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278 Commits

Author SHA1 Message Date
Danila Fedorin e4f87175a0 Remove IsDecidable record in favor of a plain definition 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-17 19:43:24 -07:00
Danila Fedorin e3b8cc39f1 Put the fixed point algorithm code into its own file 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-16 13:39:35 -07:00
Danila Fedorin cbebe599b2 Prove that it's a least fixed point 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-16 13:07:31 -07:00
Danila Fedorin c338fa3ee5 Implement the fixed point algorithm 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-16 00:23:44 -07:00
Danila Fedorin 866bc9124a Add a lemma about chains of length h+1 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-16 00:23:30 -07:00
Danila Fedorin 266c3dd81e Prove that a finite height lattice is bounded below 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-15 21:07:14 -07:00
Danila Fedorin 5cab39ca82 Prove that AxB is a finite height semilattice 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-03 23:56:39 -07:00
Danila Fedorin fb86d3f84f Generalize chains to allow equivalences 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-03 21:05:57 -07:00
Danila Fedorin 67e96b27cf Add congruence instances for < and <= on semilattices 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-03 19:33:04 -07:00
Danila Fedorin c9ec50c0ca Add a congruence requirement on Lattice. 2023-09-03 17:08:37 -07:00
Danila Fedorin eee814ae3c Add congruence for Map union and intersect 2023-09-03 16:57:56 -07:00
Danila Fedorin 29fb828ee2 Extract the equivalence code into its own module 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-02 20:36:12 -07:00
Danila Fedorin b6292bf9bd Prove that a lattice of height h1+h2 exists for products 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-20 21:53:27 -07:00
Danila Fedorin acf4a04814 Prove the chain mapping property 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-20 20:49:08 -07:00
Danila Fedorin 561d0f343a Move < definition to Semilattice 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-20 19:57:26 -07:00
Danila Fedorin 421f187e8b Clean up the Lattice definitions a fair bit 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-20 19:02:47 -07:00
Danila Fedorin e62f429b86 Add instances for decidability and finite height lattices 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-20 18:35:57 -07:00
Danila Fedorin 99cc5af243 Prove that Map equivalence is decidable 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-19 16:30:53 -07:00
Danila Fedorin 3755a31bee Remove the starter files in NatMap 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-19 14:22:40 -07:00
Danila Fedorin 46c084d24c Add the beginnings of a formalization of chains 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-19 14:22:03 -07:00
Danila Fedorin c848f443e0 Add a lattice instance for Map 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-05 18:33:49 -07:00
Danila Fedorin 7b93654c4f Prove the second absorption law for maps 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-05 17:54:33 -07:00
Danila Fedorin dc405b989f Prove one absorption law 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-05 14:13:06 -07:00
Danila Fedorin 990a785463 Add a witness for Map being an intersect semilattice 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-05 12:48:44 -07:00
Danila Fedorin d3e0db449c Prove semilattice properties for intersect 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-05 12:40:30 -07:00
Danila Fedorin 12e76527cc Prove provenance for intersection 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-05 00:36:41 -07:00
Danila Fedorin 1780cdbda4 Add more properties of update(s) and start work on provenance 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-05 00:02:50 -07:00
Danila Fedorin 66dfe14207 Prove that restrict needs the key in both maps 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-04 00:07:10 -07:00
Danila Fedorin 56147cfc82 Implement map intersection 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-08-03 23:46:26 -07:00
Danila Fedorin 7e1f70210b Remove trailing space 2023-07-30 22:26:05 -07:00
Danila Fedorin 77e2572157 Tweak the style of the Semilattice instance 2023-07-30 21:50:28 -07:00
Danila Fedorin 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
Danila Fedorin a4eaa6269f Prove idempotence 2023-07-30 20:11:02 -07:00
Danila Fedorin fceee34cee Finish associativity proof 2023-07-30 19:54:38 -07:00
Danila Fedorin eca6181494 List all the cases for the other direction 2023-07-30 19:25:46 -07:00
Danila Fedorin 2c839db924 Prove associativity of maps (in one direction) 2023-07-30 19:09:16 -07:00
Danila Fedorin 1e4e8000cf Rename union-preserves to properly match what's being preserved 2023-07-30 17:57:06 -07:00
Danila Fedorin 70b85c99cc Rename the new provenance type and remove the old version 2023-07-30 16:45:02 -07:00
Danila Fedorin 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
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