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prototype with annotation concept
package generic
@concept{*
T has [ func * (T other) -> T
func unit -> T
func inverse -> T ],
"T should have methods *, unit, and inverse in order to be considered element of a Group",
axiom opTest: T a, T b, T c {%
if (a * (b * c) != (a * b) * c) ||
(c * (b * a) != (c * b) * a {
^"T is not associative"
}
^Nil
%},
axiom unitTest: T a, T b, T c {%
if (a * a unit != a unit * a) ||
(b * a unit != b unit * b) ||
(a unit * b unit != c unit * c unit) {
^"The unit element of T is not an identity"
}
^Nil
%},
axiom inverseTest: T a, T b, T c {%
if (a * a inverse != b unit) ||
(a unit != b inverse * b) ||
(c inverse * c != T unit) {
^"The inverse operation is not working properly"
}
^Nil
%}
*}
object GroupWork<T>
func work: T a, T b, T c {
assert (a inverse * a ) asInt == 0;
assert (a * a inverse) asInt == 0;
assert (a unit * b) == b && (a unit * b unit * c unit) == a unit;
assert ((c inverse * b inverse * a inverse) * a * b * c) asInt == 0;
assert ((c inverse * b inverse * a inverse) * a * b * c) == a unit;
assert ((c inverse * b inverse * a inverse) * a * b * c) asInt == 0;
assert ((c inverse * b inverse * a inverse) * a * b * c) == a unit;
/*
printexpr a asInt;
printexpr a inverse asInt;
printexpr a unit asInt;
printexpr (a * a inverse) asInt;
printexpr (a * a unit) asInt;
printexpr ((b inverse * a inverse) * a * b) asInt;
printexpr ((c inverse * b inverse * a inverse) * a * b * c) asInt;
printexpr (b inverse * b) asInt;
printexpr (c * b * a * ( a inverse * b inverse * c inverse )) asInt;
*/
}
func workout: T a, T b, T c {
/*
printexpr ((b inverse * a inverse) * a * b) asInt;
printexpr ((c inverse * b inverse * a inverse) * a * b * c) asInt;
printexpr (b inverse * b) asInt;
printexpr (c * b * a * ( a inverse * b inverse * c inverse )) asInt;
*/
let tunit = T unit;
assert c * b * a * ( a inverse * b inverse * c inverse ) == tunit;
assert a*(b*c) == (a*b)*c;
assert c*(b*a) == (c*b)*a;
}
end
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