Advanced Programming Languages CS6110 Spring 2012 Lecture 1

Goals of the Course This course is designed to teach the elements of a mathematically rigorous semantics for programming languages.1 Based on this semantics it is possible to prove that certain programming languages behave according to precise mathematical rules if they are implemented properly. It is also possible to prove that compilers implementing these languages are correct [13] according to their mathematical semantics. On this basis, computer scientists can now prove that programs have predictable behavior and precise mathematical properties. The level of these languages ranges from C to Haskell and ML, but not all programming languages have a mathematical semantics; in this course we focus on those that do. Mathematical Semantics One of the main reasons that the topics covered in this course are considered valuable in graduate computer science education is that the material is a model for how we create software artifacts such as programming languages that are mathematical objects as well as useful tools.2 Computer science shares with physics this property that some elements of the subject are both useful tools for thought, such as physical theories, and mathematical objects as well. Computer science is also in the remarkable position tha