The Function Passing Model: Types, Proofs, and Semantics

We formalize our programming model in the context of a typed lambda calculus with records. Figure 1 shows the abstract syntax of our core language. Besides standard terms, the language includes terms related to (a) spores, (b) silos, and (c) futures. The spore term creates a new spore. It contains a list of variable definitions, the spore header, and a closure which may only refer to its parameter and variables in the spore header. The spawn term creates a new host capable of hosting silos. The populate term initializes a new silo on a given host with a given data value. The map, flatMap, and persist terms create lineages of silo transformations represented as silo references. The send term forces the materialization of the silo corresponding to its argument silo reference; send returns a future which is asynchronously completed with the silo’s value. The await term waits for the completion of its argument future and returns the future’s value. Locations ι are used to refer to futures and hosts, both of which can be created dynamically using the above terms. Values in our language are as expected: besides abstractions and record values they include spore values, locations, and silo references. Locations and silo references are not part of the “surface syntax” of our language; they are only introduced by evaluation (see Section 1.1). Silo reference values are values of a simple datatype with constructors Mat, Mapped, FMapped, and Persist. The constructors include all information required for materializing a silo with the result of applying the described transformations. Therefore, a silo reference value is also called the lineage of its corresponding silo. We defer a detailed explanation of the transformations described by a lineage to the following Section 1.1. In addition to standard function and record types, the language has types for spores, hosts, silo references, and futures. A spore type T ⇒ T ′ { type C = T } includes the types T of the variables declared in the header of the spore.