It is argued in this study that (i) progress in the philosophy ofmathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study ...

Teaching axiomatic mathematics on a computer bas traditionally involved the construction of derivations in a formal system. Heretofore theseforrnal systems have simply been adopted from mathematical logic. Such systems were designed, however, to make it easy to prove results about the system rather than to make it easy to prove results in the system. This paper describes a camputerprogram for t...

This chapter complements the chapters on technical reviews and software reliability engineering in Volume 1 of the handbook. It is primarily concerned with the veri cation of code by means of testing, but an example of an informal proof of a program is also given. A practitioner's view of testing is taken throughout, including an overview of how testing is done at Microsoft.

The evidence of the impact of informal care provision on the health of carers presents a complex and contested picture, depending on the characteristics of the care studied, including its duration, which has been relatively short in previous research (up to 4 years). Drawing on data from the Office for National Statistics Longitudinal Study, a 1% sample of linked Census records for respondents ...

Formal specification practice involve specifications which are finite. We study the concept of finiteness for specifications within the general framework of the so-called π-institutions, which constitute an abstract categorical proof oriented formalization of the informal concept of logical system. In this paper we argue that finite specifications can be captured abstractly by the concept of fi...

We present a detailed description of a machine-assisted veriication of an algorithm for self-stabilizing mutual exclusion that is due to Dijkstra Dij74]. This veriication was constructed using PVS. We compare the mechanical veriication to the informal proof sketch on which it is based. This comparison yields several observations regarding the challenges of formalizing and mechanically verifying...

We describe an implementation of a pointfree proof of the Alaoglu and the Hahn-Banach theorems in Type Theory. The proofs described here are formalisations of the proofs presented in \The Hahn-Banach Theorem in Type Theory" 4]. The implementation was partially developed simultaneously with 4] and it was a help in the development of the informal proofs.

In a call-by-value language with first-class continuations, the usual CBV fixpoint combinator can be expressed in terms of a simpler iteration primitive. We give an informal derivation of this correspondence, together with a formal correctness proof. We also present a number of generalizations and possible applications.

This paper presents the verification of a generational copying garbage collector for the CakeML runtime system. The proof is split into an algorithm proof and an implementation proof. The algorithm proof follows the structure of the informal intuition for the generational collector’s correctness, namely, a partial collection cycle in a generational collector is the same as running a full collec...

Logic of Proofs (LP) has been introduced in [2] as a collection of all valid formulas in the propositional language with labeled logical connectives [[t]]( ) where t is a proof term with the intended reading of [[t]]F as \t is a proof of F". LP is supplied with a natural axiom system, completeness and decidability theorems. LP may express some constructions of logic which have been formulated o...