(2016)We interrupt this program to note a possible solution for several of these languages here.

I code a really dumb set abstraction in a few languages. In each version one can add an element to a set and query membership. Some versions also allow set union. All these values are immutable. The particular implementation is inefficient—a linked list of elements; we are concerned about efficiency of abstraction here, not efficient set representation. Set union is significant here because it requires bringing two element lists together—synergy.

There is another dichotomy:

• A set of values and a set of operators for those values.
• A set of values each carrying ‘methods’ that one can invoke passing another value of the same ‘class’.

OCaml

The module type in OCaml is a class of types that have in common some abstract type called set a value em of that type, and a function from int & set to set, and another function of the same type. The toy module here is called Set and is accessible only thru the filter of the module type Sett. A module type is a compile time notion rather like a Java Interface. It is string enough, I think, to allow for v-tables. That a value of type set is a list of ints is not available at the call sites. This code does not use the features referred to by the “O” of “OCaml”. A more typical synergy app in OCaml. Then see this!

Scheme

I know of no Scheme except perhaps, Scheme48, that provides efficient synergy. Given either of the two efficient synergy mechanisms that I am aware of (safe & seals) I propose to explore several object styles for Scheme. I do not expect a correlation between synergy mechanism and object styles.

• In this version the set is delivered as a pair of functions, one to add, and one to query. There is no union and thus no required synergy. It is done by simple closures.
• Here we build on the safe apparatus and deliver a function from four symbols to four ‘methods’. If s is such a pack then:
  • ((s 'add) b) yields the set s∪{x}.
  • ((s 'query) x) yields x∈s.
  • ((s 'union) t) yields s∪t.
  • (s 'badge) yields the badge for s and is both useless and harmless to anyone but those from the set clan who hold it closely.

There is a problem of invoking procedures from untrusted sources. It may not return or it might return too many times. I am not confident that my code continues to work correctly in the latter case. At least in the former case I do not misbehave. I shall assume for now a function once that takes a procedure and returns another procedure that never returns twice. I leave for another time whether this needs to be primitive.

C++

See this.