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The Suspension Calculus and its Relationship to Other Explicit Treatments of Substitution in Lambda Calculi
The intrinsic treatment of binding in the lambda calculus makes it an ideal
data structure for representing syntactic objects with binding such as
formulas, proofs, types, and programs. Supporting such a data structure in an
implementation is made difficult by the complexity of the substitution
operation relative to lambda terms. In this paper we present the suspension
calculus, an explicit treatment of meta level binding in the lambda calculus.
We prove properties of this calculus which make it a suitable replacement for
the lambda calculus in implementation. Finally, we compare the suspension
calculus with other explicit treatments of substitution.Comment: 84 page