The mechanical evaluation of expressions

Landin shows how many mathematical concepts—including function definitions, “where”-clauses, sums, and integrals—can be rendered in -calculus notation. He proposes to represent mathematical expressions as -terms, writing function and operator applications in a unified way (e.g., and ). He terms such expressions applicative expressions.

Landin observes that functions may be treated as values. For example, after introducing the idea of rendering integrals in -calculus notation—/e.g./, could be written as —he says that the -expression representing the integrand is itself a function, and hence could be replaced with another one, even one not written directly in -calculus notation—/e.g./, we could render the previous integral as just .

At the end, Landin introduces the SECD machine, an abstract machine that serves as a compilation target for applicative expressions.