### Abstract

The propositions-as-types correspondence is ordinarily presented as linking the metatheory of typed λ-calculi and the proof theory of intuitionistic logic. Griffin observed that this correspondence could be extended to classical logic through the use of control operators. This observation set off a flurry of further research, leading to the development of Parigots λμ-calculus. In this work, we formalise λμ- calculus in Isabelle/HOL and prove several metatheoretical properties such as type preservation and progress.

### License

BSD License

### Topics

- Computer science/Programming languages/Lambda calculi

### Session LambdaMu

- Syntax
- Types
- DeBruijn
- Substitution
- Reduction
- ContextFacts
- TypePreservation
- Progress
- Peirce

## Cite

×

LambdaMu-AFP

    @article{LambdaMu-AFP,
      author  = {Cristina Matache and Victor B. F. Gomes and Dominic P. Mulligan},
      title   = {The LambdaMu-calculus},
      journal = {Archive of Formal Proofs},
      month   = {August},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/LambdaMu.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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