2c839db924
Prove associativity of maps (in one direction)
2023-07-30 19:09:16 -07:00
1e4e8000cf
Rename union-preserves to properly match what's being preserved
2023-07-30 17:57:06 -07:00
70b85c99cc
Rename the new provenance type and remove the old version
2023-07-30 16:45:02 -07:00
de2f202bdf
Use an expression-based provenance to make enumerating cases easier
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This should come in handy for the associativity proof.
2023-07-30 16:43:07 -07:00
6039c1dfab
Rename 'merge' to 'union'
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-30 15:18:09 -07:00
d786e6bf48
Eschew proof-by-symmetry
2023-07-30 14:16:35 -07:00
af0066eaa7
Rearrange a few functions
2023-07-30 13:49:38 -07:00
eaee73236f
More tweaks to naming and style
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-30 13:46:52 -07:00
26db4cc86c
Remove unnecessary -right prefix in theorem name.
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-30 13:21:03 -07:00
b066db9829
Use inferred variables for proofs where possible
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-30 13:19:15 -07:00
4033a1b33d
Prove most of commutativity by relying on in-dec.
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The "no" case still needs to be dismissed, but that can probably
be done by some lemma about keys in maps.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-28 00:05:41 -07:00
77b8b6fad9
Finally prove the provenance properties of merge.
2023-07-26 20:58:41 -07:00
461732244a
Finish all in/not-in proofs.
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-26 20:40:28 -07:00
12217e6928
Reformat the code to roughly fit into 80 columns.
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-26 17:31:09 -07:00
489b0532df
Add intermediate state for insertion proofs
2023-07-25 22:58:42 -07:00
6b51cd4050
Reorganize a bit and start on provenance
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-25 19:56:47 -07:00
88a712fa98
Implement the more powerful Map-functional theorem
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-25 18:22:24 -07:00
c9ab1152c4
Minor cleanup of Map module
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-25 00:10:57 -07:00
850984ec15
Do away with implicit arguments in some places where they can't be inferred
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-24 23:58:14 -07:00
4aea9a0358
Migrate Maps to including a uniqueness proof
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-24 23:55:09 -07:00
c2bc1c5421
Move the implementation details into a private module
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-24 23:12:04 -07:00
232bd65809
Add uniqueness preservation proof for merge
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-24 23:02:43 -07:00
87a476ab9e
Add proofs of uniqueness preservation for map insert
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-24 22:51:40 -07:00
c50195942d
Start moving away from purely list-based maps.
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The eventual goal is to make a map be a list and a proof
that all the keys are unique.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-24 20:38:34 -07:00
f2e72b54ce
Define unique as a data type to match stdlib All and Any
2023-07-23 21:34:24 -07:00
d9c18fe483
Prove that maps are functional assuming uniqueness
2023-07-23 17:50:25 -07:00
ab7ed2039a
Add a generic Map module and prove its induced equivalence relation
2023-07-23 00:51:34 -07:00
8febffc8e3
Add an equivalence constraint on lattice relations.
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-15 15:16:51 -07:00
971d75bb2b
Parameterize by equivalence type
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-15 14:40:11 -07:00
46ff4465f2
Git rid of the bundles (for now) use IsWhatever
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-15 13:12:21 -07:00
7b993827bf
Delete the unneeded <= relation from instances
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-15 12:18:50 -07:00
09d2125aea
Add note to self
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 22:45:17 -07:00
cdca2528e9
Add a lattice instance for products
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 21:49:47 -07:00
3b29ee0f74
Add a Semilattice isntance for Products.
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 21:20:16 -07:00
1ee6682c1a
Factor the Semilattice instances for Nat into their own module
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 19:59:07 -07:00
c9b514e9af
Add a preorder instance for product
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 19:42:29 -07:00
2b3d429631
Get started on a semilattice instances for products
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 18:42:29 -07:00
bac68b95f1
Add a Lattice instance for natural numbers.
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 18:18:17 -07:00
c6dddb177e
Get started on a lattice instance for naturals.
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-13 23:22:29 -07:00
422ea93edb
Finish up the Nat semilattices
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-13 21:55:51 -07:00
97a3f25fd2
[WIP] Start lattice and semilattice proofs for Nat
2023-04-06 23:08:49 -07:00
8b805be9d3
Add a map from natural numbers for use as a lattice transformer
2023-04-04 21:08:41 -07:00
27eeead350
Add typeclasses for (semi)lattices and order
2023-04-04 21:08:31 -07:00
