Semantics of Data Types

Volume 173 of the series Lecture Notes in Computer Science pp 197-214


Deriving structural induction in LCF

  • Lawrence PaulsonAffiliated withComputer Laboratory, University of Cambridge

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The fixed-point theory of computation allows a variety of recursive data structures. Constructor functions may be lazy or strict; types may be mutually recursive and satisfy equational constraints. Structural induction for these types follows from fixed-point induction; induction for lazy types is only sound for a subclass of formulas.

Structural induction is derived and discussed for several types, including lazy lists, finite lists, syntax trees for expressions, and finite sets. Experience with the LCF theorem prover is described.

The paper is a condensation of “Structural Induction in LCF” [12].