This repository contains exercises from the subject Mathematical Foundations for Computing(FMC) done in the Haskell functional programming language.
We start by defining, in the "nat.hs" file, the Nat data type. We then define some functions used for this type of data, such as: addition, multiplication, exponentiation, among others. All of them recursively. The possible forms of a Nat are the O or a success of some Nat S. These things are not the natural things themselves, which mathematicians use in pure mathematics or science. They are just things that seem familiar to us with the natural numbers we know, but they don't need to respect the axioms, or rather, they don't even know that the axioms exist. We dont need know how the natural numbers behave.It's just things that we build with recursion that look like a thing called a natural number.
When defining some funtions for the Nats, we came across some situations that would be interesting return a Bool value insted of Nat value. The language C, reuse the type Int to implement the type Bool. But this is not a good idea, in some cases they can be confused. Whenever we need a new data type to represent and manipulate in our functions, we wil create them. We can create: "weekday", "Bool", "Empty", "Void"... datatypes.
That is, always we need a type to our function, we will create this type(if its does not exist). This make it easy to avoid ambiguity and makes our function more readble and makes more sense.
We define in haskell the list type which has two constructors Nil or Empty and Cons. The Nil you can thought that is the start of the list and the cons like the continuation of the list. The constructor cons takes with it an object(any data type).
We define the specification(in integer theory subject) and here we implement these specification. So we need define who is the zero, the one, who is the operations defined in the specifications(these operations need respect the axioms). For example, it does not matter how the sum function works, what matter is that it takes two integers and return an integer(according to specification).
We define two main types of trees: BinTree and LTree. The LTree is the tree that we are acquainted, the tree that apear when you search for "tree data structure". The BinTree is a tree where the knot has no information, its just a knot.
Here we define ordenation functions seen in algorithms subject.
First:
ghci
Second:
:l name-file.hs
if you alredy did the "second" step, compile with:
:r
Test functin:
search 3 (Fork (Fork (Tip 2) (Tip 0)) (Tip 3))