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Foundation: Horn clause logic with equality which consists of predicates and Horn clauses for logic programming, and functions and equations for functional programming. A full integration of both programming models, so any functional expression can be used in a goal literal and arbitrary predicates can occur in conditions of equations.

Operational semantics based on lazy narrowing; provides some higher-order features.

Multiparadigm declarative programming language seamlessly merges functional, logic, and concurrent programming paradigms; covers the most important operational principles in the area of integrated functional logic languages.

Declarative, general-purpose language, merges best features of functional and logic languages. Has types and modules, higher-order and meta-programming facilities, declarative input/output. Set of system modules provides many operations on standard data types: integers, lists, characters, strings, sets, programs.

Michael Hanus's pages on amalgamating functional and logic programming.

Strongly typed, weakly moded, constraint-logic functional language designed to support construction, extension, and use of new constraint solvers.

Generic functional logic language: functions defined by conditional rewrite rules, predicates defined by Horn clauses whose bodies may contain equations, disequations, or classical atomic formulae. Extant version uses extension of SLD-resolution merged with innermost narrowing.

Relational-Functional Language: logic-programming language with call-by-value (eager) expressions of non-deterministic, non-ground functions; clauses are Hornish, succeeding with true(s), or footed, returning any value(s), and define operations (relations, functions) allowing (apply-reducible) higher-order syntax with arbitrary terms (constants, structures, variables) as operators.