Classical Proofs as Parallel Programs

Classical Proofs and Programs

Classical Proofs as Programs, Cut Elimination as Computation

We show that the SN and CR cut-elimination procedure on Gentzen-style classical logic LKT/LKQ, as presented in Danos et al.(1994), is isomorphic to call-by-name (CBN) and call-by-value (CBV) reduction system respectively. Our method is simple. We assign typed -terms on intuitionistic decoration of LKT/LKQ so as to simulate the cut-elimination procedure by -contraction | i.e. we simulate cutelim...

Simplifying Programs Extracted from Classical Proofs

Curry-Howard isomorphism extended to classical logic by associating the rule of double-negation elimination with the control operator C allows to view a natural deduction derivation of a Π2 formula as a program. However, programs produced by this method are often hard to understand, in part because of the presence of control operators. In this paper, we show how to simplify such programs and ma...

Proofs as Efficient Programs

There may, indeed, be other uses of the system than its use as a logic. Logic and theory of computation have been intertwined since their first days. The formalized notion(s) of effective computation are at first technical tools for the investigation of first order systems, and only ten years later – in the hands of John von Neumann – become the blueprints of engineered physical devices. Genera...

Programs as proofs

The Curry-Howard correspondence is about a relationship between types and programs on the one hand and propositions and proofs on the other. The implications for programming language design and program verification is an active field of research. Transformer-like semantics of internal definitions that combine a defining computation and an application will be presented. By specialisation for a g...