4 Registering primitives

This module allows new primitives to be registered, by specifying for each a modified function definition, augmenting the primal computation with a backpropagator.

A transformation is associated with a particular binding (and not, for instance, a procedure value or a symbolic name).

An existing binding can be registered as a primitive with register-primitive!, and a binding can be imported into a module as a newly-registered primitive with require/backprop or require/primal+backprop.

Once a primitive is registered, the augmented definition is available from any other module in the namespace where that binding is available (that is, registering a primitive is an effect visible across module boundaries).

Once registered, the augmented definition is available from any other module in the same namespace that uses the binding.

prim-id is an identifier that binds a procedure.

prim-augmented-def is the syntax to use for the augmented definition of prim-id in differentiated code. It should evaluate to a function that takes the same number of arguments as prim-id and returns a proc-result struct, whose primal field contains the result of evaluting prim-id at the arguments given, and whose backprop field contains a backpropagator function.

The function can share work between the primal and backpropagator.

Associating derivative information with a function confers no overhead to calls to the undifferentiated function.