DanilaFe/agda-spa
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Author SHA1 Message Date
Danila Fedorin
bf74b35c14 Add proof of Lattice preservation 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-29 21:19:48 -07:00
Danila Fedorin
7b24bae29a Start on the homomorphism / isomorphism proofs 2023-09-29 20:45:13 -07:00
Danila Fedorin
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
Danila Fedorin
4a90a57388 Clean up imports a bit 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-23 16:39:11 -07:00
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
845a8a2236 Move the Map into Lattice/Map 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-23 15:06:43 -07:00
Danila Fedorin
f27dec8904 Add proof of fixed-height chain 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-23 12:33:48 -07:00
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
d338241319 Add a meet operation, too 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-17 20:01:32 -07:00
Danila Fedorin
03c0b12a3c Start formalizing the bottom/top lattice 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2023-09-17 19:50:21 -07:00
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