private LambdaExpression Subst(LambdaExpression expr, Variable variable, LambdaExpression subst, HashSet <Variable> variables)
{
if (expr is Variable)
{
if (expr.Equals(variable))
{
return(Rename(variables, subst));
}
return(null);
}
if (expr is Abstraction)
{
var abstraction = expr as Abstraction;
if (variables.Contains(abstraction.Variable))
{
throw new Exception("Assert");
}
variables.Add(abstraction.Variable);
var r0 = Subst(abstraction.Expression, variable, subst, variables);
variables.Remove(abstraction.Variable);
if (r0 == null)
{
return(abstraction);
}
return(new Abstraction(abstraction.Variable, r0));
}
if (expr is Application)
{
var application = expr as Application;
var s0 = Subst(application.Left, variable, subst, variables);
var s1 = Subst(application.Right, variable, subst, variables);
if (s0 == null && s1 == null)
{
return(null);
}
return(new Application(s0 ?? application.Left, s1 ?? application.Right));
}
throw new NotImplementedException(expr.GetType().Name + " doesn't support subst");
}