A definition for finite sets in Agda
I am new to Agda.  I'm reading the paper "Dependent Types at Work" by Ana Bove and Peter Dybjer.  I don't understand the discussion of Finite Sets (on page 15 in my copy).

The paper defines a `Fin` type:

    data Fin : Nat -> Set where
        fzero : {n : Nat} -> Fin (succ n)
        fsucc : {n : Nat} -> Fin n -> Fin (succ n)


I must be missing something obvious.  I don't understand how this definition works.  Could someone simply translate the definition of `Fin` into everyday English?  That might be all I need to understand this part of the paper.

Thanks for taking the time to read my question.  I appreciate it.
A definition for finite sets in Agda
===

I am new to Agda.  I'm reading the paper "Dependent Types at Work" by Ana Bove and Peter Dybjer.  I don't understand the discussion of Finite Sets (on page 15 in my copy).

The paper defines a `Fin` type:

    data Fin : Nat -> Set where
        fzero : {n : Nat} -> Fin (succ n)
        fsucc : {n : Nat} -> Fin n -> Fin (succ n)


I must be missing something obvious.  I don't understand how this definition works.  Could someone simply translate the definition of `Fin` into everyday English?  That might be all I need to understand this part of the paper.

Thanks for taking the time to read my question.  I appreciate it.