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https://github.com/nadia-polikarpova/cyclegg
Cyclic theorem prover for equalitional reasoning using egraphs
https://github.com/nadia-polikarpova/cyclegg
Last synced: about 1 month ago
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Cyclic theorem prover for equalitional reasoning using egraphs
- Host: GitHub
- URL: https://github.com/nadia-polikarpova/cyclegg
- Owner: nadia-polikarpova
- Created: 2022-03-06T15:01:52.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2023-10-24T18:40:53.000Z (8 months ago)
- Last Synced: 2024-02-11T12:37:38.341Z (5 months ago)
- Language: Rust
- Size: 346 KB
- Stars: 22
- Watchers: 1
- Forks: 3
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Lists
- awesome-rust-formalized-reasoning - cyclegg - cyclic theorem prover for equational reasoning using egraph. (Projects / Provers and Solvers)
README
`cyclegg` is a theorem prover for equational reasoning.
It is based on the ideas from [CycleQ](https://github.com/ec-jones/cycleq)
but implements them on top of egraphs and equality saturation in order to avoid backtracking proof search.
To prove commutativity of addition, run:
```
cargo run -- examples/add.ceg
```
### TODO
#### Organizational
- Add flag for grounding
- Create goals inside parser, do not expose RawGoal
- Decouple proof generation from proof search (e.g. put Defs, Proof term somewhere else)
- Make partial applications without $ work
- Move from SymbolLang to a proper language.
- See babble for inspiration (https://github.com/dcao/babble/blob/main/src/ast_node.rs)
- Emit a proof data structure
- Right now we just emit strings that are (mostly) valid LiquidHaskell.
- Creating a proper equational proof data structure would allow us to emit to other backends.
- It would also be cleaner.
#### Search
- Canonical forms for termination checking:
- Grounding for cyclic mode: extend the domain of grounding_instantiations to include new vars; instantiate sides of all lemmas
- In cyclic mode: use multi-patterns instead of requiring that the premise has no extra vars?
- Blocking variables analysis
#### Proofs
- Conditional props proof generation
- Add explanation for conditional unions (cannot just `union_trusted`).
- Include the premise into the LH precondition
- This can be accomplished by taking a witness of the precondition as an argument.
- How to include the proof of the condition holding?
- To use a conditional lemma you need a witness of the condition. We can take the e-graph from
which we are getting the explanation and ask it to explain why the e-classes of the condition
are equal and use those to build a proof. In LH this would look something like
```haskell
let conditionWitness = condLHS
==. condLHS'
? lemma lemmaArgs
==. condRHS
*** QED
in conditionalLemma conditionWitness args
```
# Comparison to CycleQ
Results generated from a282086 using the command (prop52 removed because its
proof was made easier by a bug)
``` shell
cargo run --release -- examples/cycleq.ceg -t 10 --save-results
```
and compared to results from CycleQ.
All results come from runs on a Macbook Air M2.
N.B. We have cyclic proofs for prop_30 (49ms) and prop_73 (5364ms) but not with
uncyclegg but these are believed unsound.
N.B. The cyclegg timing is a little suspect (e.g. I time `prop_56` as taking
201ms instead of 5000 ms using cyclegg).
| Name | Cycleq result | Uncyclegg result | Cycleq time (ms) | Cyclegg time (ms) | Uncyclegg time (ms) |
| ------- | ---------------- | ------------- | ---------------- | ----------------- | ------------------- |
| prop_01 | Valid | Valid | 0.673 | 0.837… | 0.589… |
| prop_02 | Unknown | Valid | -1.000 | 7.748… | 1.684… |
| prop_03 | Unknown | Valid | -1.000 | 3.529… | 2.117… |
| prop_04 | Unknown | Valid | -1.000 | 3.090… | 1.654… |
| prop_06 | Valid | Valid | 0.134 | 0.202… | 0.142… |
| prop_07 | Valid | Valid | 0.210 | 0.191… | 0.142… |
| prop_08 | Valid | Valid | 1.270 | 0.237… | 0.166… |
| prop_09 | Valid | Valid | 0.641 | 0.783… | 0.350… |
| prop_10 | Valid | Valid | 0.079 | 0.141… | 0.108… |
| prop_11 | Valid | Valid | 0.014 | 0.029… | 0.025… |
| prop_12 | Valid | Valid | 1.007 | 0.504… | 0.343… |
| prop_13 | Valid | Valid | 0.047 | 0.034… | 0.029… |
| prop_14 | Unknown | Valid | -1.000 | 1.963… | 0.400… |
| prop_15 | Unknown | Valid | -1.000 | 2.072… | 1.029… |
| prop_17 | Valid | Valid | 0.051 | 0.151… | 0.120… |
| prop_18 | Valid | Valid | 0.163 | 0.170… | 0.126… |
| prop_19 | Valid | Valid | 0.847 | 0.480… | 0.333… |
| prop_21 | Valid | Valid | 0.143 | 0.170… | 0.123… |
| prop_22 | Valid | Valid | 1.591 | 1.110… | 0.593… |
| prop_23 | Valid | Valid | 1.104 | 0.422… | 0.212… |
| prop_24 | Valid | Valid | 1.445 | 1.146… | 0.442… |
| prop_25 | Valid | Valid | 0.640 | 0.716… | 0.430… |
| prop_28 | Unknown | Valid | -1.000 | 2.503… | 0.995… |
| prop_29 | Unknown | Valid | -1.000 | 4.213… | 2.262… |
| prop_31 | Valid | Valid | 1.352 | 1.210… | 0.586… |
| prop_32 | Valid | Valid | 1.071 | 0.452… | 0.202… |
| prop_33 | Valid | Valid | 0.427 | 0.417… | 0.271… |
| prop_34 | Valid | Valid | 0.709 | 0.524… | 0.351… |
| prop_35 | Valid | Valid | 0.059 | 0.319… | 0.126… |
| prop_36 | Valid | Valid | 0.188 | 0.332… | 0.125… |
| prop_37 | Unknown | Valid | -1.000 | 1.310… | 1.402… |
| prop_38 | Unknown | Valid | -1.000 | 6.999… | 1.343… |
| prop_39 | Unknown | Valid | -1.000 | 2.048… | 0.250… |
| prop_40 | Valid | Valid | 0.014 | 0.024… | 0.020… |
| prop_41 | Valid | Valid | 0.978 | 0.476… | 0.280… |
| prop_42 | Valid | Valid | 0.067 | 0.029… | 0.025… |
| prop_43 | Unknown | Valid | -1.000 | 0.593… | 0.306… |
| prop_44 | Valid | Valid | 0.193 | 0.552… | 0.420… |
| prop_45 | Valid | Valid | 0.101 | 0.032… | 0.027… |
| prop_46 | Valid | Valid | 0.020 | 0.021… | 0.018… |
| prop_49 | Valid | Valid | 231.569 | 2.492… | 1.021… |
| prop_50 | Valid | Valid | 21.207 | 0.796… | 0.425… |
| prop_51 | Valid | Valid | 1.855 | 0.453… | 0.459… |
| prop_55 | Valid | Valid | 1.516 | 0.631… | 0.381… |
| prop_56 | Valid | Valid | 1,615.585 | 5,194.048… | 12.648… |
| prop_57 | Valid | Valid | 35.090 | 3.122… | 4.161… |
| prop_58 | Valid | Valid | 3.633 | 0.910… | 0.651… |
| prop_61 | Valid | Valid | 163.463 | 2.073… | 0.874… |
| prop_64 | Valid | Valid | 0.660 | 0.413… | 0.393… |
| prop_67 | Valid | Valid | 1.045 | 0.653… | 0.366… |
| prop_75 | Unknown | Valid | -1.000 | 2,770.103… | 17.077… |
| prop_79 | Valid | Valid | 507.399 | 1.054… | 0.284… |
| prop_80 | Valid | Valid | 1.082 | 0.682… | 0.415… |
| prop_82 | Valid | Valid | 2.437 | 1.176… | 0.726… |
| prop_83 | Valid | Valid | 2.687 | 7.345… | 1.645… |
| prop_84 | Valid | Valid | 7.110 | 1.412… | 0.847… |
| prop_86 | Unknown | Valid | -1.000 | 0.768… | 0.219… |
| prop_87 | Unknown | Valid | -1.000 | 1.698… | 0.398… |
| prop_88 | Unknown | Valid | -1.000 | 1.157… | 0.405… |
| prop_89 | Unknown | Valid | -1.000 | 1.606… | 0.360… |
| prop_90 | Unknown | Valid | -1.000 | 0.630… | 0.312… |