LiquidHaskell

Abstract

Haskell has many delightful features. Perhaps the one most beloved by its users is its type system that allows developers to specify and verify a variety of program properties at compile time. However, many properties, typically those that depend on relationships between program values are impossible, or at the very least, cumbersome to encode within the existing type system. Many such properties can be verified using a combination of Refinement Types and external SMT solvers. We describe the refinement type checker LIQUIDHASKELL, which we have used to specify and verify a variety of properties of over 10,000 lines of Haskell code from various popular libraries, including containers, hscolour, bytestring, text, vector-algorithms and xmonad. First, we present a high-level overview of LIQUIDHASKELL, through a tour of its features. Second, we present a qualitative discussion of the kinds of properties that can be checked -ranging from generic application independent criteria like totality and termination, to application specific concerns like memory safety and data structure correctness invariants. Finally, we present a quantitative evaluation of the approach, with a view towards measuring the efficiency and programmer effort required for verification, and discuss the limitations of the approach.

An Introduction to Liquid Haskell

“…Liquid Haskell (LH) was first introduced in [17,18]. It represents the application of the Liquid Type theory to a full-fledged functional language like Haskell.…”

“…Liquid Haskell has been applied to over 10.000 lines of Haskell code belonging to different popular libraries, as reported in [17]. The properties specified and proved range from totality and termination of functions, to safe access of indexed structures, and preservation of data type invariants.…”

“…The properties specified and proved range from totality and termination of functions, to safe access of indexed structures, and preservation of data type invariants. In sections 5 and 6 we show a selection of case studies taken from [17] and from the above cited tutorial.…”

“…This tutorial aims at exposing the reader to a first contact with the Liquid Types technology [14], and in particular with its application to the language Haskell, a type-checker known as Liquid Haskell [17,18]. In the view of this author, Liquid Types should be regarded as a computer-assisted verification system that may increase the reliability of programs by paying a fraction of the effort needed by doing formal verification by hand.…”

“…The Liquid Types were originally developed in a functional language framework, and later on they were applied to some imperative languages such as C [13]. Recently, they have been incorporated to Haskell [17,18] in the form of a static type-checker which is independent of the compilers. The Hindley-Milner Haskell type system, and its extension to type classes, combine very well with the Liquid Types approach, which supports polymorphism, algebraic types, and lambda abstractions.…”