In this work we present a theoretical model for differentiable programming. We construct an algebraic language that encapsulates formal semantics of differentiable programs by way of Operational ...

Abstract: We propose, and axiomatize, an extended version of the situation calculus [12] for temporal reasoning in a logic programming framework. This extended language provides for a linear temporal ...

Exercise 1.1. Implement logical or and and functions. Exercise 1.3. Implement times without using plus. Exercise 1.4. Define a term for raising one number to the power of another. Exercise 1.5. Define ...

For the last few lectures, we've been studing the semantics of IMP, a fairly simple imperative language we created because it roughly emulated what we think a "normal" language looks like—it has ...

Abstract: Sir Isaac Newton, one of the greatest scientists and mathematicians of all time, introduced the notion of a vector to define the existence of gravitational forces, the motion of the planets ...

At the end of Lecture 6 we tried our hand at "baking in" booleans into the lambda calculus, to try to ease the pain of writing everything using Church encodings. This seemed like a natural evolution ...

Want to model the progress of a disease over a month's time? Sure, just write a calculus equation that would model the statistics of the disease's progression for one ...