The -calculus is good tool for exploring type systems, invaluable both in the foundations of mathematics and for practical programming languages. A further generalisation and systematic presentation of the class of type systems found in the -cube. Combinators Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The connections between the lambda-calculus and programming languages are diverse and pervasive.
Type systems are an important aspect of programming language design.
The -cube A graphical presentation of the relationship between combinatory logic, lambda calculi and related logical systems. My attempt to explain the fundamental ontological intuition on which modern mathematics is founded. HOST is my presently preferred pragmatic set theoretic foundation system . I have some notes on new classical logical foundation systems , including Pure Functions . Also some ancient writings with ontological discussions .