String diagrams for closed categories

Wanted: a coherent graphical language for (non-compact) closed categories , ideally based on string diagrams.

Literature

String diagrams

  • Baez & Stay, 2010: Physics, topology, logic, and computation: a Rosetta stone (doi, arxiv)
    • Introduces a “clasp and bubble” notation for closed categories
    • In a compact closed category, deleting the clasps and bubbles recovers the usual graphical language
  • Coecke et al, 2013: Lambek vs Lambek: Functorial vector space semantics and string diagrams for Lambek calculus (doi, arxiv)
    • Applies the “clasp-string calculus” to Lambek monoids
  • Wijnholds, 2014, MSc thesis: Categorical foundations for extended compositional distributional models of meaning (pdf)
    • Identifies coherence problems with clasp-string language
    • Advocates proof nets as alternative

Category theory, miscellaneous

  • Jeffrey, 1998: Premonoidal categories and a graphical view of programs (online )
    • Graphical syntax for abstraction and recursion, among other things
    • String diagrams not mentioned but are closely related—a great starting point!

Computer science

  • Yau & Grabow, 1981: A model for representing programs using hierarchical graphs (doi)
    • Cited by Harandi & Ning, 1990: Knowledge-based program analysis (doi)