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<h2 id="demo">Demo</h2>
<pre><code>(func $Factorial_f (param i32 i32) (result i32) (local i32)
;;> fn f(i: Int(32), j: Int(32)): Int(32) = {
;;| val res: Int(32) =
;;| (i + j);
;;| res
;;| }
;;> i
local.get 0
;;> j
local.get 1
;;> (i + j)
i32.add
;;> val res: Int(32)
local.set 2
;;> res
local.get 2
)
(func $Factorial_fact (param i32) (result i32)
;;> fn fact(i: Int(32)): Int(32) = {
;;| (if((i < 2)) {
;;| 1
;;| } else {
;;| (i * fact((i - 1)))
;;| })
;;| }
;;> i
local.get 0
;;> 2
i32.const 2
;;> (i < 2)
i32.lt_s
;;> (if((i < 2)) {
;;| 1
;;| } else {
;;| (i * fact((i - 1)))
;;| })
if (result i32)
;;> 1
i32.const 1
else
;;> i
local.get 0
;;> fact((i - 1))
;;> i
local.get 0
;;> 1
i32.const 1
;;> (i - 1)
i32.sub
call $Factorial_fact
;;> (i * fact((i - 1)))
i32.mul
end
)</code></pre>
<h2 id="wasm-basics">WASM basics</h2>
<h3 id="stack-machine">Stack machine</h3>
<ul>
<li>WASM is a stack based machine.</li>
<li>WASM has types. We will use exclusively i32.</li>
<li>Instructions can push or pop values from the stack.
<ul>
<li>i32.const x : push x to the stack.</li>
<li>i32.add : pop 2 values, add them and push the result.</li>
<li>drop : pop a value and ignore it.</li>
</ul></li>
<li>Locals can store values inside a function. Useful for val definitions among others.
<ul>
<li>local.get x : get xth local</li>
<li>local.set x : set xth local</li>
</ul></li>
<li>Globals store program wide values.
<ul>
<li>global.get x : get xth global</li>
<li>global.set x : set xth global</li>
</ul></li>
<li>Control flow.
<ul>
<li>if : pop value from stack, if 0 goto else otherwise continue.</li>
<li>call : pop arguments from the stack, jump to function.</li>
</ul></li>
</ul>
<h2 id="function-calls">Function calls</h2>
<p>How to call a function: - Push the required number of arguments on the stack. - Call the function. The call instruction will pop the arguments and place them in the locals. - The result will be placed on top of the stack.</p>
<pre><code>(func $f (param i32 i32) (result i32)
local.get 0
local.get 1
i32.add
)
(
i32.const 3 ;; arg 0
i32.const 4 ;; arg 1
;; A
call $f
;; B
)
A:
| |
| 4 | <-- arg 1
| 3 | <-- arg 0
|-------|
B:
| |
| |
| 7 | <-- result
|-------|
</code></pre>
<h2 id="store">Store</h2>
<pre><code>Store 3 at address 48
| |
| |
| |
|--------| <-- bottom of the stack
`i32.const 48`
| |
| |
| 48 | <-- address
|--------| <-- bottom of the stack
`i32.const 3`
| |
| 3 | <-- value
| 48 | <-- address
|--------| <-- bottom of the stack
`i32.store` pops 2 values from the stack
| |
| |
| |
|--------| <-- bottom of the stack
Heap
| address | 0 | 1 | 2 | .. | 47 | 48 | 49 | .. |
|---------|----|----|----|----|----|----|----|----|
| value | 0 | 0 | 0 | .. | 0 | 3 | 0 | .. |
^
value written</code></pre>
<h2 id="values">Values</h2>
<p>Very similar to java.</p>
<ul>
<li>Ints are represented simply with an i32.</li>
<li>Bools are represented with an i32, false = 0, true = 1.</li>
<li>Unit is represented with an i32 with value 0.</li>
</ul>
<h3 id="strings">Strings</h3>
<pre><code>| address | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 |
|---------|----|----|----|----|----|----|----|----|
| value | 104| 101| 108| 108| 111| 33 | 0 | 0 |
| ascii | h | e | l | l | o | ! | \0 | |
| |
| |
| 24 | <-- pointer to string
|--------| <-- bottom of the stack
</code></pre>
<h3 id="adts">ADTs</h3>
<ul>
<li>store the value on the heap to reduced the size to the size of a pointer.</li>
<li>store which constructor the value holds.</li>
</ul>
<div class="sourceCode" id="cb5"><pre class="sourceCode scala"><code class="sourceCode scala"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> <span class="fu">getList</span><span class="op">():</span> <span class="ex">List</span> <span class="op">=</span> <span class="op">{</span> <span class="op">...</span> <span class="op">}</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="kw">val</span> ls<span class="op">:</span> <span class="ex">List</span> <span class="op">=</span> <span class="fu">getList</span><span class="op">();</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="co">// What is the size of list here?</span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="co">// Is it a Nil or a Cons?</span></span></code></pre></div>
<pre><code>Cons(42, Nil())
| address | value |
|---------|---------|
| 0 | 1 | \
| 1 | | | constructor id.
| 2 | | | Cons
| 3 | | /
| 4 | 42 | \
| 5 | | | first member: int
| 6 | | | 42
| 7 | | /
| 8 | 1234 | \
| 9 | | | seconder member: pointer to Nil
| 10 | | | 1234
| 11 | | /
Field offset = 4 + 4 * field number
==> Utils.scala:adtField
</code></pre>
<h2 id="allocation">Allocation</h2>
<p>Utils.scala:memoryBoundary is the index of a global variable that holds a pointer to the next free bytes.</p>
<h3 id="example-in-pseudocode">Example in pseudocode:</h3>
<p>Start of the program:</p>
<pre><code>global.set(memoryBoundary, 0)</code></pre>
<p>We want to allocate “hello!” = 7 bytes (don’t forget the null terminator).</p>
<p>Store current memory pointer as pointer to our new string:</p>
<pre><code>hello_string = global.get(memoryBoundary)</code></pre>
<p>Increment the memory boundary by 7 (size of string).</p>
<pre><code>global.set(memoryBoundary, global.get(memoryBoundary) + 7)</code></pre>
<h3 id="with-webassembly-instructions">With webassembly instructions:</h3>
<pre><code>;; With memoryBoundary = 0.
;; Load the current boundary for string
global.get 0
;; Load it again for the arithmetic
global.get 0
;; length of string
i32.const 7
;; base + length = new boundary
i32.add
;; store new boundary
global.set 0
;; now the string pointer is on the stack, we just
;; need to copy the character's bytes into it.
...</code></pre>
<h2 id="pattern-matching">Pattern matching</h2>
<p>A pattern matching expression:</p>
<pre><code>e match {
case p1 => e1
...
case pn => en
}</code></pre>
<p>can be considered to be equivalent to the following pseudocode:</p>
<pre><code>val v = e;
if (matchAndBind(v, p1)) e1
else if (matchAndBind(v, p2)) e2
else if ...
else if (matchAndBind(v, pn)) en
else error("Match error!")</code></pre>
<p>matchAndBind is equivalent to this:</p>
<pre><code>WildcardPattern:
"case _ => ..."
matchAndBind(v, _) = true
IdPattern:
"case id => ..."
matchAndBind(v, id) = { id = v; true }
LiteralPattern:
"case 3 => ..."
matchAndBind(v, lit) = { v == lit }
CaseClassPattern:
"case Cons(x, _) => ..."
matchAndBind(C_1(v_1, ..., v_n), C_2(p_1, ..., p_m)) = {
C_1 == C_2 &&
matchAndBind(v_1, p_1) &&
...
matchAndBind(v_m, p_m)
}</code></pre>
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