zia: Interpreter for the Zia programming language.

The Zia project aims to develop a programming language that can be used to program the itself. Instead of storing the source code as plain text and editing the raw text (which can easily break the program), the runtime environment of the interpreter (the Context) can be saved to disk and used in other programs. All the programming is done using an interactive shell such as IZia. The commands sent are interpreted based on the Context. They are used to incrementally modify, test and debug the Context.

Expressions for Zia commands represent a binary tree where parentheses group a pair of expressions and a space separates a pair of expressions.

e.g. (ll lr) (rl rr)
represents the following binary tree: / \ / \ / \ / \ / \ ll lr rl rr

The leaves of the tree can be any unicode string without spaces or parentheses. These symbols may be recognised by the intepreter as concepts or if not used to label new concepts.

Currently, only the lowest-level functionality has been implemented. It's important that programs are represented consistently and transparently within the Context in order to achieve a self-describing system. The syntax shown below may appear awkward but more convenient syntax will be possible once more functionality is added. For example, the need to group pairs of expressions in parentheses will be alleviated by functionality to set the relative precedence and associativity of concepts.

So far there are 4 built-in concepts. A new Context labels these with the symbols below but the labels can be changed to different symbols (e.g. for different languages or disciplines).

Let concept, symbol: let

let is used to set a relation as true. It can be further explained in its use below.

Label concept, symbol: label_of

label_of a is the expression for the label of the concept which is labelled with the symbol a. It can be further explained in its use below.

Reduction concept, symbol: ->

-> can be used to specify reduction rules for concepts given by expressions. let (a (-> b)) represents the command to specify the rule that the concept labelled by a reduces to the concept labelled by b.

-> is also used to express the reduction of a concept. a -> expresses the concept b because of the previous command but b -> expresses b because no reduction rule exists for b.

Labels of concepts reduce to a command to print the symbol that the concept is labelled with. (label_of a) -> expresses the command to print a as output. (label_of (a ->)) -> expresses the command to print b as output.

You can modify existing reduction rules. For example you can change the reduction rule for a by let (a (-> c)); (label_of (a ->)) -> will now print c. You could also execute let (a (-> a)) and so (label_of (a ->)) -> now prints a.

The intepreter will let you know if reduction rule commands are redundant. let (a (-> a)) is redundant because a already reduces to itself. Executing let (a (-> b)) twice will print an error on the second time.

Definition concept, symbol: :=

:= can be used to label a binary tree of concepts or relabel a concept. For example let (c (:= (a b))) means graphically: c / \ a b The command (label_of (c :=)) -> then prints a b. The command (label_of (a :=)) -> prints a. We can change the symbol of b to e using let (e (:= b)). (label_of (c :=)) -> would then print a e and (label_of (a ->)) -> would print e. Because a reduces to e, (label_of (c ->)) -> prints e e. If let (c (-> f)) is executed, an error message is printed explaining some of the components of c (a and e) reduce. This would break the coherence between the reduction of a concept and its composition's reductions. Should c reduce to f or e e? Maintaining this coherence is important for a consistent lazy reduction of syntax trees.

To make sure concepts can be fully reduced, commands like let (i (:= (i j))) are not accepted by the interpreter nor are commands like let (i (-> (i j))). More subtley let (e (:= (a d))) is not accepted because the reduction of a d is e d and so (label_of (e ->)) -> would print e d, (label_of ((e d) ->)) -> would print (e d) d etc. Successive reductions could never terminate if this kind of command was accepted.

API

The current implementation exposes the Context type that can be used in an interface such as IZia. Importing the following traits allows the corresponding methods to be called with Context.

```rust trait ContextMaker { fn new() -> Self { // Constructs a new Context and labels the 4 built-in concepts. } }

trait Execute { fn execute(&mut self, command: &str) -> String { // Executes the commands given by the user that may modify the Context and outputs a // String that maybe empty, an error message or the answer to a query. } } ```