robsimmons / dusa / 9492069169

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Commit Message

Significantly refactor and simplify flattening transformation, unify handling of builtins and functional predicates (#23)

## Background

### Functional predicates

I originally introduced **functional predicates** with the observation
that it's pretty nice to be able to write

```
size is 3.
color 1 is red.
color 2 is blue.
color 3 is green.
color 4 is orange.

a (color N) :- b N, N < size.
```

where the last rule is a shorthand for 

```
a Color :- b N, size is Size, N < Size, color N is Color.
```

Expanding out this shorthand is done in a step called the _flattening
transformation_.

### Built-in operatons

I also originally introduced **built-in operations** in a way that had a
complicated interaction with the term-matching infrastructure, so that,
for example, matching the term `3` against the pattern `succ X` with
`succ` registered as the `NAT_SUCC` operator would result in X being
bound to 2.

This introduced complexity into a pretty core part of the system,
**and** it wasn't clear what should happen if you try to write things
like `succ "Hello world"`.

One correct, well-understood, and uniform way to handle this sort of
operation is by treating the successor operator as an infinite relation
of the form `succ X is Y`, with the following entries:

```
succ 0 is 1.
succ 1 is 2.
succ 2 is 3.
...
```

This PR unifies the way both functional predicates and built-in
relations get treated by the static checker and the flattening
transformation.

## Built-ins are now uniformly treated as relations

Without this PR, Dusa doesn't allow you to write built-in operations as
relations. The following isn't allowed, for example:

```
#builtin NAT_SUCC succ
a 3.
b Y :- a X, succ X is Y.
```

In Dusa 0.0.14 and below, built-ins can only be referenced in their
functional form, not their relational form, even though the program was
compiling everything into the relational form. This is fixed, and... (continued)

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