func Test1(t *testing.T) {
//Test $a \cdot b \cdot b^{-1} \cdot c = a\cdot c$
a, b, c := gt.NewNamed("a"), gt.NewNamed("b"), gt.NewNamed("c")
d := gt.Compose(a, gt.Compose(b, gt.Compose(gt.Inverse(b), c)))
h := gt.Compose(a, c)
id := func(a gt.Element) gt.Element { return a }
proofForth := func(x gt.Element) gt.Element {
return x.ToComposite().Map(id, func(el gt.Element) gt.Element {
y := el.ToComposite().Associate()
return y.Map(func(el gt.Element) gt.Element {
return el.ToComposite().Annihilate()
}, id).Simplify()
})
}
v := gt.VerifyForth(d, h, proofForth)
if !v {
t.Fatal("proofForth is not verified")
}
}
func Test2(t *testing.T) {
a, b := gt.NewNamed("a"), gt.NewNamed("b")
d := gt.Compose(a, b)
//Try to cheat verifier:
proofForth := func(x gt.Element) gt.Element {
return x.ToComposite().Left()
}
v := gt.VerifyForth(d, a, proofForth)
if v {
t.Fatal("proofForth is verified although it is not a proof")
}
}