PEPM '91 Proceedings of the 1991 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
How to prove equivalence of term rewriting systems without induction
Theoretical Computer Science
Undecidable properties of deterministic top-down tree transducers
Theoretical Computer Science
Term rewriting and all that
Journal of Symbolic Computation
Advanced topics in term rewriting
Advanced topics in term rewriting
Unravelings and Ultra-properties
ALP '96 Proceedings of the 5th International Conference on Algebraic and Logic Programming
Operational termination of conditional term rewriting systems
Information Processing Letters
A Method for Automatic Program Inversion Based on LR(0) Parsing
Fundamenta Informaticae - Program Transformation: Theoretical Foundations and Basic Techniques. Part 1
Bidirectionalization transformation based on automatic derivation of view complement functions
ICFP '07 Proceedings of the 12th ACM SIGPLAN international conference on Functional programming
Semi-inversion of functional parameters
PEPM '08 Proceedings of the 2008 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Automatic partial inversion of inductively sequential functions
IFL'06 Proceedings of the 18th international conference on Implementation and application of functional languages
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Partial inversion of constructor term rewriting systems
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Semi-inversion of guarded equations
GPCE'05 Proceedings of the 4th international conference on Generative Programming and Component Engineering
The program inverter LRinv and its structure
PADL'05 Proceedings of the 7th international conference on Practical Aspects of Declarative Languages
Computationally equivalent elimination of conditions
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Slothrop: Knuth-Bendix completion with a modern termination checker
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Proving injectivity of functions via program inversion in term rewriting
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
A grammar-based approach to invertible programs
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
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Given a constructor term rewriting system that defines injective functions, the inversion compiler proposed by Nishida, Sakai and Sakabe generates a conditional term rewriting system that defines the inverse relations of the injective functions, and then the compiler unravels the conditional system into an unconditional term rewriting system. In general, the resulting unconditional system is not (innermost-)confluent even if the conditional system is (innermost-)confluent. In this paper, we propose a modification of the Knuth-Bendix completion procedure, which is used as a post-processor of the inversion compiler. Given a confluent and operationally terminating conditional system, the procedure takes the resulting unconditional systems as input. When the procedure halts successfully, it returns convergent systems that are computationally equivalent to the conditional systems. To adapt the modified procedure to the conditional systems that are not confluent but innermost-confluent, we propose a simplified variant of the modified procedure. We report that the implementations of the procedures succeed in generating innermost-convergent inverse systems for all the examples we tried.