1 Introduction Induction-recursion is a powerful definition method in intuitionistic type theory in the sense of Scott ("Constructive Validity") [31] and Martin-L"of [17, 18, 19]. The first occurrence of formal induction-recursion is Martin-L"of's definition of a universe `a la Tarski [19], which consists of a set U

Abstract. We introduce the Casl Consistency Checker (CCC), a tool that supports consistency proofs in the algebraic specification language Casl. CCC is a faithful implementation of a previously described consistency calculus. Its system architecture combines flexibility with correctness ensured by encapsulation in a type system. CCC offers tactics, tactical combinators, forward and backward proof, and a number of specialised static checkers, as well as a connection to the Casl proof tool HOL-Casl to discharge proof obligations. We demonstrate the viability of CCC by an extended example taken from the Casl standard library of basic datatypes. 1

. This paper describes the design of a meta-logical framework that supports the representation and verication of deductive systems which are prevalent in the areas of programming languages, type theory, and logics. It extends the logical framework LF [HHP93] by a meta-logic M + 2 whose soundness follows from a realizability argument. The metalogical framework is implemented in the Twelf system [PS99]. 1 Introduction The logical framework LF [HHP93] has been designed as a meta-language for representing deductive systems. It allows concise encodings of many inference systems, such as natural deduction, sequent calculi, type systems, operational semantics, compilers, etc. The logical framework derives its expressive power from dependent types together with higher-order representation techniques which directly support common concepts in deductive systems such as variable binding, capture-avoiding substitutions, parametric and hypothetical judgments and substitution properties. Th...

It is easy to imagine machines that can communicate using spoken natural language. Constructing such machines is more difficult. The available methods for development of interactive speech applications are costly, and current research is mainly focused on producing more sophisticated systems, rather than on making it easier to build them. This thesis describes how components used in interactive speech applications can be automatically derived from natural language grammars written in Grammatical Framework (GF). By using techniques borrowed from the field of programming language implementation, we can generate speech recognition language models, multimodal fusion and fission components, and support code for abstract syntax transformations. By automatically generating these components, we can reduce duplicated work, ensure consistency, make it easier to build multilingual systems, improve linguistic quality, enable re-use across system domains, and make systems more portable.