This PR derives the linear order on string positions (`String.Pos.Raw`,
`String.Pos`, `String.Slice.Pos`) via `Std.LinearOrderPackage`, which
ensures that all data-carrying and propositional instances are present.
Previously, we were misssing some, like `Ord`.
This PR adds `String.Slice.Subslice`, which is an unbundled version of
`String.Slice`.
This type is of interest because it is the correct type for string
searching and splitting operations to land in.
This PR just adds the type with minimal API. Additional API and
subsequent refactoring of the searching and splitting API is left for
future PRs.
This PR introduces the functions `(String|Slice).posGE` and
`(String|Slice).posGT` will full verification and deprecates
`Slice.findNextPos` in favor of `Slice.posGT`.
The KMP implementation is adapted to use these two new functions.
Various useful string and order lemmas are added along the way.
Also add a `simp` attribute to `Std.le_refl` and fix the resulting
fallout (yes, this would have been better as a separate PR).
This PR introduces a function `String.split` which is based on
`String.Slice.split` and therefore supports all pattern types and
returns a `Std.Iter String.Slice`.
This supersedes the functions `String.splitOn` and `String.splitToList`,
and we remove all all uses of these functions from core. They will be
deprecated in a future PR.
Migrating from `String.splitOn` and `String.splitToList` is easy: we
introduce functions `Iter.toStringList` and `Iter.toStringArray` that
can be used to conveniently go from `Std.Iter String.Slice` to `List
String` and `Array String`, so for example `s.splitOn "foo"` can be
replaced by `s.split "foo" |>.toStringList`.
This PR removes all uses of `String.Iterator` from core, preferring
`String.ValidPos` instead.
In an upcoming PR, `String.Iterator` will be renamed to
`String.Legacy.Iterator`.
This PR defines `String.Slice.replace` and redefines `String.replace` to
use the `Slice` version.
The new implementation is generic in the pattern, so it supports things
like `"education".replace isVowel "☃!" = "☃!d☃!c☃!t☃!☃!n"`. Since it
uses the `ForwardSearcher` infrastructure, `String` patterns are
searched using KMP, unlike the previous implementation which had
quadratic runtime. As a side effect, the behavior when replacing an
empty string now matches that of most other programming languages,
namely `"abc".replace "" "k" = "kakbkck"`.
This PR adds the basic infrastructure to perform termination proofs
about `String.ValidPos` and `String.Slice.Pos`.
We choose approach where the intended way to do termination arguments is
to argue about the position itself rather than some projection of it
like `remainingBytes`.
The types `String.ValidPos` and `String.Slice.Pos` are equipped with a
`WellFoundedRelation` instance given by the greater-than relation. This
means that if a function takes a position `p` and performs a recursive
call on `q`, then the decreasing obligation will be `p < q`. This works
well in the common case where `q` is `p.next h`, in which case the goal
`p < p.next h` is solved by the simplifier.
For stepping through a string backwards, we introduce a type synonym
with a `WellFoundedRelation` instance given by the less-than relation.
This means that if a function takes a position `p` and performs a
recursive call on `q` and specifies `termination_by p.down`, then the
decreasing obligation will be `q < p`. This works well in the case where
`q` is `p.prev h`, in which case the goal `p.prev h < p` is solved by
the simplifier.
For termination arguments invoving multiple strings, the lower-level
primitive `p.remainingBytes` (landing in `Nat`) is also available.
In a future PR, we will additionally provide the necessary typeclasses
instances to register `String.ValidPos` and `String.Slice.Pos` with
`grind` to make complex termination arguments more convenient in user
code.
This PR splits some low-hanging fruit out of `Init.Data.String.Basic`:
basic material about `String.Pos.Raw`, `String.Substrig`, and
`String.Iterator`.
More splitting required and the remaining material is quite unorganized,
but it's a start.
This PR cuts some edges from the import graph.
Specifically:
- `TreeMap` and `HashMap` no longer depend on `String`, so now the
expensive things are all in parallel instead of partially in sequence
- `Omega` no longer relies on `List` lemmas
- The section of the import graph between `Init.Omega` and
`Init.Data.Bitvec.Lemmas` is cleaned up a bit
This PR redefines `String` to be the type of byte arrays `b` for which
`b.IsValidUtf8`.
This moves the data model of strings much closer to the actual data
representation at runtime.
In the near future, we will
- provide variants of `String.Pos` and `Substring` that only allow for
valid positions
- redefine all `String` functions to be much closer to their C++
implementations
In the near-to-medium future we will then provide comprehensive
verification of `String` based on these refactors.
This PR prepares for a future reorganization of the import hierarchy so
that `Init.Data.String.Basic` can import `Init.Data.UInt.Bitwise` and
`Init.Data.Array.Lemmas`.
This PR adjusts the experimental module system to make `private` the
default visibility modifier in `module`s, introducing `public` as a new
modifier instead. `public section` can be used to revert the default for
an entire section, though this is more intended to ease gradual adoption
of the new semantics such as in `Init` (and soon `Std`) where they
should be replaced by a future decl-by-decl re-review of visibilities.
for SSFT24 summer school: https://github.com/david-christiansen/ssft24
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Kim Morrison <scott.morrison@gmail.com>
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
