### Abstract

This Isabelle/HOL formalization defines Knuth–Bendix orders for higher-order terms without lambda-abstraction and proves many useful properties about them. The main order fully coincides with the standard transfinite KBO with subterm coefficients on first-order terms. It appears promising as the basis of a higher-order superposition calculus.

### License

BSD License

### Topics

- Logic/Rewriting

### Session Lambda_Free_KBOs

- Lambda_Free_KBO_Util
- Lambda_Free_KBO_App
- Lambda_Free_KBO_Std
- Lambda_Free_KBO_Basic
- Lambda_Free_TKBO_Coefs
- Lambda_Encoding_KBO
- Lambda_Free_KBOs

### Depends on

- Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms
- Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals
- Executable Multivariate Polynomials
- Regular Sets and Expressions

## Cite

×

Lambda_Free_KBOs-AFP

    @article{Lambda_Free_KBOs-AFP,
      author  = {Heiko Becker and Jasmin Christian Blanchette and Uwe Waldmann and Daniel Wand},
      title   = {Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms},
      journal = {Archive of Formal Proofs},
      month   = {November},
      year    = {2016},
      note    = {\url{https://isa-afp.org/entries/Lambda_Free_KBOs.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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