Functional maps
A functional map in AbstractAlgebra is a map which can be applied by evaluating a Julia function or closure. It is represented by a map object that contains such a function/closure, usually in a field called image_fn
.
All functional maps belong to the map class FunctionalMap
.
A generic concrete type Generic.FunctionalMap
is provided by the Generic module to implement a generic functional map type. This allows for functional maps that contain no extra data, other than a Julia function/closure.
Custom map types can also be defined which have map class FunctionalMap
.
Functional map interface
All functional map types must define their supertypes as in the following example:
mutable struct MyFunctionalMap{D, C} <: Map{D, C, FunctionalMap, MyFunctionalMap}
# some fields
image_fn::Function
end
Of course MyFunctionalMap
need not be parameterised if the types D
and C
of the domain and codomain objects are known.
Required functions for functional maps
The following functions must be defined for all functional map types or classes:
image_fn(M::Map(MyFunctionalMap))
Return the Julia function or closure that corresponds to application of the map $M$. This function only needs to be provided if this function is not stored in an image_fn
field of the MyFunctionalMap
type.
Generic functional maps
The Generic module provides a concrete type FunctionalMap
which merely keeps track of a Julia function/closure implementing the map.
Such maps can be constructed using the following function:
AbstractAlgebra.map_from_func
— Methodmap_from_func(image_fn::Function, domain, codomain)
Construct the generic functional map with domain and codomain given by the parent objects $R$ and $S$ corresponding to the Julia function $f$.
Examples
julia> f = map_from_func(x -> x + 1, ZZ, ZZ)
Map defined by a Julia function
from integers
to integers
julia> f(ZZ(2))
3