Superdeduction in Lambda-Bar-Mu-Mu-Tilde

Superdeduction in Lambda-Bar-Mu-Mu-Tilde

Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term language and a cut-elimination reduction already exist for superdeduction, both based on Christian Urban’s work on classical sequent calculus. However the compu...

Strong normalization of lambda-bar-mu-mu-tilde-calculus with explicit substitutions

Strong Normalization of lambda-mu-mu/tilde-Calculus with Explicit Substitutions

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Lambda and mu-symmetries

Symmetry analysis is a standard and powerful method in the analysis of differential equations, and in the determination of explicit solutions of nonlinear ones. It was remarked by Muriel and Romero [10] (see also the work by Pucci and Saccomandi [14]) that for ODEs the notion of symmetry can be somehow relaxed to that of lambda-symmetry (see below), still retaining the relevant properties for s...

Expressibility in the Lambda Calculus with Mu

We address a problem connected to the unfolding semantics of functional programming languages: give a useful characterization of those infinite λ-terms that are λletrec-expressible in the sense that they arise as infinite unfoldings of terms in λletrec, the λ-calculus with letrec. We provide two characterizations, using concepts we introduce for infinite λ-terms: regularity, strong regularity, ...