Rea (rea.Rea)

Reference

Type abbreviations

type 'a ok = [

| `Ok of 'a

]

Success type abbreviation.

type 'e error = [

| `Error of 'e

]

Failure type abbreviation.

type ('e, 'a) res = [

| 'a ok
| 'e error

]

Result type abbreviation.

type ('l, 'r) branch = [

| `Fst of 'l
| `Snd of 'r

]

Choice type abbrevation.

type ('d, 'c) cps = ('d -> 'c) -> 'c

Continuation passing style function type abbreviation.

type 'a op'1 = 'a -> 'a

Unary operation type abbreviation.

type 'a op'2 = 'a -> 'a -> 'a

Binary operation type abbreviation.

type 'a lazy_op'2 = (unit -> 'a) -> (unit -> 'a) -> 'a

Lazy binary operation type abbrevation.

Abstract effect framework

The effect framework in this section is almost entirely free of concrete implementation details and should theoretically be usable in a wide variety of contexts including for wrapping existing monadic libraries.

The effect framework can also be extended by users. Consider the map effect. It consists of

the map'm effect signature type abbreviation,
the map' capability mix-in,
the map combinator, and
the derived implementation in monad'd.

And, of course, various interpreters implement the map' capability. The bottom line is that nothing prevents user defined extensions following the same pattern.

type nothing = |

Empty variant type used to ensure that no errors can be left unhandled.

type ('R, +'e, +'a) s

Abstract effect signature represents the application ('e, 'a) 'R of the higher-kinded effect representation type constructor 'R to the error 'e and answer 'a types.

Basic use of this framework should rarely require one to refer to this type, but this type will appear in inferred types. When writing type signatures the effect reader type abbreviation er should be preferred.

type ('R, 'e, 'a, 'D) er = 'D -> ('R, 'e, 'a) s

Effect reader takes a dictionary 'D of capabilities and returns an effect with the signature ('R, 'e, 'a) s.

Laziness

Effect readers are functions that take a dictionary of capabilities. This allows a form of laziness via η-expansion and effect signatures are designed to allow implementations to delay invoking the effect reader functions until the effects are really needed.

val eta'0 : (unit -> 'D -> 'a) -> 'D -> 'a

eta'0 @@ fun () -> body is equivalent to fun d -> body d.

Consider the following fib implementation:

let rec fib n = eta'0 @@ fun () ->
  if n <= 1 then
    pure n
  else
    lift'2 (+) (fib (n - 2)) (fib (n - 1))

The eta'0 @@ fun () -> ... makes it so that fib n returns in O(1) time without building the complete computation tree.

val eta'1 : ('b1 -> 'd -> 'a) -> 'b1 -> 'd -> 'a

eta'1 fn is equivalent to fun x d -> fn x d.

Consider the following list traversal implementation:

let rec map_er xyE = eta'1 @@ function
  | [] -> pure []
  | x :: xs ->
    let+ y = xyE x
    and+ ys = map_er xyE xs in
    y :: ys

The eta'1 @@ function ... makes it so that map_er xyE xs returns in O(1) time without going through the whole list to compute a complete computation tree for it.

val eta'2 : ('b1 -> 'b2 -> 'd -> 'a) -> 'b1 -> 'b2 -> 'd -> 'a

eta'2 fn is equivalent to fun x y d -> fn x y d.

Running

val run : 'd -> ('d -> 'a) -> 'a

run d xE is equivalent to xE d.

Functors

type ('R, 'e, 'a, 'b, 'D) map'm =
  ('b -> 'a) ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a) s

map effect signature.

class virtual ['R, 'D] map' : object ... end

map capability mix-in.

class ['R, 'O, 'D] map'of : ['R, 'O] map' -> object ... end

map capability projection.

class virtual ['R, 'D] functr' : object ... end

Functor offers the map capability.

val map : 
  ('b -> 'a) ->
  ('R, 'e, 'b, ['R, 'D] map' as 'D) er ->
  ('R, 'e, 'a, 'D) er

map xy xE effect.

val let+ : 
  ('R, 'e, 'b, ['R, 'D] map' as 'D) er ->
  ('b -> 'a) ->
  ('R, 'e, 'a, 'D) er

( let+ ) xE xy is equivalent to map xy xE.

val (>>-) : 
  ('R, 'e, 'b, ['R, 'D] map' as 'D) er ->
  ('b -> 'a) ->
  ('R, 'e, 'a, 'D) er

xE >>- xy is equivalent to map xy xE.

val (>->) : 
  ('a -> ('R, 'e, 'b, ['R, 'D] map' as 'D) er) ->
  ('b -> 'c) ->
  'a ->
  ('R, 'e, 'c, 'D) er

xyE >-> yz is equivalent to fun x -> map yz (xyE x).

val lift'1 : 
  ('b -> 'a) ->
  ('R, 'e, 'b, ['R, 'D] map' as 'D) er ->
  ('R, 'e, 'a, 'D) er

lift'1 xy xE is equivalent to map xy xE.

Pointed functors

type ('R, 'e, 'a, 'D) pure'm = 'a -> ('R, 'e, 'a) s

pure effect signature.

class virtual ['R, 'D] pure' : object ... end

pure capability mix-in.

class ['R, 'O, 'D] pure'of : ['R, 'O] pure' -> object ... end

pure capability projection.

class virtual ['R, 'D] pointed' : object ... end

Pointed functor offers the map, and pure capabilities.

class ['R, 'O, 'D] pointed'of : ['R, 'O] pointed' -> object ... end

map and pure capability projection.

val pure : 'a -> ('R, 'e, 'a, ['R, 'D] pure' as 'D) er

pure value effect.

val pure'0 : (unit -> 'a) -> ('R, 'e, 'a, ['R, 'D] pure' as 'D) er

pure'0 (fun () -> exp) is equivalent to eta'0 (fun () -> pure exp).

val pure'1 : ('b1 -> 'a) -> 'b1 -> ('R, 'e, 'a, ['R, 'D] pure' as 'D) er

pure'1 fn x1 is equivalent to eta'0 (fun () -> pure (fn x1)).

val pure'2 : 
  ('b1 -> 'b2 -> 'a) ->
  'b1 ->
  'b2 ->
  ('R, 'e, 'a, ['R, 'D] pure' as 'D) er

pure'2 fn x1 x2 x3 is equivalent to eta'0 (fun () -> pure (fn x1 x2)).

val pure'3 : 
  ('b1 -> 'b2 -> 'b3 -> 'a) ->
  'b1 ->
  'b2 ->
  'b3 ->
  ('R, 'e, 'a, ['R, 'D] pure' as 'D) er

pure'3 fn x1 x2 x3 is equivalent to eta'0 (fun () -> pure (fn x1 x2 x3)).

val pure'4 : 
  ('b1 -> 'b2 -> 'b3 -> 'b4 -> 'a) ->
  'b1 ->
  'b2 ->
  'b3 ->
  'b4 ->
  ('R, 'e, 'a, ['R, 'D] pure' as 'D) er

pure'4 fn x1 x2 x3 x4 is equivalent to eta'0 (fun () -> pure (fn x1 x2 x3 x4)).

val return : 'a -> ('R, 'e, 'a, ['R, 'D] pure' as 'D) er

return value is equivalent to pure value.

val unit : ('R, 'e, unit, ['R, 'D] pure' as 'D) er

unit is equivalent to pure ().

val do_unless : bool -> ('R, 'e, unit, ['R, 'D] pure' as 'D) er op'1

do_unless b uE is equivalent to if b then unit else uE.

val do_when : bool -> ('R, 'e, unit, ['R, 'D] pure' as 'D) er op'1

do_when b uE is equivalent to if b then uE else unit.

Applicative functors

type ('R, 'e, 'a, 'b, 'D) pair'm =
  ('R, 'e, 'a, 'D) er ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a * 'b) s

pair effect signature.

class virtual ['R, 'D] pair' : object ... end

pair capability mix-in.

class ['R, 'O, 'D] pair'of : ['R, 'O] pair' -> object ... end

pair capability projection.

class virtual ['R, 'D] product' : object ... end

Product functor offers the map, and pair capabilities.

class ['R, 'O, 'D] product'of : ['R, 'O] product' -> object ... end

map and pair capability projection.

class virtual ['R, 'D] applicative' : object ... end

Applicative functor offers the map, pure, and pair capabilities.

class ['R, 'O, 'D] applicative'of : ['R, 'O] applicative' -> object ... end

map, pure, and pair capability projection.

val pair : 
  ('R, 'e, 'a, ['R, 'D] pair' as 'D) er ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a * 'b, 'D) er

pair xE yE effect.

val and+ : 
  ('R, 'e, 'a, ['R, 'D] pair' as 'D) er ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a * 'b, 'D) er

( and+ ) xE yE is equivalent to pair xE yE.

val (<*>) : 
  ('R, 'e, 'a, ['R, 'D] pair' as 'D) er ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a * 'b, 'D) er

xE <*> yE is equivalent to pair xE yE.

val tuple'2 : 
  ('R, 'e, 'a, ['R, 'D] pair' as 'D) er ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a * 'b, 'D) er

tuple'2 x1E x2E is equivalent to pair x1E x2E.

val tuple'3 : 
  ('R, 'e, 'a1, ['R, 'D] product' as 'D) er ->
  ('R, 'e, 'a2, 'D) er ->
  ('R, 'e, 'a3, 'D) er ->
  ('R, 'e, 'a1 * 'a2 * 'a3, 'D) er

tuple'3 x1E x2E x3E is equivalent to map (fun (x1, (x2, x3)) -> (x1, x2, x3)) (pair x1E (pair x2E x3E)).

val tuple'4 : 
  ('R, 'e, 'a1, ['R, 'D] product' as 'D) er ->
  ('R, 'e, 'a2, 'D) er ->
  ('R, 'e, 'a3, 'D) er ->
  ('R, 'e, 'a4, 'D) er ->
  ('R, 'e, 'a1 * 'a2 * 'a3 * 'a4, 'D) er

tuple'4 x1E x2E x3E x4E is like tuple'3, but for 4 elements.

val tuple'5 : 
  ('R, 'e, 'a1, ['R, 'D] product' as 'D) er ->
  ('R, 'e, 'a2, 'D) er ->
  ('R, 'e, 'a3, 'D) er ->
  ('R, 'e, 'a4, 'D) er ->
  ('R, 'e, 'a5, 'D) er ->
  ('R, 'e, 'a1 * 'a2 * 'a3 * 'a4 * 'a5, 'D) er

tuple'5 x1E x2E x3E x4E x5E is like tuple'3, but for 5 elements.

val tuple'6 : 
  ('R, 'e, 'a1, ['R, 'D] product' as 'D) er ->
  ('R, 'e, 'a2, 'D) er ->
  ('R, 'e, 'a3, 'D) er ->
  ('R, 'e, 'a4, 'D) er ->
  ('R, 'e, 'a5, 'D) er ->
  ('R, 'e, 'a6, 'D) er ->
  ('R, 'e, 'a1 * 'a2 * 'a3 * 'a4 * 'a5 * 'a6, 'D) er

tuple'6 x1E x2E x3E x4E x5E x6E is like tuple'3, but for 6 elements.

val map_er'1 : ('b -> 'd -> 'a) -> 'b -> 'd -> 'a

map_er'1 is a synonym for eta'1.

val map_er'2 : 
  ('b1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('b2 -> ('R, 'e, 'a2, 'D) er) ->
  ('b1 * 'b2) ->
  ('R, 'e, 'a1 * 'a2, 'D) er

2-tuple traversal.

val map_er'3 : 
  ('b1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('b2 -> ('R, 'e, 'a2, 'D) er) ->
  ('b3 -> ('R, 'e, 'a3, 'D) er) ->
  ('b1 * 'b2 * 'b3) ->
  ('R, 'e, 'a1 * 'a2 * 'a3, 'D) er

3-tuple traversal.

val map_er'4 : 
  ('b1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('b2 -> ('R, 'e, 'a2, 'D) er) ->
  ('b3 -> ('R, 'e, 'a3, 'D) er) ->
  ('b4 -> ('R, 'e, 'a4, 'D) er) ->
  ('b1 * 'b2 * 'b3 * 'b4) ->
  ('R, 'e, 'a1 * 'a2 * 'a3 * 'a4, 'D) er

4-tuple traversal.

val map_er'5 : 
  ('b1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('b2 -> ('R, 'e, 'a2, 'D) er) ->
  ('b3 -> ('R, 'e, 'a3, 'D) er) ->
  ('b4 -> ('R, 'e, 'a4, 'D) er) ->
  ('b5 -> ('R, 'e, 'a5, 'D) er) ->
  ('b1 * 'b2 * 'b3 * 'b4 * 'b5) ->
  ('R, 'e, 'a1 * 'a2 * 'a3 * 'a4 * 'a5, 'D) er

5-tuple traversal.

val map_er'6 : 
  ('b1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('b2 -> ('R, 'e, 'a2, 'D) er) ->
  ('b3 -> ('R, 'e, 'a3, 'D) er) ->
  ('b4 -> ('R, 'e, 'a4, 'D) er) ->
  ('b5 -> ('R, 'e, 'a5, 'D) er) ->
  ('b6 -> ('R, 'e, 'a6, 'D) er) ->
  ('b1 * 'b2 * 'b3 * 'b4 * 'b5 * 'b6) ->
  ('R, 'e, 'a1 * 'a2 * 'a3 * 'a4 * 'a5 * 'a6, 'D) er

6-tuple traversal.

val map_eq_er'1 : ('a -> 'd -> 'a) -> 'a -> 'd -> 'a

map_eq_er'1 is a synonym for eta'1.

val map_eq_er'2 : 
  ('a1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('a2 -> ('R, 'e, 'a2, 'D) er) ->
  ('a1 * 'a2) ->
  ('R, 'e, 'a1 * 'a2, 'D) er

Physical equality preserving 2-tuple traversal.

val map_eq_er'3 : 
  ('a1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('a2 -> ('R, 'e, 'a2, 'D) er) ->
  ('a3 -> ('R, 'e, 'a3, 'D) er) ->
  ('a1 * 'a2 * 'a3) ->
  ('R, 'e, 'a1 * 'a2 * 'a3, 'D) er

Physical equality preserving 3-tuple traversal.

val map_eq_er'4 : 
  ('a1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('a2 -> ('R, 'e, 'a2, 'D) er) ->
  ('a3 -> ('R, 'e, 'a3, 'D) er) ->
  ('a4 -> ('R, 'e, 'a4, 'D) er) ->
  ('a1 * 'a2 * 'a3 * 'a4) ->
  ('R, 'e, 'a1 * 'a2 * 'a3 * 'a4, 'D) er

Physical equality preserving 4-tuple traversal.

val map_eq_er'5 : 
  ('a1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('a2 -> ('R, 'e, 'a2, 'D) er) ->
  ('a3 -> ('R, 'e, 'a3, 'D) er) ->
  ('a4 -> ('R, 'e, 'a4, 'D) er) ->
  ('a5 -> ('R, 'e, 'a5, 'D) er) ->
  ('a1 * 'a2 * 'a3 * 'a4 * 'a5) ->
  ('R, 'e, 'a1 * 'a2 * 'a3 * 'a4 * 'a5, 'D) er

Physical equality preserving 5-tuple traversal.

val map_eq_er'6 : 
  ('a1 -> ('R, 'e, 'a1, ['R, 'D] product' as 'D) er) ->
  ('a2 -> ('R, 'e, 'a2, 'D) er) ->
  ('a3 -> ('R, 'e, 'a3, 'D) er) ->
  ('a4 -> ('R, 'e, 'a4, 'D) er) ->
  ('a5 -> ('R, 'e, 'a5, 'D) er) ->
  ('a6 -> ('R, 'e, 'a6, 'D) er) ->
  ('a1 * 'a2 * 'a3 * 'a4 * 'a5 * 'a6) ->
  ('R, 'e, 'a1 * 'a2 * 'a3 * 'a4 * 'a5 * 'a6, 'D) er

Physical equality preserving 6-tuple traversal.

val lift'2 : 
  ('b1 -> 'b2 -> 'a) ->
  ('R, 'e, 'b1, ['R, 'D] product' as 'D) er ->
  ('R, 'e, 'b2, 'D) er ->
  ('R, 'e, 'a, 'D) er

lift'2 xyz xE yE is equivalent to map (fun (x, y) -> xyz x y) (pair xE yE).

val lift'3 : 
  ('b1 -> 'b2 -> 'b3 -> 'a) ->
  ('R, 'e, 'b1, ['R, 'D] product' as 'D) er ->
  ('R, 'e, 'b2, 'D) er ->
  ('R, 'e, 'b3, 'D) er ->
  ('R, 'e, 'a, 'D) er

Lift 3-parameter function to operate on effect readers.

val lift'4 : 
  ('b1 -> 'b2 -> 'b3 -> 'b4 -> 'a) ->
  ('R, 'e, 'b1, ['R, 'D] product' as 'D) er ->
  ('R, 'e, 'b2, 'D) er ->
  ('R, 'e, 'b3, 'D) er ->
  ('R, 'e, 'b4, 'D) er ->
  ('R, 'e, 'a, 'D) er

Lift 4-parameter function to operate on effect readers.

val lift'5 : 
  ('b1 -> 'b2 -> 'b3 -> 'b4 -> 'b5 -> 'a) ->
  ('R, 'e, 'b1, ['R, 'D] product' as 'D) er ->
  ('R, 'e, 'b2, 'D) er ->
  ('R, 'e, 'b3, 'D) er ->
  ('R, 'e, 'b4, 'D) er ->
  ('R, 'e, 'b5, 'D) er ->
  ('R, 'e, 'a, 'D) er

Lift 5-parameter function to operate on effect readers.

val lift'6 : 
  ('b1 -> 'b2 -> 'b3 -> 'b4 -> 'b5 -> 'b6 -> 'a) ->
  ('R, 'e, 'b1, ['R, 'D] product' as 'D) er ->
  ('R, 'e, 'b2, 'D) er ->
  ('R, 'e, 'b3, 'D) er ->
  ('R, 'e, 'b4, 'D) er ->
  ('R, 'e, 'b5, 'D) er ->
  ('R, 'e, 'b6, 'D) er ->
  ('R, 'e, 'a, 'D) er

Lift 6-parameter function to operate on effect readers.

Selective functors

type ('R, 'e, 'a, 'b, 'c, 'D) branch'm =
  ('R, 'e, 'b -> 'a, 'D) er ->
  ('R, 'e, 'c -> 'a, 'D) er ->
  ('R, 'e, ('b, 'c) branch, 'D) er ->
  ('R, 'e, 'a) s

branch effect signature.

class virtual ['R, 'D] branch' : object ... end

branch capability mix-in.

class ['R, 'O, 'D] branch'of : ['R, 'O] branch' -> object ... end

branch capability projection.

class virtual ['R, 'D] selective' : object ... end

Selective functor offers the map, pure, pair, and branch capabilities.

class ['R, 'O, 'D] selective'of : ['R, 'O] selective' -> object ... end

map, pure, pair, and branch capability projection.

val branch : 
  ('R, 'e, 'b -> 'a, 'D) er ->
  ('R, 'e, 'c -> 'a, 'D) er ->
  ('R, 'e, ('b, 'c) branch, ['R, 'D] branch' as 'D) er ->
  ('R, 'e, 'a, 'D) er

branch baE caE bcE effect.

val if_else_s : 
  ('R, 'e, 'a, 'D) er ->
  ('R, 'e, 'a, 'D) er ->
  ('R, 'e, bool, ['R, 'D] selective' as 'D) er ->
  ('R, 'e, 'a, 'D) er

if_else_s tE eE cE is equivalent to

branch
  (map const eE)
  (map const tE)
  (map (function true  -> `Fst ()
               | false -> `Snd ())
       cE)

Sequencing functors

type ('R, 'e, 'a, 'b, 'D) bind'm =
  ('R, 'e, 'b, 'D) er ->
  ('b -> ('R, 'e, 'a, 'D) er) ->
  ('R, 'e, 'a) s

bind effect signature.

class virtual ['R, 'D] bind' : object ... end

bind capability mix-in.

class ['R, 'O, 'D] bind'of : ['R, 'O] bind' -> object ... end

bind capability projection.

class virtual ['R, 'D] monad' : object ... end

Monad offers the map, pure, pair, branch, and bind capabilities.

class ['R, 'O, 'D] monad'of : ['R, 'O] monad' -> object ... end

map, pure, pair, branch, and bind capability projection.

class virtual ['R, 'D] monad'd : object ... end

Implements defaults for map, pair, and branch in terms of pure and bind.

val bind : 
  ('R, 'e, 'b, ['R, 'D] bind' as 'D) er ->
  ('b -> ('R, 'e, 'a, 'D) er) ->
  ('R, 'e, 'a, 'D) er

bind xE xyE effect.

val (>>=) : 
  ('R, 'e, 'b, ['R, 'D] bind' as 'D) er ->
  ('b -> ('R, 'e, 'a, 'D) er) ->
  ('R, 'e, 'a, 'D) er

xE >>= xyE is equivalent to bind xE xyE.

val let* : 
  ('R, 'e, 'b, ['R, 'D] bind' as 'D) er ->
  ('b -> ('R, 'e, 'a, 'D) er) ->
  ('R, 'e, 'a, 'D) er

( let* ) xE xyE is equivalent to bind xyE xE.

val and* : 
  ('R, 'e, 'a, ['R, 'D] pair' as 'D) er ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a * 'b, 'D) er

( and* ) xE yE is equivalent to pair xE yE.

val join : 
  ('R, 'e, ('R, 'e, 'a, ['R, 'D] bind' as 'D) er, 'D) er ->
  ('R, 'e, 'a, 'D) er

join xEE is equivalent to bind xEE (fun xE -> xE).

val (>>) : ('R, 'e, unit, ['R, 'D] bind' as 'D) er -> ('R, 'e, 'a, 'D) er op'1

uE >> xE is equivalent to bind uE (fun () -> xE).

val (>=>) : 
  ('a -> ('R, 'e, 'b, ['R, 'D] bind' as 'D) er) ->
  ('b -> ('R, 'e, 'c, 'D) er) ->
  'a ->
  ('R, 'e, 'c, 'D) er

xyE >=> yzE is equivalent to fun x -> bind (xyE x) yzE.

val (|||) : ('R, 'e, bool, ['R, 'D] monad' as 'D) er op'2

lE ||| rE is equivalent to bind lE (function true -> pure true | false -> rE).

val (&&&) : ('R, 'e, bool, ['R, 'D] monad' as 'D) er op'2

lE &&& rE is equivalent to bind lE (function true -> rE | false -> pure true).

Alternatives

type ('R, 'e, 'a, 'D) zero'm = ('R, 'e, 'a) s

zero effect signature.

class virtual ['R, 'D] zero' : object ... end

zero capability mix-in.

class ['R, 'O, 'D] zero'of : ['R, 'O] zero' -> object ... end

zero capability projection.

type ('R, 'e, 'a, 'D) alt'm =
  ('R, 'e, 'a, 'D) er ->
  ('R, 'e, 'a, 'D) er ->
  ('R, 'e, 'a) s

alt effect signature.

class virtual ['R, 'D] alt' : object ... end

alt capability mix-in.

class ['R, 'O, 'D] alt'of : ['R, 'O] alt' -> object ... end

alt capability projection.

class virtual ['R, 'D] plus' : object ... end

Plus offers the zero and alt capabilities.

class ['R, 'O, 'D] plus'of : ['R, 'O] plus' -> object ... end

zero and alt capability projection.

val zero : ('R, 'e, 'a, ['R, 'D] zero' as 'D) er

zero effect.

val alt : ('R, 'e, 'a, ['R, 'D] alt' as 'D) er op'2

alt lE rE effect.

val (<|>) : ('R, 'e, 'a, ['R, 'D] alt' as 'D) er op'2

lE <|> rE is equivalent to alt lE rE.

val iota : int -> ('R, 'e, int, < ('R, 'D) pure' ; ('R, 'D) plus'.. > as 'D) er

iota n is equivalent to zero <|> pure 0 <|> ... <|> pure (n-1).

val filter : 
  ('a -> bool) ->
  ('R, 'e, 'a, < ('R, 'D) monad' ; ('R, 'D) zero'.. > as 'D) er ->
  ('R, 'e, 'a, 'D) er

filter p

Error handling

type ('R, 'e, 'a, 'D) fail'm = 'e -> ('R, 'e, 'a) s

fail effect signature.

class virtual ['R, 'D] fail' : object ... end

fail capability mix-in.

class virtual ['R, 'O, 'D] fail'of : ['R, 'O] fail' -> object ... end

fail capability projection.

type ('R, 'e, 'f, 'a, 'b, 'D) tryin'm =
  ('f -> ('R, 'e, 'a, 'D) er) ->
  ('b -> ('R, 'e, 'a, 'D) er) ->
  ('R, 'f, 'b, 'D) er ->
  ('R, 'e, 'a) s

tryin effect signature.

class virtual ['R, 'D] tryin' : object ... end

tryin capability mix-in.

class virtual ['R, 'O, 'D] tryin'of : ['R, 'O] tryin' -> object ... end

tryin capability projection.

class virtual ['R, 'D] errors' : object ... end

Error handling offers the fail, and tryin.

class virtual ['R, 'O, 'D] errors'of : ['R, 'O] errors' -> object ... end

fail and tryin capability projection.

val fail : 'e -> ('R, 'e, 'a, ['R, 'D] fail' as 'D) er

fail error effect.

val tryin : 
  ('f -> ('R, 'e, 'a, ['R, 'D] tryin' as 'D) er) ->
  ('b -> ('R, 'e, 'a, 'D) er) ->
  ('R, 'f, 'b, 'D) er ->
  ('R, 'e, 'a, 'D) er

tryin exE yxE xE effect.

val catch : 
  ('R, 'e, 'a, < ('R, 'D) pure' ; ('R, 'D) tryin'.. > as 'D) er ->
  ('R, 'f, ('e, 'a) res, 'D) er

catch xE is equivalent to tryIn (fun e -> pure (`Error e)) (fun x -> pure (`Ok x)) xE.

val handle : 
  ('f -> ('R, 'e, 'a, < ('R, 'D) pure' ; ('R, 'D) tryin'.. > as 'D) er) ->
  ('R, 'f, 'a, 'D) er ->
  ('R, 'e, 'a, 'D) er

handle exE xE is equivalent to tryin exE pure xE

val finally : 
  ('R, 'e, unit, < ('R, 'D) monad' ; ('R, 'D) errors'.. > as 'D) er ->
  ('R, 'e, 'a, 'D) er op'1

finally uE xE is equivalent to tryin (fun e -> bind uE (fun () -> fail e)) (fun x -> bind uE (fun () -> pure x)) xE.

val map_error : 
  ('f -> 'e) ->
  ('R, 'f, 'a, < ('R, 'D) pure' ; ('R, 'D) errors'.. > as 'D) er ->
  ('R, 'e, 'a, 'D) er

map_error fe xE is equivalent to tryin (fun f -> fail (fe e)) pure xE.

val gen_error : 
  ('R, nothing, 'a, < ('R, 'D) pure' ; ('R, 'D) errors'.. > as 'D) er ->
  ('R, 'e, 'a, 'D) er

gen_error xE is equivalent to map_error (function (_: nothing) -> .) xE.

Asynchronicity

type ('R, 'e, 'a, 'b, 'D) par'm = ('R, 'e, 'a, 'b, 'D) pair'm

par effect signature.

class virtual ['R, 'D] par' : object ... end

par effect signature.

class ['R, 'O, 'D] par'of : ['R, 'O] par' -> object ... end

par capability projection.

val par : 
  ('R, 'e, 'a, ['R, 'D] par' as 'D) er ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a * 'b, 'D) er

par xE yE effect.

val let&+ : 
  ('R, 'e, 'b, ['R, 'D] map' as 'D) er ->
  ('b -> 'a) ->
  ('R, 'e, 'a, 'D) er

( let&+ ) xE xy is equivalent to map xy xE.

val and&+ : 
  ('R, 'e, 'a, ['R, 'D] par' as 'D) er ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a * 'b, 'D) er

( and&+ ) xE yE is equivalent to par xE yE.

val let&* : 
  ('R, 'e, 'b, ['R, 'D] bind' as 'D) er ->
  ('b -> ('R, 'e, 'a, 'D) er) ->
  ('R, 'e, 'a, 'D) er

( let&* ) xE xyE is equivalent to bind xyE xE.

val and&* : 
  ('R, 'e, 'a, ['R, 'D] par' as 'D) er ->
  ('R, 'e, 'b, 'D) er ->
  ('R, 'e, 'a * 'b, 'D) er

( and&* ) xE yE is equivalent to par xE yE.

type ('R, 'e, 'a, 'D) suspend'm = (('e, 'a) res, unit) cps -> ('R, 'e, 'a) s

suspend effect signature.

class virtual ['R, 'D] suspend' : object ... end

suspend capability mix-in.

class ['R, 'O, 'D] suspend'of : ['R, 'O] suspend' -> object ... end

suspend capability projection.

val suspend : 
  (('e, 'a) res, unit) cps ->
  ('R, 'e, 'a, ['R, 'D] suspend' as 'D) er

suspend with_resume effect.

type ('R, 'e, 'D) spawn'm = ('R, nothing, unit, 'D) er -> ('R, 'e, unit) s

spawn effect signature.

class virtual ['R, 'D] spawn' : object ... end

spawn effect capability.

class ['R, 'O, 'D] spawn'of : ['R, 'O] spawn' -> object ... end

spawn capability projection.

class virtual ['R, 'D] sync' : object ... end

monad' and errors' effect capabilities.

class ['R, 'O, 'D] sync'of : ['R, 'O] sync' -> object ... end

sync' capability projection.

class virtual ['R, 'D] async' : object ... end

monad', errors', suspend', par', and spawn' effect capabilites.

class ['R, 'O, 'D] async'of : ['R, 'O] async' -> object ... end

async' capability projection.

val spawn : 
  ('R, nothing, unit, ['R, 'D] spawn' as 'D) er ->
  ('R, 'e, unit, 'D) er

spawn uE effect.

class virtual ['R, 'D] par'd : object ... end

Implements par.

module Memo : sig ... end

Memoized lazy computation for asynchronous programming.

module Mut : sig ... end

Mutable ref cells for asynchronous programming.

Environment

The environment or reader is built-in to the effect system in the form of the capability dictionary. Thanks to OCaml's structural objects, it is possible to extend the dictionary for user needs.

Dictionary

val env : ('R, 'e, ['R, 'D] pure' as 'D, 'D) er

env effect returns the dictionary 'd of capabilities.

val env_as : (['R, 'D] pure' as 'D -> 'a) -> ('R, 'e, 'a, 'D) er

env_as fn effect returns the value of type 'a computed from the dictionary of capabilities of type 'd.

val mapping_env : ('D -> 'S) -> ('R, 'e, 'a, 'S) er -> ('R, 'e, 'a, 'D) er

mapping_env fn er effect executes the effect er with the dictionary of capabilities of type 'D mapped through the given function fn.

val setting_env : 's -> ('R, 'e, 'a, 's) er -> ('R, 'e, 'a, 'D) er

setting_env s er effect executes the effect er with the given dictionary s of capabilities.

Properties

module Prop : sig ... end

An abstraction for accessing instance variables or properties of objects.

val prop : (unit -> 'a) -> ('a -> unit) -> 'a Prop.t

prop get set is equivalent to Prop.make get set.

val get : (['R, 'D] pure' as 'D -> 'a Prop.t) -> ('R, 'e, 'a, 'D) er

get prop_of effect returns the value of the property from the dictionary of capabilities of type 'd.

val get_as : 
  (['R, 'D] pure' as 'D -> 'b Prop.t) ->
  ('b -> 'a) ->
  ('R, 'e, 'a, 'D) er

get_as prop_of fn

val mapping : 
  (< .. > as 'D -> 'p Prop.t) ->
  'p op'1 ->
  ('R, 'e, 'a, 'D) er op'1

mapping prop_of fn xE effect executes the effect xE with the property of the dictionary of capabilities mapped through the given function.

val setting : (< .. > as 'D -> 'p Prop.t) -> 'p -> ('R, 'e, 'a, 'D) er op'1

setting prop_of value xE effect executess the effect xE with the property of the dictionary of capabilities set to given value.

Mutable properties

val read : 
  ('D -> 'v Mut.t Prop.t) ->
  ('R, 'e, 'v, < ('R, 'D) monad' ; ('R, 'D) suspend'.. > as 'D) er

read prop_of effect.

val mutate : 
  ('D -> 'v Mut.t Prop.t) ->
  'v op'1 ->
  ('R, 'e, unit, < ('R, 'D) monad' ; ('R, 'D) suspend'.. > as 'D) er

mutate prop_of vv effect.

val modify : 
  ('D -> 'v Mut.t Prop.t) ->
  ('v -> 'v * 'a) ->
  ('R, 'e, 'a, < ('R, 'D) monad' ; ('R, 'D) suspend'.. > as 'D) er

modify prop_of vva effect.

val try_mutate : 
  ('D -> 'v Mut.t Prop.t) ->
  ('v -> ('R, 'e, 'v, 'D) er) ->
  ('R,
    'e,
    unit,
    < ('R, 'D) monad'
    ; ('R, 'D) errors'
    ; ('R, 'D) suspend'.. > as 'D)
    er

try_mutate prop_of vvE effect.

val try_modify : 
  ('D -> 'v Mut.t Prop.t) ->
  ('v -> ('R, 'e, 'v * 'a, 'D) er) ->
  ('R,
    'e,
    'a,
    < ('R, 'D) monad'
    ; ('R, 'D) errors'
    ; ('R, 'D) suspend'.. > as 'D)
    er

try_modify prop_of vvaE effect.

val cloning : 
  ('D -> 'v Mut.t Prop.t) ->
  ('R, 'e, 'a, < ('R, 'D) monad' ; ('R, 'D) suspend'.. > as 'D) er op'1

cloning prop_of xE effect.

Interpreters

Users can and often should implement their own interpreters that only allow specific limited sets of effects. This package is intended to only provide the core framework for effectul programming.

for Stdlib

module StdRea : sig ... end

Stdlib extension modules.

Data types

module Constant : sig ... end

Constant functor, products, and applicatives.

module Identity : sig ... end

Identity monad.

Tail recursive

module Tailrec : sig ... end

A self tail recursive interpreter usable with Js_of_ocaml.

Traversals

module Traverse : sig ... end

Data type traversal use cases.