Dear colleagues,

Let me advertise talks given by our guests: Georg Struth on algebraic techniques in program analysis; and Bart Jacobs on categorical quantum logic. No registration is necessary; see you there!

Best regards, Ichiro Hasuo Group website: http://www-mmm.is.s.u-tokyo.ac.jp/

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Thu 29 May 2014, 16:30-18:00

Georg Struth (U. Sheffield), Build Your Own Program Analysis Tool

理学部7号館2階 214教室 Room 214, School of Science Bldg. No. 7

アクセス： https://www-mmm.is.s.u-tokyo.ac.jp/indexj.html （一番下） Access: http://www-mmm.is.s.u-tokyo.ac.jp/ (see bottom)

We present a principled way of designing program analysis tools within interactive proof assistants such as Coq or Isabelle; inparticular tools for the construction and verification of sequential and concurrent programs. We use algebras of programs to capture the control flow of programs and to derive Hoare-style inference rules, verification conditions, or transformation and refinement laws. We model their data flow by linking these algebras with denotational models of programs, including relations, predicate transformers, or sets of traces and by enriching these with notions of store and state, with data types, assignment and process interference.

This separation of concern makes the approach open, modular and highly automatic. Its implementation in Isabelle/HOL is particularly simple. It yields lightweight tools which are themselves correct by construction and can be combined with various programming languages and integrated into different formal methods.

We illustrate the approach through three examples: a verification tool for while programs based on Kleene algebra with tests, its extension to a Morgan-style program refinement tool, and a prototype for verifying and constructing shared variable concurrent programs based on a new variant of concurrent Kleene algebra. Time permitting, we

will outline how more powerful program analysis tools can be obtained from more expressive algebras.

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Mon 2 Jun 2014, 15:30-17:00

Bart Jacobs (Radboud U. Njimegen), Axiomatising categorical quantum logic

化学東館 236教室（理学部7号館の隣．ご存知ない方は先に理学部7号館415へお越しください） Room 236, Chemistry Building East (“Kagaku-Higashikan”). If not familiar come first to Rm 415, School of Science Bldg. No. 7

アクセス： https://www-mmm.is.s.u-tokyo.ac.jp/indexj.html （一番下） Access: http://www-mmm.is.s.u-tokyo.ac.jp/ (see bottom)

This talk describes several assumptions on a category that together yield a proposal for a categorical structure for quantum logic. The assumptions and consequences describe the differences and similarities between classical, probabilistic, and quantum logic. The leading examples are the category Sets, the Kleisli category of the distribution monad, and the opposite of the category of C*-algebras and (completely) positive unital maps.