A draft of a new paper on Menlder-style recursion schemes (in consideration to submit to TYPES'14 post-proceedings) is available online, powered by ShareLaTeX. We’d appreciate any feedback.

This paper contains a bug fix for $mcata_1$ (or $\it\text{msf}it_{\star\to\star}$ in this paper) in “A hierarchy of Mendler-style recursion schemes”, an interesting example of its use over an indexed mixed-variant datatype, and more rigorous theoretic elaboration of its $F_\omega$ embedding.

Moreover, we introduce ongoing work of two new Mendler-style recursion scheme. One of them is Mendler-style iteration over Parametric Higher-Order Abstract Syntax (PHOAS), inspired by Parametric Compositional Data Types (PCDT). We named our recursion scheme $\it\text{mphit}$, which stands for Mendler-style parametric higher-order iteration. I’ll perhaps write a separate post on this.