Introduction to higher order categorical logic
Introduction to higher order categorical logic
Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
On observational equivalence and algebraic specification
Journal of Computer and System Sciences
Algebraic specifications of reachable higher-order algebras
Lecture notes in Computer Science on Recent trends in data type specification
Proofs and types
Handbook of theoretical computer science (vol. B)
Universal algebra in higher types
Theoretical Computer Science
Handbook of logic in computer science (vol. 1)
Handbook of logic in computer science (vol. 2)
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
On the power of higher-order algebraic specification methods
Information and Computation
A completeness theorem for the expressive power of higher-order algebraic specifications
Journal of Computer and System Sciences - special issue on complexity theory
Fundamentals of Algebraic Specification I
Fundamentals of Algebraic Specification I
Completeness of many-sorted equational logic
ACM SIGPLAN Notices
A Process Calculus with Finitary Comprehended Terms
Theory of Computing Systems
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We introduce a necessary and sufficient condition for the ω-extensionality rule of higher-order equational logic to be conservative over first-order many-sorted equational logic for ground first-order equations. This gives a precise condition under which computation in the higher-order initial model by term rewriting is possible. The condition is then generalised to characterise a normal form for higher-order equational proofs in which extensionality inferences occur only as the final proof inferences. The main result is based on a notion of observational equivalence between higher-order elements induced by a topology of finite information on such elements. Applied to extensional higher-order algebras with countable first-order carrier sets, the finite information topology is metric and second countable in every type.