Extend important types and functions

docs/src/broadcast_background.md

@@ -96,3 +96,51 @@ If you want to avoid adding dots for selected function calls in expr, splice
 those function calls in with `$`. For example, `@. sqrt(abs($sort(x)))` is
 equivalent to `sqrt.(abs.(sort(x)))` (no dot for sort).
 
+## Important `Base.Broadcast` types and functions
+
+There are some important types and functions that are helpful for understanding
+Julia's broadcasting.
+
+ - `Base.Broadcast.Broadcasted` (or just `Broadcasted`)
+ - `Base.Broadcast.broadcasted` (or just `broadcasted`, please note the difference in capitalization)
+ - `Base.Broadcast.instantiate` (or just `instantiate`)
+ - `Base.Broadcast.materialize` (or just `materialize`)
+ - `Base.Broadcast.materialize!` (or just `materialize!`)
+ - `Base.Broadcast.copyto` (or just `copyto`)
+ - `Base.Broadcast.copyto!` (or just `copyto!`)
+
+For brevity, we'll use a suffix `(!)` to denote the functional or in-place
+methods.
+
+The default type in Julia Base's broadcast software layer is `Broadcasted`. This
+is a "lazy" object that contains
+
+ - `style`, used for [traits](https://en.wikipedia.org/wiki/Trait_(computer_programming)), or dispatch
+ - `f`, the function to be broadcasted
+ - `args`, the arguments to the function `f`
+ - `axes`, the "shape" or "size" of the broadcasted object, when materialized
+
+When broadcast expressions are _lowered_ (a step in the Julia compilation
+procedure), they are lowered to `broadcasted` calls, which are then passed to
+`materialize(!)`. For example:
+
+```@example
+a = [1]
+Base.Meta.@lower @. a+=1
+```
+
+!!! note
+
+    The result of `Base.Meta.@lower` is an intermediate representation (IR) of
+    the given expression.
+
+The responsibility of `broadcasted`, here, is to return `Broadcasted` objects.
+This function allows users to overload `broadcasted` to return special types of
+`Broadcasted` objects.
+
+
+Finally, `materialize(!)` does two things:
+
+ - Calls `instantiate`, which reconstructs a new `Broadcasted`
+   object with the `axes` populated (by default it's populated with `nothing`).
+ - Calls `copyto(!)`, which executes the broadcasted expression per element.