Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Term rewriting and all that
An algebraic generalization of Frege structures—binding algebras
Theoretical Computer Science
Semantic analysis of normalisation by evaluation for typed lambda calculus
Proceedings of the 4th ACM SIGPLAN international conference on Principles and practice of declarative programming
Abstract Syntax and Variable Binding
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Term rewriting with variable binding: an initial algebra approach
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Electronic Notes in Theoretical Computer Science (ENTCS)
Second-Order and Dependently-Sorted Abstract Syntax
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Term Equational Systems and Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
On the construction of free algebras for equational systems
Theoretical Computer Science
Journal of Logic and Computation
Second-order algebraic theories
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Mathematical models of computational and combinatorial structures
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Second-order algebraic theories
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Polymorphic abstract syntax via Grothendieck construction
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Discrete generalised polynomial functors
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
An algebraic presentation of predicate logic
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
Instances of Computational Effects: An Algebraic Perspective
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
Multiversal Polymorphic Algebraic Theories: Syntax, Semantics, Translations, and Equational Logic
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We extend universal algebra and its equational logic from first to second order as follows. 1. We consider second-order equational presentations as specified by identities between second-order terms, with both variables and parameterised metavariables over signatures of variable-binding operators. 2. We develop an algebraic model theory for second-order equational presentations, generalising the semantics of (first-order) algebraic theories and of (untyped and simply-typed) lambda calculi. 3. We introduce a deductive system, Second-Order Equational Logic, for reasoning about the equality of second-order terms. Our development is novel in that this equational logic is synthesised from the model theory. Hence it is necessarily sound. 4. Second-Order Equational Logic is shown to be a conservative extension of Birkhoff's (First-Order) Equational Logic. 5. Two completeness results are established: the semantic completeness of equational derivability, and the derivability completeness of (bidirectional) Second-Order Term Rewriting.