The tail-recursion modulo cons<\/i> transformation can rewrite functions that are not quite tail-recursive into a tail-recursive form that can be executed efficiently. In this article we generalize tail recursion modulo cons<\/i> (TRMc) to modulo contexts<\/i> (TRMC), and calculate a general TRMC algorithm from its specification. We can instantiate our general algorithm by providing an implementation of application and composition on abstract contexts, and showing that our context<\/i> laws_ hold. We provide some known instantiations of TRMC, namely modulo evaluation contexts<\/i> (CPS), and associative operations<\/i>, and further instantiantions not so commonly associated with TRMC, such as defunctionalized<\/i> evaluation contexts, monoids<\/i>, semirings<\/i>, exponents<\/i>, and cons products<\/i>. We study the modulo cons<\/i> instantiation in particular and prove that an instantiation using Minamide\u2019s hole calculus is sound. We also calculate a second instantiation in terms of the Perceus heap semantics to precisely reason about the soundness of in-place update. While all previous approaches to TRMc fail in the presence of non-linear control (for example induced by call\/cc, shift\/reset or algebraic effect handlers), we can elegantly extend the heap semantics to a hybrid approach which dynamically adapts to non-linear control flow. We have a full implementation of hybrid TRMc in the Koka language and our benchmark shows the TRMc transformed functions are always as fast or faster than using manual alternatives.<\/p>\n","protected":false},"excerpt":{"rendered":"
The tail-recursion modulo cons transformation can rewrite functions that are not quite tail-recursive into a tail-recursive form that can be executed efficiently. In this article we generalize tail recursion modulo cons (TRMc) to modulo contexts (TRMC), and calculate a general TRMC algorithm from its specification. We can instantiate our general algorithm by providing an implementation 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