# ReverseDiffSource internals¶

All the core of the functions in the package ( differentiation, removal of neutral statements, factorization of identical calls) rely on 2 structures:

1. The ExNode composite type that represents either:
• a single operation (a function call)
• an external reference (a variable that can be a parameter for derivation or a reference to a variable outside the scope of the expression)
• a constant
ExNodes have parents which are typically the arguments of the function. Collectively they make a DAG but with several additions :
• the order of arguments (parent nodes) is significant ( a ^ b is not the same as b ^ a)
• there needs to be additionnal ordering information as statements not related sometimes need to execute in a specific order, this information is in the precedence field.
1. The ExGraph composite type that stores
• ExNodes in a vector (in the order of execution),
• information on how to map ExNodes to variable names (used and set),
• and optionnaly information on how to map nodes to ‘outer’ nodes. This last mapping is necessary when the ExGraph is embedded in another parent graph ( for example the inner scope of for loops is represented as a subgraph).

## Showing the code graph¶

Starting from an expression, it is possible to have a dump of the nodes composing its equivalent graph with the (unexported) tograph() call:

ex = quote
a = 1 + x
2 * exp(-a)
end

g = ReverseDiffSource.tograph(ex)

node | symbol     | ext ? | type       | parents  | precedence | main  | value         |
---- | ---------- | ----- | ---------- | -------- | ---------- | ----- | ------------- |
1    |            |       | [constant] |          |            | 1     | (Float64) NaN |
2    | x >>       |       | [external] |          |            | :x    | (Float64) NaN |
3    | a <<       |       | [call]     | 11, 1, 2 |            | :call | (Float64) NaN |
4    |            |       | [constant] |          |            | 2     | (Float64) NaN |
5    |            |       | [call]     | 8, 3     |            | :call | (Float64) NaN |
6    |            |       | [call]     | 10, 5    |            | :call | (Float64) NaN |
7    | nothing << |       | [call]     | 9, 4, 6  |            | :call | (Float64) NaN |
8    |            |       | [constant] |          |            | -     | (Float64) NaN |
9    |            |       | [constant] |          |            | *     | (Float64) NaN |
10   |            |       | [constant] |          |            | exp   | (Float64) NaN |
11   |            |       | [constant] |          |            | +     | (Float64) NaN |


Additionnaly, the plot() function (also unexported) will generate a GrapViz compatible graph description :

using GraphViz

Graph( ReverseDiffSource.plot( g ))

Should produce :