### Abstract

We formalize a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory includes many properties of the standard operators on terms: substitution, swapping and freshness. It also includes bindings-aware induction and recursion principles and support for semantic interpretation. This work has been presented in the ITP 2017 paper “A Formalized General Theory of Syntax with Bindings”.

### License

BSD License

### Topics

- Computer science/Programming languages/Lambda calculi
- Computer science/Functional programming
- Logic/General logic/Mechanization of proofs

### Session Binding_Syntax_Theory

- Preliminaries
- QuasiTerms_Swap_Fresh
- QuasiTerms_PickFresh_Alpha
- QuasiTerms_Environments_Substitution
- Pick
- Equiv_Relation2
- Transition_QuasiTerms_Terms
- Terms
- Well_Sorted_Terms
- Iteration
- Semantic_Domains
- Recursion

## Cite

×

Binding_Syntax_Theory-AFP

    @article{Binding_Syntax_Theory-AFP,
      author  = {Lorenzo Gheri and Andrei Popescu},
      title   = {A General Theory of Syntax with Bindings},
      journal = {Archive of Formal Proofs},
      month   = {April},
      year    = {2019},
      note    = {\url{https://isa-afp.org/entries/Binding_Syntax_Theory.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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