Lazy Data Structures

  • OCaml is by default eager
    • function parameters are evaluated to values before calling functions
    • Pairs, records, and variants all have their internals computed to values recursively.
  • But, sometimes laziness can be both useful and more efficient
    • for lazy funcation call, no need to compute arguments that are not used
    • It allows for construction of “infinite” lists, etc
      • Don’t compute the nth element until it is asked for
      • But, once it is computed, cache it (a form of memoizing)
      • Just don’t ask for all infinitely many elements!

Super simple encoding of laziness in OCaml

  • OCaml has no built-in Laziness (Haskell does)
  • But it can be encoded via a thunk
let frozen_add = fun () -> printf "Have a smiley day!\n"; 4 + 3
let thaw e = e ()
thaw frozen_add;; (* 4+3 not computed until here *)
  • This encoding is in fact just “call by name”, laziness means memoizing the result.

The Base.Lazy module

  • Base.Lazy is a much more usable sugar for the above
# open Lazy;;
# let l = lazy(printf "Have a smiley day!\n";2+3);;
val l : int lazy_t = <lazy> (* lazy_t is the wrapper type *)
# force l;;
Have a smiley day!
- : int = 5
# let f lv =  (force lv) + (force lv);;
val f : int lazy_t -> int = <fun>
# f l;;
Have a smiley day! (* this is printed only once, the 2nd force uses cached 5 value *)
- : int = 10
  • Fact: laziness is just a “wrapper” on a computation
  • So: Lazy is in fact (yet) another monad - !
    • We won’t get into Lazy.bind etc here but lets make an infinite stream of fib’s.
open Core
open Lazy
type 'a stream = Cons of 'a * 'a stream Lazy.t (* List MUST be infinite *)

let rec all_ones : int stream = Cons(1,lazy(all_ones))

let rec ints n : int stream = Cons(n,lazy(ints (n+1)))

(* Code to get the nth element of a lazy list *)

let rec nth (Cons(hd, tl) : 'a stream) (n : int) :'a =
  if n = 0 then hd
  else nth (force tl) (n-1)

(* A more interesting example - shows memoization, this is not exponential *)

let rec fib : int stream = 
  let rec fib_rest (Cons(hd, tl) : int stream) : (int stream) = 
   let Cons(hd',_) = force tl in
    Cons (hd + hd', lazy(fib_rest (force tl))) in
  Cons(1, lazy(Cons(1, lazy(fib_rest fib))))
  • One thing not clear from the code is that a Lazy will not be recomputed
  • Once the list is “unrolled” by one call it doesn’t need to be “re-unrolled”
  • This is a form of caching / memoization built into Lazy
    • (but not in our crude encoding of it above)
  • Note that becuase of that the above nth function will in fact be linear, not exponential

Asynchronous Programming

Concurrency is needed for two main reasons

  1. You want to run things in parallel for speed gain (multi-core, cluster, etc)
  2. You are waiting for a result from an I/O action
    • Disk read/write, network request, remote API call, etc
    • (Sometimes also awaiting for internal actions such as time-outs)

In OCaml

  • Concurrency for speed gain is a work in progress, look for a release in a year or two
  • Concurrency to support asynchronous waiting: Async library (which is based on the Lwt library)

Local concurrency for speed

  • This is usually done via threads
  • fork off another computation with its own runtime stack etc but share the heap
  • But, threads are notoriously difficult to debug
    • 100’s of patches have been added to help (channels, monitors, locks, ownership types, etc etc etc) but still hard
  • So, better to use a simpler system focused on waiting for I/O if that is all you really need


  • Async is another Jane Street library
  • It is based on the notion of a promise
  • Promises have been around for a very long time but are gaining in popularity
  • Many languages have libraries implementing some form
  • In Async they are called deferreds, of type Deferred.t


  • A Deferred.t is an action returning a result
  • Until the action is forced, it won’t run (like laziness)
  • When it is forced a result will be returned which is an option
    • None will mean failure; I/O always needs failure case
  • Here is an example using Async.Reader.file_contents
    • reads a whole file into a string
    • but, calls to it immediately return
    • The file is not in fact read until the deferred is run
    • This is a special file operation function part of Async to support deferreds.
# #require "async";;
# #require "ppx_jane";;
# open Async;;
# let eventual_string = Reader.file_contents "";;
val eventual_string : string Deferred.t = <abstr>
# Deferred.peek eventual_string;;
- : string option = None (* nothing has been done to force the Deferred to run *)
# eventual_string;; (* .. utop forces it to run implicitly - like Lazy.force but implicit *)
- : string =
# Deferred.peek eventual_string;;
- : string option =
  • An odd thing about the above is let-defining a Deferred will not run it
    • but, if it is directly fed into the top loop it will implicitly run
    • this is becuase utop when it sees a direct deferred will run it and return the result

(Note the Async examples we base on Real World OCaml Chapter 15 which has a lot more than what we are covering)

The Async monad

  • Lazy and Option we saw it was often not hard to avoid the bind/return view
  • This is also possible with Async but often I/O actions are sequenced and bind/return is thus very helpful.
# let uppercase_file (filename : string) : (unit Deferred.t) =
    let%bind s = Reader.file_contents filename in filename ~contents:(String.uppercase s)
# uppercase_file "t.txt" (* this will implicitly run the Deferred above *)
- : unit = ()
# Reader.file_contents "t.txt"
- : string = "HELLO FOLKS!"

Deferred.return does the normal wrapping thing, it defers a normal value

let d = return(10);;
val d : int Deferred.t = <abstr>
# d;;
- : int = 10


  • Deferred’s are in fact implemented with Ivars
  • Think of it as “the implementation of a promise”
  • Often you can use library functions that are Deferred aware
  • But using Ivar you can write your own
  • Here is an example based on RWOC:
# let ivar = Ivar.create () (* Create an Ivar; think of it like a ref cell *)
val ivar : '_weak1 Ivar.t =
  {Async_kernel__.Types.Ivar.cell = Async_kernel__Types.Cell.Empty}
# let def = ivar  (* Read the contents of the promise -- an empty one now! *)
val def : '_weak2 Deferred.t = <abstr>
# Deferred.peek def
- : '_weak3 option = None (* It is nothing.  Typing `def;;` now will loop forever! *)
# Ivar.fill ivar "Hello" (* Fill a promise explicitly *)
- : unit = ()
# Deferred.peek def
- : string option = Some "Hello" (* Indeed it got filled *)
- : string = "Hello"

Making the monadic bind and return`

  • Let us show how bind can be defined with Ivars
  • This will give us the complete picture of the monad
  • Uses upon : 'a Deferred.t -> ('a -> unit) -> unit
    • takes an Ivar (a promise), and when it is fulfilled runs the ('a -> unit) code
let bind' (d: 'a Deferred.t) ~(f:('a -> 'b Deferred.t)) : 'b Deferred.t =
    let i = Ivar.create () in
    upon d (fun x -> (* Run this first function when d is determined *)
             upon (f x) (* then run f x *)
                  (fun y -> Ivar.fill i y)
           ); (* call the promise "filled" when f x is determined *) i (* this returns a Deferred so users can pull on it *)

We covered the basic concepts of Async above. See Real World OCaml Chapter 15 for larger examples including asynchronous http.