The Memorist Tale: Every Thunk Every Cost All At Once

Lazy evaluation offers great flexibility by computing only what is necessary. However, analysing the cost of lazy programs is notoriously challenging, as computation occurs out of order and depends on future demands. Recent work has proposed alternative semantics for modelling lazy evaluation cost that avoid reasoning about program states. However, existing approaches either rely on nondeterminism or require complex bidirectional semantics. We present the Memorist Semantics, a novel semantics for analysing the cost of lazy programs by explicitly tracking the cost and dependencies of every subterm. Our semantics annotates components of a term with fine-grained cost and usage information, yielding a deterministic semantics that can be expressed through a simple monadic interface. We formalize the semantics in Rocq and verify its soundness with respect to the existing Clairvoyance Semantics. Similar to prior formalized semantics, our semantics is defined for a total, typed language with built-in structural recursion and without support for first-class functions. We outline ideas for possible extensions.