Mathematical Aspects of Functional Programming

Functional languages, in which the programmer gives a more mathematical description of the problem to be solved, provide the basis for greater abstraction in software design. For the language implementor, these languages allow semantic analysis to be carried out in a mathematical context. The price for this abstraction is the need for the implementor to solve significantly more difficult problems, in type checking, pattern matching, optimization and garbage collection, than would be the case for traditional imperative languages. This talk will survey some of the mathematical structures and algorithms that underlie the analysis and implementation of functional programming languages.