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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 Edinburgh 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 system is based on such an interpretation of LF. We have considered whether a conventional… (More)

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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