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These became duplicates of their non-barred counterparts.
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One can use PartialShapeShape instead, so there is limited utility for
this type. It is not used directly and there also is no PartialVecShape.
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Albeit long, this commit is relatively boring.
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Add IsShaped and Shaped records describing shapely types as in Jay95.
Implement bff on Shaped and rewrite PartialVecVec to use the vector
shape retaining all proofs on the vector implementation.
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This allows bff to be more precise with regard to its failure modes,
even though we are not yet making use of that projected precision. It
allows inserting a default value for entries that could not be recovered
in a shape changing update as described in VoigtlaenderHMW13.
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It allows defining get functions that are only defined for some vector
lengths. It retains backwards compatibility with the previous state via
a VecVec compatibility module. The biggest benefit is that now standard
library functions such as tail, take and drop can be passed to bff.
Conflicts: heavy
BFF.agda (imports, bff type clash)
Bidir.agda (imports, heavy bff type clash in theorem-{1,2} and
lemma-get-mapMV)
Generic.agda (imports)
Precond.agda (imports, bff type clash in assoc-enough)
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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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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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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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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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This is another step towards permitting arbitrary Setoids in bff.
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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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It is unused, has no proofs and starts to get into the way of
refactoring the union function type.
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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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Also adapt depending modules. Long lines generally become shorter. The
misleading name "EqInst" (hiding the decidability) got discarded.
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And update Bidir and Precond, cause they import BFF.
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This should make it easier to see what is assumed.
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The case is not interesting, because it is too restricted. The defined
get-type requires a bijection between input length and output length.
Since it requires polymorphism we get a reverse get-len via free
theorems and both compositions are required to be identities. Thus the
case is restricted without providing new insights.
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It is a definition based on Vec but with less assumptions. The VecBFF
has therefore been renamed to VecRevBFF.
VecBFF uses get : \forall n \exists m -> Vec A n -> Vec a m
VecRevBFF uses get : \forall m \exists n -> Vec A n -> Vec a m
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