Commit Graph

252 Commits

Author SHA1 Message Date
ce3fa182fe Start formalizing monotonic function predicates
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-12 23:49:33 -07:00
71cb97ad8c Reorder some definitions
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-12 23:27:17 -07:00
57606636a7 Slightly format some code
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-12 23:22:31 -07:00
da2f7f51d7 Get Language typechecking again, finally
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-12 23:21:05 -07:00
2db11dcfc7 Use concatenation to represent adding new nodes
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-12 22:04:43 -07:00
3e2719d45f Turn old proof into a hole to clean up later.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-08 22:45:04 -07:00
78252b6c9e Add proof of node preservation for adding edges.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-08 22:43:07 -07:00
85fdf544b9 Translate informal proof of (node) transitivity into formal one.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-08 20:57:08 -07:00
4f14a7b765 Successfully prove that monotonic updates preserve existing indices
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-08 00:24:52 -07:00
bc5b4b7d9e Explicitly write metas for missing functions
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-08 00:16:10 -07:00
520b2b514c Clear up vector reindexing
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-08 00:12:50 -07:00
f7ac22257e Beat head against the vector-cast wall.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-07 23:44:35 -07:00
b72ad070ba Try using index-based comparisons
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-07 23:18:46 -07:00
195537fe15 Implement graph construction using <*>, map, and update.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-07 20:26:38 -07:00
d4b0796715 Intermediate commit. Switch to *-based definition of <=.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-07 19:51:59 -07:00
b505063771 Start working on proofs of Graph-related things
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-04-04 20:34:28 -07:00
844c99336a Intermediate commit: add while loops and start trying to formalize them. 2024-04-03 22:31:23 -07:00
5d56a7ce2d Fix comments in Forward.agda
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-23 12:09:14 -07:00
2e096bd64e Extract common parts of forward analyses into Forward.agda
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-22 17:50:29 -07:00
1a7b2a1736 Adjust behavior of eval to not require constant 'k in vars' threading
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-22 17:15:40 -07:00
f0da9a9020 Move more code out of Sign and into Main
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-11 13:07:42 -07:00
040c13caba Use instances to simplify printing code
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-11 12:50:05 -07:00
56da61b339 Delete the bundles since they did not turn out all that useful
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-11 12:14:53 -07:00
3e88a64ed9 Add some debugging code to sign analysis to print the results
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 22:23:45 -07:00
8a85c4497c Prove that evaluation is monotonic and complete sign analysis
Other than monotonicity of plus and minus, god damn it.

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 21:25:46 -07:00
8964ba59a1 Prove monotonicity of eval
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 20:29:05 -07:00
96f3ceaeb2 Use the previous join function directly in GeneralizedUpdate
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 19:41:02 -07:00
237250cf72 Stop using modules in 'Sign' analysis
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 19:23:48 -07:00
8515491327 Simplify AboveBelow a bit to avoid nested modules
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 18:43:10 -07:00
3305de4710 Remove need for explicit arguments in map derivatives
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 18:35:29 -07:00
f21ebdcf46 Start working on the evaluation operation.
Proving monotonicity is the main hurdle here.

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 18:13:01 -07:00
0705df708e Prove that variables in a program all come from the program's code
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 16:41:21 -07:00
51accb6438 Define 'minus', too -- with no monotonicity proof.
I'm still thinking about how this should be achieved most easily.

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 16:40:49 -07:00
afe5bac2dc Commit result of (unsuccessfully) trying to prove monotonicity of plus.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-10 13:54:19 -07:00
fdc40632bf Add a way to retrieve the code for a particular state
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 23:09:50 -08:00
f84a1c923c Prove that the 'join' transformation is monotonic
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 23:06:47 -08:00
1b1b80465c Use named modules to avoid having to pass redundant parameters
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 21:46:15 -08:00
56c72e1388 Delete unused homomorphism proof that was broken by an Agda update.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 14:07:56 -08:00
0c30f8be48 Start on sign analysis (mostly just imports)
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 14:00:10 -08:00
75f981cb75 Define simple sequential-only programs
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 13:59:48 -08:00
ca99e18184 Tweak exports from finite value bundle to avoid (some) redundant arguments
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 13:59:22 -08:00
702cf2c298 Expose more functionaity from the set lattice
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 13:58:40 -08:00
0c088ca2ae Prove multi-key access monotonicity in finite maps
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 13:58:07 -08:00
bc138d87f0 Prove things about key-based access in map
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 13:57:29 -08:00
311ed75186 Expose more helpers from 'Map'
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 13:57:02 -08:00
1ccc6f08e5 Add more properties of uniqueness
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-09 13:54:01 -08:00
332b7616cf Prove that foldr is monotonic when input lists are pairwise monotonic
This should help prove that "join" is monotonic

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-07 21:53:45 -08:00
7905d106e2 Tweak signature of 'forget' to simplify proofs
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-07 20:04:33 -08:00
34203840c8 Use the new provenance function to clean up some proofs
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-07 19:59:14 -08:00
48983c55b1 Prove exercise 4.26 from the textbook
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-06 00:35:29 -08:00