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Aard custom (#49)

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* Merge changes to docs

* Fix typo

* Correct SUMMARY so it compiles; update .gitignore

* Clean up statements.md

Make syntax and notation consistent with Rust source code.

* Fix statements for Merkle trees and compound types

* First draft of custom statements and small updates to signedpod.md

* Update book/src/merkletree.md

Co-authored-by: Ahmad Afuni <root@ahmadafuni.com>

* merklestatements correct typo

Co-authored-by: Ahmad Afuni <root@ahmadafuni.com>

* add todo for gadget ids

Co-authored-by: Ahmad Afuni <root@ahmadafuni.com>

* Separate out custom statements version 1

* More details on custom statements version 1

* new file custom2

* Partial draft of version 2

* First draft of version 2 spec, it's kind of a mess

* Another version of the custom predicates spec

* Update book/src/custom2.md

Co-authored-by: Eduard S. <eduardsanou@posteo.net>

* Simple example of deduction rule applied in circuit

* Implement Edu's comments on custom predicates

* Backend predicates must be defined in groups

* Add more examples

* Two diff statements using same constant

* Remove deprecated example

---------

Co-authored-by: Ahmad Afuni <root@ahmadafuni.com>
Co-authored-by: Eduard S. <eduardsanou@posteo.net>
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# Ethdos custom predicate, using binary AND and OR: example of a recursive group
```
eth_dos_distance(src_or, src_key, dst_or, dst_key, distance_or, distance_key) = or<
eth_dos_distance_ind_0(src_or, src_key, dst_or, dst_key, distance_or, distance_key),
eth_dos_distance_base(src_or, src_key, dst_or, dst_key, distance_or, distance_key)
>
eth_dos_distance_base(src_or, src_key, dst_or, dst_key, distance_or, distance_key) = and<
eq(src_or, src_key, dst_or, dst_key),
ValueOf(distance_or, distance_key, 0)
>
eth_dos_distance_ind_0(src_or, src_key, dst_or, dst_key, distance_or, distance_key) = and<
eth_dos_distance(src_or, src_key, intermed_or, intermed_key, shorter_distance_or, shorter_distance_key)
// distance == shorter_distance + 1
ValueOf(one_or, one_key, 1)
SumOf(distance_or, distance_key, shorter_distance_or, shorter_distance_key, one_or, one_key)
// intermed is a friend of dst
eth_friend(intermed_or, intermed_key, dst_or, dst_key)
>
```
This group includes three statements.
When the definition is serialized for hashing, the statements are renamed to SELF.1, SELF.2, SELF.3.
With this renaming and the wildcards, the first of the three definitions becomes:
```
SELF.1( *1, *2, *3, *4, *5, *6 ) = or<
SELF.2( *1, *2, *3, *4, *5, *6 ) ,
SELF.3( *1, *2, *3, *4, *5, *6 )
>
```
and similarly for the other two definitions.
The above definition is serialized in-circuit and hashed with a zk-friendly hash to generate the "group hash", a unique cryptographic identifier for the group.
Then the individual statements in the group are identified as:
```
eth_dos_distance = groupHASH.1
eth_dos_distance_base = groupHASH.2
eth_dos_distance_ind = groupHASH.3
```