Partial functions in type theory
Notre Dame Journal of Formal Logic 33 (4):493-516 (1992)
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William M. Farmer (1995). Reasoning About Partial Functions with the Aid of a Computer. Erkenntnis 43 (3):279 - 294.
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William M. Farmer (1990). A Partial Functions Version of Church's Simple Theory of Types. Journal of Symbolic Logic 55 (3):1269-1291.
Erik Palmgren (1991). A Construction of Type: Type in Martin-Löf's Partial Type Theory with One Universe. Journal of Symbolic Logic 56 (3):1012-1015.
Paul Oppenheimer & Edward N. Zalta (2011). Relations Vs Functions at the Foundations of Logic: Type-Theoretic Considerations. Journal of Logic and Computation 21:351-374.
Pavel Naumov (2005). On Modal Logics of Partial Recursive Functions. Studia Logica 81 (3):295 - 309.
Gerard R. Renardel & de Lavalette (1984). Descriptions in Mathematical Logic. Studia Logica 43 (3).
Jaap van Oosten (2011). Partial Combinatory Algebras of Functions. Notre Dame Journal of Formal Logic 52 (4):431-448.
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