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Hierarchy Builder: algebraic hierarchies made easy in Coq with Elpi
It is nowadays customary to organize libraries of machine checked proofs around
hierarchies of algebraic structures [2, 6, 8, 16, 18, 23, 27]. One influential example is the …
hierarchies of algebraic structures [2, 6, 8, 16, 18, 23, 27]. One influential example is the …
On algebraic hierarchies in mathematical repository of Mizar
Mathematics, especially algebra, uses plenty of structures: groups, rings, integral domains,
fields, vector spaces to name a few of the most basic ones. Classes of structures are closely …
fields, vector spaces to name a few of the most basic ones. Classes of structures are closely …
Type-theoretic signatures for algebraic theories and inductive types
A Kovács - ar** a mathematical theory,
knowledge about a such a theory may reside in many places and in many forms within a …
knowledge about a such a theory may reside in many places and in many forms within a …
Rapid prototy** formal systems in MMT: 5 case studies
Logical frameworks are meta-formalisms in which the syntax and semantics of object logics
and related formal systems can be defined. This allows object logics to inherit …
and related formal systems can be defined. This allows object logics to inherit …
Leveraging the information contained in theory presentations
A theorem prover without an extensive library is much less useful to its potential users.
Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic …
Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic …
A language feature to unbundle data at will (short paper)
Programming languages with sufficiently expressive type systems provide users with
different means of data 'bundling'. Specifically, in dependently-typed languages such as …
different means of data 'bundling'. Specifically, in dependently-typed languages such as …
Diagram combinators in MMT
Formal libraries, especially large ones, usually employ modularity to build and maintain
large theories efficiently. Although the techniques used to achieve modularity vary between …
large theories efficiently. Although the techniques used to achieve modularity vary between …
Automatically proving equivalence by type-safe reflection
One difficulty with reasoning and programming with dependent types is that proof
obligations arise naturally once programs become even moderately sized. For example …
obligations arise naturally once programs become even moderately sized. For example …
Simple Type Theory
B Farmer - Springer
2 Answers to Readers' Questions 6 2.1 Why Logic?............................ 6 2.2 Why a Practical
Logic?..................... 6 2.3 Why Simple Type Theory?................... 7 2.4 Why not First-Order …
Logic?..................... 6 2.3 Why Simple Type Theory?................... 7 2.4 Why not First-Order …