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123 Commits

Author SHA1 Message Date
Danila Fedorin
d99d4a2893 [WIP] Demonstrate partial lattice construction 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 19:51:27 +02:00
Danila Fedorin
fbb98de40f Prove the other absorption law 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 19:26:03 +02:00
Danila Fedorin
706b593d1d Write a lemma to wrangle PartialAbsorb proofs 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 19:14:49 +02:00
Danila Fedorin
45606679f5 Prove one of the absorption laws 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 18:32:23 +02:00
Danila Fedorin
7e099a2561 Delete debugging code 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:18:31 +02:00
Danila Fedorin
2808759338 Add instances of semilattice proofs 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:18:19 +02:00
Danila Fedorin
42bb8f8792 Extend laws on Path' to Path versions 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:17:59 +02:00
Danila Fedorin
05e693594d Prove idempotence of meet and join 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:17:25 +02:00
Danila Fedorin
90e0046707 Prove missing congruence law 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:17:01 +02:00
Danila Fedorin
13eee93255 Remove whitespace errors 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 15:26:41 +02:00
Danila Fedorin
6243326665 Prove associativity of meet 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 15:21:59 +02:00
Danila Fedorin
7b2114cd0f Use a convenience function for creating the "greatest path" 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 15:21:43 +02:00
Danila Fedorin
36ae125e1e Prove associativity 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-22 18:05:08 +02:00
Danila Fedorin
6055a79e6a Prove a side lemma about nothing/just 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-22 18:04:53 +02:00
Danila Fedorin
01f7f678d3 Prove congruence of various operations 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-22 18:02:45 +02:00
Danila Fedorin
14f1494fc3 Provide a definition of partial congruence 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-22 18:01:48 +02:00
Danila Fedorin
d3bac2fe60 Switch to representing least/greatest with absorption 
It's more convenient this way to require non-partiality.

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-22 17:59:54 +02:00
Danila Fedorin
5705f256fd Prove some quasi-homomorphism properties 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-11 15:49:56 +02:00
Danila Fedorin
d59ae90cef Lock down more equivalence relation proofs 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-11 15:46:18 +02:00
Danila Fedorin
c1c34c69a5 Strengthen absorption laws 
If x \/ y is defined, x /\ (x \/ y) has to be defined,
too. Previously, we stated them in terms of
"if x /\ (x \/ y) is defined", which is not right.

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-11 15:44:29 +02:00
Danila Fedorin
d2faada90a Add a left and right version of identity 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-11 15:43:27 +02:00
Danila Fedorin
7fdbf0397d Prove idempotence of value combining 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-05 16:57:24 -07:00
Danila Fedorin
fdef8c0a60 Prove commutativity and associativity of value joining 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-05 16:49:38 -07:00
Danila Fedorin
c48bd0272e Define "less than or equal" for partial lattices and prove some properties 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-05 14:53:00 -07:00
Danila Fedorin
d251915772 Show that lifted equality preserves equivalences 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-05 14:52:40 -07:00
Danila Fedorin
da6e82d04b Add helper definitions for partial commutativity, associativity, reflexivity 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-02 15:11:12 -05:00
Danila Fedorin
dd101c6e9b Start working on a general lattice builder framework 2025-06-29 10:35:37 -07:00
Danila Fedorin
a611dd0f31 Add 'ExtendBelow' lattice, which adds new bottom to lattices 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-04-20 19:13:07 -07:00
Danila Fedorin
33cc0f9fe9 Implement constant analysis 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-05 19:39:12 -08:00
Danila Fedorin
ca375976b7 Re-export members of isLattice together with the record where needed 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 22:43:13 -08:00
Danila Fedorin
c0238fea25 Clean up how proofs of fixed height are imported 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 22:34:49 -08:00
Danila Fedorin
1432dfa669 Clean up FiniteMap module structure a bit 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 22:28:47 -08:00
Danila Fedorin
ffe9d193d9 Parameterize FiniteMap by its keys right away 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 22:19:02 -08:00
Danila Fedorin
cf824dc744 Switch product to using instances 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 21:33:59 -08:00
Danila Fedorin
70847d51db Swich AboveBelow to using instances 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 21:23:07 -08:00
Danila Fedorin
d96eb97b69 Switch maps (and consequently most of the code) to using instances 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 21:16:22 -08:00
Danila Fedorin
d90b544436 Use binary operator for decidable equality consistently 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 19:08:28 -08:00
Danila Fedorin
b0488c9cc6 Make 'IsDecidable' into a record to aid instance search 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 18:58:56 -08:00
Danila Fedorin
8abf6f8670 Make 'isLattice' for simple types be an instance 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-01-04 17:27:38 -08:00
Danila Fedorin
4da9b6d3cd Fuse 'FiniteMap' and 'FiniteValueMap' 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-12-31 19:21:23 -08:00
Danila Fedorin
69d1ecebae Prove that the bottom map's valyes are all bottoms 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-09 20:48:32 -07:00
Danila Fedorin
b78cb91f2a Strengthen lemma about IterProd bottom to definition equality 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-09 20:20:11 -07:00
Danila Fedorin
16fa4cd1d8 Use records rather than nested pairs to represent 'fixed height' 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-09 20:11:04 -07:00
Danila Fedorin
95669b2c65 Prove that the iterated product is made from iterated bottom elements 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-09 19:45:15 -07:00
Danila Fedorin
6857f60465 Rename the min/max elements top bottom and top in Prod 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-09 19:08:46 -07:00
Danila Fedorin
f4392b32c0 Finish the last proof obligation for trace walking 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-09 19:01:36 -07:00
Danila Fedorin
794c04eee9 Prove the foldr-implies lemma 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-09 18:37:50 -07:00
Danila Fedorin
a22c0c9252 Prove a property of multi-key lookup 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-09 17:56:26 -07:00
Danila Fedorin
cfa3375de5 Expose more functions from FiniteMap 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-08 20:50:05 -07:00
Danila Fedorin
6b116ed960 Forward some map function to Finite{,Value}Map 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-05-08 20:34:15 -07:00