Calculi for intuitionistic normal modal logic (2007)

by Y Kakutani
Venue:In Proceedings of Programming and Programming Languages
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Call-by-name and call-by-value in normal modal logic

by Yoshihiko Kakutani
"... Abstract. This paper provides a call-by-name and a call-by-value calculus, both of which have a Curry-Howard correspondence to the minimal normal logic K. The calculi are extensions of the λµ-calculi, and their semantics are given by CPS transformations into a calculus corresponding to the intuition ..."
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Abstract. This paper provides a call-by-name and a call-by-value calculus, both of which have a Curry-Howard correspondence to the minimal normal logic K. The calculi are extensions of the λµ-calculi, and their semantics are given by CPS transformations into a calculus corresponding to the intuitionistic fragment of K. The duality between call-by-name and call-by-value with modalities is investigated in our calculi. 1