Until now namespaces were stored as (reversed) lists of strings.
It led to:
* confusing code where we work on the underlying representation of
namespaces rather than say what we mean (using `isSuffixOf` to mean
`isParentOf`)
* potentially introducing errors by not respecting the invariant cf.
bug report #616 (but also name generation in the scheme backend
although that did not lead to bugs as it was self-consistent AFAICT)
* ad-hoc code to circumvent overlapping interface implementation when
showing / pretty-printing namespaces
This PR introduces a `Namespace` newtype containing a list of strings.
Nested namespaces are still stored in reverse order but the exposed
interface aims to support programming by saying what we mean
(`isParentOf`, `isApproximationOf`, `X <.> Y` computes to `X.Y`, etc.)
irrespective of the underlying representation.
Until now namespaces were stored as (reversed) lists of strings.
It led to:
* confusing code where we work on the representation rather than say
what we mean (e.g. using `isSuffixOf` to mean `isParentOf`)
* potentially introducing errors by not respecting the invariant cf.
bug report #616 (but also name generation in the scheme backend
although that did not lead to bugs as it was self-consistent AFAICT)
* ad-hoc code to circumvent overlapping interface implementations when
showing / pretty-printing namespaces
This introduces a Namespace newtype containing non-empty lists of
strings. Nested namespaces are still stored in reverse order but the
exposed interface aims to support programming by saying what we mean
(`isParentOf`, `isApproximationOf`, `X <.> Y` computes to `X.Y`, etc.)
irrespective of the underlying representation.
Main change
===========
The main change is to the type of function dealing with an untouched
segment of the local scope. e.g.
```
weak : {outer, vars : _} -> (ns : List Name) ->
tm (outer ++ inner) -> tm (outer ++ ns ++ inner)
```
Instead we now write
```
weak : SizeOf ns -> tm (outer ++ inner) -> tm (outer ++ ns ++ inner)
```
meaning that we do not need the values of `outer`, `inner` and `ns`
at runtime. Instead we only demand a `SizeOf ns` which is a `Nat`
together with an (erased) proof that `ns` is of that length.
Other modifications
===================
Quadratic behaviour
-------------------
A side effect of this refactor is the removal of two sources of
quadratic behaviour. They typically arise in a situation where
work is done on a scope of the form
```
outer ++ done ++ ns ++ inner
```
When `ns` is non-empty, some work is performed and then the variable
is moved to the pile of things we are `done` with. This leads to
recursive calls of the form `f done` -> `f (done ++ [v])` leading
to a cost quadratic in the size of `ns`.
Now that we only care about `SizeOf done`, the recursive call is
(once all the runtime irrelevant content is erased) for the form
`f n` -> `f (S n)`!
More runtime irrelevance
------------------------
In some places we used to rely on a list of names `vars` being
available. However once we only care about the length of `vars`,
the fact it is not available is not a limitation.
For instance a `SizeOf vars` can be reconstructed from an environment
assigning values to `vars` even if `vars` is irrelevant. Indeed the
size of the environment is the same as that of `vars`.
For lack of a better place, I've put it in `Syntax.PreorderReasoning`
These equations are natural in equational reasoning, but less so when
rewriting, so that's why it's there
