Introduction

The preceding illustration can be generalized to a full matrix/computer algebra system (similar to Matlab for instance) with applications to a full range of domains (e.g. signal/image processing, neural networks, etc.)

To proceed, let's define some other remarkable functions to:

• Get the sum of a list of values and its generalization called "reduce" or "fold" (e.g. how to use the "sum" template to get the min/max of a list ?).
• Repeat a function f to a value x (what is called the fixpoint of f, and can be use to solve equations for instance with bissection method).

The "sum" function can be written as follow:

let rec sum xs = 
  match xs with
    | []    -> 0
    | v::vs -> v+(sum vs) 

printfn "%A" (sum [1;2;3])

The elements (0,+) can be considered as parameters and replaced by (1,*), (99,min), (-99,max), ([],insert), etc.

let rec reduce v0 op xs = 
  match xs with
    | []    -> v0
    | v::vs -> op v (reduce v0 op vs) 

let sum = reduce 0 (+)
let max = reduce (-9) (fun x r -> if x>r then x else r)

printfn "%A" (sum [1;2;3])
printfn "%A" (max [1;2;3])

source

As an exercice, try to define functions on matrixes (i.e. list of lists).