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sync spec & code (#107)

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* sync spec & code

* move primitives (merkletree) into the backend

* comment on the ops spec and link to issue #108

* typo

* fix github-ci mdbook-publish pages
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book/src/operations.md
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@ -9,23 +9,37 @@ The following table summarises the natively-supported operations:
|------|-----------------------|---------------------|-----------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------|
| 0 | `None` | | | `None` |
| 1 | `NewEntry`[^newentry] | `(key, value)` | | `ValueOf(ak, value)`, where `ak` has key `key` and origin ID 1 |
| 2 | `EntryEq` | `s1`, `s2` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `value1 = value2` | `Eq(ak1, ak2)` |
| 3 | `SymmetricEq` | `s` | `s = Equal(ak1, ak2)` | `Eq(ak2, ak1)` |
| 4 | `TransitiveEq` | `s1`, `s2` | `s1 = Equal(ak1, ak2)`, `s2 = Equal(ak3, ak4)`, `ak2 = ak3` | `Eq(ak1, ak4)` |
| 5 | `EntryNEq` | `s1`, `s2` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `value1 != value2` | `NEq(ak1, ak2)` |
| 6 | `SymmetricNEq` | `s` | `s = NotEqual(ak1, ak2)` | `NEq(ak2, ak1)` |
| 7 | `GtToNEq` | `s` | `s = Gt(ak1, ak2)` | `NEq(ak1, ak2)` |
| 8 | `LEqToNEq` | `s` | `s = LEq(ak1, ak2)` | `NEq(ak1, ak2)` |
| 9 | `EntryGt` | `s1`, `s2` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `value1 > value2` | `Gt(ak1, ak2)` |
| 10 | `TransitiveGt` | `s1`, `s2` | `s1 = Gt(ak1, ak2)`, `s2 = Gt(ak3, ak4)`, `ak2 = ak3` | `Gt(ak1, ak4)` |
| 11 | `EntryLEq` | `s1`, `s2` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `value1 <= value2` | `LEq(ak1, ak2)` |
| 12 | `TransitiveLEq` | `s1`, `s2` | `s1 = LEq(ak1, ak2)`, `s2 = LEq(ak3, ak4)`, `ak2 = ak3` | `LEq(ak1, ak4)` |
| 13 | `EntryContains` | `s1`, `s2`, `proof` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `merkle_includes(value1, value2, proof) = true` | `Contains(ak1, ak2)` |
| 14 | `RenameContains` | `s1`, `s2` | `s1 = Contains(ak1, ak2)`, `s2 = Equal(ak3, ak4)`, `ak1 = ak3` | `Contains(ak4, ak2)` |
| 15 | `EntrySintains` | `s1`, `s2`, `proof` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `merkle_excludes(value1, value2, proof) = true` | `Sintains(ak1, ak2)` |
| 16 | `RenameSintains` | `s1`, `s2` | `s1 = Sintains(ak1, ak2)`, `s2 = Equal(ak3, ak4)`, `ak1 = ak3` | `Sintains(ak4, ak2)` |
| 17 | `SumOf` | `s1`, `s2`, `s3` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `s3 = ValueOf(ak3, value3)`, `value1 = value2 + value3` | `SumOf(ak1, ak2, ak3)` |
| 18 | `ProductOf` | `s1`, `s2`, `s3` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `s3 = ValueOf(ak3, value3)`, `value1 = value2 * value3` | `ProductOf(ak1, ak2, ak3)` |
| 19 | `MaxOf` | `s1`, `s2`, `s3` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `s3 = ValueOf(ak3, value3)`, `value1 = max(value2, value3)` | `MaxOf(ak1, ak2, ak3)` |
| 2 | `CopyStatement` | `s` | | |
| 3 | `EntryEq` | `s1`, `s2` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `value1 = value2` | `Eq(ak1, ak2)` |
| 4 | `EntryNEq` | `s1`, `s2` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `value1 != value2` | `NEq(ak1, ak2)` |
| 5 | `EntryGt` | `s1`, `s2` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `value1 > value2` | `Gt(ak1, ak2)` |
| 6 | `EntryLEq` | `s1`, `s2` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `value1 <= value2` | `LEq(ak1, ak2)` |
| 7 | `TransitiveEq` | `s1`, `s2` | `s1 = Equal(ak1, ak2)`, `s2 = Equal(ak3, ak4)`, `ak2 = ak3` | `Eq(ak1, ak4)` |
| 8 | `GtToNEq` | `s` | `s = Gt(ak1, ak2)` | `NEq(ak1, ak2)` |
| 9 | `LtToNEq` | `s` | `s = Lt(ak1, ak2)` | `NEq(ak1, ak2)` |
| 10 | `EntryContains` | `s1`, `s2`, `proof` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `merkle_includes(value1, value2, proof) = true` | `Contains(ak1, ak2)` |
| 11 | `EntrySintains` | `s1`, `s2`, `proof` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `merkle_excludes(value1, value2, proof) = true` | `Sintains(ak1, ak2)` |
| 12 | `RenameContains` | `s1`, `s2` | `s1 = Contains(ak1, ak2)`, `s2 = Equal(ak3, ak4)`, `ak1 = ak3` | `Contains(ak4, ak2)` |
| 13 | `SumOf` | `s1`, `s2`, `s3` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `s3 = ValueOf(ak3, value3)`, `value1 = value2 + value3` | `SumOf(ak1, ak2, ak3)` |
| 14 | `ProductOf` | `s1`, `s2`, `s3` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `s3 = ValueOf(ak3, value3)`, `value1 = value2 * value3` | `ProductOf(ak1, ak2, ak3)` |
| 15 | `MaxOf` | `s1`, `s2`, `s3` | `s1 = ValueOf(ak1, value1)`, `s2 = ValueOf(ak2, value2)`, `s3 = ValueOf(ak3, value3)`, `value1 = max(value2, value3)` | `MaxOf(ak1, ak2, ak3)` |
<!-- NOTE: should we 'uniformize' the names? eg. currently we have `EntryGt` and `GtToNEq` -->
<br><br>
<span style="color:green"><b>WIP</b>. The following table defines more operations that are not yet [implemented](https://github.com/0xPARC/pod2/blob/main/src/middleware/operation.rs#L20).<br>
Issue keeping track of the operations: [#108](https://github.com/0xPARC/pod2/issues/108).
</span><br>
| Code | Identifier | Args | Condition | Output |
|------|------------------|------------|----------------------------------------------------------------|----------------------|
| | `SymmetricEq` | `s` | `s = Equal(ak1, ak2)` | `Eq(ak2, ak1)` |
| | `SymmetricNEq` | `s` | `s = NotEqual(ak1, ak2)` | `NEq(ak2, ak1)` |
| | `RenameSintains` | `s1`, `s2` | `s1 = Sintains(ak1, ak2)`, `s2 = Equal(ak3, ak4)`, `ak1 = ak3` | `Sintains(ak4, ak2)` |
| | `TransitiveEq` | `s1`, `s2` | `s1 = Equal(ak1, ak2)`, `s2 = Equal(ak3, ak4)`, `ak2 = ak3` | `Eq(ak1, ak4)` |
| | `TransitiveGt` | `s1`, `s2` | `s1 = Gt(ak1, ak2)`, `s2 = Gt(ak3, ak4)`, `ak2 = ak3` | `Gt(ak1, ak4)` |
| | `TransitiveLEq` | `s1`, `s2` | `s1 = LEq(ak1, ak2)`, `s2 = LEq(ak3, ak4)`, `ak2 = ak3` | `LEq(ak1, ak4)` |
| | `LEqToNEq` | `s` | `s = LEq(ak1, ak2)` | `NEq(ak1, ak2)` |
[^newentry]: Since new key-value pairs are not constrained, this operation will have no arguments in-circuit.