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The Very Model of a Modern Metamodeler

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Philosophers have been talking about metaphysics since Aristotle. Logicians have used metalanguages for 80 years. And, in the last 50 years, computer scientists have produced metaobjects, metaclasses and metamodels. “Going meta” is now even part of the popular culture. What is this all about?

It is about the incredibly powerful human ability to reflect on what we are doing. Bringing this capability to our modeling languages, we can create languages able to express their own definitions. But, with real semantic formalization, we also open up the possibility of creating tools that can reflect on the very models they are being used to create. What might this mean for the next generation of modeling languages and tools?

This presentations goes meta, to reflect on reflection and try to figure it out.

Published in: Software
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The Very Model of a Modern Metamodeler

  1. 1. The Very Model of a Modern Metamodeler MODELSWARD 2019, Prague, Czech Republic 22 February 2019 Ed Seidewitz Chief Technology Officer Model Driven Solutions
  2. 2. Page 2 Going “Meta” 22 February 2018 Pickles by Brian Crane for October 04, 2018
  3. 3. Page 3 Metaphysics 22 February 2018 Wrote a series of books collectively called Physics (Φυσικὴ, “On nature”). Followed by unnamed books later collectively called Metaphysics (μετά Φυσικὴ, “After Physics”). Metaphysics is a reflection on the “why of things”. Nature Reflections on nature (“2nd philosophy”) Reflections on reflections on nature (“1st philosophy”) Aristotle 4th century BC “Meta”
  4. 4. Page 4 Metalanguage 22 February 2018 David Hilbert 1862 – 1943 In 1920, introduced metamathematics, a project to use mathematical methods to study mathematics. A metalanguage was used to discuss the language of mathematics. Mathematical logicians now commonly use metalanguage to mean the language used to define a formal logic language. World Mathematics (language) Metamathematics (metalanguage)
  5. 5. Page 5 Metacircularity (1) 22 February 2018 Kurt Gödel 1906 – 1978 In 1931, published two incompleteness theorems. Used Gödel numbering to reduce number theory proofs to arithmetic operations. Proved the existence of a theorem stating This theorem cannot be proved, which, if false, is inconsistent, and, if true, cannot be proved in number theory! World Mathematics (language) Metamathematics (metalanguage)
  6. 6. Page 6 Metacircularity (2) 22 February 2018 https://www.flickr.com/photos/null0/272015955/ (cropped) CC BY-SA 2.0 John McCarthy 1927 – 2011 In 1960, published Recursive Functions of Symbolic Expressions and Their Computation by Machine, on the design of Lisp, a “list processing” language. Encoding Lisp meta-expressions as symbolic expressions (lists), Lisp can be implemented in itself metacircularly. Lisp programmers actually use S-expressions. Lists Lisp program (S-expressions) Lisp definition (M-expressions) Machine code Steve Russell 1937 – present Implemented Lisp eval on the IBM 704. https://commons.wikimedia.org/wiki/File:Len_Shustek,_CHM_2011.jpg (cropped) CC BY-SA 2.0
  7. 7. Page 7 Metaclass 22 February 2018 Smalltalk 1980 Developed in the 1970s at Xerox PARC by Alan Kay, Dan Ingalls, Adele Goldberg and others. Object-oriented programming language in which “everything is an object.” The first publicly released version, Smalltalk-80, introduced metaclasses. Objects Class Metaclass instance of instance of Bytecode
  8. 8. Page 8 Metaobject 22 February 2018 Metaobject Protocol 1991 A metaobject protocol (MOP) gives “users the ability to incrementally modify [a programming] language’s behavior an implementation.” This is done by allowing extensions to the metaobjects that represent language elements. The Art of the Metaobject Protocol, by Kiczales, des Rivières and Bobrow, describes the MOP for the Common Lisp Object System (CLOS). Objects Class Metaclass instance of instance of Metaobject extension Metaclass extension
  9. 9. Page 9 Metamodel 22 February 2018 Meta Object Facility (MOF) 1999 – 2016 MOF is “the basis for metamodel [abstract syntax] definition in [Object Management Group’s] family of [modeling] languages”. Since MOF 2.0, “based on a simplification of [the] class modeling capabilities” of UML. Date: November 2016 OMG Meta Object Facility (MOF) Core Specification Version 2.5.1 OMG Document Number: formal/2016-11-01 Standard document URL: http://www.omg.org/spec/MOF/2.5.1 Associated Normative Machine-Readable Files: http://www.omg.org/spec/MOF/20131001/MOF.xmi Associated Non-normative Machine-Readable Files: http://www.omg.org/spec/MOF/20131001/CMOFConstraints.ocl http://www.omg.org/spec/MOF/20131001/EMOFConstraints.ocl “Real world” system Model (in UML) Metamodel (for UML) “instance of” “instance of” M0 M1 M2 M3 Four metalayer architecture (deemphasized in MOF 2.x) Meta-metamodel (for MOF) “instance of”
  10. 10. Page 10 Metasemantic Protocol 22 February 2018 ad/2017-12-02 RFP Template: ab/15-06-01 OMG RFP 9 December 2017 1 Object Management Group 109 Highland Avenue Needham, MA 02494 USA Telephone: +1-781-444-0404 Facsimile: +1-781-444-0320 rfp@omg.org Systems Modeling Language (SysML®) v2 Request For Proposal (RFP) OMG Document: ad/2017-12-02 Letters of Intent due: 24 September, 2018 Submissions due: 4 November, 2019 Systems Modeling Language (SysML) v2 2017 – ? Since 2006, SysML has been the OMG-standard UML profile for systems engineering. In 2017, OMG issue a Request for Proposals (RFP) for SysML version 2. To meet user needs, SysML v2 requires a syntactically and semantically user-extensible metamodel. “Real world” system Model (in SysML) Metamodel (for SysML) “instance of” “instance of” Semantic extension Semantic model library Builds on Kernel Modeling Language (KerML) work by Bock, Cole, Galey and others.
  11. 11. Page 11 System Model 22 February 2018 2435.0 A block is a class whose instances are objects. A value type is a class whose instances are values. An object has identity and has properties that can change over time. A value does not have identity separate from its value and is immutable over time. Both classes and features have instances.
  12. 12. Page 12 2435.0 Semantic Model Library 22 February 2018 Library model System model System “Block” and “value type” are just syntactic markers for classes that descend from the library classes Object and Value. Features of classes also specialize (“subset”) general library features.
  13. 13. Page 13 Quantities and Units Domain Model Library 22 February 2018 Base Quantities and Units The base library model can be extended with library models for specific subject domains. An individual is a model of a class constrained to a single instance. Generic functions on numeric values can also operate on quantity values.
  14. 14. Page 14 Quantities Units Usage 22 February 2018 Library model System model System 2435.0 The domain library adds modeling capabilities to the base language.
  15. 15. Page 15 Gone “Meta”! General-purpose modeling languages… …with rigourous semantics …allowing for domain-specific specialization …through semantic model libraries and metasemantic protocols 22 February 2018 We need to activate our metacomic protocol!

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