The idea of a syntax algebra, is that, a computer language whose syntax is similar to that of mathematical formalism, that it is just like equations or formulas, that one can manipulate them meaningfully. (somewhat similar to the idea of term rewriting system)
Contrast it with the ad hoc syntax of haskell or ocaml, whose syntax are so ad hoc and non-systematic — total garbage. [see OCaml Syntax Sucks]
by the way, the picture is from:
[A Galois Connection Calculus for Abstract Interpretation By Patrick Cousot And Radhia Cousot. At
https://www.di.ens.fr/~rcousot/publications.www/CousotCousot-POPL14-ACM-p2-3-2014.pdf , accessed on 2016-09-03 ]
[local copy CousotCousot-POPL14-ACM-p2-3-2014.pdf ]
abstract: We introduce a Galois connection calculus for language independent specification of abstract interpretations used in programming language semantics, formal verification, and static analysis.
I don't know what's “Galois connection calculus”.
[via [ twitter whitequark ] [ 2016-09-03 https://twitter.com/whitequark/status/771851320374366208 ] ]
here's a easy introduction. [Order Theory, Galois Connections and Abstract Interpretation By David Henriques Carnegie Mellon University. At http://www.cs.cmu.edu/~emc/15414-f11/lecture/lec19_GaloisConnections.pdf [local copy lec19_GaloisConnections.pdf ]〕