HasCasl: Integrated higher-order specification and program development

Abstract

a b s t r a c tWe lay out the design of HasCasl, a higher order extension of the algebraic specification language Casl that serves both as a wide-spectrum language for the rigorous specification and development of software, in particular but not exclusively in modern functional programming languages, and as an expressive standard language for higher-order logic. Distinctive features of HasCasl include partial higher order functions, higher order subtyping, shallow polymorphism, and an extensive type-class mechanism. Moreover, HasCasl provides dedicated specification support for monad-based functional-imperative programming with generic side effects, including a monad-based generic Hoare logic. IntroductionThe rigorous development of software from abstract requirements to executable code calls for wide-spectrum languages that are sufficiently powerful and flexible to support both an expressive specification logic and concepts appearing in advanced programming languages, including modern functional languages such as Haskell [59], but also imperative and object-oriented languages. Here, we discuss the design of such a wide-spectrum language, HasCasl. HasCasl is an extension of the standard algebraic specification language Casl (Common Algebraic Specification Language) [6,53] developed by the Common Framework Initiative (CoFI) of IFIP WG 1.3, and as such has been adopted by IFIP WG 1.3. It arguably constitutes 'the' natural higher order extension of Casl, and is intended, beyond its purpose as a software specification language, as an expressive standard language for higher order logic. In particular, HasCasl is presently the most expressive language in the logic graph underlying the Bremen heterogeneous tool set Hets [48] and as such serves as a central hub for the interchange of theories between various formalisms in the tool.The core of HasCasl is a higher order logic of partial functions built on top of Moggi's partial λ-calculus [44]. The semantics and proof theory of this logic have been developed in a companion paper [76]; essentially, one arrives at an intuitionistic partial higher order logic without choice principles (even without unique choice). The full HasCasl logic extends the core logic by subtyping and type-classed based shallow polymorphism, including higher-order type constructors and constructor classes; the semantics of the latter is based on models explicitly incorporating signature extensions [70]. Support for general recursive functions is bootstrapped in the style of HOLCF [64] by specifying a theory of fixed point recursion on complete partial orders. Extensive syntactical sugaring of these concepts yields an executable sublanguage which is in close correspondence with a large subset of Haskell.Part of the technical difficulties arising in the development of these concepts stems from the above-mentioned lack of unique choice in the core logic; in particular, additional effort is required in the construction of inductive datatypes and in setting up the theory of complete partial orders. We beli...

Just do it

“…Others have come to the same conclusion; for example, Schröder and Mossakowski's monad-independent Hoare logic [29] similarly defines Hoare triples in terms of 'global evaluation formulae', which are analogous to our assertions.…”

“…It has been embedded into the Coq proof system as an axiomatic extension called Ynot [18], and used as the basis for an implementation of separation logic [19]. Similarly, Schröder and Mossakowski [29] develop a monad-independent Hoare logic within the HASCASL algebraic specification language, and use this logic for reasoning about dynamic references. Either of these approaches makes a sound basis for certified development of effectful programs in the Hoare-Floyd style.…”

“…But if we were to extend the MonadCount class in Section 3 with an operation reset to reset the counter, this would be copyable but not discardable; in a similar 'latch' monad, set and reset methods would be copyable but not relatively commutable; and the probabilistic operation coin in Section 8.2 is discardable but not copyable. (Schröder and Mossakowski [29] call queries 'pure'; however, in general, queries are not 'pure' in the sense of being instances of return.) To illustrate the assertional style, recall the Towers of Hanoi problem from Section 3.…”

Refinement in hybridised institutions

“…), to the ones underlying specification and programming languages or used for describing particular systems from different domains. Well-known examples include probabilistic logics [BKI05], quantum logics [CMSS06], hidden and observational logics [BD94,BH06], coalgebraic logics [C06], as well as logics for reasoning about process algebras [MR06], functional [ST12,SM09] and imperative programing languages [ST12].…”

Carnap, Goguen, and the Hyperontologies: Logical Pluralism and Heterogeneous Structuring in Ontology Design

“…Concerning typed variants, [30] presents an institution for a higher-order logic extending Church's type theory [39] with polymorphism; this is basically the higher-order logic used in modern interactive theorem provers like Isabelle/HOL [152]. A feature of Isabelle/HOL that is not covered by this logic is type classes; the institution of HasCasl [169] is a polymorphic higher-order logic featuring type classes, as well as partial functions and subsorting; moreover, it is intuitionistic.…”