Feasible Computation with Higher Types

We restrict recursion in finite types so as to characterize the polynomial time computable functions. The restrictions are obtained by enriching the type structure with the formation of types ρ → σ and terms λ $${\bar x^\rho }r$$ ρ r as well as $$\rho \relbar\joinrel\mathrel\circ \sigma $$ and λx ρ r. Here we use two sorts of typed variables: complete ones $${\bar x^\rho }$$ ρ and incomplete ones x ρ.