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HWhile is an educational programming language designed for teaching the basics of programming, computability and complexity theory. HWhile's simplicity makes it extremely easy to learn. It has just 3 statement types: while loops, conditionals and assignment. It has a single data type: the binary tree, which supports just a few operations: construct a new binary tree out of two subtrees ('cons'), and retrieval of the left and right subtrees of a binary tree ('hd' and 'tl'). HWhile has fully specified syntax and semantics.

An example

All HWhile programs have a single input and a single output, each a binary tree. The example program below adds together two natural numbers X, Y (represented by trees) that are passed in coupled in the binary tree XY.

add                         // - 'add' is the name of the program.
read XY {                   // - The input binary tree is the variable 'XY'.
    X := hd XY;             // - Extract the arguments X, Y.
    Y := tl XY;
    while X {               // - Perform the addition by repeatedly
        Y := cons nil Y;    //   subtracting from X and adding to Y until X
        X := tl X           //   is the the empty tree (representing 0).
} write Y                   // - Output the final value of Y as the result.

HWhile also includes some convenience features for dealing with programs-as-data, as well as syntactic sugar for natural numbers and lists. Switch statements and external macro calls, and tree equality testing are also supported as syntactic sugar.

HWhile supports (almost fully) the version of While used in Bernhard Reus’ textbook [Limits of Computation - From a Programming Perspective](http:limits.bernhardreus.com) and has been developed in co-operation with Bernhard to support students on the corresponding module at Sussex University. This version also allows one to translate while programs into programs as data. For this to work, all the syntax sugar (extensions) of a While program has to be removed again.

More about the syntax and the semantics (and usage) of the While language can be found in Bernhard’s textbook (Chapter 3-5), and we also include a summary below.


Installing Prerequisites

All the tools required to compile and run HWhile are included in the Haskell Platform. Make sure you install the full version as opposed to the core version.

Note that you may need to add the Haskell Platform's binaries to your system's path variable. If you're on windows this should happen automatically. Otherwise some configuration may be required.

Installing HWhile

Once the Haskell Platform is installed and configured correctly, you can install HWhile by running:

stack install hwhile

This will download HWhile and its depenencies (if necessary) and compile and install them.


If installed correctly, HWhile can be run with the command:

hwhile <FLAG> <FILE> <EXPR>

For example:

hwhile -i examples/count.while "[1, 2, 3]"

This example takes a list of numbers as its argument and outputs their sum, so you should see 6 as the output.


There are syntax highlighting extensions available for Sublime Text and VS Code.


Informally, the syntax of HWhile is summarised as:

PROG ::= programName read inputName { CMD; CMD; ... } write outputName
CMD  ::= var := EXP
      |  while EXP { CMD; CMD; ... }
      |  if EXP { CMD; CMD; ... }
      |  if EXP { CMD; CMD; ... } else { CMD; CMD; ... }
EXP  ::= nil | cons EXP EXP | hd EXP | tl EXP | (EXP) | var

A HWhile program reads its input into the variable inputName, which may then occur in the following CMDs. The value of the variable outputName is the output of program. All variables have the initial value of nil. For the while and if statements, the tree nil is falsy and all other trees are truthy.

The grammar below gives exactly the concrete syntax of this implementation, including syntactic sugar:

PROG  ::= ID read ID BLOCK write ID

BLOCK ::= { CMDS }
        | {}

        | CMD

CMD   ::= ID := EXP                     // Assignment
        | while EXP BLOCK               // While loops
        | if EXP BLOCK else BLOCK       // If-then-else statements
        | if EXP BLOCK                  // If-then statements
        | ID := <ID> EXP                // Macro calls
        | switch EXP { CASES            // Switch statements

        | default : CMDS }
        | }

EXP   ::= LIT
        | cons EXP EXP
        | hd EXP
        | tl EXP
        | (EXP)
        | EXP = EXP
        | ID
        | []
        | [ EXP LIST

        | ]

LIT   ::= nil
        | true
        | false
        | <LIT.LIT>
        | NAT
        | @asgn
        | @:=
        | @doAsgn
        | @while
        | @doWhile
        | @if
        | @doIf
        | @var
        | @quote
        | @hd
        | @doHd
        | @tl
        | @doTl
        | @cons
        | @doCons

NAT   ::= 0|[1-9][0-9]+

ID    ::= [a-zA-Z_'][a-zA-Z0-9_']*

Command line input must conform to the following grammar:

INP    ::= nil
        | true
        | false
        | <LIT.LIT>
        | NAT
        | []
        | [ INP INPLST
        | @asgn
        | @:=
        | @doAsgn
        | @while
        | @doWhile
        | @if
        | @doIf
        | @var
        | @quote
        | @hd
        | @doHd
        | @tl
        | @doTl
        | @cons
        | @doCons

        | ]


The semantics of HWhile programs are defined by functions. These functions take a program construct - an expression, block, command or program, and a store - a function of type X -> T that maps variable names to trees.

We first define two functions over stores - addition, which adds a new binding, and lookup, which retrieves the tree bound to the given name.

σ + (x -> T) = σ, x -> T       if x ∉ σ
             | σ', x -> T, σ'' if σ = σ', x -> U, σ''

σ(x) = T   if σ = σ', x -> T, σ''
     | nil if x ∉ σ

Semantics for expressions are defined as follows:

[e] : EXP -> (X -> T) -> T

[x] σ = σ(x)
[hd e] σ = nil if [e] σ = nil
         | H   if [e] σ = <H.T>
[tl e] σ = nil if [e] σ = nil
         | T   if [e] σ = <H.T>
[e = e'] σ = nil if [e] σ /= [e'] σ
           | T   if [e] σ  = [e'] σ where T /= nil
[cons e e'] σ = <H.T> where H = [e] σ, T = [e'] σ

For blocks:

[b] : BLOCK -> (X -> T) -> (X -> T)

[{}] σ = σ
[{c; cs}] σ = [{cs}] ([c] σ)

For commands, we define semantics only for pure commands (assignment, while loops and if-then-else statements). The semantics for switch statements and macro calls are given by translation to pure commands. The semantics for pure commands are given as follows:

[c] : CMD -> (X -> T) -> (X -> T)

[x := e] σ = σ + (x -> [e] σ)
[while e b] σ = σ                   if [e] σ  = nil
              | [while e b] ([b] σ) if [e] σ /= nil
[if e b else b'] σ = [b]  σ if [e] σ /= nil
                   | [b'] σ if [e] σ  = nil

The translations for if-then statements, switch statements and macros are defined as follows:

if e b = if e b else {}

switch e {} = {}
switch e { default : cs } = { cs }
switch e1 { case e2 : cs cases } =
    { if e1 = e2 { cs } else switch e1 { cases } }

x := <macro> e = z := e; disjoin(cmds, z, y); x := y
where macro.while = macro read z { cmds } write y

The function disjoin renames the variable names in cmds such that there are no names in common with the program in which the macro call occurs, except for the read-variable z and the write-variable y.

Finally, the semantics for programs are defined as follows:

[p] : PROG -> T -> T

[n read x b write y] T = ([b] (x -> T))(y)