CASL
The CoFI Algebraic Specification Language1
Summary

by The CoFITask Group on Language Design

20 May 1997

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Abstract

This Summary is the basis for the Design Proposal [LD97a] for CASL, the CoFI Algebraic Specification Language. It is being submitted for approval to the sponsoring IFIP Working Group on Foundations of System Specification, WG 1.3. All comments on the Proposed Design of CASL and on this summary should be sent to the CoFI Language Design mailing list(cofi-language@brics.dk).

Deadline for comments to be considered at the IFIP WG 1.3 Meeting:

12 noon on Friday, 30 May, 1997.

The language CASL is central to CoFI: it is a reasonably expressive algebraic language for specifying requirements and design for conventional software. From CASL, simpler CoFI languages (e.g., for interfacing with existing tools) are to be obtained by restriction, and CASL is to be incorporated in more advanced CoFI languages (e.g., for specifying reactive systems). CASL strikes a balance between simplicity and expressiveness. The main features of its design are as follows:

Many-sorted basic specifications in CASL denote classes of many-sorted partial first-order structures: algebras where the functions are partial or total, and where also predicates are allowed. Axioms are first-order formulae built from definedness assertions and both strong and existential equations. Sort generation constraints can be stated. Datatype declarations are provided for concise specification of sorts together with some constructors and (optional) selectors. Subsorted basic specifications provide moreover a simple treatment of subsorts, interpreting subsort inclusion as embedding.

Structured specifications allow translation, reduction, union, and extension of specifications. Extensions may be required to be conservative and/or free; initiality constraints are a special case. A simple form of generic (parametrized) specifications is provided, together with instantiation involving parameter-fitting translations.

Architectural specifications express that the specified software is to be composed from separately-developed, reusable units with clear interfaces.

Finally, libraries allow the (distributed) storage and retrieval of named specifications.

This Summary of CASL gives the abstract syntax, and informally describes its intended semantics. It is accompanied by the Rationale for CoFI [CoF97], the Rationale for the Proposed Design of CASL [LD97b], a draft of the Formal Semantics of CASL [Sem97a], and two proposals for Concrete Syntax, with Examples of CASL specifications [KB97][VBC97].

Contents

  • About this document
  • Contributors
  • Structure
  • Part I: Basic Specifications
  • 1 Basic Concepts
  • 1.1 Signatures
  • 1.2 Models
  • 1.3 Sentences
  • 1.4 Satisfaction
  • 2 Basic Constructs
  • 2.1 Signature Declarations
  • 2.1.1 Sorts
  • 2.1.2 Constants and Functions
  • 2.1.3 Predicates
  • 2.1.4 Datatype Declarations
  • 2.2 Variable Declarations
  • 2.3 Axioms and Terms
  • 2.3.1 Quantifiers
  • 2.3.2 Logical Connectives
  • 2.3.3 Atomic Formulae and Terms
  • 2.4 Sort Generation
  • 2.5 Local Basic Specifications
  • 3 Subsorting Concepts
  • 3.1 Signatures
  • 3.2 Models
  • 3.3 Subsorted Sentences
  • 4 Subsorting Constructs
  • 4.1 Subsort Declarations
  • 4.2 Axioms and Terms
  • 4.3 Datatype Declarations
  • 4.4 Subsort Definitions
  • Part II: Structured Specifications
  • 5 Structuring Concepts
  • 6 Structuring Constructs
  • 6.1 Structured Specifications
  • 6.1.1 Translations and Reductions
  • 6.1.2 Unions and Extensions
  • 6.2 Named and Generic Specifications
  • Part III: Architectural Specifications
  • 7 Architectural Concepts
  • 8 Architectural Constructs
  • 8.1 Unit Declarations and Definitions
  • 8.2 Unit Compositions
  • Part IV: Specification Libraries
  • 9 Library Concepts
  • 10 Library Constructs
  • 10.1 Libraries
  • 10.2 Distributed Libraries and Downloading
  • Appendices:
  • Appendix A: Abstract Syntax
  • Identifiers
  • Basic Specifications
  • Basic Specifications with Subsorts
  • Structured Specifications
  • Named and Generic Specifications
  • Architectural and Unit Specifications
  • Specification Libraries
  • Appendix B: Bibliography
  • References
  • Appendix C: Changes from the Tentative Design
  • Index
  • Footnotes

  • CoFI Document: CASL/Summary-v0.97 --Version 0.97-- 20 May 1997.
    Comments to cofi-language@brics.dk