Design and Implementation of Deterministic Higher-order Patterns

We introduce a class of deterministic higher-order patterns to Template Haskell for supporting declarative transformational programming with more elegant binding of pattern variables. Higher-order patterns are capable of checking and binding subtrees far from the root, which is useful for program manipulation. However, there are three major problems. First, it is difficult to explain why a particular desired matching result cannot be obtained because of the complicated higherorder matching algorithm. Second, the general higher-order matching algorithm is of high cost, which may be exponential time at worst. Third, the (possibly infinite) nondeterministic solutions of higher-order matching prevents it from being used in a functional setting. To resolve these problems, we impose reasonable restrictions on higher-order patterns to gain predictability, efficiency and determinism. We show that our deterministic higher-order patterns are powerful to support concise specification and efficient implementation of various kinds of program transformations for optimizations.