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Focused proof systems provide means for reducing and struc-turing the non-determinism involved in searching for sequent calculus proofs. We present a focused proof system for a first-order logic with in-ductive and co-inductive definitions in which the introduction rules are partitioned into an asynchronous phase and a synchronous phase. These focused… (More)

Dependently typed λ-calculi such as the Logical Framework (LF) can encode relationships between terms in types and can naturally capture correspondences between formulas and their proofs. Such calculi can also be given a logic programming interpretation: the Twelf system is based on such an interpretation of LF. We consider here whether a conventional… (More)

- Zachary Snow
- ICLP
- 2010

Dependently typed λ-calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the " formulas-as-types " notion, such calculi can also encode the correspondence between formulas and their proofs in typing judgments. As such, these calculi provide a natural yet powerful means for specifying… (More)

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