Could Automatic Differentiation learn by applying learnable weights to the compiled S-expression atoms - Backpropagating Errors applied with Stochastic Gradient

Could Automatic Differentiation learn by applying learnable weights to the compiled S-expression atoms - Backpropagating Errors applied with Stochastic Gradient Descent ? A program would constrain a task with functional statements, which is then compiled to weighted s-expressions which learn the specific task from training data. A sort of Neural-net functional program hybrid.