Commit Graph

203 Commits

Author SHA1 Message Date
7e5cc1b316 Add an 'iterated product' lattice for A x A ... x A x B.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-02-11 14:19:41 -08:00
33b7bc37f0 Add a 'FiniteHeightLattice' bundle
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-02-11 14:19:41 -08:00
6fe8dc2a02 Add an 'iterate' function to Utils
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-02-11 14:19:41 -08:00
ec31333e9a Add a 'Finite Map' lattice
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-02-11 14:19:41 -08:00
ad26d20274 Add facts about equal-key maps
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-02-11 12:45:43 -08:00
2b27e397b6 Add another utility proof
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-02-11 12:45:33 -08:00
d718338759 Clean up 'Map' to hide implementation details, extract code
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-02-10 16:51:43 -08:00
1b8c88b1a2 Expose only a 'public' "keys" function from Map
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-02-10 16:35:21 -08:00
a55c786a51 Tentatively start working on a language to analyze 2024-02-07 22:51:08 -08:00
512cd22be5 Fix definition of 'less than' to not involve a third variable.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-02-07 21:04:13 -08:00
9646096c75 Fix uses of 'absurd' in Fixedpoint.agda 2023-11-23 14:15:40 -08:00
bf74b35c14 Add proof of Lattice preservation
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-29 21:19:48 -07:00
7b24bae29a Start on the homomorphism / isomorphism proofs 2023-09-29 20:45:13 -07:00
3c346dcd15 Add a 'set' lattice backed by maps
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-23 17:12:12 -07:00
4a90a57388 Clean up imports a bit
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-23 16:39:11 -07:00
6cd37a212f Move the product instances into its own file
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-23 16:34:30 -07:00
8eaec3facd Provide a 'fixed height' predicate from Lattice for convenience
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-23 16:20:58 -07:00
dce21b3696 Moved the Nat lattice instance into an actual file
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-23 15:34:59 -07:00
5d54e62c3a Move the lattice etc. instances into Lattice.Map
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-23 15:08:04 -07:00
845a8a2236 Move the Map into Lattice/Map
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-23 15:06:43 -07:00
f27dec8904 Add proof of fixed-height chain
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-23 12:33:48 -07:00
fa7e2b5bb6 Add a proof that AboveBelow is a fixed-height lattice (phew!)
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-18 22:34:58 -07:00
c0db2ccd46 Add a lattice instance for the AboveBelow type
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-18 20:56:08 -07:00
d338241319 Add a meet operation, too
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-17 20:01:32 -07:00
03c0b12a3c Start formalizing the bottom/top lattice
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-17 19:50:21 -07:00
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
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
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
c338fa3ee5 Implement the fixed point algorithm
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-16 00:23:44 -07:00
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
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
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
fb86d3f84f Generalize chains to allow equivalences
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-09-03 21:05:57 -07:00
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
c9ec50c0ca Add a congruence requirement on Lattice. 2023-09-03 17:08:37 -07:00
eee814ae3c Add congruence for Map union and intersect 2023-09-03 16:57:56 -07:00
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
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
acf4a04814 Prove the chain mapping property
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-08-20 20:49:08 -07:00
561d0f343a Move < definition to Semilattice
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-08-20 19:57:26 -07:00
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
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
99cc5af243 Prove that Map equivalence is decidable
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-08-19 16:30:53 -07:00
3755a31bee Remove the starter files in NatMap
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-08-19 14:22:40 -07:00
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
c848f443e0 Add a lattice instance for Map
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-08-05 18:33:49 -07:00
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
dc405b989f Prove one absorption law
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-08-05 14:13:06 -07:00
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
d3e0db449c Prove semilattice properties for intersect
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-08-05 12:40:30 -07:00