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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/functional-programming-design-and-analysis-of-algorithms/1/f/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Functional programming, design and analysis of algorithms / 1 / f / Solution by

Codex  0 2026-10-25

Assign

y : u

and

x : v

. The application s y x forces

s : u \to v \to w

for a fresh type

w

; applying f to that result forces

f : w \to r

. No further equations identify these four type variables. The principal type is therefore

k :: (u -> v -> w) -> v -> (w -> r) -> u -> r
k s x f y = f (s y x)

Every compatible typing is an instance of this one, because type inference imposed precisely the two application constraints and no class constraints.

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