# Research Summary on Implementing Functional Patterns by Synthesizing Inverse Functions

In this research summary we present our recent work on implementing functional patterns with inverse functions in the lazy functional-logic programming language Curry. Our goal is the synthesis of the inverse of any given function in Curry itself. The setting of a functional-logic language especially allows the inversion of non-injective functions. In general, inverse computation is a non-trivial problem in lazy programming languages due to their non-strict semantics. We are so far able to directly derive the inverse function for a limited class of functions, namely those consisting of rules that do not involve both extra variables and non-linear right-hand sides. Because the synthesized definitions are based on standard code, known optimizations techniques can be applied to them. For all other functions we can still provide an inverse function by using non-strict unification.

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