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Applications of Game Semantics: From Program Analysis to Hardware Synthesis
"... After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design. 1. C ..."
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After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design. 1. Chronology, methodology, ideology Game Semantics is a denotational semantics in the conventional sense: for any term, it assigns a certain mathematical object as its meaning, which is constructed compositionally from the meanings of its subterms in a way that is independent of the operational semantics of the object language. What makes Game Semantics particular, peculiar maybe, is that the mathematical objects it operates with
Functional Reachability
"... Abstract—What is reachability in higherorder functional programs? We formulate reachability as a decision problem in the setting of the prototypical functional language PCF, and show that even in the recursionfree fragment generated from a finite base type, several versions of the reachability pro ..."
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Abstract—What is reachability in higherorder functional programs? We formulate reachability as a decision problem in the setting of the prototypical functional language PCF, and show that even in the recursionfree fragment generated from a finite base type, several versions of the reachability problem are undecidable from order 4 onwards, and several other versions are reducible to each other. We characterise a version of the reachability problem in terms of a new class of tree automata introduced by Stirling at FoSSaCS 2009, called Alternating Dependency Tree Automata (ADTA). As a corollary, we prove that the ADTA nonemptiness problem is undecidable, thus resolving an open problem raised by Stirling. However, by restricting to contexts constructible from a finite set of variable names, we show that the corresponding solution set of a given instance of the reachability problem is regular. Hence the relativised reachability problem is decidable. I.
Verification of HigherOrder Computation: A GameSemantic Approach
"... Abstract. We survey recent developments in an approach to the verification of higherorder computation based on game semantics. Higherorder recursion schemes are in essence (programs of) the simplytyped lambda calculus with recursion, generated from uninterpreted firstorder symbols. They are a hig ..."
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Abstract. We survey recent developments in an approach to the verification of higherorder computation based on game semantics. Higherorder recursion schemes are in essence (programs of) the simplytyped lambda calculus with recursion, generated from uninterpreted firstorder symbols. They are a highly expressive definitional device for infinite structures such as word languages and infinite ranked trees. As applications of a representation theory of innocent strategies based on traversals, we present a recent advance in the model checking of trees generated by recursion schemes, and the first machine characterization of recursion schemes (by a new variant class of higherorder pushdown automata called collapsible pushdown automata). We conclude with some speculative remarks about reachability checking of functional programs. A theme of the work is the fruitful interplay of ideas between the neighbouring fields of semantics and verification. Game semantics has emerged as a powerful paradigm for giving semantics
Evaluation is MSOL compatible
"... We consider simplytyped lambda calculus with fixpoint operators. Evaluation of a term gives as a result the Böhm tree of the term. We show that evaluation is compatible with monadic secondorder logic (MSOL). This means that for a fixed finite vocabulary of terms, the MSOL properties of Böhm trees ..."
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We consider simplytyped lambda calculus with fixpoint operators. Evaluation of a term gives as a result the Böhm tree of the term. We show that evaluation is compatible with monadic secondorder logic (MSOL). This means that for a fixed finite vocabulary of terms, the MSOL properties of Böhm trees of terms are effectively MSOL properties of terms themselves. Theorems of this kind have been known for some graph operations: unfolding, and Muchnik iteration. Similarly to those results, our main theorem has diverse applications. It can be used to show decidability results, to construct classes of graphs with decidable MSOL theory, or to obtain MSOL formulas expressing behavioral properties of terms. Another application is decidability of a controlflow synthesis problem. 1