We present a simulation of quantum systems where the state vectors and observables are polymorphic Haskell functions. The model is not restricted to qubits: It admits state spaces of infinite dimension, but with finite number of degrees of freedom. (So, the subject is quantum mechanics, and not quantum field theory). Since the state vectors and operators are not represented or manipulated as symbolic formulae, they are opaque and they cannot be treated as classical data.

We expect from the reader a moderate familiarity with elementary quantum theory, but the part about quantum computing is kept at a basic level.