A quantitative model for simply typed λ-calculus

We use a simplified version of the framework of resource monoids, introduced by Dal Lago and Hofmann (2005, 2011), to interpret simply typed λ -calculus with constants zero and successor. We then use this model to prove a simple quantitative result about bounding the size of the normal form of λ -terms. While the bound itself is already known, this is to our knowledge the first semantic proof of this fact. Our use of resource monoids differs from the other instances found in the literature, in that it measures the size of λ -terms rather than time complexity.