c1c34c69a5
Strengthen absorption laws
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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
d2faada90a
Add a left and right version of identity
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-07-11 15:43:27 +02:00
7fdbf0397d
Prove idempotence of value combining
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-07-05 16:57:24 -07:00
fdef8c0a60
Prove commutativity and associativity of value joining
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-07-05 16:49:38 -07:00
c48bd0272e
Define "less than or equal" for partial lattices and prove some properties
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-07-05 14:53:00 -07:00
d251915772
Show that lifted equality preserves equivalences
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-07-05 14:52:40 -07:00
da6e82d04b
Add helper definitions for partial commutativity, associativity, reflexivity
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-07-02 15:11:12 -05:00
dd101c6e9b
Start working on a general lattice builder framework
2025-06-29 10:35:37 -07:00
a611dd0f31
Add 'ExtendBelow' lattice, which adds new bottom to lattices
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-04-20 19:13:07 -07:00
33cc0f9fe9
Implement constant analysis
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-05 19:39:12 -08:00
9f2790c500
Actually force proof of 'analyze-correct'
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-05 19:39:12 -08:00
105321971f
Slightly help along implicit inference by moving binary less-than
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-05 19:39:12 -08:00
236c92a5ef
Add definitions about monotonicity to Lattice
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-05 19:39:12 -08:00
ca375976b7
Re-export members of isLattice together with the record where needed
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 22:43:13 -08:00
c0238fea25
Clean up how proofs of fixed height are imported
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 22:34:49 -08:00
1432dfa669
Clean up FiniteMap module structure a bit
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 22:28:47 -08:00
ffe9d193d9
Parameterize FiniteMap by its keys right away
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 22:19:02 -08:00
cf824dc744
Switch product to using instances
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 21:33:59 -08:00
70847d51db
Swich AboveBelow to using instances
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 21:23:07 -08:00
d96eb97b69
Switch maps (and consequently most of the code) to using instances
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 21:16:22 -08:00
d90b544436
Use binary operator for decidable equality consistently
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 19:08:28 -08:00
b0488c9cc6
Make 'IsDecidable' into a record to aid instance search
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 18:58:56 -08:00
8abf6f8670
Make 'isLattice' for simple types be an instance
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2025-01-04 17:27:38 -08:00
4da9b6d3cd
Fuse 'FiniteMap' and 'FiniteValueMap'
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-12-31 19:21:23 -08:00
c2c04e3ecd
Rewrite Forward analysis to use statement-based evaluators.
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To keep old (expression-based) analyses working, switch to using
instance search and provide "adapters" that auto-construct statement
analyzers from expression analyzers.
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-12-31 17:31:01 -08:00
f01df5af4b
Slightly tweak module style in Forward.agda
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-12-31 12:55:29 -08:00
b28994e1d2
Tighten exported definitions in Forward.agda
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-12-31 00:29:39 -08:00
10332351ea
Use instance search to avoid multiply-nested modules
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-12-31 00:21:10 -08:00
9131214880
Slightly clean up import for in-dec for Graph edges
2024-11-16 15:15:42 -08:00
4fba1fe79a
Remove unused 'singleton' calls for if/else CFGs
2024-11-16 14:42:16 -08:00
828b652d3b
Rename 'a' to 'b' in fixedpoint algorithm proof
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-08-18 10:28:45 -10:00
12971450e3
Add guardedness to Main directly
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-08-08 13:28:25 -07:00
7d2928ed81
Prove that the sign analysis is correct
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-10 22:31:47 -07:00
5f946de5e8
Remove last remaining assumption for correctness
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-10 21:30:56 -07:00
04bafb2d55
Prove that the inputs to wrap are empty
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-10 21:25:40 -07:00
e0248397b7
Prove that predecessors imply edges
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 23:18:51 -07:00
41ada43047
Move predecessor code into Graphs
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 23:13:49 -07:00
a081edb881
Add a proof about filter's distributivity
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 23:06:49 -07:00
3d2a507f2f
Almost prove correctness
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 22:49:53 -07:00
82027ecd04
Move predecessor computation into Graphs
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 21:26:32 -07:00
734e82ff6d
Wrap generated graphs to ensure entry and exit nodes have no extra edges
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 21:08:32 -07:00
69d1ecebae
Prove that the bottom map's valyes are all bottoms
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 20:48:32 -07:00
b78cb91f2a
Strengthen lemma about IterProd bottom to definition equality
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 20:20:11 -07:00
16fa4cd1d8
Use records rather than nested pairs to represent 'fixed height'
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 20:11:04 -07:00
95669b2c65
Prove that the iterated product is made from iterated bottom elements
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 19:45:15 -07:00
6857f60465
Rename the min/max elements top bottom and top in Prod
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 19:08:46 -07:00
f4392b32c0
Finish the last proof obligation for trace walking
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 19:01:36 -07:00
794c04eee9
Prove the foldr-implies lemma
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 18:37:50 -07:00
80069e76e6
Prove the recursive step of trace walking
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 17:56:47 -07:00
a22c0c9252
Prove a property of multi-key lookup
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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-05-09 17:56:26 -07:00
