• Coq

  • Referenced in 1526 articles [sw00161]
  • management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems ... machine-checked proofs. Typical applications include the formalization of programming languages semantics (e.g. the CompCert ... EAL7 certification in industrial context), the formalization of mathematics (e.g. the full formalization...
  • Isabelle/HOL

  • Referenced in 833 articles [sw01569]
  • assistant. It allows mathematical formulas to be expressed in a formal language and provides tools ... calculus. The main application is the formalization of mathematical proofs and in particular formal verification...
  • Isabelle

  • Referenced in 541 articles [sw00454]
  • assistant. It allows mathematical formulas to be expressed in a formal language and provides tools ... calculus. The main application is the formalization of mathematical proofs and in particular formal verification...
  • HOL Light

  • Referenced in 257 articles [sw06580]
  • some non-trivial tasks in the formalization of mathematics and industrial formal verification...
  • LEGO

  • Referenced in 105 articles [sw09685]
  • bringing the level of formalization closer to that of informal mathematics. The higher-order power ... types, provide an expressive language for formalization of mathematical problems and program specification and development...
  • Isar

  • Referenced in 125 articles [sw04599]
  • Despite this success in actually formalizing parts of mathematics and computer science, there are still ... semi-automated reasoning (Isar) approach to readable formal proof documents sets out to bridge...
  • MPTP 0.2

  • Referenced in 42 articles [sw02589]
  • project is to make the large formal Mizar Mathematical Library (MML) available to current first ... Mizar proof constructs into the TPTP formalism. The proofs using second-order Mizar schemes ... inductive or deductive system trained on formal mathematics can be sometimes smarter than MML authors...
  • Isabelle/ZF

  • Referenced in 55 articles [sw04973]
  • assistant. It allows mathematical formulas to be expressed in a formal language and provides tools ... calculus. The main application is the formalization of mathematical proofs and in particular formal verification...
  • ETPS

  • Referenced in 145 articles [sw06302]
  • partial automation of various mathematical activities, promoting development of formal theories in a wide variety ... textbook: Peter B. Andrews, An Introduction to Mathematical Logic and Type Theory: To Truth Through ... ETPS: A System to Help Students Write Formal Proofs (postscript...
  • Nuprl

  • Referenced in 371 articles [sw06751]
  • system is a framework for reasoning about mathematics and programming. Over the years its design ... base and supports the cooperation of independent formal tools...
  • C-CoRN

  • Referenced in 33 articles [sw06752]
  • computer based library of constructive mathematics, formalized in the theorem prover Coq. Background: There ... this: we put mathematics on a computer in an active (formalized ... constructive theorem prover), but mainly because constructive mathematics has the additional bonus of providing (actual ... CoRN grew out of the FTA project, formalizing the Fundamental Theorem of Algebra...
  • Flyspeck

  • Referenced in 98 articles [sw10277]
  • Flyspeck informal mathematical text as a narrative linked to the formal development. To make this...
  • MoMM

  • Referenced in 31 articles [sw04655]
  • world’s largest body of formalized mathematics - the Mizar Mathematical Library (MML), which uses...
  • Matita

  • Referenced in 64 articles [sw06140]
  • machine collaboration. It provides a formal language where mathematical definitions, executable algorithms and theorems cohexist...
  • MPTP

  • Referenced in 21 articles [sw02489]
  • existence of large integral bodies of formalized mathematics. Then we proceed to describe the implementation ... makes the largest existing corpus of formalized mathematics available to theorem provers. MPTP (Mizar Problems...
  • Ott

  • Referenced in 25 articles [sw00663]
  • either for informal mathematics or the formal mathematics of a proof assistant -- make it much...
  • MBase

  • Referenced in 17 articles [sw08724]
  • that offers a universal repository of formalized mathematics where the formal representation allows semantics-based ... propose a methodology for developing representation formalisms for mathematical knowledge bases. We propose to concretely ... that is well-suited both for formalizing mathematical practice and supporting efficient inference services. This...
  • MMT

  • Referenced in 38 articles [sw07136]
  • provides an interface layer between formally rigorous mathematical systems, and knowledge management services which...
  • MegaWave

  • Referenced in 24 articles [sw04428]
  • inspired from and are a mathematical formalization of the Gestalt theory. Gestalt theory, which ... never been formalized is a rigorous realm of vision psychology developed between ... From the mathematical viewpoint the closest field to it is stochastic geometry, involving basic probability...
  • MizarMode

  • Referenced in 15 articles [sw01973]
  • tool for the Mizar way of formalizing mathematics The Emacs authoring environment for Mizar (MizarMode ... maintaining a very large body of formalized mathematics. par Mizar is a non-programmable ... long-term and large-scale formalization effort. MizarMode has been designed with...