Fungi: A typed functional language for programs that name their own cached dependency graphs

Fungi serves as the target language for IODyn. Unlike IODyn, the incremental features of Fungi are explicit. In particular, Fungi provides language affordances for

• first-class names,
• first class name-functions,
• input/output collections whose types are indexed by sets of names (e.g., to uniquely identify positions in a list), and
• functions whose types are indexed by what cached data and computations they read and write. Though the semantics of Fungi are effectful, wherein it allocates programmer-named values and computations, and reads these objects from memory later, the behavior of Fungi is functional: the key invariant of its type-and-effects system.

More precisely, Fungi provides two languages: One for the Archivist (the functional subset), and an imperative "wrapper" language for the Editor, who is permitted to mutate the Archivist's input, and then indicate where the output of archivist computations should be incrementally repaired, on demand.

(Status:)

• We have implemented the AST structure, concrete syntax (via Rust macros for now); see src/tgt_ast.rs, and test/tgt_ast.rs
• We are beginning the basic type system, and then, the refinement types and decision procedures.
• For technical background and formal definitions, see the latest draft of the technical report.
• We are presently implementing these formalisms; the deductive proof rules for index equivalence and apartness do not indicate an obvious algorithm, or obvious encoding into SMT. Creating these decision procedures is a key research challenge.