Logic Programming Techniques: Automated Proof Search and Unification

This lecture introduces logic programming concepts, focusing on automated proof search techniques in LTAC, existential variables, and unification. The instructor begins by discussing the basic functionalities of LTAC for automatic proof search, highlighting the importance of existential variables in logic programming. The lecture progresses to the concept of unification, explaining how it plays a crucial role in logic programming and proof construction. The instructor provides examples of defining inductive relations, particularly the addition function, and demonstrates how to prove equivalences between different definitions. The lecture also covers advanced proof techniques, including the use of tactics like auto and eauto for simplifying proofs. The instructor emphasizes the significance of understanding the underlying principles of proof search and the application of tactics in Coq. Throughout the lecture, various examples are presented to illustrate the practical application of these concepts in logic programming, culminating in a discussion on synthesizing programs and evaluating expressions in Coq.