3 Evaluation and Efficiency 2 3.1 Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Evaluation of Functional Programs . . . . . . . . . . . . . . . . . 2 3.2.1 Referential transparency . . . . . . . . . . . . . . . . . . . 3 3.2.2 Substitution model . . . . . . . . . . . . . . . . . . . . . . 3 3.2.3 Time and space complexity . . . . . . . . . . . . . . . . . 7 3.2.4 ...

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a recursively defined function: one is for its recursive calls and the other is for its calls outside its definition. Bimorphic recursion in this paper can be neste...

Scheduling transformations reorder operations in a program to improve locality and/or parallelism. There are mature loop transformation frameworks such as the polyhedral model for composing and applying instance-wise scheduling nests.In recent years, there have been efforts build nested recursion loops, but these cannot employ full power of nests since they overly-restrictive representations. T...

The termination of rewrite systems for parameter recursion, simple nested recursion and unnested multiple recursion is shown by using monotone interpretations both on the ordinals below the first primitive recursively closed ordinal and on the natural numbers. We show that the resulting derivation lengths are primitive recursive. As a corollary we obtain transparent and illuminating proofs of t...

We identify the Baker-Campbell-Hausdorff recursion driven by a weight λ=1 Rota-Baxter operator with Magnus expansion relative to post-Lie structure naturally associated corresponding algebra. Post-Lie and BCH-recursion are reviewed before proof of main result.