API

@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)

@leaf T

Define functor for the type T so that isleaf(x::T) == true.

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.children(x)

Return the children of x as defined by functor. Equivalent to functor(x)[1].

Functors.isleaf(x)

Return true if x has no children according to functor.

Examples

julia> Functors.isleaf(1)
true

julia> Functors.isleaf([2, 3, 4])
true

julia> Functors.isleaf(["five", [6, 7]])
false

julia> Functors.isleaf([])
false

julia> Functors.isleaf((8, 9))
false

julia> Functors.isleaf(())
true

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])

fleaves(x; exclude = isleaf)

Traverse x by recursing each child of x as defined by functor and collecting the leaves into a flat array, ordered by a breadth-first traversal of x, respecting the iteration order of children calls.

The exclude function is used to determine whether to recurse into a node, therefore identifying the leaves as the nodes for which exclude returns true.

See also fcollect for a similar function that collects all nodes instead.

Examples

julia> struct Bar; x; end

julia> @functor Bar

julia> struct TypeWithNoChildren; x; y; end

julia> m = (a = Bar([1,2,3]), b = TypeWithNoChildren(4, 5));

julia> fleaves(m)
2-element Vector{Any}:
 [1, 2, 3]
 TypeWithNoChildren(4, 5)

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

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.

See also fmap_with_path and fmapstructure.

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, Tuples, NamedTuples, 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 call fmap(f, x, ys...; walk = mywalk) will wrap mywalk in ExcludeWalk then CachedWalk. Here, ExcludeWalk is responsible for applying f at excluded nodes. For a low-level interface for executing a user-constructed walk, see execute.

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"))

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)

" fmapwithpath(f, x, ys...; exclude = isleaf, walk = DefaultWalkWithPath(), [prune])

Like fmap, but also passes a KeyPath to f for each node in the recursion. The KeyPath is a tuple of the indices used to reach the current node from the root of the recursion. The KeyPath is constructed by the walk function, and can be used to reconstruct the path to the current node from the root of the recursion.

f has to accept two arguments: the associated KeyPath and the value of the current node.

exclude also receives the KeyPath as its first argument and a node as its second. It should return true if the recursion should not continue on its children and f applied to it.

prune is used to control the behaviour when the same node appears twice, see fmap for more information.

Examples

julia> x = ([1, 2, 3], 4, (a=5, b=Dict("A"=>6, "B"=>7), c=Dict("C"=>8, "D"=>9)));

julia> exclude(kp, x) = kp == KeyPath(3, :c) || Functors.isleaf(x);

julia> fmap_with_path((kp, x) -> x isa Dict ? nothing : x.^2, x; exclude = exclude)
([1, 4, 9], 16, (a = 25, b = Dict("B" => 49, "A" => 36), c = nothing))

fmapstructure(f, x, ys...; exclude = isleaf, [prune])

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.

See also fmap and fmapstructure_with_path.

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)])

fmapstructure_with_path(f, x, ys...; [exclude, prune])

Like fmap_with_path, but doesn't preserve the type of custom structs. Instead, it returns a named tuple, a tuple, an array, a dict, or a nested set of these.

See also fmapstructure.

AbstractWalk

Any walk for use with fmap should inherit from this type. A walk subtyping AbstractWalk must satisfy the walk function interface:

struct MyWalk <: AbstractWalk end

function (::MyWalk)(recurse, x, ys...)
  # implement this
end

The walk function is called on a node x in a Functors tree. It may also be passed associated nodes ys... in other Functors trees. The walk function recurses further into (x, ys...) by calling recurse on the child nodes. The choice of which nodes to recurse and in what order is custom to the walk.

execute(walk, x, ys...)

Execute a walk that recursively calls itself, starting at a node x in a Functors tree, as well as optional associated nodes ys... in other Functors trees. Any custom walk function that subtypes Functors.AbstractWalk is permitted.

DefaultWalk()

The default walk behavior for Functors.jl. Walks all the Functors.children of trees (x, ys...) based on the structure of x. The resulting mapped child nodes are restructured into the type of x.

See fmap for more information.

StructuralWalk()

A structural variant of Functors.DefaultWalk. The recursion behavior is identical, but the mapped children are not restructured.

See fmapstructure for more information.

ExcludeWalk(walk, fn, exclude)

A walk that recurses nodes (x, ys...) according to walk, except when exclude(x) is true. Then, fn(x, ys...) is applied instead of recursing further.

Typically wraps an existing walk for use with fmap.

CachedWalk(walk[; prune])

A walk that recurses nodes (x, ys...) according to walk and storing the output of the recursion in a cache indexed by x (based on object ID). Whenever the cache already contains x, either:

• prune is specified, then it is returned, or
• prune is unspecified, and the previously cached recursion of (x, ys...) returned.

Typically wraps an existing walk for use with fmap.

CollectWalk()

A walk that recurses into a node x via Functors.children, storing the recursion history in a cache. The resulting ordered recursion history is returned.

See fcollect for more information.

AnonymousWalk(walk_fn)

Wrap a walk_fn so that AnonymousWalk(walk_fn) isa AbstractWalk. This type only exists for backwards compatability and should not be directly used. Attempting to wrap an existing AbstractWalk is a no-op (i.e. it is not wrapped).

IterateWalk()

A walk that walks all the Functors.children of trees (x, ys...) and concatenates the iterators of the children via Iterators.flatten. The resulting iterator is returned.

When used with fmap, the provided function f should return an iterator. For example, to iterate through the square of every scalar value:

julia> x = ([1, 2, 3], 4, (5, 6, [7, 8]));

julia> make_iterator(x) = x isa AbstractVector ? x.^2 : (x^2,);

julia> iter = fmap(make_iterator, x; walk=Functors.IterateWalk(), cache=nothing);

julia> collect(iter)
8-element Vector{Int64}:
  1
  4
  9
 16
 25
 36
 49
 64

We can also simultaneously iterate through multiple functors:

julia> y = ([8, 7, 6], 5, (4, 3, [2, 1]));

julia> make_zipped_iterator(x, y) = zip(make_iterator(x), make_iterator(y));

julia> zipped_iter = fmap(make_zipped_iterator, x, y; walk=Functors.IterateWalk(), cache=nothing);

julia> collect(zipped_iter)
8-element Vector{Tuple{Int64, Int64}}:
 (1, 64)
 (4, 49)
 (9, 36)
 (16, 25)
 (25, 16)
 (36, 9)
 (49, 4)
 (64, 1)

KeyPath(keys...)

A type for representing a path of keys to a value in a nested structure. Can be constructed with a sequence of keys, or by concatenating other KeyPaths. Keys can be of type Symbol, String, or Int.

For custom types, access through symbol keys is assumed to be done with getproperty. For consistency, the method Base.propertynames is used to get the viable property names.

For string and integer keys instead, the access is done with getindex.

See also getkeypath, haskeypath.

Examples

julia> kp = KeyPath(:b, 3)
KeyPath(:b, 3)

julia> KeyPath(:a, kp, :c, 4) # construct mixing keys and keypaths
KeyPath(:a, :b, 3, :c, 4)

julia> struct T
           a
           b
       end

julia> function Base.getproperty(x::T, k::Symbol)
            if k in fieldnames(T)
                return getfield(x, k)
            elseif k === :ab
                return "ab"
            else        
                error()
            end
        end;

julia> Base.propertynames(::T) = (:a, :b, :ab);

julia> x = T(3, Dict(:c => 4, :d => 5));

julia> getkeypath(x, KeyPath(:ab)) # equivalent to x.ab
"ab"

julia> getkeypath(x, KeyPath(:b, :c)) # equivalent to (x.b)[:c]
4

haskeypath(x, kp::KeyPath)

Return true if x has a value at the path kp.

See also KeyPath and getkeypath.

Examples

```jldoctest julia> x = Dict(:a => 3, :b => Dict(:c => 4, "d" => [5, 6, 7])) Dict{Any,Any} with 2 entries: :a => 3 :b => Dict{Any,Any}(:c=>4,"d"=>[5, 6, 7])

julia> haskeypath(x, KeyPath(:a)) true

julia> haskeypath(x, KeyPath(:b, "d", 1)) true

julia> haskeypath(x, KeyPath(:b, "d", 4)) false

getkeypath(x, kp::KeyPath)

Return the value in x at the path kp.

See also KeyPath and haskeypath.

Examples

julia> x = Dict(:a => 3, :b => Dict(:c => 4, "d" => [5, 6, 7]))
Dict{Symbol, Any} with 2 entries:
  :a => 3
  :b => Dict{Any, Any}(:c=>4, "d"=>[5, 6, 7])

julia> getkeypath(x, KeyPath(:b, "d", 2))
6