We present the linear type theory λΠ⊸ &⊤ as the formal basis for LLF, a conservative
extension of the logical framework LF. LLF combines the expressive power of dependent …

The theory of cut-free sequent proofs has been used to motivate and justify the design of a
number of logic programming languages. Two such languages, λProlog and its linear logic …

Deductive systems, given via axioms and rules of inference, are a common conceptual tool
in mathematical logic and computer science. They are used to specify many varieties of …

For many given systems of logic, it is possible to identify, via systematic proof-theoretic
analyses, a fragment which can be used as a basis for a logic programming language. Such …

Logic programming can be given a foundation in sequent calculus by viewing computation
as the process of building a cut-free sequent proof bottom-up. The first accounts of logic …

We present new variants of known proofs of cut elimination for intuitionistic and classical
sequent calculi. In both cases the proofs proceed by three nested structural inductions …

We present the spine calculus S→⊸ &⊤ as an efficient representation for the linear λ-
calculus λ→⊸ &⊤ which includes unrestricted functions (→) linear functions (⊸) additive …

Proof theory is the area of mathematics which studies the concepts of mathematical proof
and mathematical provability [Bus98]. It is mainly concerned with the formal syntax of logical …

Modern programming languages such as Lisp, Scheme and ML permit procedures to be
encapsulated within data in such a way that they can subsequently be retrieved and used to …

Linear logical frameworks with subexponentials have been used for the specification of,
among other systems, proof systems, concurrent programming languages and linear …