Extensional equality preservation and verified generic programming

In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets of specifications or abstract data types (ADTs). Functors and monads are at the core of many applications of functional programming. This raises the question of what useful ADTs for verified functors and monads could look like. The functorial map of many important monads preserves extensional equality. For instance, if $f, g : A \rightarrow B$ are extensionally equal, that is, $\forall x \in A, \ f \ x = g \ x$, then $map \ f : List \ A \rightarrow List \ B$ and $map \ g$ are also extensionally equal. This suggests that preservation of extensional equality could be a useful principle in verified generic programming. We explore this possibility with a minimalist approach: we deal with (the lack of) extensional equality in Martin-L\"of's intensional type theories without extending the theories or using full-fledged setoids. Perhaps surprisingly, this minimal approach turns out to be extremely useful. It allows one to derive simple generic proofs of monadic laws but also verified, generic results in dynamical systems and control theory. In turn, these results avoid tedious code duplication and ad-hoc proofs. Thus, our work is a contribution towards pragmatic, verified generic programming.Comment: Manuscript ID: JFP-2020-003

Foundational nonuniform (co)datatypes for higher-order logic

Nonuniform (or “nested” or “heterogeneous”) datatypes are recursively defined types in which the type arguments vary recursively. They arise in the implementation of finger trees and other efficient functional data structures. We show how to reduce a large class of nonuniform datatypes and codatatypes to uniform types in higher-order logic. We programmed this reduction in the Isabelle/HOL proof assistant, thereby enriching its specification language. Moreover, we derive (co)recusion and (co)induction principles based on a weak variant of parametricity

Foundational nonuniform (co)datatypes for higher-order logic

Nonuniform (or “nested” or “heterogeneous”) datatypes are recursively defined types in which the type arguments vary recursively. They arise in the implementation of finger trees and other efficient functional data structures. We show how to reduce a large class of nonuniform datatypes and codatatypes to uniform types in higher-order logic. We programmed this reduction in the Isabelle/HOL proof assistant, thereby enriching its specification language. Moreover, we derive (co)recusion and (co)induction principles based on a weak variant of parametricity

Cotransforming Grammars with Shared Packed Parse Forests

SPPF (shared packed parse forest) is the best known graph representation of a parse forest (family of related parse trees) used in parsing with ambiguous/conjunctive grammars. Systematic general purpose transformations of SPPFs have never been investigated and are considered to be an open problem in software language engineering. In this paper, we motivate the necessity of having a transformation operator suite for SPPFs and extend the state of the art grammar transformation operator suite to metamodel/model (grammar/graph) cotransformations

LMS-Verify: abstraction without regret for verified systems programming

Performance critical software is almost always developed in C, as programmers do not trust high-level languages to deliver the same reliable performance. This is bad because low-level code in unsafe languages attracts security vulnerabilities and because development is far less productive, with PL advances mostly lost on programmers operating under tight performance constraints. High-level languages provide memory safety out of the box, but they are deemed too slow and unpredictable for serious system software. Recent years have seen a surge in staging and generative programming: the key idea is to use high-level languages and their abstraction power as glorified macro systems to compose code fragments in first-order, potentially domain-specific, intermediate languages, from which fast C can be emitted. But what about security? Since the end result is still C code, the safety guarantees of the high-level host language are lost. In this paper, we extend this generative approach to emit ACSL specifications along with C code. We demonstrate that staging achieves ``abstraction without regret'' for verification: we show how high-level programming models, in particular higher-order composable contracts from dynamic languages, can be used at generation time to compose and generate first-order specifications that can be statically checked by existing tools. We also show how type classes can automatically attach invariants to data types, reducing the need for repetitive manual annotations. We evaluate our system on several case studies that varyingly exercise verification of memory safety, overflow safety, and functional correctness. We feature an HTTP parser that is (1) fast (2) high-level: implemented using staged parser combinators (3) secure: with verified memory safety. This result is significant, as input parsing is a key attack vector, and vulnerabilities related to HTTP parsing have been documented in all widely-used web servers.</jats:p

Proceedings of the Workshop on Algorithmic Aspects of Advanced Programming Languages: WAAAPL'99: Paris, France, September 30, 1999

The first Workshop on Algorithmic Aspects of Advanced Programming Languages was held on September 30, 1999, in Paris, France, in conjunction with the PLI'99 conferences and workshops. The choice of programming languages has a huge effect on the algorithms and data structures that are to be implemented in that language. Traditionally, algorithms and data structures have been studied in the context of imperative languages. This workshop considers the algorithmic implications of choosing an advanced functional or logic programming language instead. A total of eight papers were selected for presentation at the workshop, together with an invited lecture by Robert Harper. We would like to thank Dider Remv, general chair of PLI'99, for his assistance in organizing this workshop