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This is an introduction to proof theory of nonclassical logic, which is directed at people who have just started the study of nonclassical logics, using proof-theoretic methods. In our paper, we willâ€¦ (More)

- Hendrik Pieter Barendregt, Martin W. Bunder, Wil Dekkers
- J. Symb. Log.
- 1993

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considersâ€¦ (More)

- Bruce Bates, Martin W. Bunder, Keith P. Tognetti
- Eur. J. Comb.
- 2010

Links between the Calkin-Wilif tree and the Stern-Brocot tree are discussed answering the questions: What is the jth vertex in the nth level of the Calkin-Wilf tree? A simple mechanism is describedâ€¦ (More)

- Bruce Bates, Martin W. Bunder, Keith P. Tognetti
- Eur. J. Comb.
- 2010

In this paper we discover an efficient method for answering two related questions involving the Sternâ€“Brocot tree: What is the jth term in the nth level of the tree? andWhat is the exact position ofâ€¦ (More)

- Wil Dekkers, Martin W. Bunder, Hendrik Pieter Barendregt
- Arch. Math. Log.
- 1998

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considersâ€¦ (More)

- Martin W. Bunder, Wil Dekkers
- J. Symb. Log.
- 2001

Pure Type Systems. PTSs, introduced as a generalisation of the type systems of Barendregt's lambda-cube, provide a foundation for actual proof assistants, aiming at the mechanic verification ofâ€¦ (More)

- Martin W. Bunder
- 1973

- Martin W. Bunder, Keith P. Tognetti, Glen E. Wheeler
- Discrete Mathematics
- 2008

The Binary Reflected Gray Code function b is defined as follows: If m is a nonnegative integer, then b(m) is the integer obtained when initial zeros are omitted from the binary reflected Gray code ofâ€¦ (More)

- Martin W. Bunder
- J. Symb. Log.
- 1990

A computer handles A-terms more easily if these are translated into combinatory terms. This translation process is called bracket abstraction. The simplest abstraction algorithm-the (fab) algorithmâ€¦ (More)

- Wil Dekkers, Martin W. Bunder, Hendrik Pieter Barendregt
- J. Symb. Log.
- 1998

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. In a precedingâ€¦ (More)