Arity raising, also known as variable splitting or flattening, is the program optimization which transforms a function of one argument into a function of several arguments by decomposing the structure of the original one argument into individual components in that structure. This optimization eliminates the need for the structuring of the components and also allows more arguments to be passed in registers during a function call. We present a formal specification of arity raising for a higher-order functional language. This specification supports the general arity raising of functions, even for functions which are passed as arguments or returned as values. We define a practical algorithm, based on algorithm W, which implements arity raising, and we prove this algorithm sound with respect to the deductive system. These results provide a declarative framework for reasoning about arity raising and support a richer form of the transformation than is currently found in compilers for functional languages.

We present a formal specification of unCurrying for a higherorder, functional language with ML-style let-polymorphism. This specification supports the general unCurrying of functions, even for functions which are passed as arguments or returned as values. The specification also supports partial unCurrying of any consecutive parameters of a function, rather than only unCurrying all of a function's parameters. We present the specification as a deductive system which axiomatizes a judgment relating a source term with an unCurried form of the term. We prove that this system relates only typable terms and that it is correct with respect to an operational semantics. We define a practical algorithm, based on algorithm W, which implements the unCurrying and prove this algorithm sound and complete with respect to the deductive system. This algorithm generates maximally unCurried forms of source terms. These results provide a declarative framework for reasoning about unCurrying and support a richer form of unCurrying than is currently found in compilers for functional languages.

In this paper, we note and analyze a key trade-off: as the complexity of caches increases (higher set-associativity, larger block size, and larger overall size), the power consumed by a cache access increases.However, because the hit rate also increases, the number of main memory accesses decreases and thus the power consumed by a memory access decreases.Recent papers which consider the power consumption of caches tend to ignore hit rates.This is unfortunate, because it is undesirable to have energy-efficient caches which are also very slow.Hit rates also play a key role in truly evaluating the energy efficiency of a cache, because low hit rates lead to more frequent main memory accesses which consume more power than cache accesses.