CLICS II addresses the following key issues in the area of the unification of formalisms:
- Modularity: A key issue in the applicability of formalisms to large-scale examples is the ability to structure theories so as to be able to reuse components
- Simplicity: The high level of expertise required is a barrier to the wide-spread use of formal methods. Internal logic provides a potentially very attractive approach, ie that one sets up a theory within some convenient "universe" (such as aa topos), in such a way that much of the mathematical infrastructure of the theory is absorbed into the setting, so that a "user" of the theory can take a very naive view of it
- Statics vs. Dynamics: Traditionally, a sharp distinction has been drawn between the dichotomies denotational / operational, declarative / procedural and logical / computational. A number of recent developments give rise to new ideas for finding a middle ground between these dichotomies; namely, a logical and geometric perspective on the dynamics of computation. This promises a number of exciting applications: deeper structural insights into execution paradigms, leading ultimately to improved architectures; extending useful type disciplines from functional languages to the concurrent process paradigm; extracting computational content from apparently non-constructive reasoning; and developing new geometrical paradigms for symbolic computation.
APPROACH AND METHODS
CLICS II aims to make decisive progress in four main areas: domain theory, semantics and logics of programming languages, concurrency and linear logic, and type theory and constructive mathematics. The cooperation between partners will be organised around a number of specialised workshops focusing on specific themes: sequentiality and stability, duality in domain theory, logic of inductive and recursive datatypes, subtypes and polymorphism in higher-order languages, higher order modal program logics, monadic programming language semantics, applied linear logic, computational content of classical logic, symbolic computation. Each theme addresses issues that span across several or all the main objectives of the project.
The new formalisms and logic systems which result from the project should contribute to future developments in high-level programming language design and in mechanised checking or derivation of proofs of correctness of computer systems. The main potential for exploitation will lie in the fundamental insights and methods made available for more applied work.
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