The Power of Tightness for Call-By-Push-Value

We propose tight type systems for Call-by-Name (CBN) and Call-by-Value (CBV) that can be both encoded in a tight type system for Call-by-Push-Value (CBPV). All such systems are quantitative, in the sense that they provide exact information about the length of normalization sequences to normal form (discriminated between multiplicative and exponential steps) as well as the size of these normal forms.