DanilaFe/agda-spa
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107 Commits

Author SHA1 Message Date
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
Danila Fedorin
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
Danila Fedorin
040c13caba Use instances to simplify printing code 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-03-11 12:50:05 -07:00
Danila Fedorin
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
Danila Fedorin
8964ba59a1 Prove monotonicity of eval 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-03-10 20:29:05 -07:00
Danila Fedorin
237250cf72 Stop using modules in 'Sign' analysis 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-03-10 19:23:48 -07:00
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
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
Danila Fedorin
311ed75186 Expose more helpers from 'Map' 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2024-03-09 13:57:02 -08:00