Focused Linear Logic and the λ-calculus

Focused Linear Logic and the λ-calculus

Linear logic enjoys strong symmetries inherited from classical logic while providing a constructive framework comparable to intuitionistic logic. However, the computational interpretation of sequent calculus presentations of linear logic remains problematic, mostly because of the many rule permutations allowed in the sequent calculus. We address this problem by providing a simple interpretation...

Linear-algebraic Λ-calculus

With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an interpreter/simulator) is provided for this language in the form of a term rewrite system. The linear-algebraic λ-calculus hereby constructed is linear in a different...

Jumping around the box: Graphical and operational studies on λ-calculus and Linear Logic

A Parigot-style Linear Λ-calculus for Full Intuitionistic Linear Logic

This paper describes a natural deduction formulation for Full Intuitionistic Linear Logic (FILL), an intriguing variation of multiplicative linear logic, due to Hyland and de Paiva. The system FILL resembles intuitionistic logic, in that all its connectives are independent, but resembles classical logic in that its sequent-calculus formulation has intrinsic multiple conclusions. From the intrin...

Models of λ-Calculus and the Weak MSO Logic∗

We study the Weak MSO logic in relationship to infinitary λ-calculus. We show that for every formula φ of Weak MSO there exists a finitary model of infinitary λ-calculus recognizing the set of infinitary λ-terms whose Böhm tree satisfies φ. The model is effective, in the sense that for every λY -term we can effectively compute its value in the model. In particular, given a finite λY -term, one ...