Generating Recursors

This repository contains a small project in progress to generate recursors for inductive types.

• preliminary.v
• naming.v naming functions and scheme for the named definition
• commons.v functions building terms common to many files
• preprocess_parameters.v computes uniform parameters and converts gather relevant information
• preprocess_debruijn_to_named.v fully names the deburijn variables present in the interface
• postprocess_named_to_debruijn.v converts a named term to one defined using debruijn variables
• generate_rec_call computes rec call, if any, both for types and terms
• generate_types.v generates the types that are used for the term and type of the recursor
• generate_rec_type.v generates the type of the recursor of a mutual inductive type given a fully named mdecl. It handles:
  • basics
  • parameters
  • indices
  • mutual
  • non uniform parameters
  • nested on param (no indices)
  • nested on param (has indices)
  • LetIn in args
  • rec call on LetIn
  • relevance
  • universe constrains
  • sort poly
• generate_rec_term.v generates the type of the recursor of a mutual inductive type given a fully named mdecl. It handles:
  • basics
  • parameters
  • indices
  • mutual
  • non uniform parameters
  • nested on param (no indices)
  • nested on param (has indices)
  • LetIn in args
  • rec call on LetIn
  • relevance
  • universe constrains
  • sort poly
• unit_tests.v provide a testing functions with different mode of testing and examples

There is then a folder of unit tests. It contains:

• t01_basic_types: basic inductive types like bool / nat etc...
• t02_uniform_param_types: inductive types with uniform parmeters like list
• t03_indexed_param_types: inductive types with indices like vec
• t04_mutual_types: basic mutual inductive types like even and odd
• t05_uniform_param_types: inductive types with non uniform parameters like nu_list :

Inductive nu_list (A : Type) : Type :=
| nu_nil : nu_list A
| nu_cons : nu_list (A * A) -> nu_list A.

• t06_nested_types: nested inductive types like RoseTree
• t07_let_types: inductive types with let in in the type of the constructors
• t08_metacoq_types: types from MetaCoq