@TECHREPORT{Moggi88thepartial, author = {Eugenio Moggi}, title = {The Partial Lambda-Calculus}, institution = {}, year = {1988} }

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Abstract

This thesis investigates various formal systems for reasoning about partial functions or partial elements, with particular emphasis on lambda calculi for partial functions. Beeson's (intuitionistic) logic of partial terms (LPT) is taken as the basic formal system and some of its metamathematical properties are established (for later application). Three different flavours of Scott's logic of partial elements (LPE) are considered and it is shown that they are conservative extensions of LPT. This result, we argue, corroborates the choice of LPT as the basic formal system. Variants of LPT are introduced for reasoning about partial terms with a restriction operator (LPT + ¯), monotonic partial functions (monLPT), -terms ( p -calculus) and Y-terms ( p ¯Y-calculus). The expressive powers of some (in)equational fragments are compared in LPT and its variants. Two equational formal systems are related to some of the logics above: Obtulowicz's p-equational logic is related to LPT + ¯ and Plotkin...