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right so um this is totally a work in progress talk um a piece of material so um please ask questions give me the ideas how to take it further so whats this about the idea here is um data types or inductive data types especially independently languages are absolutely wonderful so heres a simple example weve got uh the data type of natural numbers and its defined by zero and success and then if we have dependent types or inductive families we can uh do interesting things like talk about properties of those values uh by defining other inductively defined things very simple one were going to find the even numbers to be a corrupt collection or property of natural numbers where we say that zero is even and we say that uh the successor of a number is even if the predecessor is on so we have mutually definedness with this auxiliary odd um as well which says that if a number is even then what if we could use negation in our data types what if we could say instead of saying defining this s