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143
Nominal algebra
, 2006
"... Nominal terms are a termlanguage used to accurately and expressively represent systems with binding. We present Nominal Algebra (NA), a theory of algebraic equality on nominal terms. Builtin support for binding in the presence of metavariables allows NA to closely mirror informal mathematical us ..."
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Cited by 8 (2 self)
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Nominal terms are a termlanguage used to accurately and expressively represent systems with binding. We present Nominal Algebra (NA), a theory of algebraic equality on nominal terms. Builtin support for binding in the presence of metavariables allows NA to closely mirror informal mathematical
Nominal Algebra and the HSP Theorem
"... Nominal algebra is a logic of equality developed to reason algebraically in the presence of binding. In previous work it has been shown how nominal algebra can be used to specify and reason algebraically about systems with binding, such as firstorder logic, the lambdacalculus, or process calculi. ..."
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Cited by 11 (5 self)
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Nominal algebra is a logic of equality developed to reason algebraically in the presence of binding. In previous work it has been shown how nominal algebra can be used to specify and reason algebraically about systems with binding, such as firstorder logic, the lambdacalculus, or process calculi
The lambdacalculus is nominal algebraic
"... The λcalculus is fundamental in the study of logic and computation. Partly this is because it is a tool to study functions and functions are an important object of study in this field. Partly this is because the λcalculus seems to be, for homo sapiens, an ergonomic formal syntax. ..."
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Cited by 1 (1 self)
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The λcalculus is fundamental in the study of logic and computation. Partly this is because it is a tool to study functions and functions are an important object of study in this field. Partly this is because the λcalculus seems to be, for homo sapiens, an ergonomic formal syntax.
NOMINAL ALGEBRA AND THE HSP THEOREM (TECHNICAL REPORT)
"... Abstract. Nominal algebra is a logic of equality developed to reason algebraically in the presence of binding. In previous work the authors have shown how nominal algebra can be used to specify and reason algebraically about systems with binding, such as firstorder logic, the λcalculus, or process ..."
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Abstract. Nominal algebra is a logic of equality developed to reason algebraically in the presence of binding. In previous work the authors have shown how nominal algebra can be used to specify and reason algebraically about systems with binding, such as firstorder logic, the λ
An axiomatic approach to metareasoning on nominal algebras in HOAS
 Leeuwen (Eds.), 28th International Colloquium on Automata, Languages and Programming, ICALP 2001
, 2001
"... We present a logical framework # for reasoning on a very general class of languages featuring binding operators, called nominal algebras, presented in higherorder abstract syntax (HOAS). # is based on an axiomatic syntactic standpoint and it consists of a simple types theory a la Church extended wi ..."
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Cited by 21 (1 self)
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We present a logical framework # for reasoning on a very general class of languages featuring binding operators, called nominal algebras, presented in higherorder abstract syntax (HOAS). # is based on an axiomatic syntactic standpoint and it consists of a simple types theory a la Church extended
Captureavoiding Substitution as a Nominal Algebra
 Formal Aspects of Computing
, 2008
"... Abstract. Substitution is fundamental to computer science, underlying for example quantifiers in predicate logic and betareduction in the lambdacalculus. So is substitution something we define on syntax on a casebycase basis, or can we turn the idea of ‘substitution ’ into a mathematical objec ..."
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Cited by 15 (5 self)
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ematical object? We exploit the new framework of Nominal Algebra to axiomatise substitution. We prove our axioms sound and complete with respect to a canonical model; this turns out to be quite hard, involving subtle use of results of rewriting and algebra. 1
Finite and infinite support in nominal algebra and logic: nominal completeness theorems for free
 Journal of Symbolic Logic
, 2012
"... By operations on models we show how to relate completeness with respect to permissivenominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissivenominal models, so the construction hinges on generating from an insta ..."
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Cited by 2 (1 self)
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By operations on models we show how to relate completeness with respect to permissivenominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissivenominal models, so the construction hinges on generating from
Under consideration for publication in Formal Aspects of Computing CaptureAvoiding Substitution as a Nominal Algebra
"... Abstract. Substitution is fundamental to the theory of logic and computation. Is substitution something that we define on syntax on a casebycase basis, or can we turn the idea of substitution into a mathematical object? We give axioms for substitution and prove them sound and complete with respect ..."
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with respect to a canonical model. As corollaries we obtain a useful conservativity result, and prove that equalityuptosubstitution is a decidable relation on terms. These results involve subtle use of techniques both from rewriting and algebra. A special feature of our method is the use of nominal
On Universal Algebra over Nominal Sets
"... ... theorem for algebras over nominal sets. We isolate a ‘uniform’ fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into ‘uniform’ theories and systematically prove ..."
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Cited by 9 (1 self)
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... theorem for algebras over nominal sets. We isolate a ‘uniform’ fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into ‘uniform’ theories and systematically
Results 1  10
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143