## Sunday, April 7, 2019

### Announcing ghc-lib 0.20190404

Announcing ghc-lib 0.20190404

On behalf of Digital Asset I am excited to share with you the latest release of ghc-lib.

As described in detail in the ghc-lib README, the ghc-lib project lets you use the GHC API for parsing and analyzing Haskell code without tying you to a specific GHC version.

## What's new

The GHC source code in this release is updated to GHC HEAD as of April the 4th, 2019. Accordingly, the mini-hlint example in the ghc-lib repo was adjusted to accomodate GHC API changes to the ParseResult datatype and parser error handling.

By far the biggest change though is this : the ghc-lib project now provides two packages, ghc-lib-parser and ghc-lib. The packages are released on Hackage, and can be installed as usual e.g. cabal install ghc-lib.

Some projects don't require the ability to compile Haskell to GHC's Core language. If lexical analysis alone is sufficient for your project's needs, then the ghc-lib-parser package alone will do for that. The build time for ghc-lib-parser is roughly half of the combined build times of ghc-lib-parser and ghc-lib. That is, in this case, switching to the new release will decrease the build time for your project. Note that if your project does require compiling Haskell to Core, then your project will now depend on both the ghc-lib-parser and ghc-lib packages.

The ghc-lib package "re-exports" the modules of the ghc-lib-parser package. So, if you depend upon the ghc-lib package, you'll get the ghc-lib-parser modules "for free". Sadly though, at this time, package import syntax (and we do recommend using package import syntax for these packages) doesn't quite work like you'd expect so that if you, import "ghc-lib" DynFlags for example, this will fail because DynFlags is in fact in the ghc-lib-parser package. In this case, you'd write, import "ghc-lib-parser" DynFlags and all would be well. The mini-compile example in the ghc-lib repo demonstrates mixing modules from both packages.

Digital Asset make extensive use of the ghc-lib packages in the DAML smart contract language compiler and hope you continue to benefit from this project too!

## Wednesday, March 20, 2019

### Bush fixing Travis and GitLab

Bush fixing Travis and CI

Ever had one of those days?

You are not alone!

This Saturday 9th March 2019, the GHC devs are going to announce that git://git.haskell.org/ghc.git has been decommissioned. The new official upstream GHC will be https://gitlab.haskell.org/ghc/ghc.

Sadly (for us) this broke ghc-lib CI's Travis linux configuration.

What does our CI do? The ghc-lib CI script pulls down the latest GHC sources and builds and tests them as a ghc-lib. The details of the problem are that Travis gives you a broken Ubuntu where cloning the official URL fails with a TLS “handshake error”. More generally, any Travis job that tries to git clone over the https protocol from a GitLab remote will fail the same way.

This .travis.yml shows a workaround. The idea is to spin up a container before install that doesn’t have this problem and clone from there. The essential bits are:

services:
- docker

# [Why we git clone on linux here]
# At this time, git clone https://gitlab.haskell.org/ghc/ghc.git
# from within CI.hs does not work on on linux. This appears to be a
# known Travis/ubuntu SSL verification issue. We've tried many less
# drastic workarounds. This grand hack is the only way we've found so
# far that can be made to work.
before_install:
- |
if [[ "$TRAVIS_OS_NAME" == "linux" ]]; then docker pull alpine/git docker run -ti --rm -v${HOME}:/root -v $(pwd):/git \ alpine/git clone https://gitlab.haskell.org/ghc/ghc.git /git/ghc --recursive fi  Note, MacOS docker services aren’t supported but that’s OK! The TLS handshake problem doesn’t exhibit in that configuration. Update : It turns out that while this issue exists in Ubuntu 14.04 which Travis uses by default, it is “fixed” in Ubuntu 16.04. So by writing dist: xenial in your .travis.yml file, the above workaround can be avoided. ## Saturday, February 23, 2019 ### Adding a GHC Language Extension Adding a GHC Language Extension This note summarizes the essential mechanics of adding a new language extension to GHC. The example code will illustrate adding a Foo extension. ## Implementing the extension The first step is to add a Foo constructor to the Extension type in libraries/ghc-boot-th/GHC/LanguageExtensions/Type.hs. data Extension = Cpp | OverlappingInstances ... | Foo  The next job is to extend xFlagsDeps in compiler/main/DynFlags.hs. xFlagsDeps = [ flagSpec "AllowAmbiguousTypes" LangExt.AllowAmbiguousTypes, ... flagSpec "Foo" LangExt.Foo ] That's all it takes. With these two changes, it is now possible to enable Foo in Haskell source files by writing {-# LANGUAGE Foo #-} or from a compile command by passing the argument -XFoo. ## Testing for the extension ### Lexer In compiler/parser/Lexer.x, locate data ExtBits and add a constructor for Foo. data ExtBits = FfiBit | ... | FooBit  Next, extend the where clause of function mkParserFlags' with a case for Foo. langExtBits = FfiBit xoptBit LangExt.ForeignFunctionInterface .|. InterruptibleFfiBit xoptBit LangExt.InterruptibleFFI ... .|. FooBit xoptBit LangExt.FooBit   The function xtest is then the basic building block for testing if Foo is enabled. For example, this specific function tests a bitmap for the on/off status of the Foo bit. fooEnabled :: ExtsBitMap -> Bool fooEnabled = xtest FooBit  In practice, testing for a language extension in the lexer is called from a function computing a lexer action. Suppose foo to be such a function and the action it computes depends somehow on whether the Foo language extension is in effect. Putting it all together, schematically it will have the following form. foo :: (FastString -> Token) -> Action foo con span buf len = do exts <- getExts if FooBit xtest exts then ... else ...  ### Parser This utility computes a monadic expression testing for the on/off state of a bit in a parser state monad. extension :: (ExtsBitmap -> Bool) -> P Bool extension p = P$ \s -> POk s (p $! (pExtsBitmap . options) s)  An expression of this kind can be evaluated in the semantic action of a parse rule in compiler/parser/Parser.y. Here's an example of how one might be used. foo :: { () } : 'foo' {} | {- empty -} {% do foo_required <- extension fooEnabled when foo_required$ do
loc <- fileSrcSpan
parseErrorSDoc loc \$ text "Missing foo"
}


### Renaming, type-checking and de-sugaring

All of renaming, typechecking and desurgaring occur in the contexts of TcRnIf _ _ monads. Function xoptM :: Extension -> TcRnIf gbl lcl Bool is provided for extension testing in such contexts. Here's a schematic of how such a test might be used in a renaming function.

import GHC.LanguageExtensions

updateFoos :: [AvailInfo] -> RnM (TcGlbEnv, TcLclEnv)
updateFoos info = do
(globals, locals) <- getEnvs
opt_Foo <- xoptM Foo
if not opt_Foo then
return (globals, locals)
else
let globals' = ...
locals' = ...
return (globals', locals')


## Sunday, June 10, 2018

### Bucket Sort

Bucket Sort

Bucket sort assumes input generated by a random process that distributes elements uniformly over the interval [0, 1).

The idea of bucket sort is to divide [0, 1) into n equal-sized subintervals or buckets, and then distribute the n input numbers into the buckets. To produce the output, sort the numbers in each bucket and then go through the buckets in order. Sorting a bucket can be done with insertion sort.

let rec insert x = function
| [] -> [x]
| h :: tl as ls ->
if x < h then x :: ls else h :: insert x tl

let rec insertion_sort = function
| [] | [_] as ls -> ls
| h :: tl -> insert h (insertion_sort tl)


This code for bucket sort assumes the input is an n-element array a and that each element 0 ≤ a.(i) < 1. The code requires an auxillary array b.(0 .. n - 1) of lists (buckets).

let bucket_sort a =
let n = Array.length a in
let b = Array.make n [] in
Array.iter
(fun x ->
let i =
int_of_float (
floor (float_of_int n *. x)
) in
Array.set b i (x :: Array.get b i)
) a;
Array.iteri
(fun i l ->
Array.set b i (insertion_sort l)
) b;
Array.fold_left (fun acc bucket -> acc @ bucket) [] b
;;
bucket_sort [| 0.78; 0.17; 0.39; 0.26; 0.72; 0.94
; 0.21; 0.12; 0.23; 0.68|]

Bucket sort runs in linear time on the average.

References:
[1] "Introduction to Algorithms" Section 9.4:Bucket Sort -- Cormen et. al. (Second ed.) 2001.

## Sunday, May 20, 2018

### Dijkstra's algorithm

Shortest Path

This article assumes familiarity with Dijkstra's shortest path algorithm. For a refresher, see [1]. The code assumes open Core is in effect and is online here.

The first part of the program organizes our thoughts about what we are setting out to compute. The signature summarizes the notion (for our purposes) of a graph definition in modular form. A module implementing this signature defines a type vertex_t for vertices, a type t for graphs and type extern_t : a representation of a t for interaction between an implemening module and its "outside world".

module type Graph_sig = sig
type vertex_t [@@deriving sexp]
type t [@@deriving sexp]
type extern_t

type load_error = [ Duplicate_vertex of vertex_t ] [@@deriving sexp]

val of_adjacency : extern_t -> [ Ok of t | Load_error of load_error ]
val to_adjacency : t -> extern_t

module Dijkstra : sig
type state

type error = [
| Relax of vertex_t
] [@@deriving sexp]
exception Error of error [@@deriving sexp]

val dijkstra : vertex_t -> t -> [ Ok of state | Error of error ]
val d : state -> (vertex_t * float) list
val shortest_paths : state -> (vertex_t * vertex_t list) list
end

end

A realization of Graph_sig provides "conversion" functions of_adjacency/to_adjacency between the types extern_t and t and nests a module Dijkstra. The signature of the sub-module Dijkstra requires concrete modules provide a type state and an implementation of Dijkstra's algorithm in terms of the function signature val dijkstra : vertex_t -> t -> [ Ok of state | Error of error ].

For reusability, the strategy for implementing graphs will be generic programming via functors over modules implementing s vertex type.

An implementation of the module type GRAPH defines a module type VERT which is required to provide a comparable type t. It further defines a module type S that is exactly module type Graph_sig above. Lastly, modules of type GRAPH provide a functor Make that maps any module of type VERT to new module of type S fixing extern_t to an adjacency list representation in terms of the native OCaml type 'a list and float to represent weights on edges.

module type GRAPH = sig
module type VERT = sig
type t[@@deriving sexp]
include Comparable.S with type t := t
end

module type S = sig
include Graph_sig
end

module Make : functor (V : VERT) ->
S with type vertex_t = V.t
and type extern_t = (V.t * (V.t * float) list) list
end

The two module types Graph_sig and GRAPH together provide the specification for the program. module Graph in the next section implements this specification.

Implementation of module Graph is in outline this.

module Graph : GRAPH = struct
module type VERT = sig
type t[@@deriving sexp]
include Comparable.S with type t := t
end

module type S = sig
include Graph_sig
end

module Make : functor (V : VERT) ->
S with type vertex_t = V.t
and type extern_t = (V.t * (V.t * float) list) list
=

functor (V : VERT) -> struct
...
end
end

As per the requirements of GRAPH the module types VERT and S are provided as is the functor Make. It is the code that is ellided by the ... above in the definition of Make that is now the focus.

Modules produced by applications of Make satisfy S. This requires suitable definitions of types vertext_t, t and extern_t. The modules Map and Set are available due to modules of type VERT being comparable in their type t.

      module Map = V.Map
module Set = V.Set

type vertex_t = V.t [@@deriving sexp]
type t = (vertex_t * float) list Map.t [@@deriving sexp]
type extern_t = (vertex_t * (vertex_t * float) list) list
type load_error = [ Duplicate_vertex of vertex_t ] [@@deriving sexp]


While the external representation extern_t of graphs is chosen to be an adjacency list representation in terms of association lists, the internal representation t is a vertex map of adjacency lists providing logarithmic loookup complexity. The conversion functions between the two representations "come for free" via module Map.

      let to_adjacency g = Map.to_alist g

let of_adjacency_exn l =  match Map.of_alist l with
| Ok t -> t
| Duplicate_key c -> raise (Load_error (Duplicate_vertex c))

try
Ok (of_adjacency_exn l)
with


At this point the "scaffolding" for Dijkstra's algorithm, that part of GRAPH dealing with the representation of graphs is implemented.

The interpretation of Dijkstra's algorithm we adopt is functional : the idea is we loop over vertices relaxing their edges until all shortest paths are known. What we know on any recursive iteration of the loop is a current "state" (of the computation) and each iteration produces a new state. This next definition is the formal definition of type state.

      module Dijkstra = struct

type state = {
src    :                  vertex_t
; g      :                         t
; d      :               float Map.t
; pred   :            vertex_t Map.t
; s      :                     Set.t
; v_s    : (vertex_t * float) Heap.t
}

The fields of this record are:
• src : vertex_t, the source vertex;
• g : t, G the graph;
• d : float Map.t, d the shortest path weight estimates;
• pre : vertex_t Map.t, π the predecessor relation;
• s : Set.t, the set S of nodes for which the lower bound shortest path weight is known;
• v_s : (vertex_t * float) Heap.t, V - {S}, , the set of nodes of g for which the lower bound of the shortest path weight is not yet known ordered on their estimates.

Function invocation init src g compuates an initial state for the graph g containing the source node src. In the initial state, d is everywhere except for src which is 0. Set S (i.e. s) and the predecessor relation π (i.e. pred) are empty and the set V - {S} (i.e. v_s) contains all nodes.

        let init src g =
let init x = match V.equal src x with
| true -> 0.0 | false -> Float.infinity in
let d = List.fold (Map.keys g) ~init:Map.empty
~f:(fun acc x -> Map.set acc ~key:x ~data:(init x)) in
{
src
; g
; s = Set.empty
; d
; pred = Map.empty
; v_s = Heap.of_list (Map.to_alist d)
~cmp:(fun (_, e1) (_, e2) -> Float.compare e1 e2)
}


Relaxing an edge (u, v) with weight w (u, v) tests whether the shortest path to v so far can be improved by going through u and if so, updating d (v) and π (v) accordingly.

        type error = [
| Relax of vertex_t
] [@@deriving sexp]
exception Error of error [@@deriving sexp]

let relax state (u, v, w) =
let {d; pred; v_s; _} = state in
let dv = match Map.find d v with
| Some dv -> dv
| None -> raise (Error (Relax v)) in
let du = match Map.find d u with
| Some du -> du
| None -> raise (Error (Relax u)) in
if dv > du +. w then
let dv = du +. w in
(match Heap.find_elt v_s ~f:(fun (n, _) -> V.equal n v) with
| Some tok -> ignore (Heap.update v_s tok (v, dv))
| None -> raise (Error (Relax v))
);
{ state with
d = Map.change d v
~f:(function
| Some _ -> Some dv
| None -> raise (Error (Relax v))
)
; pred = Map.set (Map.remove pred v) ~key:v ~data:u
}
else state

Here, relaxation can result in a linear heap update operation. A better implementation might seek to avoid that.

One iteration of the body of the loop of Dijkstra's algorithm consists of the node in V - {S} with the least shortest path weight estimate being moved to S and its edges relaxed.

        let dijkstra_exn src g =
let rec loop ({s; v_s; _} as state) =
match Heap.is_empty v_s with
| true -> state
| false ->
let u = fst (Heap.pop_exn v_s) in
loop (
List.fold (Map.find_exn g u)
~init:{ state with s = Set.add s u }
~f:(fun state (v, w) -> relax state (u, v, w))
)
in loop (init src g)

let dijkstra src g =
try
Ok (dijkstra_exn src g)
with
| Error err -> Error err


The shortest path estimates contained by a value of state is given by the projection d.

        let d state = Map.to_alist (state.d)


The shortest paths themselves are easily computed as,

   let path state n =
let rec loop acc x =
(match V.equal x state.src with
| true -> x :: acc
| false -> loop (x :: acc) (Map.find_exn state.pred x)
) in
loop [] n

let shortest_paths state =
List.map (Map.keys state.g) ~f:(fun n -> (n, path state n))
end
end

which completes the implementation of Make.

The following program produces a concrete instance of the shortest path problem (with some evaluation output from the top-level).

module G : Graph.S with
type vertex_t = char and type extern_t = (char * (char * float) list) list
=
Graph.Make (Char)

let g : G.t =
[ 's', ['u',  3.0; 'x', 5.0]
; 'u', ['x',  2.0; 'v', 6.0]
; 'x', ['v',  4.0; 'y', 6.0; 'u', 1.0]
; 'v', ['y',  2.0]
; 'y', ['v',  7.0]
]
with
| Ok g -> g
| Load_error e -> failwiths "Graph load error : %s" e G.sexp_of_load_error
;;
let s = match (G.Dijkstra.dijkstra 's' g) with
| Ok s -> s
| Error e -> failwiths "Error : %s" e G.Dijkstra.sexp_of_error

;; G.Dijkstra.d s
- : (char * float) list =
[('s', 0.); ('u', 3.); ('v', 9.); ('x', 5.); ('y', 11.)]

;; G.Dijkstra.shortest_paths s
- : (char * char list) list =
[('s', ['s']); ('u', ['s'; 'u']); ('v', ['s'; 'u'; 'v']); ('x', ['s'; 'x']);
('y', ['s'; 'x'; 'y'])]


References:
[1] "Introduction to Algorithms" Section 24.3:Dijkstra's algorithm -- Cormen et. al. (Second ed.) 2001.

## Saturday, December 9, 2017

### How to migrate your ppx to OCaml migrate parsetree

OCaml migrate parse tree

## OCaml migrate parse tree

Earlier this year, this blog post [2] explored the implementation of a small preprocessor extension (ppx).

The code of the above article worked well enough at the time but as written, exhibits a problem : new releases of the OCaml compiler are generally accompanied by evolutions of the OCaml parse tree. The effect of this is, a ppx written against a specific version of the compiler will "break" in the presence of later releases of the compiler. As pointed out in [3], the use of ppx's in the OCaml eco-system these days is ubiquitous. If each new release of the OCaml compiler required sychronized updates of each and every ppx in opam, getting new releases of the compiler out would soon become a near impossibilty.

Mitigation of the above problem is provided by the ocaml-migrate-parsetree library. The library provides the means to convert parsetrees from one OCaml version to another. This allows the ppx rewriter to write against a specific version of the parsetree and lets the library take care of rolling parsetrees backwards and forwards in versions as necessary. In this way, the resulting ppx is "forward compatible" with newer OCaml versions without requiring ppx code updates.

To get the ppx_id_of code from the earlier blog post usable with ocaml-migrate-parsetree required a couple of small tweaks to make it OCaml 4.02.0 compatible. The changes from the original code were slight and not of significant enough interest to be worth presenting here. What is worth looking at is what it then took to switch the code to use ocaml-migrate-parsetree. The answer is : very little!

open Migrate_parsetree
open OCaml_402.Ast

open Ast_mapper
open Ast_helper
open Asttypes
open Parsetree
open Longident

(* The original ppx as written before goes here!
.                    .                   .
.                    .                   .
.                    .                   .
*)

let () = Driver.register ~name:"id_of" (module OCaml_402) id_of_mapper

The complete code for this article is available online here and as a bonus, includes a minimal jbuilder build system demonstrating just how well the OCaml tool-chain comes together these days.

## Saturday, November 11, 2017

### Towers of Hanoi

Towers of Hanoi

The "towers of Hanoi" problem is stated like this. There are three pegs labelled a, b and c. On peg a there is a stack of n disks of increasing size, the largest at the bottom, each with a hole in the middle to accomodate the peg. The problem is to transfer the stack of disks to peg c, one disk at a time, in such a way as to ensure that no disk is ever placed on top of a smaller disk.

The problem is amenable to a divide and conquer strategy : "Move the top n - 1 disks from peg a to peg b, move the remaining largest disk from peg a to peg c then, move the n - 1 disks on peg b to peg c."

let rec towers n from to_ spare =
if n > 0 then
begin
towers (n - 1) from spare to_;
Printf.printf
"Move the top disk from peg %c to peg %c\n" from to_;
towers (n - 1) spare to_ from
end
else
()
;;

For example, the invocation let () = towers 3 'a' 'c' 'b' will generate the recipie
Move the top disk from peg a to peg c
Move the top disk from peg a to peg b
Move the top disk from peg c to peg b
Move the top disk from peg a to peg c
Move the top disk from peg b to peg a
Move the top disk from peg b to peg c
Move the top disk from peg a to peg c


Let T(n) be the time complexity of towers (x, y, z), when the characteristic operation is the moving of a disk from one peg to another. The time complexity of towers(n - 1, x, y z) is T(n - 1) by definition and no further investigation is needed. T(0) = 0 because the test n > 0 fails and no disks are moved. For larger n, the expression towers (n - 1, from, spare, to_) is evaluated with cost T(n - 1) followed by Printf.printf "Move the top disk from peg %c to peg %c\n" from to_  with cost 1 and finally, towers(n - 1, spare, to_, from)` again with cost T(n - 1).

Summing these contributions gives the recurrence relation T(n) = 2T(n - 1) + 1 where T(0) = 0.

Repeated substituition can be used to arrive at a closed form for T(n), since, T(n) = 2T(n - 1) + 1 = 2[2T(n - 2) + 1] + 1 = 2[2[2T(n - 3) +1] + 1] + 1 = 23T(n - 3) + 22 + 21 + 20 (provided n ≥ 3), expanding the brackets in a way that elucidates the emerging pattern. If this substitution is repeated i times then clearly the result is T(n) = 2iT(n - i) + 2i - 1 + 2i - 2 + ··· + 20 (n ≥ i). The largest possible value i can take is n and if i = n then T(n - i) = T(0) = 0 and so we arrive at T(n) = 2n0 + 2n - 1 + ··· + 20. This is the sum of a geometric series with the well known solution 2n - 1 (use induction to establish that last result or more directly, just compute 2T(n) - T(n)). And so, the time complexity (the number of disk moves needed) for n disks is T(n) = 2n - 1.

References:
Algorithms and Data Structures Design, Correctness, Analysis by Jeffrey Kingston, 2nd ed. 1998