Erratum to: "A new framework for declarative programming": [Theoret. Comput. Sci. 300 (2003) 91-160]

We propose a new framework for the syntax and semantics of Weak Hereditarily Harrop logic programming with constraints, based on resolution over -categories: 9nite product categories with canonical structure. Constraint information is directly built-in to the notion of signature via categorical syntax. Many-sorted equational constraints are a special case of the formalism which combines features of uniform logic programming languages (modules and hypothetical implication) with those of constraint logic programming. Using the canonical structure supplied by -categories, we de9ne a diagrammatic generalization of formulas, goals, programs and resolution proofs up to equality (rather than just up to isomorphism). We extend the Kowalski–van Emden 9xed point interpretation, a cornerstone of declarative semantics, to an operational, non-ground, categorical semantics based on indexing over sorts and programs. We also introduce a topos-theoretic declarative semantics and show soundness and completeness of resolution proofs and of a sequent calculus over the categorical signature. We conclude with a discussion of semantic perspectives on uniform logic programming. PII of original article S0304-3975(01)00308-5 ∗ Corresponding author. E-mail addresses: [email protected] (S.E. Finkelstein), [email protected] (P. Freyd), [email protected] (J. Lipton). 0304-3975/$ see front matter c © 2003 Published by Elsevier B.V. doi:10.1016/j.tcs.2003.09.011