Niveau: Supérieur, Doctorat, Bac+8
Nominal Abstraction Andrew Gacek?,a, Dale Millerb, Gopalan Nadathura a Department of Computer Science and Engineering, University of Minnesota b INRIA Saclay - Ile-de-France & LIX/Ecole polytechnique Abstract Recursive relational specifications are commonly used to describe the computational struc- ture 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 abstrac- tion 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 establish- ing properties of typing calculi and of arbitrarily cascading substitutions that play a role in reducibility arguments. Key words: generic judgments, higher-order abstract syntax, ?-tree syntax, proof search, reasoning about operational semantics ?4-192 EE/CS Building, 200 Union Street SE, Minneapolis, MN 55455 Email addresses: agacek@cs.
- unique nominal constant
- generic judgments
- nominal abstraction
- terms
- proof theory
- currently allow
- based reasoning
- abstraction into
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- rules