\subsection{ss:destructive-substitution}{Destructive substitutions}

(Introduced in OCaml 3.12, generalized in 4.06)

\begin{syntax}
mod-constraint:
          ...
        | 'type' [type-params] typeconstr-name ':=' typexpr
        | 'module' module-path ':=' extended-module-path
\end{syntax}

A ``destructive'' substitution (@'with' ... ':=' ...@) behaves essentially like
normal signature constraints (@'with' ... '=' ...@), but it additionally removes
the redefined type or module from the signature.

Prior to OCaml 4.06, there were a number of restrictions: one could only remove
types and modules at the outermost level (not inside submodules), and in the
case of @'with type'@ the definition had to be another type constructor with the
same type parameters.

A natural application of destructive substitution is merging two
signatures sharing a type name.
\begin{caml_example*}{verbatim}
module type Printable = sig
  type t
  val print : Format.formatter -> t -> unit
end
module type Comparable = sig
  type t
  val compare : t -> t -> int
end
module type PrintableComparable = sig
  include Printable
  include Comparable with type t := t
end
\end{caml_example*}

One can also use this to completely remove a field:
\begin{caml_example}{verbatim}
module type S = Comparable with type t := int
\end{caml_example}
or to rename one:
\begin{caml_example}{verbatim}
module type S = sig
  type u
  include Comparable with type t := u
end
\end{caml_example}

Note that you can also remove manifest types, by substituting with the
same type.
\begin{caml_example}{verbatim}
module type ComparableInt = Comparable with type t = int ;;
module type CompareInt = ComparableInt with type t := int
\end{caml_example}

\subsection{ss:local-substitution}{Local substitution declarations}

(Introduced in OCaml 4.08)

\begin{syntax}
specification:
          ...
        | 'type' type-subst { 'and' type-subst }
        | 'module' module-name ':=' extended-module-path
        | 'module' 'type' module-name ':=' module-type

;

type-subst:
          [type-params] typeconstr-name ':=' typexpr { type-constraint }
\end{syntax}


Local substitutions behave like destructive substitutions (@'with' ... ':=' ...@)
but instead of being applied to a whole signature after the fact, they are
introduced during the specification of the signature, and will apply to all the
items that follow.

This provides a convenient way to introduce local names for types and modules
when defining a signature:

\begin{caml_example}{verbatim}
module type S = sig
  type t
  module Sub : sig
    type outer := t
    type t
    val to_outer : t -> outer
  end
end
\end{caml_example}

Note that, unlike type declarations, type substitution declarations are not
recursive, so substitutions like the following are rejected:

\begin{caml_example}{toplevel}
module type S = sig
  type 'a poly_list := [ `Cons of 'a * 'a poly_list | `Nil ]
end [@@expect error];;
\end{caml_example}

\subsection{ss:module-type-substitution}{Module type substitutions}

(Introduced in OCaml 4.13)

\begin{syntax}
mod-constraint:
          ...
        | 'module ' 'type' modtype-path  '=' module-type
        | 'module ' 'type' modtype-path  ':=' module-type
\end{syntax}

Module type substitution essentially behaves like type substitutions.
They are useful to refine an abstract module type in a signature into
a concrete module type,

\begin{caml_example}{toplevel}
module type ENDO = sig
  module type T
  module F: T -> T
end
module Endo(X: sig module type T end): ENDO with module type T = X.T =
struct
    module type T = X.T
    module F(X:T) = X
 end;;
\end{caml_example}

It is also possible to substitute a concrete module type with an
equivalent module types.

\begin{caml_example*}{verbatim}
module type A = sig
  type x
  module type R = sig
    type a = A of x
    type b
  end
end
module type S = sig
  type a = A of int
  type b
end
module type B = A with type x = int and module type R = S
\end{caml_example*}
However, such substitutions are never necessary.

Destructive module type substitution removes the module type substitution
from the signature
\begin{caml_example}{toplevel}
module type ENDO' = ENDO with module type T := ENDO;;
\end{caml_example}
If the right hand side of the substitution is not a path, then the destructive
substitution is only valid if the left-hand side of the substitution is never
used as the type of a first-class module in the original module type.

\begin{caml_example}{verbatim}[error]
module type T = sig module type S val x: (module S) end
module type Error = T with module type S := sig end
\end{caml_example}
