Foundations of logic programming
Foundations of logic programming
Automatic verification of pointer programs using monadic second-order logic
Proceedings of the ACM SIGPLAN 1997 conference on Programming language design and implementation
Term rewriting and all that
Linear Second-Order Unification and Context Unification with Tree-Regular Constraints
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Hardware Verification using Monadic Second-Order Logic
Proceedings of the 7th International Conference on Computer Aided Verification
On Equality Up-to Constraints over Finite Trees, Context Unification, and One-Step Rewriting
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Correction of functional logic programs
ESOP'03 Proceedings of the 12th European conference on Programming
Inductive synthesis of equational programs
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Solving first order formulae of pseudo-regular theory
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
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This paper deals with a class of second order formulae where the only predicate is joinability modulo a conditional term rewrite system, first order variables range over ground terms and second order variables are interpreted as relations on ground terms (i.e. sets of tuples of ground terms). We define a generic algorithm that decides the satisfiability of positive second order joinability formulae when an algorithm is known to finitely represent solutions of first order formulae. When the answer is positive, the algorithm computes one particular instance for the second order variables. We apply this technique to the class of positive second order pseudo-regular formulae. The result is then a logic program that represents the instance of the second order variables. We define a transformation to translate this instance into a CTRS. This result can be used to automatically synthesize a program that defines a relation from its specification.