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Coinductive bigstep operational semantics
 In European Symposium on Programming (ESOP 2006
, 2006
"... Abstract. This paper illustrates the use of coinductive definitions and proofs in bigstep operational semantics, enabling the latter to describe diverging evaluations in addition to terminating evaluations. We show applications to proofs of type soundness and to proofs of semantic preservation for ..."
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Cited by 36 (6 self)
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Abstract. This paper illustrates the use of coinductive definitions and proofs in bigstep operational semantics, enabling the latter to describe diverging evaluations in addition to terminating evaluations. We show applications to proofs of type soundness and to proofs of semantic preservation for compilers. 1
Deciding Monadic Theories of Hyperalgebraic Trees
"... We show that the monadic secondorder theory of any infinite tree generated by a higherorder grammar of level 2 subject to a certain syntactic restriction is decidable. By this we extend the result of Courcelle [7] that the MSO theory of a tree generated by a grammar of level 1 (algebraic) is decid ..."
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Cited by 12 (4 self)
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We show that the monadic secondorder theory of any infinite tree generated by a higherorder grammar of level 2 subject to a certain syntactic restriction is decidable. By this we extend the result of Courcelle [7] that the MSO theory of a tree generated by a grammar of level 1 (algebraic) is decidable. To this end, we develop a technique of representing infinite trees by infinite lambda terms, in such a way that the MSO theory of a tree can be interpreted in the MSO theory of a lambda term.
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"... They first noticed that Gold’s limiting recursive functions which was originally introduced to formulate the learning processes of machines, serve as approximation algorithms. Here, Gold’s limiting recursive function is of the form $f(x) $ such that $f(x)=y \Leftrightarrow\exists t_{0}\forall t>t_{0 ..."
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They first noticed that Gold’s limiting recursive functions which was originally introduced to formulate the learning processes of machines, serve as approximation algorithms. Here, Gold’s limiting recursive function is of the form $f(x) $ such that $f(x)=y \Leftrightarrow\exists t_{0}\forall t>t_{0}.g(t,x)=y\Leftrightarrow\lim_{t}g(t, x)=y$, $t $ where $g(t, x) $ is called a guessing function, and is a limit variable. Then, they proved that some limiting recursive functions approximate arealizer of a semiclassical principle $\neg\neg\exists y\forall x.g(x, y)=0arrow\exists y\forall x.g(x, y)=0$. Also, they showed impressive usages of the semiclassical principle for mathematics and for software synthesis. In this way, NakataHayashi opened up the possibility that limiting operations provide readability interpretation of semiclassical logical systems. They formulated the set of the limiting recursive functions as a Basic Recursive hnction Theory(brft, for short. Wagner[19] and Strong[16]). Then NakataHayashi carried out their readability interpretation using the BRFT.
DOI: 10.1007/11693024_5 Coinductive bigstep operational semantics
"... Abstract. This paper illustrates the use of coinductive definitions and proofs in bigstep operational semantics, enabling the latter to describe diverging evaluations in addition to terminating evaluations. We show applications to proofs of type soundness and to proofs of semantic preservation for ..."
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Abstract. This paper illustrates the use of coinductive definitions and proofs in bigstep operational semantics, enabling the latter to describe diverging evaluations in addition to terminating evaluations. We show applications to proofs of type soundness and to proofs of semantic preservation for compilers. inria00289545, version 1 21 Jun 2008 1