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## 25 enum

```%--------------------------------------------------%
% vim: ft=mercury ts=4 sw=4 et
%--------------------------------------------------%
% Copyright (C) 2000, 2005-2006 The University of Melbourne.
% Copyright (C) 2014-2015, 2017-2018, 2022 The Mercury team.
%--------------------------------------------------%
%
% File: enum.m.
% Author: stayl.
% Stability: medium
%
% This module provides the typeclass enum, which describes types
% which can be converted to and from integers without loss of information.
%
%--------------------------------------------------%
%--------------------------------------------------%

:- module enum.
:- interface.

% A type T can be declared to be a member of the enum typeclass if
%
% - all values X of type T can be converted to an int N using
%   the instance's to_int member function, with each distinct X
%   being translated by to_int to a distinct N; and
%
% - for all values N of type int that are equal to to_int(X) for some X,
%   from_int(N) = X.
%
% - for all values N of type int that are not equal to to_int(X) for any X,
%   from_int(N) should fail.
%
% In mathematical notation, the following must hold:
%
%   all [X] (X = from_int(to_int(X)))
%   all [X, Y] (to_int(X) = to_int(Y)) => X = Y)
%   all [N] (some [X] N = to_int(X) => from_int(N) = X)
%   all [N] (not (some [X] N = to_int(X))) => from_int(N) fails
%
:- typeclass enum(T) where [
func to_int(T) = int,
func from_int(int) = T is semidet
].

% This is another version of the above typeclass, which maps
% values of type T to *unsigned* integers.
%
% The other difference is that the from_uint method is a semidet
% *predicate*, not a semidet *function*. This is because programmers
% are more likely to expect predicates to be able to fail than functions.
%
:- typeclass uenum(T) where [
func to_uint(T) = uint,
pred from_uint(uint::in, T::out) is semidet
].

% det_from_int(I) returns the result of from_int(I), but throws an
% exception if from_int fails.
%
:- func det_from_int(int) = T <= enum(T).
:- func det_from_uint(uint) = T <= uenum(T).

%--------------------------------------------------%
%--------------------------------------------------%

```

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