Remove frule for getindex(::Tuple, i) (#680)

* Remove frule for getindex(::Tuple, i)

Having this chain rule is sub-optimal, because it prevents early-SROA
in Diffractor-like systems that would like to perform some optimizations
before applying AD (but can't do any optimization on functions that
have custom rules). By letting it go down to the `getfield`, regular
SROA can apply. Any AD system should handle `getfield` anyway, so
I don't think there's a strong reason to have this.

Similar reasoning applies to the reverse rules also, but they
aren't currently actively causing me problems, so this PR only
removes the frule, since I don't think many other packages are
using them. We can revisit the rrules later.

* Also remove the rules for first/tail

For similar reasons as getindex, having a rule for first/tail is
suboptimal because it supresses early SROA. Tail is particularly
problematic, because it is used in the implementation of the
```
x, y... = abc
```
syntax, of which users expect early elimination.

* add getfield rule and remove tests for deleted rules

---------

Co-authored-by: Oscar Smith <oscardssmith@gmail.com>

src/rulesets/Base/indexing.jl

@@ -1,14 +1,6 @@
-#####
-##### getindex(::Tuple)
-#####
-
-function frule((_, ẋ), ::typeof(getindex), x::Tuple, i::Integer)
-    return x[i], ẋ[i]
-end
-
-function frule((_, ẋ), ::typeof(getindex), x::Tuple, i)
-    y = x[i]
-    return y, Tangent{typeof(y)}(ẋ[i]...)
+# Int rather than Int64/Integer is intentional
+function frule((_, ẋ), ::typeof(getfield), x::Tuple, i::Int)
+    return x.i, ẋ.i
 end
 
 "for a given tuple type, returns a Val{N} where N is the length of the tuple"
@@ -77,7 +69,7 @@ end
 """
     ∇getindex(x, dy, inds...)
 
-For the `rrule` of `y = x[inds...]`, this function is roughly 
+For the `rrule` of `y = x[inds...]`, this function is roughly
 `setindex(zero(x), dy, inds...)`, returning the array `dx`.
 Differentiable. Includes `ProjectTo(x)(dx)`.
 """
@@ -191,29 +183,6 @@ function ∇getindex!(dx::AbstractGPUArray, dy, inds...)
     return dx
 end
 
-#####
-##### first, tail
-#####
-
-function frule((_, ẋ), ::typeof(first), x::Tuple)
-    return first(x), first(ẋ)
-end
-
-function rrule(::typeof(first), x::T) where {T<:Tuple}
-    first_back(dy) = (NoTangent(), Tangent{T}(ntuple(j -> j == 1 ? dy : NoTangent(), _tuple_N(T))...))
-    return first(x), first_back
-end
-
-function frule((_, ẋ), ::typeof(Base.tail), x::Tuple)
-    y = Base.tail(x)
-    return y, Tangent{typeof(y)}(Base.tail(ẋ)...)
-end
-
-function rrule(::typeof(Base.tail), x::T) where {T<:Tuple}
-    tail_pullback(dy) = (NoTangent(), Tangent{T}(NoTangent(), dy...))
-    return Base.tail(x), tail_pullback
-end
-
 #####
 ##### view
 #####

test/rulesets/Base/indexing.jl

@@ -3,12 +3,7 @@
         x = (1.2, 3.4, 5.6)
         x2 = (rand(2), (a=1.0, b=x))
 
-        # Forward
-        test_frule(getindex, x, 2)
-        test_frule(getindex, x2, 1)
-        test_frule(getindex, x, 1:2)
-        test_frule(getindex, x2, :)
-
+        # don't test Forward because this will be handled by lowering to getfield
         # Reverse
         test_rrule(getindex, x, 2)
         @test_skip test_rrule(getindex, x2, 1, check_inferred=false)  # method ambiguity, maybe fixed by https://github.com/JuliaDiff/ChainRulesTestUtils.jl/pull/253
@@ -168,22 +163,7 @@
     end
 end
 
-@testset "first & tail" begin
-    x = (1.2, 3.4, 5.6)
-    x2 = (rand(2), (a=1.0, b=x))
-
-    test_frule(first, x)
-    test_frule(first, x2)
-
-    test_rrule(first, x)
-    # test_rrule(first, x2) # MethodError: (::ChainRulesTestUtils.var"#test_approx##kw")(::NamedTuple{(:rtol, :atol), Tuple{Float64, Float64}}, ::typeof(test_approx), ::NoTangent, ::Tangent{NamedTuple{(:a, :b), Tuple{Float64, Tuple{Float64, Float64, Float64}}}, NamedTuple{(:a, :b), Tuple{Float64, Tangent{Tuple{Float64, Float64, Float64}, Tuple{Float64, Float64, Float64}}}}}, ::String) is ambiguous
-
-    test_frule(Base.tail, x, check_inferred=false) # return type Tuple{Tuple{Float64, Float64}, Tangent{Tuple{Float64, Float64}, Tuple{Float64, Float64}}} does not match inferred return type Tuple{Tuple{Float64, Float64}, Tangent{Tuple{Float64, Float64}}}
-    test_frule(Base.tail, x2, check_inferred=false)
-
-    test_rrule(Base.tail, x)
-    test_rrule(Base.tail, x2)
-end
+# first & tail handled by getfield rules
 
 @testset "view" begin
     test_frule(view, rand(3, 4), :, 1)