current setting of MAX_TUPLE_SPLAT)
negated() = !(f())
negated(x1) = !(f(x1))
negated(x1,x2) = !(f(x1,x2))
negated(x1,x2,x3) = !(f(x1,x2,x3))
negated(x1,x2,x3,x4) = !(f(x1,x2,x3,x4))
negated(x1,x2,x3,x4,x5) = !(f(x1,x2,x3,x4,x5))
negated(x1,x2,x3,x4,x5,x6) = !(f(x1,x2,x3,x4,x5,x6))
negated(x1,x2,x3,x4,x5,x6,x7) = !(f(x1,x2,x3,x4,x5,x6,x7))
negated(x1,x2,x3,x4,x5,x6,x7,x8) = !(f(x1,x2,x3,x4,x5,x6,x7,x8))
negated(x1,x2,x3,x4,x5,x6,x7,x8,x9) = !(f(x1,x2,x3,x4,x5,x6,x7,x8,x9))
negated(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10) =
!(f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10))
negated(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11) =
!(f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11))
negated(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12) =
!(f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12))
negated(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13) =
!(f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13))
negated(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14) =
!(f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14))
negated(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15) =
!(f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15))
negated(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16) =
!(f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16))

negated(xs...) = !(f(xs...))

return negated # This name is remembered and visible at the REPL
end

# array shape rules

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4 changes: 2 additions & 2 deletions doc/stdlib/base.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -674,13 +674,13 @@ Generic Functions

Creates a composition of two functions (or functor objects), such that ``(f ∘ g)(x...) == f(g(x...))``\ . The ``∘`` symbol can be accessed at the REPL using ``\circ``\ .

By default, an anonymous function ``(x...) -> f(g(x...))`` is returned, but this may be specialized to create any functionally-equivalent callable object.
By default, a function equivalent to ``(x...) -> f(g(x...))`` is returned, but this may be specialized to create any functionally-equivalent, callable object.

.. function:: !(f::Function)

.. Docstring generated from Julia source

Returns a new function which applies boolean not to the output of ``f``\ , equal to ``(x...) -> !f(x...)``\ .
Returns a new function which applies boolean not to the output of ``f``\ , equivalent to ``(x...) -> !f(x...)``\ .

Syntax
------
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