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The Abella interactive theorem prover (system description
 In Fourth International Joint Conference on Automated Reasoning
, 2008
"... Abella [3] is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a twolevel logic approach to specification and reasoning. One level is defined by a specification logic which s ..."
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Abella [3] is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a twolevel logic approach to specification and reasoning. One level is defined by a specification logic which supports a transparent
The Bedwyr system for model checking over syntactic expressions
 21th Conference on Automated Deduction, LNAI 4603, 391–397
, 2007
"... Bedwyr is a generalization of logic programming that allows model checking directly on syntactic expressions possibly containing bindings. This system, written in OCaml, is a direct implementation of two recent advances in the theory of proof search. The first is centered on the fact that both finit ..."
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Cited by 28 (17 self)
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Bedwyr is a generalization of logic programming that allows model checking directly on syntactic expressions possibly containing bindings. This system, written in OCaml, is a direct implementation of two recent advances in the theory of proof search. The first is centered on the fact that both finite success and finite failure can be captured in the sequent calculus by incorporating inference rules for definitions that allow fixed points to be explored. As a result, proof search in such a sequent calculus can capture simple model checking problems as well as may and must behavior in operational semantics. The second is that higherorder abstract syntax is directly supported using termlevel λbinders and the quantifier known as ∇. These features allow reasoning directly on expressions containing bound variables. 2
Mixing finite success and finite failure in an automated prover
 In Proceedings of ESHOL’05: Empirically Successful Automated Reasoning in HigherOrder Logics, pages 79 – 98
, 2005
"... Abstract. The operational semantics and typing judgements of modern programming and specification languages are often defined using relations and proof systems. In simple settings, logic programming languages can be used to provide rather direct and natural interpreters for such operational semantic ..."
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Abstract. The operational semantics and typing judgements of modern programming and specification languages are often defined using relations and proof systems. In simple settings, logic programming languages can be used to provide rather direct and natural interpreters for such operational semantics. More complex features of specifications such as names and their bindings, proof rules with negative premises, and the exhaustive enumeration of state spaces, all pose significant challenges to conventional logic programming systems. In this paper, we describe a simple architecture for the implementation of deduction systems that allows a specification to interleave between finite success and finite failure. The implementation techniques for this prover are largely common ones from higherorder logic programming, i.e., logic variables, (higherorder pattern) unification, backtracking (using streambased computation), and abstract syntax based on simply typed λterms. We present a particular instance of this prover’s architecture and its prototype implementation, Level 0/1, based on the dual interpretation of (finite) success and finite failure in proof search. We show how Level 0/1 provides a highlevel and declarative implementation of model checking and bisimulation checking for the (finite) πcalculus. 1
Proof search specifications of bisimulation and modal logics for the πcalculus
 ACM Trans. on Computational Logic
"... We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allo ..."
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We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within πcalculus expressions and their executions (proofs). We shall illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no sideconditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for onestep transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode the πcalculus with replications, in an extended logic with induction and coinduction.
System description: Abella – A system for reasoning about computations
 In Fourth International Joint Conference on Automated Reasoning
, 2008
"... Abella [Gac08] is an interactive theorem prover for reasoning about the properties ..."
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Cited by 3 (2 self)
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Abella [Gac08] is an interactive theorem prover for reasoning about the properties
Automation of HigherOrder Logic
 THE HANDBOOK OF THE HISTORY OF LOGIC, EDS. D. GABBAY & J. WOODS; VOLUME 9: LOGIC AND COMPUTATION, EDITOR JÖRG SIEKMANN
, 2014
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Optimizing the runtime processing of types in a higherorder logic programming language
 Proceedings of the 12th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR’05
, 2005
"... Abstract. The traditional purpose of types in programming languages of providing correctness assurances at compile time is increasingly being supplemented by a direct role for them in the computational process. In the specific context of typed logic programming, this is manifest in their effect on t ..."
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Abstract. The traditional purpose of types in programming languages of providing correctness assurances at compile time is increasingly being supplemented by a direct role for them in the computational process. In the specific context of typed logic programming, this is manifest in their effect on the unification operation. Their influence takes two different forms. First, in a situation where polymorphism is permitted, type information is needed to determine if different occurrences of the same name in fact denote an identical constant. Second, type information may determine the specific form of a binding for a variable. When types are needed for the second purpose as in the case of higherorder unification, these have to be available with every variable and constant. However, in many situations such as firstorder and higherorder pattern unification it turns out that types have no impact on the variable binding process. As a consequence, type examination is needed in these situations only for the first of the two purposes described and even here a careful preprocessing can considerably reduce their runtime footprint. We develop a scheme for treating types in these contexts that exploits this observation. Under this scheme, type information is elided in most cases and is embedded into term structure when this is not entirely possible. Our approach obviates types when properties known as definitional genericity and type preservation are satisfied and has the advantage of working even when these conditions are violated. 1
The Australian National University
"... We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allo ..."
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We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within πcalculus expressions and their executions (proofs). We illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no sideconditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for onestep transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode