Name
Abstract | ||
|---|---|---|
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such descriptions: the interpretation of atomic judgments through recursive definitions and an encoding of binding constructs via generic judgments. However, logics encompassing these two features do not currently allow for the definition of relations that embody dynamic aspects related to binding, a capability needed in many reasoning tasks. We propose a new relation between terms called nominal abstraction as a means for overcoming this deficiency. We incorporate nominal abstraction into a rich logic also including definitions, generic quantification, induction, and co-induction that we then prove to be consistent. We present examples to show that this logic can provide elegant treatments of binding contexts that appear in many proofs, such as those establishing properties of typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.ic.2010.09.004 | Information and Computation/information and Control |
Keywords | DocType | Volume |
proof search,Generic judgments,reasoning about operational semantics,Reasoning about operational semantics,generic quantification,nominal abstraction,Higher-order abstract syntax,λ -Tree syntax,generic judgment,reasoning task,binding context,rich logic,higher-order abstract syntax,Proof search,generic judgments,binding construct,atomic judgment,Recursive relational specification,logic-based reasoning | Journal | 209 |
Issue | ISSN | Citations |
1 | Information and Computation | 9 |
PageRank | References | Authors |
0.55 | 34 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrew Gacek | 1 | 252 | 16.87 |
| Dale Miller | 2 | 90 | 5.17 |
| Gopalan Nadathur | 3 | 1047 | 117.85 |