Corrigendum for --- M. J. Frade, A. Saabas, T. Uustalu. Bidirectional data-flow analyses, type-systematically. In Proc. of PEPM 2009, pp. 141-149. ACM Press, 2009. doi:10.1145/1480945.1480965 --- p 145, col 1, Thm 1: The Galois connection described here is actually not coreflective. Accordingly, these corrections are needed to rectify the statements: in (5): replace "form a coreflective Galois connection" with "form a Galois connection"; delete "Moreover, or any joins-closed relation R, f2R(R2f^{\from}(R), R2f^{\to}(R)) \subseteq R"; in (6): replace "we have R = f2R(R2f^{\from}(R), R2f^{\to}(R))" with "we have R \subseteq f2R(R2f^{\from}(R), R2f^{\to}(R))". Yasuaki Morita spotted this error. A coreflection is obtained by confining to those joins-closed relations R that satisfy the following "butterfly" property: for all d0,d,d1,d0',d',d1' \in D, if d0 \leq d \leq d1 and d0' \leq d' \leq d1' and (d0,d1') \in R and (d1,d0') \in R, then (d,d') \in R (*) These make the image of right adjoint f2R. A reflection is obtained by confining to those pairs of monotone functions f^{\from}, f^{\to} that satisfy the inequations for all d' \in D, f^{\from}(d') \leq f^{\from}(d' \meet f^{\to}(f^{\from}(d'))) for all d \in D, f^{\to}(d) \leq f^{\to} (d \meet f^{\from}(f^{\to}(d))) (**) These make the image of the left adjoint \langle R2f^{\from}, R2f^{\to} \rangle. These narrower posets of joins-closed relations and pairs of monotone functions (satisfying (*) and (**) respectively) are isomorphic. We are currently (in Apr. 2024) writing a paper where we explain this and a lot more. p 148, fig 8, col 2: The clause for [dup]^{\to}(e::es) contains a typo. Read es for *.