Travesty.Bi_traversable_types
The main groups of signatures provided by this module are:
We also define other signatures, mostly for internal book-keeping. They may be useful elsewhere, however.
These signatures form the inner body of the On_monad
functor in the main signatures. They all have names ending with _on_monad
, and assume the existence of a monad M
.
While they aren't interesting on their own, they do contain (in slightly abstract form) the specific functions needed to build, and provided on building, bi-traversable containers.
Here, we define some signatures for bi-traversable structures in an arity-generic way. We then specialise them for arity-0 and arity-1 types.
Unlike in Traversal_types
, we don't (yet) have any specific types for monadic bi-traversals; this is because we don't derive any operations that only work on monads.
module type Basic_generic_on_applicative = sig ... end
Basic_generic_on_applicative
describes applicative bi-traversal on types of any arity.
module type Generic_on_applicative = sig ... end
Generic_on_applicative
extends Generic
to contain various derived operators; we use it to derive the signatures of the various On
modules.
module type Basic0_on_applicative = sig ... end
Basic0_on_applicative
is the inner signature of an applicative bi-traversal over arity-0 types.
module type Basic1_left_on_applicative = sig ... end
Basic1_left_on_applicative
is the inner signature of an applicative bi-traversal over arity-1 types with a floating left type and fixed right type.
module type Basic1_right_on_applicative = sig ... end
Basic1_right_on_applicative
is the inner signature of a monadic bi-traversal over arity-1 types with a floating right type and fixed left type.
module type Basic2_on_applicative = sig ... end
Basic2_on_applicative
is the inner signature of a monadic bi-traversal over arity-2 types with a floating right type and fixed left type.
We now define basic signatures that generalise the above signatures over all monads.
These signatures form the input to functors that provide derived operations, chaining, type-fixing, and conversion to bi-mappable and regular traversable containers.
The basic signatures are Basic0
, which defines traversal across an arity-0 type t
(with a fixed, associated element type elt
); Basic1_left
and Basic1_right
, which fix the right and left element type respectively (leaving the named type floating); and Basic2
, which defines traversal across an arity-2 type ('l, 'r) t
with left element type 'l
and right element type 'r
.
module type Basic0 = sig ... end
Basic0
is the basic signature of an arity-0 bi-traversable type.
module type Basic1_left = sig ... end
Basic1_left
is the basic signature of an arity-1 bi-traversable type with a floating left type and fixed right type.
module type Basic1_right = sig ... end
Basic1_right
is the basic signature of an arity-1 bi-traversable type with a floating right type and fixed left type.
module type Basic2 = sig ... end
Basic2
is the signature of an arity-2 bi-traversable type with floating left and right types.
The signatures below include various functions we can derive from bi-mappable types.
module type Generic = sig ... end
Generic
is a generic interface for bi-mappable types, used to build S0
(arity-0) and S1
(arity-1).
module type S0 = sig ... end
S0
is the full signature of an arity-0 bi-traversable type.
module type S1_left = sig ... end
S1_left
is the full signature of an arity-1 bi-traversable type with a floating left type and fixed right type.
module type S1_right = sig ... end
S1_right
is the full signature of an arity-1 bi-traversable type with a floating right type and fixed left type.
module type S2 = sig ... end
S2
is the full signature of an arity-2 bi-traversable type with floating left and right types.