Commit Graph

249 Commits

Author SHA1 Message Date
7e1f70210b Remove trailing space 2023-07-30 22:26:05 -07:00
77e2572157 Tweak the style of the Semilattice instance 2023-07-30 21:50:28 -07:00
1b7a3f02eb Add an instance of Semilattice for Map.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-30 20:36:19 -07:00
a4eaa6269f Prove idempotence 2023-07-30 20:11:02 -07:00
fceee34cee Finish associativity proof 2023-07-30 19:54:38 -07:00
eca6181494 List all the cases for the other direction 2023-07-30 19:25:46 -07:00
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
This should come in handy for the associativity proof.
2023-07-30 16:43:07 -07:00
6039c1dfab Rename 'merge' to 'union'
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
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.
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
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.
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.
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.
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
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
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-25 18:22:24 -07:00
c9ab1152c4 Minor cleanup of Map module
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
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
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
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-24 23:12:04 -07:00
232bd65809 Add uniqueness preservation proof for merge
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
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.
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.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-15 15:16:51 -07:00
971d75bb2b Parameterize by equivalence type
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
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-15 13:12:21 -07:00
7b993827bf Delete the unneeded <= relation from instances
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-15 12:18:50 -07:00
09d2125aea Add note to self
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 22:45:17 -07:00
cdca2528e9 Add a lattice instance for products
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 21:49:47 -07:00
3b29ee0f74 Add a Semilattice isntance for Products.
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
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-14 19:59:07 -07:00
c9b514e9af Add a preorder instance for product
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
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.
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.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-13 23:22:29 -07:00
422ea93edb Finish up the Nat semilattices
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