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<title>8.7 Substituting inside a signature</title>
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<h2 class="section" id="s:signature-substitution"><a class="section-anchor" href="#s:signature-substitution" aria-hidden="true"></a>8.7 Substituting inside a signature</h2>
<ul>
<li><a href="signaturesubstitution.html#ss%3Adestructive-substitution">8.7.1 Destructive substitutions</a>
</li><li><a href="signaturesubstitution.html#ss%3Alocal-substitution">8.7.2 Local substitution declarations</a>
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<h3 class="subsection" id="ss:destructive-substitution"><a class="section-anchor" href="#ss:destructive-substitution" aria-hidden="true"></a>8.7.1 Destructive substitutions</h3>
<p>(Introduced in OCaml 3.12, generalized in 4.06)</p><div class="syntax"><table class="display dcenter"><tr class="c019"><td class="dcell"><table class="c001 cellpading0"><tr><td class="c018">
<a class="syntax" href="modtypes.html#mod-constraint"><span class="c010">mod-constraint</span></a></td><td class="c015">::=</td><td class="c017">
...
</td></tr>
<tr><td class="c018"> </td><td class="c015">∣</td><td class="c017"> <span class="c004">type</span> [<a class="syntax" href="typedecl.html#type-params"><span class="c010">type-params</span></a>] <a class="syntax" href="names.html#typeconstr-name"><span class="c010">typeconstr-name</span></a> <span class="c004">:=</span> <a class="syntax" href="types.html#typexpr"><span class="c010">typexpr</span></a>
</td></tr>
<tr><td class="c018"> </td><td class="c015">∣</td><td class="c017"> <span class="c004">module</span> <a class="syntax" href="names.html#module-path"><span class="c010">module-path</span></a> <span class="c004">:=</span> <a class="syntax" href="names.html#extended-module-path"><span class="c010">extended-module-path</span></a>
</td></tr>
</table></td></tr>
</table></div><p>A “destructive” substitution (<span class="c004">with</span> ... <span class="c004">:=</span> ...) behaves essentially like
normal signature constraints (<span class="c004">with</span> ... <span class="c004">=</span> ...), but it additionally removes
the redefined type or module from the signature.</p><p>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 <span class="c004">with type</span> the definition had to be another type constructor with the
same type parameters.</p><p>A natural application of destructive substitution is merging two
signatures sharing a type name.
</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> Printable = <span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">type</span> t
<span class="ocamlkeyword">val</span> print : Format.formatter -> t -> unit
<span class="ocamlkeyword">end</span>
<span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> Comparable = <span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">type</span> t
<span class="ocamlkeyword">val</span> compare : t -> t -> int
<span class="ocamlkeyword">end</span>
<span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> PrintableComparable = <span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">include</span> Printable
<span class="ocamlkeyword">include</span> Comparable <span class="ocamlkeyword">with</span> <span class="ocamlkeyword">type</span> t := t
<span class="ocamlkeyword">end</span></div></div>
</div><p>One can also use this to completely remove a field:
</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> S = Comparable <span class="ocamlkeyword">with</span> <span class="ocamlkeyword">type</span> t := int</div>
<div class="pre caml-output ok"><span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> S = <span class="ocamlkeyword">sig</span> <span class="ocamlkeyword">val</span> compare : int -> int -> int <span class="ocamlkeyword">end</span></div></div>
</div><p>
or to rename one:
</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> S = <span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">type</span> u
<span class="ocamlkeyword">include</span> Comparable <span class="ocamlkeyword">with</span> <span class="ocamlkeyword">type</span> t := u
<span class="ocamlkeyword">end</span></div>
<div class="pre caml-output ok"><span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> S = <span class="ocamlkeyword">sig</span> <span class="ocamlkeyword">type</span> u <span class="ocamlkeyword">val</span> compare : u -> u -> int <span class="ocamlkeyword">end</span></div></div>
</div><p>Note that you can also remove manifest types, by substituting with the
same type.
</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> ComparableInt = Comparable <span class="ocamlkeyword">with</span> <span class="ocamlkeyword">type</span> t = int ;;</div>
<div class="pre caml-output ok"><span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> ComparableInt = <span class="ocamlkeyword">sig</span> <span class="ocamlkeyword">type</span> t = int <span class="ocamlkeyword">val</span> compare : t -> t -> int <span class="ocamlkeyword">end</span></div></div>
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> CompareInt = ComparableInt <span class="ocamlkeyword">with</span> <span class="ocamlkeyword">type</span> t := int</div>
<div class="pre caml-output ok"><span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> CompareInt = <span class="ocamlkeyword">sig</span> <span class="ocamlkeyword">val</span> compare : int -> int -> int <span class="ocamlkeyword">end</span></div></div>
</div>
<h3 class="subsection" id="ss:local-substitution"><a class="section-anchor" href="#ss:local-substitution" aria-hidden="true"></a>8.7.2 Local substitution declarations</h3>
<p>(Introduced in OCaml 4.08)</p><div class="syntax"><table class="display dcenter"><tr class="c019"><td class="dcell"><table class="c001 cellpading0"><tr><td class="c018">
<a class="syntax" href="modtypes.html#specification"><span class="c010">specification</span></a></td><td class="c015">::=</td><td class="c017">
...
</td></tr>
<tr><td class="c018"> </td><td class="c015">∣</td><td class="c017"> <span class="c004">type</span> <a class="syntax" href="#type-subst"><span class="c010">type-subst</span></a> { <span class="c004">and</span> <a class="syntax" href="#type-subst"><span class="c010">type-subst</span></a> }
</td></tr>
<tr><td class="c018"> </td><td class="c015">∣</td><td class="c017"> <span class="c004">module</span> <a class="syntax" href="names.html#module-name"><span class="c010">module-name</span></a> <span class="c004">:=</span> <a class="syntax" href="names.html#extended-module-path"><span class="c010">extended-module-path</span></a>
</td></tr>
<tr><td class="c018"> </td></tr>
<tr><td class="c018"><a class="syntax" id="type-subst"><span class="c010">type-subst</span></a></td><td class="c015">::=</td><td class="c017">
[<a class="syntax" href="typedecl.html#type-params"><span class="c010">type-params</span></a>] <a class="syntax" href="names.html#typeconstr-name"><span class="c010">typeconstr-name</span></a> <span class="c004">:=</span> <a class="syntax" href="types.html#typexpr"><span class="c010">typexpr</span></a> { <a class="syntax" href="typedecl.html#type-constraint"><span class="c010">type-constraint</span></a> }
</td></tr>
</table></td></tr>
</table></div><p>Local substitutions behave like destructive substitutions (<span class="c004">with</span> ... <span class="c004">:=</span> ...)
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.</p><p>This provides a convenient way to introduce local names for types and modules
when defining a signature:</p><div class="caml-example verbatim">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> S = <span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">type</span> t
<span class="ocamlkeyword">module</span> Sub : <span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">type</span> outer := t
<span class="ocamlkeyword">type</span> t
<span class="ocamlkeyword">val</span> to_outer : t -> outer
<span class="ocamlkeyword">end</span>
<span class="ocamlkeyword">end</span></div>
<div class="pre caml-output ok"><span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> S =
<span class="ocamlkeyword">sig</span> <span class="ocamlkeyword">type</span> t <span class="ocamlkeyword">module</span> Sub : <span class="ocamlkeyword">sig</span> <span class="ocamlkeyword">type</span> t <span class="ocamlkeyword">val</span> to_outer : t/1 -> t/2 <span class="ocamlkeyword">end</span> <span class="ocamlkeyword">end</span></div></div>
</div><p>Note that, unlike type declarations, type substitution declarations are not
recursive, so substitutions like the following are rejected:</p><div class="caml-example toplevel">
<div class="ocaml">
<div class="pre caml-input"> <span class="ocamlkeyword">module</span> <span class="ocamlkeyword">type</span> S = <span class="ocamlkeyword">sig</span>
<span class="ocamlkeyword">type</span> 'a poly_list := [ `Cons <span class="ocamlkeyword">of</span> 'a * 'a <span class="ocamlhighlight">poly_list</span> | `Nil ]
<span class="ocamlkeyword">end</span> ;;</div>
<div class="pre caml-output error"><span class="ocamlerror">Error</span>: Unbound type constructor poly_list</div></div>
</div>
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