eq | is the equality predicate for comparing two group elements, in case representation is not canonical | (eq a a) (eq a b) → (eq b a) if (eq a b) then (if φ(a) then φ(b)) |

op | a function of type g×g→g
where g is the set of group values | (eq (op a (op b c)) (op (op a b) c)) (eq (op a b) (op b a)) |

I | is the group identity | (eq (op I a) a) (eq (op a I) a) |

G | is some generator of the group | |

inv | is the inverse of the operation | (eq (op x (inv x)) I) |

n | number of elements in group | nG = I |

`I` could be computed as `(((fileVal "expt") op #f #f) G n)` or `(op G (inv G))` but that seems unnecessary.
`n` could be computed as
`(let c ((N 0)(g G)) (if (eq g I) N (+ 1 (c (op G g))))` but then this would not qualify for the informal term “computational group”.

A good introduction to the original signature idea.