The foundation of a generic theorem prover
Journal of Automated Reasoning
Proof General: A Generic Tool for Proof Development
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
A Refinement of de Bruijn's Formal Language of Mathematics
Journal of Logic, Language and Information
A User Interface for a Mathematical System that Allows Ambiguous Formulae
Electronic Notes in Theoretical Computer Science (ENTCS)
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Declarative Representation of Proof Terms
Journal of Automated Reasoning
A declarative language for the coq proof assistant
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
Generating counterexamples for structural inductions by exploiting nonstandard models
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Textbook proofs meet formal logic: the problem of underspecification and granularity
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Extracting computer algebra programs from statements
EUROCAST'05 Proceedings of the 10th international conference on Computer Aided Systems Theory
Teaching semantics with a proof assistant: no more LSD trip proofs
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Set Graphs. III. Proof Pearl: Claw-Free Graphs Mirrored into Transitive Hereditarily Finite Sets
Journal of Automated Reasoning
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The mathematical proof checker Mizar by Andrzej Trybulec uses a proof input language that is much more readable than the input languages of most other proof assistants. This system also differs in many other respects from most current systems. John Harrison has shown that one can have a Mizar mode on top of a tactical prover, allowing one to combine a mathematical proof language with other styles of proof checking. Currently the only fully developed Mizar mode in this style is the Isar proof language for the Isabelle theorem prover. In fact the Isar language has become the official input language to the Isabelle system, even though many users still use its low-level tactical part only. In this paper we compare Mizar and Isar. A small example, Euclid's proof of the existence of infinitely many primes, is shown in both systems. We also include slightly higher-level views of formal proof sketches. Moreover, a list of differences between Mizar and Isar is presented, highlighting the strengths of both systems from the perspective of end-users. Finally, we point out some key differences of the internal mechanisms of structured proof processing in either system.