Our contribution to CSL 04 [AM04] contains a little error, which is easily corrected by 2 elementary editing steps (replacing one character and deleting another). Definition of wellformed contexts (fifth page). Typing contexts should, in contrast to kinding contexts, only contain type variable declarations without variance information. Hence, the second rule is too liberal; we must insist on p = ◦. The corrected set of rules is then: ⋄ cxt ∆ cxt ∆, X ◦κ cxt ∆ cxt ∆ ⊢ A: ∗ ∆, x:A cxt Definition of welltyped terms (immediately following). Since wellformed typing contexts ∆ contain no variance information, hence ◦ ∆ = ∆, we might drop the “◦ ” in the instantiation rule (fifth rule). The new set of rules is consequently, (x:A) ∈ ∆ ∆ cxt ∆ ⊢ x: A ∆, X ◦κ ⊢ t: A ∆ ⊢ t: ∀X κ. A ∆, x:A ⊢ t: B ∆ ⊢ λx.t: A → B ∆ ⊢ t: ∀X κ. A ∆ ⊢ F: κ

Abstract. Pattern matching is advantageous for understanding and reasoning about function definitions, but it tends to tightly couple the interface and implementation of a datatype. Significant effort has been invested in tackling this loss of modularity; however, decoupling patterns from concrete representations while maintaining soundness of reasoning has been a challenge. Inspired by the development of invertible programming, we propose an approach to abstract datatypes based on a rightinvertible language rinv—every function has a right (or pre-) inverse. We show how this new design is able to permit a smooth incremental transition from programs with algebraic datatypes and pattern matching, to ones with proper encapsulation (implemented as abstract datatypes), while maintaining simple and sound reasoning.