theoretical hash functions

// Hash functions:
int Hash(byte[] bytes);
int Hash_Add(int hash, byte add);
int Hash_Remove(int hash, byte remove);

// With variables:
byte[] x;
byte b;

// Where & is binary concat

// Such that:
Hash(x & b) == Hash_Add(Hash(x), b)
    // String example:
    Hash("abcd") == Hash_Add(Hash("abc"), "d")  // this is very normal for hash funtions

// AND such that:
Hash(x) == Hash_Remove(Hash(b & x), b) // notice the order of b and x
    // String example:
    Hash("bcd") == Hash_Remove(Hash("abcd"), "a")

// Also, order is important. I.e.
Hash(x & b) != Hash(b & x)