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Unchecked Exceptions can be Strictly More Powerful than Call/CC
 HigherOrder and Symbolic Computation
, 1996
"... We demonstrate that in the context of staticallytyped purelyfunctional lambda calculi without recursion, unchecked exceptions (e.g., SML exceptions) can be strictly more powerful than call/cc. More precisely, we prove that a natural extension of the simplytyped lambda calculus with unchecked exce ..."
Abstract

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We demonstrate that in the context of staticallytyped purelyfunctional lambda calculi without recursion, unchecked exceptions (e.g., SML exceptions) can be strictly more powerful than call/cc. More precisely, we prove that a natural extension of the simplytyped lambda calculus with unchecked exceptions is strictly more powerful than all known sound extensions of Girard's Fomega (a superset of the simplytyped lambda calculus) with call/cc. This result is established by showing that the first language is Turing complete while the later languages permit only a subset of the recursive functions to be written. We show that our natural extension of the simplytyped lambda calculus with unchecked exceptions is Turing complete by reducing the untyped lambda calculus to it by means of a novel method for simulating recursive types using uncheckedexceptionreturning functions. The result concerning extensions of Fomega with call/cc stems from previous work of the author and Robert Harper.