LambdaN

LambdaN is a conceptual framework that combines the lambda calculus with a directed graph of computation nodes to capture functional programs with explicit data dependencies. In LambdaN, programs are expressed as families of lambda abstractions whose applications are wired into a network of nodes, each representing a function, value, or evaluation operator. This graph-structured approach aims to make sharing, incremental computation, and parallel evaluation intrinsic to the language design.

Core concepts: A node can execute a partial evaluation; edges denote data flow; reduction rules operate locally at nodes while preserving global semantics; supports both eager and lazy evaluation strategies; includes a lightweight type system with type inference and algebraic data types.

Implementation and interop: LambdaN has been described as both a theoretical model and a candidate runtime. It is often implemented as a domain-specific language or as a library embedded in existing languages, offering interop with conventional functions and data structures. Common optimizations include memoization of node results, graph rewriting to fuse adjacent operations, and exploiting parallelism across independent nodes.

Applications: The framework is proposed for research into functional programming language design, symbolic computation, and hardware mapping, where a dataflow graph maps naturally onto parallel processors or accelerators. It also serves pedagogical purposes by illustrating how lambda expressions can be embedded in a graph-based computation model.

Relation to other concepts: LambdaN draws on lambda calculus, functional programming, and dataflow programming. It shares ideas with graph reduction, semantic nets, and continuation-passing style under different reduction strategies. The concept remains largely theoretical with several experimental implementations and ongoing discussions among researchers.