Automated machine learning (AutoML) can make data scientists more productive. But if machine learning is totally automated, that leaves no room for data scientists to apply their intuition. Hence, data scientists often prefer not total but gradual automation, where they control certain choices and AutoML explores the rest. Unfortunately, gradual AutoML is cumbersome with state-of-the-art tools, requiring large non-compositional code changes. More concise compositional code can be achieved with combinators, a powerful concept from functional programming. This paper introduces a small set of orthogonal combinators for composing machinelearning operators into pipelines. It describes a translation scheme from pipelines and associated hyperparameter schemas to search spaces for AutoML optimizers. On that foundation, this paper presents Lale, an open-source sklearn-compatible AutoML library, and evaluates it with a user study.