Lambda Calculus with Explicit Recursion

AbstractThis paper is concerned with the study ofλ-calculus with explicit recursion, namely of cyclicλ-graphs. The starting point is to treat aλ-graph as a system of recursion equations involvingλ-terms and to manipulate such systems in an unrestricted manner, using equational logic, just as is possible for first-order term rewriting. Surprisingly, now the confluence property breaks down in an essential way. Confluence can be restored by introducing a restraining mechanism on the substitution operation. This leads to a family ofλ-graph calculi, which can be seen as an extension of the family ofλσ-calculi (λ-calculi with explicit substitution). While theλσ-calculi treat the let-construct as a first-class citizen, our calculi support the letrec, a feature that is essential to reason about time and space behavior of functional languages and also about compilation and optimizations of program

Functional encapsulation and type reconstruction in a strongly-typed, polymorphic language

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 181-186).by Shail Aditya Gupta.Ph.D

Properties of a First-order Functional Language with Sharing

A calculus and a model for a first-order functional language with sharing is presented. In most implementations of..