Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.Includes bibliographical references (p. 98-96).by Jakov Kuc̆an.Ph.D

Kuc̆an, Jakov

In this thesis we present two applications of using types of a typed lambda calculus to derive equation schemas, instances of which are provable by convertibility. Part 1: Retraction Approach to CPS transform: We study the continuation passing style (CPS) transform and its generalization, the computational transform, in which the notion of computation is generalized from continuation passing to an arbitrary one. To establish a relation between direct style and continuation passing style interpretation of sequential call-by-value programs, we prove the Retraction Theorem which says that a lambda term can be recovered from its continuationized form via a lambda-definable retraction. The Retraction Theorem is proved in the logic of computational lambda calculus for the simply typable terms. Part 2: Another look at &quot;Theorems for Free!&quot;: We reexamine Wadler&apos;s &quot;free theorems&quot; --- theorems about polymorphic functions derivable from the type of the function --- in an extension of Mairson&apos;s syntact..

Jakov Kucan

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Metatheorems about Convertibility in Typed Lambda Calculi: Applications to CPS transform and &quot;Free Theorems&quot;

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Metatheorems about convertibility in typed lambda calculi : applications to CPS transform and "free theorems"

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Metatheorems about convertibility in typed lambda calculi : applications to CPS transform and "free theorems"

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