Type-based Exception Analysis for Non-strict Higher-order Functional Languages with Imprecise Exception Semantics

Abstract

Most statically typed functional programming languages allow programmers to write partial functions: functions that are not defined on all the elements of their domain as specified by their type. Applying a partial function to a value on which it is not defined will raise a run-time exception, thus in practice well-typed programs can and do still go wrong.To warn programmers about such errors, contemporary compilers for functional languages employ a local and purely syntactic analysis to detect partial case-expressions-those that do not cover all possible patterns of constructors. As programs often maintain invariants on their data, restricting the potential values of the scrutinee to a subtype of its given or inferred type, many of these incomplete case-expressions are harmless. Such an analysis does not account for these invariants and will thus report many false positives, overwhelming the programmer.We develop a constraint-based type system that detects harmful sources of partiality and prove it correct with respect to an imprecise exception semantics. The analysis accurately tracks the flow of both exceptions-the manifestation of partiality gone wrong-and ordinary data through the program, as well as the dependencies between them. The latter is crucial for usable precision, but has been omitted from previously published exception analyses.

Higher-Ranked Annotation Polymorphic Dependency Analysis

“…The Dependency Core Calculus was introduced by [1] as a unifying framework for dependency analyses. Instances include binding-time analysis (see, e.g., [29]), exception analysis [17,16], secure information flow analysis [9] and static slicing [27]. They devised the Dependency Core Calculus (DCC) to which each instance of a dependency analysis can be mapped.…”

Extensible Datasort Refinements

“…Program analysis. Koot and Hage (2015) formulate a type system that analyzes where exceptions can be raised, including match exceptions raised by nonexhaustive case expressions. This system appears to be less precise than datasorts, but has advantages typical to program analysis: no type annotations are required.…”

Predicting resource consumption of higher-order workflows

“…Other papers whose approach to type and effect systems influenced our work are Gedell et al (2006), the work on exception analysis by Koot and Hage (2015), the usage analysis by Hage et al (2007), and the security analysis by Weijers et al (2014).…”