DanilaFe/agda-spa
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Author SHA1 Message Date
Danila Fedorin
2a06e6ae2d Adjust 'to' to make it easier to reason about 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-25 12:17:19 -08:00
Danila Fedorin
671ffc82df Define to-and-from functions from finite maps to tuples and prove one inverse direction 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-19 14:50:29 -08:00
Danila Fedorin
486b552b59 Try to generalize universe levels where possible 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-19 12:36:46 -08:00
Danila Fedorin
aafcb2683d Prove the transport of 'height lattice' property given an isomorphism 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-18 23:26:41 -08:00
Danila Fedorin
8c9f39ac35 Add some additional 'equivalence' definitions to Equivalence 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-18 21:46:42 -08:00
Danila Fedorin
6384f7006e Make 'lattice' public 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-18 20:18:38 -08:00
Danila Fedorin
b1c6b4c99a Expose bundles from Unit 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 21:20:05 -08:00
Danila Fedorin
5420bb808e Expose bundles from 'Prod' 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 21:16:41 -08:00
Danila Fedorin
4c0860f4c7 Expose bundle form MapSet 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 21:14:49 -08:00
Danila Fedorin
e89418d600 Expose bundle form 'Map' 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 21:12:49 -08:00
Danila Fedorin
bfb32092c2 Expose bundles and apply so renames to IterProd 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 21:10:51 -08:00
Danila Fedorin
6e26aa1580 Add a bundle to FiniteMap 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 21:02:43 -08:00
Danila Fedorin
27f40bd42e Add bundles to 'AboveBelow' 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 21:00:28 -08:00
Danila Fedorin
08f3f49640 Rename some definitions in Nat and expose bundle 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 20:56:21 -08:00
Danila Fedorin
a920608bef Tweak IterProd to expose more (including a bundle) 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 20:45:14 -08:00
Danila Fedorin
45f2babfa3 Fix typo in FixedHeightLattice definition 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 15:37:00 -08:00
Danila Fedorin
16c4d13242 Prove that iterated products are finite height 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 15:36:12 -08:00
Danila Fedorin
0ba4b46e16 Add proof of decidable equivalence for products 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 15:35:50 -08:00
Danila Fedorin
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
Danila Fedorin
33b7bc37f0 Add a 'FiniteHeightLattice' bundle 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 14:19:41 -08:00
Danila Fedorin
6fe8dc2a02 Add an 'iterate' function to Utils 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 14:19:41 -08:00
Danila Fedorin
ec31333e9a Add a 'Finite Map' lattice 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 14:19:41 -08:00
Danila Fedorin
ad26d20274 Add facts about equal-key maps 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 12:45:43 -08:00
Danila Fedorin
2b27e397b6 Add another utility proof 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-02-11 12:45:33 -08:00
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
a55c786a51 Tentatively start working on a language to analyze 2024-02-07 22:51:08 -08:00
Danila Fedorin
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
Danila Fedorin
9646096c75 Fix uses of 'absurd' in Fixedpoint.agda 2023-11-23 14:15:40 -08:00
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