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The branch enables shape updates in variety of flavours:
* explicitly passing the desired target shape
* providing a plugin sput : ℕ → ℕ → Maybe ℕ
* providing a right-inverse to getlen
It also provides a backwards compatibility function to facilitate
shape-retaining updates.
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We can now exploit getlen being rightinvertible and it works for drop
and sieve.
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For building on the sieve example.
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Unlike the original version in VoigtlaenderHMW13, we do not request an
sput : ℕ → ℕ → Maybe ℕ
function for determining the updated source shape from the original
source and updated view shape. Instead we ask the caller directly to
provide the result of sput together with a proof that its getlen matches
with the provided, updated view.
The precondition assoc-enough is not enriched in this way and still
requires a non-changing shape. I.e. it says what it said before.
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The new lemma replaces two uses of lemma-fromFunc-tabulate, because the
latter exposes the implementation of FinMapMaybe, whereas the former
argues about the behaviour of FinMapMaybe. The aim of not exposing the
implementation (apart from brevity) is to enable refactoring.
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Most of the became unused by using the convenience functions introduced
in the parent commit.
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These two features heavily interconnect. As such it makes sense to
integrate them properly. This non-trivial merge does that work. Compared
to feature-partial-getlen a few definitions moved from FreeTheorems.agda
to GetTypes.agda. Many types changed compared to both branches.
Conflicts:
BFF.agda
Bidir.agda
FreeTheorems.agda
Precond.agda
conflict in GetTypes.agda not detected by merge
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* Remove let patter , match = foo usage
* Remove Qualified.infix-symbol usage
* Add non-obvious absurd patterns
* Qualify constructors
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This branch brings three main benefits:
* Only one explicit parameter is needed to ask for a get function.
* The postulated free theorems are mostly turned into preconditions,
i.e. the only use of the postulates is in LiftGet.
* We can now convert list based get functions to vec based ones and back
including the (now) accompanying free theorem.
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This is an improved version of getVec-to-getList in that it also
transports the corresponding free theorem.
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By choosing gl₁ = suc and gl₂ = id, the tail function can now be
bidirectionalized.
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There is no way for Agda to infer these functions or even the intended
index Setoid, so making these explicit is rather required.
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This allows passing both getlen and get as a single parameter. It also
allows to make the free theorem a prerequisite instead of a postulate.
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The representation chosen is to give both an injection gl₁ and a
function gl₂ (formerly getlen), such that by choosing a non-identity for
gl₁ partiality of getlen can be expressed. An alternative would have
been to allow getlen to return a Maybe ℕ and have get return
maybe (Vec A) ⊤ (getlen n)
thus sending all inputs for which getlen yields nothing to tt. It seems
that while there is no way to obtain a such a getlen predicate from an
arbitrary index Setoid I, it should be possible to manufacture a Setoid
from a predicate. Thanks to Stefan Mehner for the insightful discussion.
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Most conflicts stem from varying imports or added functions and a
take-both approach merges them. A notable exception is theorem-2, where
a new result sequence-cong was required. Apart from that, theorem-2
could be taken almost verbatim from feature-delete albeit its type
coming from feature-decsetoid.
Conflicts:
Bidir.agda
FinMap.agda
Generic.agda
Precond.agda
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The old definition of bff had a single failure mode - assoc - and its
proof was a single cong. Now we need to show that the other failure mode
- mapM (flip lookupM ...) - is eliminated by the success of the former
resulting in a larger proof.
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The biggest piece of this puzzle was establishing
get <$> mapMV f v == mapMV f (get v)
provided that the result of mapMV is just something.
lemma-union-not-used lost a "map just", but could be retained in
structure.
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Since the generalization of lemma-checkInsert-restrict there is nothing
to show for theorem-1. So everything works with Setoids now yielding the
same results as the paper proofs.
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We can actually get semantic equality there without requiring anything
else. Indeed this was already hinted in the BX for free paper that says,
that lemma-1 holds in semantic equality.
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This is another step towards permitting arbitrary Setoids in bff.
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We get the plain Setoid for free then.
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The general idea is to enable bff to use arbitrary DecSetoids.
* assoc needs to learn about DecSetoid
* checkInsert needs to learn about DecSetoid
* InsertionResult needs to learn about Setoid
* Parameters to InsertionResult.same become weaker
* lemma-checkInsert-restrict should work with weaker same
* lemma-insert-same needs to learn about Setoid
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The union was the only user of this type and now it uses only partial
mappings. So drop remaining uses of FinMap and make everything work with
FinMapMaybe instead.
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In the presence of shape-changing updates, bff needs to shrink one of
the mappings before unifying them. As long the shape does not change,
the union becomes a disjoint union. With this insight we can adapt the
proof of theorem-1 using the adapted lemma-disjoint-union. Unfortunately
theorem-2 requires more work and assoc-enough becomes non-trivial due to
the introduction of mapMV.
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and accompanying lemmata.
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It is unused, has no proofs and starts to get into the way of
refactoring the union function type.
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agda 2.3.0.1 supported the old notation, but 2.3.2.1 needs full
qualification.
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Also rename fmap to _<$>_ to match Agda naming conventions. The imported
_>>=_ appears to have different binding, so some braces were necessary.
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This removes imports.
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