# Mathematics and Computation

## A blog about mathematics for computers

Postsby categoryby yearall

# Posts in the category Programming languages

### Runners in action

It has been almost a decade since Matija Pretnar and I posted the first blog posts about programming with algebraic effects and handlers and the programming language Eff. Since then handlers have become a well-known control mechanism in programming languages.

Handlers and monads excel at simulating effects, either in terms of other effects or as pure computations. For example, the familiar state monad implements mutable state with (pure) state-passing functions, and there are many more examples. But I have always felt that handlers and monads are not very good at explaining how a program interacts with its external environment and how it gets to perform real-world effects.

Danel Ahman and I have worked for a while on attacking the question on how to better model external resources and what programming constructs are appropriate for working with them. The time is right for us to show what we have done so far. The theoretical side of things is explained in our paper Runners in action, Danel implemented a Haskell library Haskell-Coop to go with the paper, and I implemented a programming language Coop.

### What is algebraic about algebraic effects?

Published as arXiv:1807.05923.

Abstract: This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 "Algebraic effect handlers go mainstream". It is targeted roughly at the level of a doctoral student with some amount of mathematical training, or at anyone already familiar with algebraic effects and handlers as programming concepts who would like to know what they have to do with algebra. We draw an uninterrupted line of thought between algebra and computational effects. We begin on the mathematical side of things, by reviewing the classic notions of universal algebra: signatures, algebraic theories, and their models. We then generalize and adapt the theory so that it applies to computational effects. In the last step we replace traditional mathematical notation with one that is closer to programming languages.

### The new and improved Programming languages zoo

It is my pleasure to announce the new and improved Programming languages Zoo, a potpourri of miniature but fully functioning programming language implementations. The new zoo has a decent web site, it is now hosted on GitHub, and the source code was cleaned up. Many thanks to Matija Pretnar for all the work.

The purpose of the zoo is to demonstrate design and implementation techniques, from dirty practical details to lofty theoretical considerations:

• functional, declarative, object-oriented, and procedural languages
• source code parsing with a parser generator
• recording of source code positions
• pretty-printing of values
• interactive shell (REPL) and non-interactive file processing
• untyped, statically and dynamically typed languages
• type checking and type inference
• subtyping, parametric polymorphism, and other kinds of type systems
• eager and lazy evaluation strategies
• recursive definitions
• exceptions
• interpreters and compilers
• abstract machine

There is still a lot of room for improvement and new languages. Contributions are welcome!

### Miniprolog

I have aded to the PL Zoo a mini prolog interpreter. It really is minimalistic, as it only handles pure Horn clauses. There is no arithmetic, lists, cuts, or disjunctions. Nevertheless, it ought to be possible to write a miniml interpreter in it… If anyone does it, please send me the code!

### A toy call-by-push-value language

I have added two new languages to the PL Zoo. The minor addition is miniml+error, which is just MiniML with an error exception (raised by division by 0) that cannot be caught. The purpose is to demonstrate handling of fatal errors during runtime. The more interesting new animal is levy (written by Matija Pretnar and myself), an implementation of Paul Levy’s call-by-push-value language. If you only know about Haskell’s call-by-name and ML’s call-by-value, I invite you to learn about call-by-push-value. Start by reading Paul’s FAQ.

### Sub and Poly, two new additions to the PL Zoo

I have added two new languages to the Programming Languages Zoo which demonstrate polymorphic type inference and type checking with subtypes.

### An object-oriented language Boa

I have added another language, called Boa, to the Programming Languages Zoo. It is an object-oriented language with the following features:

• integers and booleans as base types,
• first-class functions,
• dynamically typed,
• objects are extensible records with mutable fields,
• there are no classes, instead we can define “prototype” objects and extend them
to create instances.