DanilaFe/agda-spa
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Author SHA1 Message Date
Danila Fedorin
6039c1dfab Rename 'merge' to 'union' 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-30 15:18:09 -07:00
Danila Fedorin
d786e6bf48 Eschew proof-by-symmetry 2023-07-30 14:16:35 -07:00
Danila Fedorin
af0066eaa7 Rearrange a few functions 2023-07-30 13:49:38 -07:00
Danila Fedorin
eaee73236f More tweaks to naming and style 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-30 13:46:52 -07:00
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
77b8b6fad9 Finally prove the provenance properties of merge. 2023-07-26 20:58:41 -07:00
Danila Fedorin
461732244a Finish all in/not-in proofs. 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-26 20:40:28 -07:00
Danila Fedorin
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
Danila Fedorin
489b0532df Add intermediate state for insertion proofs 2023-07-25 22:58:42 -07:00
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
c9ab1152c4 Minor cleanup of Map module 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-25 00:10:57 -07:00
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
232bd65809 Add uniqueness preservation proof for merge 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-24 23:02:43 -07:00
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
f2e72b54ce Define unique as a data type to match stdlib All and Any 2023-07-23 21:34:24 -07:00
Danila Fedorin
d9c18fe483 Prove that maps are functional assuming uniqueness 2023-07-23 17:50:25 -07:00
Danila Fedorin
ab7ed2039a Add a generic Map module and prove its induced equivalence relation 2023-07-23 00:51:34 -07:00
Danila Fedorin
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
Danila Fedorin
971d75bb2b Parameterize by equivalence type 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-15 14:40:11 -07:00
Danila Fedorin
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
Danila Fedorin
7b993827bf Delete the unneeded <= relation from instances 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-15 12:18:50 -07:00
Danila Fedorin
09d2125aea Add note to self 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-14 22:45:17 -07:00
Danila Fedorin
cdca2528e9 Add a lattice instance for products 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-14 21:49:47 -07:00
Danila Fedorin
3b29ee0f74 Add a Semilattice isntance for Products. 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-14 21:20:16 -07:00
Danila Fedorin
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
Danila Fedorin
c9b514e9af Add a preorder instance for product 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-14 19:42:29 -07:00
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
422ea93edb Finish up the Nat semilattices 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-07-13 21:55:51 -07:00
Danila Fedorin
97a3f25fd2 [WIP] Start lattice and semilattice proofs for Nat 2023-04-06 23:08:49 -07:00
Danila Fedorin
8b805be9d3 Add a map from natural numbers for use as a lattice transformer 2023-04-04 21:08:41 -07:00
Danila Fedorin
27eeead350 Add typeclasses for (semi)lattices and order 2023-04-04 21:08:31 -07:00