public ITerm Substitute(string variable, ITerm expression)
{
if (variable == Variable)
{
// (λ x . t)[x := r] = λ x . t
return this;
}
else
{
var free_variables = expression.GetFreeVariables();
if (free_variables.Contains(Variable))
{
// Need to do an α-conversion.
string t = Utilities.GetFreeVariable(Body.GetFreeVariables().Union(free_variables));
return new AbstractionTerm(t, Body.Substitute(Variable, new VariableTerm(t)).Substitute(variable, expression));
}
else
{
// (λ y . t)[x := r] = λ y . (t[x := r])
return new AbstractionTerm(Variable, Body.Substitute(variable, expression));
}
}
}
