Principles of Inverse Computation and the Universal Resolving Algorithm

Abstract

We survey fundamental concepts in inverse programming and present the Universal Resolving Algorithm (URA), an algorithm for inverse computation in a first-order, functional programming language. We discuss the principles behind the algorithm, including a three-step approach based on the notion of a perfect process tree, and demonstrate our implementation with several examples. We explain the idea of a semantics modifier for inverse computation which allows us to perform inverse computation in other programming languages via interpreters.On leave from DIKU,

Dual syntax for XML languages

“…Such work is only superficially similar to our work, since this alternative syntax is fixed while our is different for each application domain. Program inversion [1] attacks reversibility in a general context, but does not provide a solution to our particular problem.…”

Reversibility in the higher-order π-calculus

“…Bennett provides an account [1] of early research on the subject. A full review of works on reversible computing, and the closely related subjects of program inversion (see, e.g., [39] and the references therein) and bidirectional transformation and languages (see, e.g., [40,41] and the references therein), is out of the scope of this paper but we can highlight works related to our three main contributions: (i) reversible languages and models, (ii) causal semantics and back and forth bisimulation, (iii) translating between reversible and irreversible computations.…”

A Grammar-Based Approach to Invertible Programs

“…In this case, treating them as language constructs with predefined inverses helps us to invert programs that contains them. For example, consider mulPrime(x 1 , x 2 ) that multiplies two primes x 1 …”

“…Abramov and Glück [1] categorized inversion methods into program inversion and inverse computation. Program inversion takes a program and returns an inverse program while inverse computation takes a program and an output and computes the corresponding input.…”

“…Although it is possible to invert all the programs based on symbolic computation with search (e.g., [1]) as in logic programs, an inverse obtained this way could perform much worse than a handwritten inverse. Thus, an inversion method should restrict itself to a certain subclass of programs for which efficient inverses can be derived.…”