Generative Semantic Lambda Calculus: A Unified Dynamical Theory of Meaning, Uncertainty, and Computation

We propose a novel computational framework: Generative-Semantic Lambda Calculus (GSλ). Unlike classical lambda calculus, which treats functions as mappings, GSλ views computational objects as "generative semantic processes," essentially a family of distributions evolving in a latent semantic space. GSλ achieves the combination and reasoning of "meaning" by introducing semantic flow, generative operators, and uncertainty structures. This framework unifies procedures, probabilistic models, and semantic interpretation, constructing a closed-loop calculus system. We present sketches of formal syntax, operational semantics, denotative semantics, and consistency and completeness theorems.