When this function type is a builtin we can call it as before, using the function pointer, but we need to do something separate for our user defined functions. We need to bind each of the arguments passed in, to each of the symbols in the formals field. Once this is done we need to evaluate the field, using the env field as an environment, and the calling environment as a parent.

A first attempt, without error checking, might look like this:

Actually this is an interesting case, and leaves us a couple of options. We could just throw an error when the argument count supplied is incorrect, but we can do something that is more fun. When too few arguments are supplied we could instead bind the first few formal arguments of the function and then return it, leaving the rest unbound.

This creates a function that has been partially evaluated and reflects our previous idea of a function being some kind of partial computation. If we start with a function that takes two arguments, and pass in a single argument, we can bind this first argument and return a new function with its first formal argument bound, and its second remaining empty.

So you can imagine functions like a little Pac-Man, not consuming all inputs at once, but iteratively eating inputs to the right, getting bigger and bigger until it is full and explodes to create something new. This isn’t actually how we’re going to implement it in code, but it is still fun to imagine.

The above function does exactly as we explained, with correct error handling added in too. First it iterates over the passed in arguments attempting to place each one in the environment. Then it checks if the environment is full, and if so evaluates, otherwise returns a copy of itself with some arguments filled.

Try defining some functions and test out how partial evaluation works.