Lab 6: Higher-Order Functions

This week you'll be getting some additional practice with higher-order functions. To start, you should know how map, filter, fold_right and fold_left work for lists. Primarily you will be generalizing these to matrices. There are two secondary objectives of this lab:

• One topic we lost due to the blizzard was modules. They're not crucial, but they certainly make programming in OCaml more comfortable. In short, a module is something like a namespace. We use the following syntax for constructing a module:

  module ModuleName = struct
    ...
  end
  

  What appears between struct and end is anything that we have considered an OCaml program thus far. For example:

  module Foo = struct
    let bar x = x + 1
  end
  

  Outside of the module definition, I can use dot notation to refer to definitions given within the module:

  let baz : int = Foo.bar 3
  

  Modules are also used to organize interfaces for functional data structures in OCaml. Lists, for example, are defined within a module, and every time you've used a list function from the standard library (e.g., List.rev) you've been referring to the module List (in which rev is defined). We'll be using OCaml's module system in this lab to organize our small interface for matrices.

• The topic of this weeks (delayed) assignment is tensors, which are a generalization of both vectors (which we can think of essentially as lists) and matrices. Understanding how to work with matrices will be useful for thinking about how to work with tensors.

As usual, please use this opportunity to clear up any confusions you have by asking the course staff questions. They're very smart folks!