Monad-independent Dynamic Logic in HasCasl

Schröder, Lutz; Mossakowski, Till

doi:10.1093/logcom/14.4.571

Cited by 18 publications

(43 citation statements)

References 21 publications

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“…This might involve the combination of particular programming language constructs and their semantics with the pure algebraic-logic semantics of Expander2 specifications. Related work has been done by combining the algebraic specification language CASL [3] with Haskell [25].…”

Section: Resultsmentioning

confidence: 99%

Expander2: Program Verification Between Interaction and Automation

Padawitz

2007

Electronic Notes in Theoretical Computer Science

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Expander2 is a flexible multi-purpose workbench for interactive rewriting, verification, constraint solving, flow graph analysis and other procedures that build up proofs or computation sequences. Moreover, tailormade interpreters display terms as two-dimensional structures ranging from trees and rooted graphs to a variety of pictorial representations that include tables, matrices, alignments, partitions, fractals and turtle systems. Proofs and computations performed with Expander2 follow the rules and the semantics of swinging types. Swinging types are based on many-sorted predicate logic and combine constructor-based types with destructor-based (e.g. state-based) ones. The former come as initial term models, the latter as final models consisting of context interpretations. Relation symbols are interpreted as least or greatest solutions of their respective axioms. This paper presents an overview of Expander2 with particular emphasis on the system's prover capabilities. It is an adaptation of [21] to the latest version of Expander2. In particular, proof rules tailor-made for transition rule specifications have been added to the system and are discussed and exemplified here for the first time.

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Section: Resultsmentioning

confidence: 99%

Expander2: Program Verification Between Interaction and Automation

Padawitz

2007

Electronic Notes in Theoretical Computer Science

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“…It is slightly modified w.r.t. the standard laws for monads, the main subtlety arising from partiality being the treatment of the first unit law [74]. The notation is (almost) identical to the one used in Haskell, i.e.…”

Section: Monads For Functional-imperative Programmingmentioning

confidence: 99%

“…12. Note that it is only thanks to the treatment of partial functions in the specification of monads that the state monad is really an instance of Monad, since stricter versions of the first monad law fail to hold for the state monad (see [74] for a more detailed discussion). Monads specified in HasCasl in the style of Fig.…”

Section: Monads For Functional-imperative Programmingmentioning

confidence: 99%

“…In preparation for the formulation of the monad-based Hoare calculus, we now summarise material from [74] on generic notions of purity (previously called side-effect freeness), to be required of stateful formulas appearing as pre-and postconditions, and global evaluation formulas (called global dynamic judgements in [74]). Informally, pure programs are those that have the following properties:…”

Section: Generic Purity and Global Evaluationmentioning

confidence: 99%

“…Definition 65 ([19,79] For details on the relation between the various notions above, see [19,74]. Here, we need mainly the notion of purity.…”

Section: Generic Purity and Global Evaluationmentioning

confidence: 99%

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HasCasl: Integrated higher-order specification and program development

Schröder

Mossakowski

2009

Theoretical Computer Science

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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...

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