# Recursive transformations from Functors.jl

Flux models are deeply nested structures, and Functors.jl provides tools needed to explore such objects, apply functions to the parameters they contain, and re-build them.

New layers should be annotated using the `Functors.@functor`

macro. This will enable `params`

to see the parameters inside, and `gpu`

to move them to the GPU.

`Functors.jl`

has its own notes on basic usage for more details. Additionally, the Advanced Model Building and Customisation page covers the use cases of `Functors`

in greater details.

`Functors.@functor`

— Macro```
@functor T
@functor T (x,)
```

Adds methods to `functor`

allowing recursion into objects of type `T`

, and reconstruction. Assumes that `T`

has a constructor accepting all of its fields, which is true unless you have provided an inner constructor which does not.

By default all fields of `T`

are considered `children`

; this can be restricted be restructed by providing a tuple of field names.

**Examples**

```
julia> struct Foo; x; y; end
julia> @functor Foo
julia> Functors.children(Foo(1,2))
(x = 1, y = 2)
julia> _, re = Functors.functor(Foo(1,2));
julia> re((10, 20))
Foo(10, 20)
julia> struct TwoThirds a; b; c; end
julia> @functor TwoThirds (a, c)
julia> ch2, re3 = Functors.functor(TwoThirds(10,20,30));
julia> ch2
(a = 10, c = 30)
julia> re3(("ten", "thirty"))
TwoThirds("ten", 20, "thirty")
julia> fmap(x -> 10x, TwoThirds(Foo(1,2), Foo(3,4), 56))
TwoThirds(Foo(10, 20), Foo(3, 4), 560)
```

`Functors.fmap`

— Function```
fmap(f, x, ys...; exclude = Functors.isleaf, walk = Functors.DefaultWalk()[, prune])
fmap(walk, f, x, ys...)
```

A structure and type preserving `map`

.

By default it transforms every leaf node (identified by `exclude`

, default `isleaf`

) by applying `f`

, and otherwise traverses `x`

recursively using `functor`

. Optionally, it may also be associated with objects `ys`

with the same tree structure. In that case, `f`

is applied to the corresponding leaf nodes in `x`

and `ys`

.

**Examples**

```
julia> fmap(string, (x=1, y=(2, 3)))
(x = "1", y = ("2", "3"))
julia> nt = (a = [1,2], b = [23, (45,), (x=6//7, y=())], c = [8,9]);
julia> fmap(println, nt)
[1, 2]
23
45
6//7
()
[8, 9]
(a = nothing, b = Any[nothing, (nothing,), (x = nothing, y = nothing)], c = nothing)
julia> fmap(println, nt; exclude = x -> x isa Array)
[1, 2]
Any[23, (45,), (x = 6//7, y = ())]
[8, 9]
(a = nothing, b = nothing, c = nothing)
julia> twice = [1, 2]; # println only acts once on this
julia> fmap(println, (i = twice, ii = 34, iii = [5, 6], iv = (twice, 34), v = 34.0))
[1, 2]
34
[5, 6]
34
34.0
(i = nothing, ii = nothing, iii = nothing, iv = (nothing, nothing), v = nothing)
julia> d1 = Dict("x" => [1,2], "y" => 3);
julia> d2 = Dict("x" => [4,5], "y" => 6, "z" => "an_extra_value");
julia> fmap(+, d1, d2) == Dict("x" => [5, 7], "y" => 9) # Note that "z" is ignored
true
```

Mutable objects which appear more than once are only handled once (by caching `f(x)`

in an `IdDict`

). Thus the relationship `x.i === x.iv[1]`

will be preserved. An immutable object which appears twice is not stored in the cache, thus `f(34)`

will be called twice, and the results will agree only if `f`

is pure.

By default, `Tuple`

s, `NamedTuple`

s, and some other container-like types in Base have children to recurse into. Arrays of numbers do not. To enable recursion into new types, you must provide a method of `functor`

, which can be done using the macro `@functor`

:

```
julia> struct Foo; x; y; end
julia> @functor Foo
julia> struct Bar; x; end
julia> @functor Bar
julia> m = Foo(Bar([1,2,3]), (4, 5, Bar(Foo(6, 7))));
julia> fmap(x -> 10x, m)
Foo(Bar([10, 20, 30]), (40, 50, Bar(Foo(60, 70))))
julia> fmap(string, m)
Foo(Bar("[1, 2, 3]"), ("4", "5", Bar(Foo("6", "7"))))
julia> fmap(string, m, exclude = v -> v isa Bar)
Foo("Bar([1, 2, 3])", (4, 5, "Bar(Foo(6, 7))"))
```

To recurse into custom types without reconstructing them afterwards, use `fmapstructure`

.

For advanced customization of the traversal behaviour, pass a custom `walk`

function that subtypes `Functors.AbstractWalk`

. The form `fmap(walk, f, x, ys...)`

can be called for custom walks. The simpler form `fmap(f, x, ys...; walk = mywalk)`

will wrap `mywalk`

in `ExcludeWalk`

then `CachedWalk`

.

```
julia> struct MyWalk <: Functors.AbstractWalk end
julia> (::MyWalk)(recurse, x) = x isa Bar ? "hello" :
Functors.DefaultWalk()(recurse, x)
julia> fmap(x -> 10x, m; walk = MyWalk())
Foo("hello", (40, 50, "hello"))
julia> fmap(MyWalk(), x -> 10x, m)
Foo("hello", (4, 5, "hello"))
```

The behaviour when the same node appears twice can be altered by giving a value to the `prune`

keyword, which is then used in place of all but the first:

```
julia> twice = [1, 2];
julia> fmap(float, (x = twice, y = [1,2], z = twice); prune = missing)
(x = [1.0, 2.0], y = [1.0, 2.0], z = missing)
```

`Functors.isleaf`

— Function`Functors.children`

— Function`Functors.children(x)`

Return the children of `x`

as defined by `functor`

. Equivalent to `functor(x)[1]`

.

`Functors.fcollect`

— Function`fcollect(x; exclude = v -> false)`

Traverse `x`

by recursing each child of `x`

as defined by `functor`

and collecting the results into a flat array, ordered by a breadth-first traversal of `x`

, respecting the iteration order of `children`

calls.

Doesn't recurse inside branches rooted at nodes `v`

for which `exclude(v) == true`

. In such cases, the root `v`

is also excluded from the result. By default, `exclude`

always yields `false`

.

See also `children`

.

**Examples**

```
julia> struct Foo; x; y; end
julia> @functor Foo
julia> struct Bar; x; end
julia> @functor Bar
julia> struct TypeWithNoChildren; x; y; end
julia> m = Foo(Bar([1,2,3]), TypeWithNoChildren(:a, :b))
Foo(Bar([1, 2, 3]), TypeWithNoChildren(:a, :b))
julia> fcollect(m)
4-element Vector{Any}:
Foo(Bar([1, 2, 3]), TypeWithNoChildren(:a, :b))
Bar([1, 2, 3])
[1, 2, 3]
TypeWithNoChildren(:a, :b)
julia> fcollect(m, exclude = v -> v isa Bar)
2-element Vector{Any}:
Foo(Bar([1, 2, 3]), TypeWithNoChildren(:a, :b))
TypeWithNoChildren(:a, :b)
julia> fcollect(m, exclude = v -> Functors.isleaf(v))
2-element Vector{Any}:
Foo(Bar([1, 2, 3]), TypeWithNoChildren(:a, :b))
Bar([1, 2, 3])
```

`Functors.functor`

— Function`Functors.functor(x) = functor(typeof(x), x)`

Returns a tuple containing, first, a `NamedTuple`

of the children of `x`

(typically its fields), and second, a reconstruction funciton. This controls the behaviour of `fmap`

.

Methods should be added to `functor(::Type{T}, x)`

for custom types, usually using the macro `@functor`

.

`Functors.fmapstructure`

— Function`fmapstructure(f, x; exclude = isleaf)`

Like `fmap`

, but doesn't preserve the type of custom structs. Instead, it returns a `NamedTuple`

(or a `Tuple`

, or an array), or a nested set of these.

Useful for when the output must not contain custom structs.

**Examples**

```
julia> struct Foo; x; y; end
julia> @functor Foo
julia> m = Foo([1,2,3], [4, (5, 6), Foo(7, 8)]);
julia> fmapstructure(x -> 2x, m)
(x = [2, 4, 6], y = Any[8, (10, 12), (x = 14, y = 16)])
julia> fmapstructure(println, m)
[1, 2, 3]
4
5
6
7
8
(x = nothing, y = Any[nothing, (nothing, nothing), (x = nothing, y = nothing)])
```