### 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

### 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