Formalnemu

Formalnemu is a formalism designed to model and reason about memory-aware computation in functional-style programming. It formalizes how results can be cached and reused to improve efficiency while preserving correctness, making explicit the interaction between computation and stored results.

A formalnemu model consists of a language L of expressions, a memory store S that represents the current state of allocated data, and an evaluation relation that maps a pair (expression, store) to a resulting value and a possibly updated store. Expressions include variables, constructors, and let-bindings, together with explicit annotations for memory effects. A separate memo table M records previously computed results for subexpressions, enabling reuse across evaluation steps and even across separate evaluations in the same session.

Semantics in formalnemu relies on reduction rules that describe how expressions are simplified to values while consulting and updating the memo table. A central feature is call-by-need evaluation: if a subexpression has a cached result, the stored value is used rather than recomputing it. The framework supports different evaluation strategies and investigates how caching interacts with purity, laziness, and potential side effects. Consistency requirements ensure that memoized results are compatible with the functional parts of the model, so that recomputation does not occur unless necessary.

An example is the evaluation of a recursive function such as Fibonacci with memoization. Computing fib(n) stores fib(k) results for k < n; subsequent requests for fib(k) reuse the stored values, reducing overall work.

Applications of formalnemu appear in theoretical studies of program optimization, formal verification of memoization correctness, and education about memory-conscious computation. Limitations include potential space growth from caching and the need to manage memory effects carefully in mixed-purity settings. See also formal semantics, memoization, and term rewriting systems.