ICFP

It is well known that there are problems associated with formal systems which attempt to combine higher order abstract syntax (HOAS) with principles of induction and recursion. We describe a formal system, called Bsyntax, which we have implemented in ...

In this paper we extend the model of program variables from the Refinement Calculus [2] in order to be able to reason more algebraically about recursive procedures with parameters and local variables. We extend the meaning of variable substitution or ...

We illustrate the benefits of using Natural Deduction in combination with weak Higher-Order Abstract Syntax for formalizing an object-based calculus with objects, cloning, method-update, types with subtyping, and side-effects, in inductive type theories ...

The task of designing and implementing a compiler can be a difficult and error-prone process. In this paper, we present a new approach based on the use of higher-order abstract syntax and term rewriting in a logical framework. All program ...

We have verified several versions of the CPS transformation in Isabelle/HOL. In our verification we adopted first-order abstract syntax with variable names so that the formalization is close to that of hand-written proofs and compilers. To simplify ...

We report on work in progress regarding a foundation for the notion of meta-variable in logical frameworks and type theories. Our proposal is to treat meta-variables as modal variables in a modal type theory, which is logically clean and justifies ...

We give a general category theoretic formulation of the approach to modelling variable binding first proposed by Fiore, Plotkin, and Turi. This general formulation allows us to include variable binding as they have it, as well as Tanaka's linear ...

Under the widely believed conjecture P≠NP, NP-complete problems cannot be solved exactly using efficient polynomial time algorithms. Furthermore, any instance of a NP-complete problem can be converted to an instance of another problem in NP in ...

Recently there has been a great deal of interest in higher-order syntax which seeks to extend standard initial algebra semantics to cover languages with variable binding by using functor categories. The canonical example studied in the literature is ...

We report on work in progress devoted to the formalization of an Ordered Logical Framework (OLF) [16] based on a two-levels architecture [10] in the Hybrid system [2]. OLF here is a second-order version of ordered linear logic to be used as a meta-...

I describe the mechanisation in HOL of some basic λ-calculus theory, using the axioms proposed by Gordon and Melham [4]. Using these as a foundation, I mechanised the proofs from Chapters 2 and 3 of Hankin [5] (equational theory and reduction theory), ...