Artificial Intelligence (AI) methods are an integral part of modern decision support systems. The best-performing predictive models used in AI-based decision support systems lack transparency. Explainable Artificial Intelligence (XAI) aims to create AI systems that can explain their rationale to human users. Local explanations in XAI can provide information about the causes of individual predictions in terms of feature importance. However, a critical drawback of existing local explanation methods is their inability to quantify the uncertainty associated with a feature's importance. This paper introduces an extension of a feature importance explanation method, Calibrated Explanations, previously only supporting classification, with support for standard regression and probabilistic regression, i.e., the probability that the target is below an arbitrary threshold. The extension for regression keeps all the benefits of Calibrated Explanations, such as calibration of the prediction from the underlying model with confidence intervals, uncertainty quantification of feature importance, and allows both factual and counterfactual explanations. Calibrated Explanations for regression provides fast, reliable, stable, and robust explanations. Calibrated Explanations for probabilistic regression provides an entirely new way of creating probabilistic explanations from any ordinary regression model, allowing dynamic selection of thresholds. The method is model agnostic with easily understood conditional rules. An implementation in Python is freely available on GitHub and for installation using both pip and conda, making the results in this paper easily replicable.

This paper presents Express, a library for manipulating dynamically typed Haskell expressions involving function application and variables. Express works as a wrapper around the Data.Dynamic module and provides additional features such as: explicit encoding of function applicaion thus delayed application between values, support for variable placeholders and expression matching. This paper shows these additions make this library useful in generating program specifications, automated testing and program synthesis.

This paper presents a new tool called Extrapolate that automatically generalizes counterexamples found by property-based testing in Haskell. Example applications show that generalized counterexamples can inform the programmer more fully and more immediately what characterises failures. Extrapolate is able to produce more general results than similar tools. Although it is intrinsically unsound, as reported generalizations are based on testing, it works well for examples drawn from previous published work in this area.

This paper presents Speculate, a tool that automatically conjectures laws involving conditional equations and inequalities about Haskell functions. Speculate enumerates expressions involving a given collection of Haskell functions, testing to separate those expressions into apparent equivalence classes. Expressions in the same equivalence class are used to conjecture equations. Representative expressions of different equivalence classes are used to conjecture conditional equations and inequalities. Speculate uses lightweight equational reasoning based on term rewriting to discard redundant laws and to avoid needless testing. Several applications demonstrate the effectiveness of Speculate.

This thesis presents techniques for discovery, refinement and generalization of properties about functional programs. These techniques work by reasoning from test results: their results are surprisingly accurate in practice, despite an inherent uncertainty in principle. These techniques are validated by corresponding implementations in Haskell and for Haskell programs: Speculate, FitSpec and Extrapolate. Speculate discovers properties given a collection of black-box function signatures. Properties discovered by Speculate include inequalities and conditional equations. These properties can contribute to program understanding, documentation and regression testing. FitSpec guides refinements of properties based on results of black-box mutation testing. These refinements include completion and minimization of property sets. Extrapolate generalizes counterexamples of test properties. Generalized counterexamples include repeated variables and side-conditions and can inform the programmer what characterizes failures. Several example applications demonstrate the effectiveness of Speculate, FitSpec and Extrapolate.