Programs are viewed as both functions to be executed and data structures to be analysed, but this has always required encoding, e.g. of a lambda-term to a syntax tree, so that a self-interpreter could not be applied to itself directly, but only to its code. Further, the code of a typed program should have a distinctive type. In tree calculus, however, program analysis is supported directly, without encodings, including the self-application of a breadth-first self-interpreter of type

bf :∀X. ∀Y. (X → Y) → (X → Y)