The Topos of Programming | Yon

The Topos of ProgrammingA topos-oriented programming language.Syntax Reference Benchmarks Native via MLIR & LLVMNo garbage collectorAGPLThe heapThe address of a value is its content.Yon allocates into xleech2, a content-addressed heap whose geometry is the Leech lattice Λ24: exactly 196,560 slots per heap. Allocation hashes the bytes; identical content returns the existing slot, so same content ⇔ same slot. Equality of arbitrarily large values is one number comparison: O(1) structural equality, by construction.String.equal: ~17 ns at 1 char and at 32,768 chars. Three orders of magnitude of size, the same per-comparison time.Benchmarkshello.yonfun main(): number { be greeting holds "ciao, mondo" // interned on the heap be _ holds String.print(greeting) return 0 }$ yonc hello.yon -o hello && ./hellociao, mondoEvery string literal is a section of the builtin String place, interned on that same heap, so two equal strings are one slot, however they were built.The paradigmWorlds are categories. Behaviour is arrows.In Topos-Oriented Programming a world is a category, a place is an object in it, and a value is a section: immutable, identified by its content. All behaviour lives in arrows. Identity is the exception, requested only where you need it. Logic is internal: truth is the subobject classifier Ω, and unknown is a citizen of the Heyting core, not an error. From the Yoneda lemma, a thing is determined by its relations; the type checker, optimizer, and allocator act on that.Read “Topos-Oriented Programming” Execution modelWhat Yon does without.Identity is explicit. Concurrency is the process. Failure is a value. The interface to a place is its arrows.

Four mechanisms common elsewhere are absent:No garbage collectorSlots are stable for the life of the process; the heap grows with distinct content only.No threadsThe unit of concurrency is the process. Spaces talk over a shared-memory wire.No exceptionsFailure is data: a place, a declaration, or a process exit, never a thrown stack.No typeclassesArrows are the interface: a place’s presheaf of observations.Future work Source: OCaml, MLIR, C