The different Types module

[mimoo]

A Types module is repeated in many places, which makes refactor quite hard to perform. In order to refactor this, let's understand where it is used and how it differs in different places:

The first one is in types.ml:

module type Types = sig
  module Checked : sig
    type ('a, 'f) t
  end

  module As_prover : sig
    type ('a, 'f) t
  end

  module Typ : sig
    include module type of Typ.T

    type ('var, 'value, 'f) t = ('var, 'value, 'f, (unit, 'f) Checked.t) Typ.t
  end

  module Provider : sig
    include module type of Provider.T

    type ('a, 'f) t =
      (('a Request.t, 'f) As_prover.t, ('a, 'f) As_prover.t) provider
  end
end

Note: it seems like we can safely remove the As_prover one. See #750

which references other types from the same file/module.

Other occurrences:

• ~ As_prover.S.Types | same as Types.Types
• ~ As_prover.Extended.Types | sames as Types.Types
• x As_prover.Make (Checked) (_): S | creates it from Checked.Types
• x As_prover.Make_extended (Checked) (_): S | creates it from Checked.Types
• x As_prover.T.Types and As_prover.Types | creates it from Checked_ast.Types
• x Checked_ast.Types (where Checked0 is the AST):

  module Types = struct
      module Checked = struct
          type ('a, 'f) t = ('a, 'f) Checked0.t
      end
  
      module As_prover = struct
          type ('a, 'f) t = ('a, 'f) As_prover0.t
      end
  
      module Typ = struct
          include Types.Typ.T
  
          type ('var, 'value, 'f) t = ('var, 'value, 'f, (unit, 'f) Checked.t) typ
      end
  
      module Provider = struct
          include Types.Provider.T
  
          type ('a, 'f) t =
          (('a Request.t, 'f) As_prover0.t, ('a, 'f) As_prover0.t) provider
      end
  end

• x Checked_ast.Basic.Types | uses Checked_ast.Types
• ~ Checked_intf.Basic.Types | uses Types.Types
• ~ Checked_intf.S.Types | uses Types.Types
• ~ Checked_intf.Extended.Types | uses Types.Types
• x Checked_runner.Simple.Types

  module Types = struct
      module Checked = struct
          type ('a, 'f) t =
          | Pure of 'a
          | Function of ('f Run_state.t -> 'f Run_state.t * 'a)
      end
  
      module As_prover = struct
          type ('a, 'f) t = ('a, 'f) As_prover.t
      end
  
      module Typ = struct
          include Types.Typ.T
  
          type ('var, 'value, 'f) t = ('var, 'value, 'f, (unit, 'f) Checked.t) typ
      end
  
      module Provider = struct
          include Types.Provider.T
  
          type ('a, 'f) t =
          (('a Request.t, 'f) As_prover.t, ('a, 'f) As_prover.t) provider
      end
  end

• x Checked_runner.Make_checked

  module Types = struct
      module Checked = struct
          type ('a, 'f) t = ('a, Backend.Field.t) Simple.Types.Checked.t
      end
  
      module As_prover = struct
          type ('a, 'f) t = ('a, 'f) As_prover.t
      end
  
      module Typ = struct
          include Types.Typ.T
  
          type ('var, 'value, 'f) t = ('var, 'value, 'f, (unit, 'f) Checked.t) typ
      end
  
      module Provider = struct
          include Types.Provider.T
  
          type ('a, 'f) t =
          (('a Request.t, 'f) As_prover.t, ('a, 'f) As_prover.t) provider
      end
  end

• ~ Checked_runner.Run_extras | uses Types.Types
• x Checked_runner.Make (_) | creates Types from Checked_ast.Types
• ~ Checked.Make (Basic: Checked_intf.Basic) (_) : Checked_intf.S | creates Types from Basic.Types
• ~ Typ.Checked_monad.Types | uses Types.Types

What I'm able to infer from this is that Types.Types defines Checked.t as abstract, and the other types are based on that. Then they can be instantiated by the different monads:

• Checked_ast uses its own Checked.t (the AST monad)
• Checked_runner uses its own Checked.t as well (the state monad)

The question I am trying to answer is the following:

• what's the pattern here? Why are we creating or passing this Types module everywhere? Especially as this module is eventually removed from the snark interface (does not appear in snark_intf.ml)
• why is Checked_runner.Make still relying on Checked_ast.Types -> this one is easy, we can simply use Checked.Types
• why is As_prover.T.Types and As_prover.Types still relying on the Checked_ast Types