Concepts

This document provides an overview of some of the key ideas in arr.ai. It strives to steer clear of syntax and semantics as much as practicable in order to focus on the concepts themselves.

Type system

A core premise of arr.ai is that the type system should be made as simple as possible, but not simpler.

Numbers, tuples and sets are sufficiently powerful to represent a rich and diverse set of information structures, including arrays, string, dictionaries and even functions.

Key to understanding the type system is to realise that, although these other "types" are visible as distinct things in arr.ai syntax (e.g., the string "abc"), they do not exist as distinct types in the language. The string "abc" is exactly the set {(@: 0, @char: 97), (@: 1, @char: 98), (@: 2, @char: 99)}. There is no distinction whatsoever between the two. The string syntax and the set syntax may be used interchangeably in any expression and the result is guaranteed to be the same. There isn't even a standard library function available to ask which representation is being used to implement a given value. In a very strong sense, strings do not exist in arr.ai. They are just syntactic sugar for a special arrangement of numbers, tuples and sets.

A bit of history: The original design of arr.ai's type system had numbers, tuples, Booleans and relations. After tossing it over for some time, it became clear that sets were not only a very important concept, but also more fundamental than relations. After much deliberation to try and model sets as a special kind of relation ({|@|, (1), (2), (3)} in current arr.ai syntax), it was decided to reverse the situation and define relations in terms of sets and tuples.

Booleans also went the way of the Dodo due to the ability to model them as special sets. The use of the empty set, {}, for false and the set with the empty tuple, {()}, for true has a precedent. In relational theory, two special relations model false and true, respectively: DUM, the empty table with no attributes, and DEE, the table with no attributes containing the tuple with no attributes. There has been some consideration towards reinstating Booleans as a core type, due to usability concerns (e.g., true prints as {()}). However, it hasn't been a major issue to date, so it will not likely happen. One possible solution is to render {()} as true, since that is just about the only use this special set has (though the same doesn't apply to {}).

Immutable values

All arr.ai values are immutable. Each arr.ai program is a single expression that defines some output as a function of its inputs. Expressions are pure, that is, they have no side effects. Even writing to a filesystem is impossible, which is why arr.ai directly supports outputting zip and tar archives.