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Constructive LinearTime Temporal Logic: Proof Systems and Kripke Semantics
"... In this paper we study a version of constructive lineartime temporal logic (LTL) with the “next ” temporal operator. The logic is originally due to Davies, who has shown that the proof system of the logic corresponds to a type system for bindingtime analysis via the CurryHoward isomorphism. Howev ..."
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In this paper we study a version of constructive lineartime temporal logic (LTL) with the “next ” temporal operator. The logic is originally due to Davies, who has shown that the proof system of the logic corresponds to a type system for bindingtime analysis via the CurryHoward isomorphism. However, he did not investigate the logic itself in detail; he has proved only that the logic augmented with negation and classical reasoning is equivalent to (the “next ” fragment of) the standard formulation of classical lineartime temporal logic. We give natural deduction, sequent calculus and Hilbertstyle proof systems for constructive LTL with conjunction, disjunction and falsehood, and show that the sequent calculus enjoys cut elimination. Moreover, we also consider Kripke semantics and prove soundness and completeness. One distinguishing feature of this logic is that distributivity of the “next ” operator over disjunction “○(A ∨ B) ⊃ ○A ∨ ○B” is rejected in view of a typetheoretic interpretation. Key words: constructive lineartime temporal logic, Kripke semantics, sequent calculus, cut elimination 1.
Tracking DataFlow with Open Closure Types
 in "LPAR 19th International Conference Logic for Programming, Artificial Intelligence, and Reasoning
, 2013
"... Abstract. Type systems hide data that is captured by function closures in function types. In most cases this is a beneficial design that enables simplicity and compositionality. However, some applications require explicit information about the data that is captured in closures. This paper introduce ..."
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Abstract. Type systems hide data that is captured by function closures in function types. In most cases this is a beneficial design that enables simplicity and compositionality. However, some applications require explicit information about the data that is captured in closures. This paper introduces open closure types, that is, function types that are decorated with type contexts. They are used to track dataflow from the environment into the function closure. A simplytyped lambda calculus is used to study the properties of the type theory of open closure types. A distinctive feature of this type theory is that an open closure type of a function can vary in different type contexts. To present an application of the type theory, it is shown that a type derivation establishes a simple noninterference property in the sense of informationflow theory. A publicly available prototype implementation of the system can be used to experiment with type derivations for example programs.