This work constitutes the proceedings of the sixth International Conference on Algebraic and Logic Programming and the third International Workshop on Higher-Order Algebra, Logic and Term Rewriting. Topics covered include functional and logic programming, higher-order methods and term rewriting.

Safe folding/unfolding with conditional narrowing.- Optimal non-deterministic functional logic computations.- A semantic basis for termination analysis of logic programs and its realization using symbolic norm constraints.- Parallelizing functional programs by generalization.- Higher-order equational unification via explicit substitutions.- Parameterised higher-order algebraic specifications.- Higher-order lazy narrowing calculus: A computation model for a higher-order functional logic language.- On composable properties of term rewriting systems.- Needed reductions with context-sensitive rewriting.- Conditional term graph rewriting.- Lazy narrowing with parametric order sorted types.- Termination of algebraic type systems: The syntactic approach.- Proof net semantics of proof search computation.- Explicit substitutions for the ??-calculus.- A left-linear variant of ??.- Perpetuality and uniform normalization.- Model generation with existentially quantified variables and constraints.- Optimal left-to-right pattern-matching automata.