CHURCH'S TYPES IN LOGICAL REASONING ON PROGRAMMING

SUMMARY In our previous paper [1] of this series we defined the basic types as the startpoint of scientific problem solving by help of logically and mathematically founded programming of mathematical machines. In this paper we extend the type system with Church’s types that enable the first step of problem solving during logical reasoning.

[1]  Bart Jacobs,et al.  Categorical Logic and Type Theory , 2001, Studies in logic and the foundations of mathematics.

[2]  Valerie Novitzká LOGICAL REASONING ABOUT PROGRAMMING OF MATHEMATICAL MACHINES , 2005 .

[3]  J. Roger Hindley,et al.  Introduction to combinators and λ-calculus , 1986, Acta Applicandae Mathematicae.

[4]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[5]  Claudio Hermida,et al.  Fibrations, logical predicates and indeterminates , 1993, CST.

[6]  J. Girard,et al.  Proofs and types , 1989 .