The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.

Starting from the analysis of the problem behind formal verification of programs and showing the need for automatic synthesis and analysis of computer programs, the book presents the logical systems to reason about programs, the way to encode specifications so to enable their computational reading. Then, the mathematics behind synthesis and analysis of computer programs is developed in depth.

The purpose of this book is to explore what a liturgical approach to the Bible looks like and what hermeneutical implications this might have: How does the liturgy celebrate, understand, and communicate Scripture? The starting point is Pope Benedict's affirmation that ""a faith-filled understanding of sacred Scripture must always refer back to the liturgy"" (Verbum Domini 52). The first part of the book (based on SC 24) provides significant examples to demonstrate: The liturgical order of readings intertextually combines Old Testament and New Testament readings using manifold hermeneutical principles, specifically how the psalms show the wide range of interpretations the liturgy employs. Prayers are biblically inspired and help to appropriate Scripture personally. The hymns convey Scripture in a poetic way. Signs and actions such as foot-washing or the Ephphetha rite enact Scripture. The study considers the Mass, the sacraments and the Liturgy of the Hours. In the second part, Benini systematically focuses on the various dimensions of liturgical hermeneutics of the Bible, which emerge from the first part. The study reflects the approaches the liturgy offers to Scripture and its liturgical reception. It explores theological aspects such as the unity of the two Testaments in Christ's paschal mystery or the anamnesis as a central category in both Scripture and liturgy. The liturgy does not understand Scripture primarily as a document of the past, but celebrates it as a current and living ""Word of the Lord,"" as a medium of encounter with God: Scripture is sacramental. Liturgical Hermeneutics of Sacred Scripture seeks to contribute not only to the comparison of the Roman, Ambrosian, and Byzantine Rite regarding the Word of God, but most of all to the overall ""liturgical approach"" to Scripture. As such, it promotes an interdisciplinary dialogue of liturgical and biblical studies.