We present a formulae-as-types interpretation of Subtractive Logic (i.e. bi-intuitionistic logic). This presentation is two-fold: we first define a very natural restriction of the λµ-calculus which is closed under reduction and whose type system is a constructive restriction of the Classical Natural Deduction. Then we extend this deduction system conservatively to Subtractive Logic. From a computational standpoint, the resulting calculus provides a type system for first-class coroutines (a restricted form of first-class continuations). Keywords: Curry-Howard isomorphism, Subtractive Logic, control operators, coroutines. 1

We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e. in presence of all the usual connectives) classical natural deduction. 1

symmetric λµ-calculus

this paper, we introduce two natural deduction systems NJ c=t and NK c=t . NJ c=t is an extension of the intuitionistic natural deduction system NJ with the catch and the throw rules, and NK c=t is an extension of the classical natural deduction system

The catch/throw mechanism in Common Lisp gives a simple control structure for non-local exits. Nakano[7, 9] and Sato[13] proposed intuitionistic calculi with inference rules which give logical interpretations of the catch/throw-constructs. Although the calculi are theoretically well-founded, we cannot use the catch/throw mechanism for handling run-time errors in a meaningful way, because of the side-condition of the implication-introduction rule (the formulation rule of the -abstract). This deficiency is critical if we use higher-order functions with the catch/throw mechanism. In this paper, we propose a new formulation of catch/throw calculi, which has no side-condition on the implication-introduction rule. By restricting the types of thrown terms to data types (non-functional types) instead, we obtain a strongly normalizing calculus for the catch/throw mechanism where we can write higher-order functions which handles run-time errors. 1. Introduction Recently, control st...

We demonstrate that in the context of statically-typed purely-functional lambda calculi without recursion, unchecked exceptions (e.g., SML exceptions) can be strictly more powerful than call/cc. More precisely, we prove that a natural extension of the simply-typed lambda calculus with unchecked exceptions is strictly more powerful than all known sound extensions of Girard's F-omega (a superset of the simply-typed lambda calculus) with call/cc. This result is established by showing that the first language is Turing complete while the later languages permit only a subset of the recursive functions to be written. We show that our natural extension of the simply-typed lambda calculus with unchecked exceptions is Turing complete by reducing the untyped lambda calculus to it by means of a novel method for simulating recursive types using unchecked-exception-returning functions. The result concerning extensions of F-omega with call/cc stems from previous work of the author and Robert Harper.

We define a very natural restriction of the λµ-calculus which is stable under reduction and whose type system is a restriction of the Classical Natural Deduction to intuitionistic logic. However, we show that this system is in some sense degenerated unless we provide a native disjunction. We prove that the system with native disjunction is conservative over DIS-logic and also that DIS-logic is constructive. From a computational standpoint, this restriction on λµ-terms prevents a coroutine from accessing the local environment of another coroutine.

s from the Third Workshop Flemming Nielson (editor) October 1993 1 Introduction The third DART workshop took place on Thursday August l9th and Friday August 20th at the Department of Computer Science (DIKU) at the University of Copenhagen; it was organized by Mads Rosendahl and others at DIKU, and Torben Amtoft and Susanne Brønberg helped producing this report. The first day comprised survey presentations whereas the second contained more research oriented talks. The primary aim of the workshop was to increase the awareness of DART participants for each other's work, to stimulate collaboration between the di#erent groups, and to inform Danish industry about the skills possessed by the groups. The DART project started in March 1991 (prematurely terminating a smaller project on Formal Implementation, Transformation and Analysis of Programs) and is funded by the Danish Research Councils as part of the Danish Research Programme on Informatics. To date it has received about 8 million Danis...

a canonical classical natural deduction system

Abstract not found