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. A pure calculus of functional abstraction and function application, with applications throughout logic and computer science. 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 work was published in 1924 in a paper entitled On the building blocks of mathematical logic .