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6cd37a212f
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Move the product instances into its own file
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-23 16:34:30 -07:00 |
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8eaec3facd
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Provide a 'fixed height' predicate from Lattice for convenience
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-23 16:20:58 -07:00 |
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dce21b3696
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Moved the Nat lattice instance into an actual file
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-23 15:34:59 -07:00 |
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5d54e62c3a
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Move the lattice etc. instances into Lattice.Map
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-23 15:08:04 -07:00 |
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845a8a2236
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Move the Map into Lattice/Map
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-23 15:06:43 -07:00 |
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f27dec8904
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Add proof of fixed-height chain
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-23 12:33:48 -07:00 |
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fa7e2b5bb6
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Add a proof that AboveBelow is a fixed-height lattice (phew!)
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-18 22:34:58 -07:00 |
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c0db2ccd46
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Add a lattice instance for the AboveBelow type
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-18 20:56:08 -07:00 |
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d338241319
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Add a meet operation, too
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-17 20:01:32 -07:00 |
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03c0b12a3c
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Start formalizing the bottom/top lattice
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-17 19:50:21 -07:00 |
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e4f87175a0
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Remove IsDecidable record in favor of a plain definition
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-17 19:43:24 -07:00 |
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e3b8cc39f1
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Put the fixed point algorithm code into its own file
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-16 13:39:35 -07:00 |
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cbebe599b2
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Prove that it's a least fixed point
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-16 13:07:31 -07:00 |
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c338fa3ee5
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Implement the fixed point algorithm
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-16 00:23:44 -07:00 |
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866bc9124a
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Add a lemma about chains of length h+1
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-16 00:23:30 -07:00 |
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266c3dd81e
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Prove that a finite height lattice is bounded below
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-15 21:07:14 -07:00 |
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5cab39ca82
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Prove that AxB is a finite height semilattice
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-03 23:56:39 -07:00 |
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fb86d3f84f
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Generalize chains to allow equivalences
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-03 21:05:57 -07:00 |
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67e96b27cf
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Add congruence instances for < and <= on semilattices
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-03 19:33:04 -07:00 |
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c9ec50c0ca
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Add a congruence requirement on Lattice.
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2023-09-03 17:08:37 -07:00 |
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eee814ae3c
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Add congruence for Map union and intersect
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2023-09-03 16:57:56 -07:00 |
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29fb828ee2
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Extract the equivalence code into its own module
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-09-02 20:36:12 -07:00 |
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b6292bf9bd
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Prove that a lattice of height h1+h2 exists for products
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-20 21:53:27 -07:00 |
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acf4a04814
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Prove the chain mapping property
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-20 20:49:08 -07:00 |
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561d0f343a
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Move < definition to Semilattice
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-20 19:57:26 -07:00 |
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421f187e8b
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Clean up the Lattice definitions a fair bit
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-20 19:02:47 -07:00 |
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e62f429b86
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Add instances for decidability and finite height lattices
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-20 18:35:57 -07:00 |
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99cc5af243
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Prove that Map equivalence is decidable
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-19 16:30:53 -07:00 |
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3755a31bee
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Remove the starter files in NatMap
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-19 14:22:40 -07:00 |
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46c084d24c
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Add the beginnings of a formalization of chains
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-19 14:22:03 -07:00 |
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c848f443e0
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Add a lattice instance for Map
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-05 18:33:49 -07:00 |
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7b93654c4f
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Prove the second absorption law for maps
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-05 17:54:33 -07:00 |
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dc405b989f
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Prove one absorption law
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-05 14:13:06 -07:00 |
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990a785463
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Add a witness for Map being an intersect semilattice
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-05 12:48:44 -07:00 |
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d3e0db449c
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Prove semilattice properties for intersect
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-05 12:40:30 -07:00 |
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12e76527cc
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Prove provenance for intersection
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-05 00:36:41 -07:00 |
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1780cdbda4
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Add more properties of update(s) and start work on provenance
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-05 00:02:50 -07:00 |
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66dfe14207
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Prove that restrict needs the key in both maps
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-04 00:07:10 -07:00 |
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56147cfc82
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Implement map intersection
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-08-03 23:46:26 -07:00 |
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7e1f70210b
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Remove trailing space
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2023-07-30 22:26:05 -07:00 |
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77e2572157
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Tweak the style of the Semilattice instance
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2023-07-30 21:50:28 -07:00 |
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1b7a3f02eb
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Add an instance of Semilattice for Map.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-07-30 20:36:19 -07:00 |
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a4eaa6269f
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Prove idempotence
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2023-07-30 20:11:02 -07:00 |
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fceee34cee
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Finish associativity proof
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2023-07-30 19:54:38 -07:00 |
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eca6181494
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List all the cases for the other direction
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2023-07-30 19:25:46 -07:00 |
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2c839db924
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Prove associativity of maps (in one direction)
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2023-07-30 19:09:16 -07:00 |
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1e4e8000cf
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Rename union-preserves to properly match what's being preserved
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2023-07-30 17:57:06 -07:00 |
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70b85c99cc
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Rename the new provenance type and remove the old version
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2023-07-30 16:45:02 -07:00 |
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de2f202bdf
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Use an expression-based provenance to make enumerating cases easier
This should come in handy for the associativity proof.
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2023-07-30 16:43:07 -07:00 |
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6039c1dfab
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Rename 'merge' to 'union'
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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2023-07-30 15:18:09 -07:00 |
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