Curiosity killed the cat, good thing cats have 9 lives…

I don’t know you, but after using a few programming languages I have too many questions about type systems, some that come to mind:

What is a type system?

What is a type?

Do we need a type system?

When do we not need one?

What is the relation between type systems and property testing? or is there one?

Why is category theory so important in advanced type systems? (I have intuition but no concrete answers yet)

Are there pure definitions and implementations for the different types of types systems?

Probably some of those questions make no sense, at least, until I understand the answers.

Thankfully, I was not alone in asking myself questions. For example this question seems to spiral into no concrete answers.

If you are looking for a post about Strong vs Weak typing and Static vs dynamic typing articles I found a this one (there are many more)

Anyway I am starting off with the first question.

What is a type system?

According to

Wikipedia In programming languages, a type system is a collection of rules that assign a property called a type to the various construct—​such as variables, expressions, functions or modules—​that a computer program is composed of.1 The main purpose of a type system is to reduce bugs in computer programs2 by defining interfaces between different parts of a computer program, and then checking that the parts have been connected in a consistent way. This checking can happen statically (at compile time), dynamically (at run time), or it can happen as a combination of static and dynamic checking. Type systems have other purposes as well, such as enabling certain compiler optimizations, allowing for multiple dispatch, providing a form of documentation, etc.

Ok, a bit generic, but helpful:

There are rules

There are constructs

A program is composed by the aforementioned constructs

type systems help prevent errors

Other definitions I found online are as simple as:

A type is a label (can’t remember who said this)

“…A type is simply a name for a collection of related values just like a food group, it’s a name for a collection of foods with related properties and a type is a name for a collection of values that we code with that have similar properties” From Erik Meijer latest course on functional programming (Lecture 2 part 1)

Benjamin C Pierce from TAPL A type system is a tractable syntactic method for proving the absence of certain program behaviours by classifying phrases according to the kinds of values they compute.

This is a more helpful

Tractable and syntactic method

absence of behaviours (perhaps runtime errors)

(perhaps runtime errors) Classification of phrases according to kind of values

As I was thinking a little about this I found this gem of a post:

@mrb_bk wondered What is a type system for This is totally worth the read. The post is based on studying TAPL. The TL;DR of the post goes like:

"The most basic property of this type system or any other is safety (also called soundness): well-typed terms do not 'go wrong.'"

What does “go wrong” means in this context?

"...it means reaching a 'stuck state' that is not designated as a final value but where the evaluation rules do not tell us what to do next."

In this context thinking of getting stuck as runtime errors is acceptable.

"What we want to know, then, is that well-typed terms do not get stuck. We show this in two steps, commonly known as the progress and preservation theorems."

The theorem definition and explanation is in the post, but I had to stop and thing about:

"Safety = Progress + Preservation"

That is where I am going to leave this for today.

Worth Reading

As a novice in this area I found The paper by [Luca Cardelli][1] is a good read .

Also this pdf by Benjamin C. Pierce contains an overview of the available literature up until year 2003.

Some other related reads

References

Feedback other resources?

Do you know of other type system resources I should look into? Do you know of any other links I should look into? Any comments? Let me know

Happy new year!!