  We present a correspondence and bisimulation between variants of
parametrically polymorphic type systems and variants of finite control
automata, such as FSA, PDA, tree automata and Turing machine. Within this
correspondence we show that two recent celebrated results on automatic
generation of fluent API are optimal in certain senses, present new results on
the studied type systems, formulate open problems, and present potential
software engineering applications, other than fluent API generation, which may
benefit from judicious use of type theory.
