Module type Hasher.S

The type that is hashed.

hash_fold_t state x mixes the content of x into the state.

By default, all our hash_fold_t functions (derived or not) should satisfy the following properties.

1. hash_fold_t state x should mix all the information present in x in the state. That is, by default, hash_fold_t will traverse the full term x (this is a significant change for Hashtbl.hash which by default stops traversing the term after after considering a small number of "significant values"). hash_fold_t must not discard the state.

2. hash_fold_t must be compatible with the associated compare function: that is, for all x y and s, compare x y = 0 must imply hash_fold_t s x = hash_fold_t s y.

3. To avoid avoid systematic collisions, hash_fold_t should expand to different sequences of built-in mixing functions for different values of x. No such sequence is allowed to be a prefix of another.

A common mistake is to implement hash_fold_t of a collection by just folding all the elements. This makes the folding sequence of a be a prefix of a @ b, thereby violating the requirement. This creates large families of collisions: all of the following collections would hash the same:

      [[]; [1;2;3]]
      [[1]; [2;3]]
      [[1; 2]; [3]]
      [[1; 2; 3]; []]
      [[1]; [2]; []; [3];]
      ...

A good way to avoid this is to mix in the size of the collection to the beginning (fold ~init:(hash_fold_int state length) ~f:hash_fold_elem). The default in our libraries is to mix the length of the structure before folding. To prevent the aforementioned collisions, one should respect this ordering.