Abst rac t . The Genericity Lemma is one of the most important motivations to take in the untyped lambda calculus the notion of solvability as a formal representation of the informal notion of undefinedness. We generalise solvability towards typed lambda calculi, and we call this generalisation: usability. We then prove the Genericity Lemma for un-usable terms. The technique of the proof is bas...

We describe a formalisation of proof theory about sequent-style calculi, based on informal work in DP96]. The formalisation uses de Bruijn nameless dummy variables (also called de Bruijn indices) dB72], and is performed within the proof assistant Coq BB + 96]. We also present a description of some of the other possible approaches to formal meta-theory, particularly an abstract named syntax and ...

A large number of published distributed deadlock detection/resolution algorithms are found to be incorrect because they have used informal approaches to prove the correctness of their algorithms. In this paper, we present a formal approach for the correctness proof and give an example of the proof. In this proposed approach, a formal model of distributed deadlock is presented with a local-time ...

This formalisation contains the proof that there is no anonymous and neutral Social Decision Scheme for at least four voters and alternatives that fulfils both SD-Efficiency and SD-Strategy-Proofness. The proof is a fully structured and quasi-human-redable one. It was derived from the (unstructured) SMT proof of the case for exactly four voters and alternatives by Brandl et al. [1]. Their proof...

In this work, we prove the lower bound ln(Hn)−ln( 5 3 ) for the partial sum of the Prime Harmonic series and, based on this, the divergence of the Prime Harmonic Series ∑n p=1[p prime] · 1 p . The proof relies on the unique squarefree decomposition of natural numbers. This proof is similar to Euler’s original proof (which was highly informal and morally questionable). Its advantage over proofs ...

The interaction between intuitions about inference, and the normative constraints that logical principles applied to mechanically-recognizable derivations impose on (informal) inference, is explored. These intuitions are evaluated in a clear testcase: informal mathematical proof. It is argued that formal derivations are not the source of our intuitions of validity, and indeed, neither is the se...

We describe some tools to support distributed cooperative design and validation of software systems. Workers at di erent sites can collaborate on tasks including speci cation, re nement, validation, veri cation, and documentation. A distributed database supports alternative and incomplete activities, and can be read using any web browser; remote proof execution, animation, and informal explanat...

We consider formal provability with structural induction and related proof principles in the λ-calculus seen as a (functional) programming language, i.e., presented with first-order abstract syntax over one-sorted variable names. Structural induction is the principal primitive proof principle of that particular syntactic framework and it is, indeed, near-ubiquitously employed in informal proofs...

Unlike computer algebra systems, automated theorem provers have not yet achieved considerable recognition and relevance in mathematical practice. A significant shortcoming of mathematical proof assistance systems is that they require the fully formal representation of mathematical content, whereas in mathematical practice an informal, natural-language-like representation where obvious parts are...