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<!DOCTYPE html>
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<section id="verifying-langname-contracts">
<h1>Verifying BitML contracts<a class="headerlink" href="#verifying-langname-contracts" title="Permalink to this headline">¶</a></h1>
<p>Other than compiling contracts to transactions, the BitML toolchain
allows to verify contracts before executing them.</p>
<p>A desirable property of smart contracts is <strong>liquidity</strong>,
which requires that the contract balance is always eventually transferred to some participant.
In a non-liquid contract, funds can be frozen forever, unavailable to anyone, hence effectively destroyed.
There are many possible flavours of liquidity, depending e.g. on which
participants are assumed to be honest, and on which are their strategies.</p>
<p>The toolchain can also verify arbitrary security proprieties,
expressed as LTL queries.</p>
<section id="liquidity">
<h2>Liquidity<a class="headerlink" href="#liquidity" title="Permalink to this headline">¶</a></h2>
<p>In the following contract, <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> and <code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code> contribute 1 BTC each
for a donation of 2 BTC to either <code class="code bitml docutils literal notranslate"><span class="pre">"C"</span></code> or <code class="code bitml docutils literal notranslate"><span class="pre">"D"</span></code>.
We want to check if the contract is liquid or not, without supplying any strategy,
i.e. without knowing which branch <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> and <code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code> will authorize.</p>
<p>This flavour of liquidity is called <strong>strategy-less</strong>.
Intuitively, it corresponds to check
if the contract is liquid for any possible strategy of any participants,
whether they are honest or not.</p>
<p>To check the liquidity of the following contract,
we add <code class="code bitml docutils literal notranslate"><span class="pre">(check-liquid)</span></code> at its end.</p>
<div class="highlight-bitml notranslate"><div class="highlight"><pre><span></span><span class="o">#</span><span class="nv">lang</span> <span class="nv">bitml</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"A"</span> <span class="s">"0339bd7fade9167e09681d68c5fc80b72166fe55bbb84211fd12bde1d57247fbe1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"B"</span> <span class="s">"034a7192e922118173906555a39f28fa1e0b65657fc7f403094da4f85701a5f809"</span><span class="p">)</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"C"</span> <span class="s">"034f5ca30056b9dd89132ca8c7583e6d82b69bc17bb2c1dfef9dea9c3467631e6b"</span><span class="p">)</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"D"</span> <span class="s">"037b60c121050e1fa6e7d5cd299ecc66d87330b2996567004f831c63ef0e2a157e"</span><span class="p">)</span>
<span class="p">(</span><span class="nf">debug-mode</span><span class="p">)</span>
<span class="p">(</span><span class="nf">contract</span>
<span class="p">(</span><span class="nf">pre</span>
<span class="p">(</span><span class="k">deposit </span><span class="s">"A"</span> <span class="mi">1</span> <span class="s">"txid:2e647d8566f00a08d276488db4f4e2d9f82dd82ef161c2078963d8deb2965e35@1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">deposit </span><span class="s">"A"</span> <span class="mi">1</span> <span class="s">"txid:625bc69c467b33e2ad70ea2817874067604eb42dd5835403f54fb6028bc70168@0"</span><span class="p">))</span>
<span class="p">(</span><span class="nf">choice</span>
<span class="p">(</span><span class="k">auth </span><span class="s">"A"</span> <span class="s">"B"</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"C"</span><span class="p">))</span>
<span class="p">(</span><span class="k">auth </span><span class="s">"A"</span> <span class="s">"B"</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"D"</span><span class="p">)))</span>
<span class="p">(</span><span class="nf">check-liquid</span><span class="p">))</span>
</pre></div>
</div>
<p>During the compilation of the contract, the tool-chain checks if it is liquid. The result is printed before the transactions in a comment-box.</p>
<div class="highlight-balzac notranslate"><div class="highlight"><pre><span></span><span class="cm">/*=============================================================================</span>
<span class="cm">Model checking result for (check-liquid)</span>
<span class="cm">Result: false</span>
<span class="cm">counterexample({[0 | nil | 'xconf U empty | empty] < ( A, B) : withdraw C + (A, B) : withdraw D, 100000000 satoshi > 'xconf,</span>
<span class="cm">'C-LockAuthControl} {{A lock withdraw C in 'xconf}[0 | nil | 'xconf U empty | empty] < Lock((A, B) : withdraw C) + (A, B) : withdraw D, 100000000 satoshi ></span>
<span class="cm">'xconf,'Rifl} {{A lock withdraw D in 'xconf}[0 | nil | 'xconf U empty | empty] < Lock((A, B) : withdraw C) + Lock((A, B) : withdraw D), 100000000 satoshi > 'xconf,'Finalize}, {[0 | nil | 'xconf U empty | empty] < Lock((A, B) : withdraw C) + Lock((A, B) : withdraw D), 100000000 satoshi > 'xconf, solution})</span>
<span class="cm">Model checking time: 143.0 ms</span>
<span class="cm">=============================================================================*/</span>
</pre></div>
</div>
<p>As we can see, the contract is not liquid.
In fact, In order to unlock the funds, <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> and <code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code> must agree on the recipient of the donation,
by giving their authorization on the same branch. This contract would be liquid
only by assuming the cooperation between <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> and <code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code>: indeed, <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> alone cannot
guarantee that the 2 BTC will eventually be donated, as <code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code> can choose a different
recipient, or even refuse to give any authorization.</p>
<p>We can try to modify the contract to handle this situations by adding a timeout branch
with <code class="code bitml docutils literal notranslate"><span class="pre">(after</span> <span class="pre">700000</span> <span class="pre">(split</span> <span class="pre">(1</span> <span class="pre">-></span> <span class="pre">(withdraw</span> <span class="pre">"A"))</span> <span class="pre">(1</span> <span class="pre">-></span> <span class="pre">(withdraw</span> <span class="pre">"B"))))</span></code>.
The new branch locks the contract until the block number 700000 is appended to the blockchain,
modeling a delay.
After the corresponding time passes, it unlocks and returns their deposits to <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> and <code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code>.</p>
<div class="highlight-bitml notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="nf">contract</span>
<span class="p">(</span><span class="nf">pre</span>
<span class="p">(</span><span class="k">deposit </span><span class="s">"A"</span> <span class="mi">1</span> <span class="s">"txid:2e647d8566f00a08d276488db4f4e2d9f82dd82ef161c2078963d8deb2965e35@1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">deposit </span><span class="s">"A"</span> <span class="mi">1</span> <span class="s">"txid:625bc69c467b33e2ad70ea2817874067604eb42dd5835403f54fb6028bc70168@0"</span><span class="p">))</span>
<span class="p">(</span><span class="nf">choice</span>
<span class="p">(</span><span class="k">auth </span><span class="s">"A"</span> <span class="s">"B"</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"C"</span><span class="p">))</span>
<span class="p">(</span><span class="k">auth </span><span class="s">"A"</span> <span class="s">"B"</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"D"</span><span class="p">))</span>
<span class="p">(</span><span class="k">after </span><span class="mi">700000</span> <span class="p">(</span><span class="k">split </span><span class="p">(</span><span class="mi">1</span> <span class="k">-> </span><span class="p">(</span><span class="k">withdraw </span><span class="s">"A"</span><span class="p">))</span> <span class="p">(</span><span class="mi">1</span> <span class="k">-> </span><span class="p">(</span><span class="k">withdraw </span><span class="s">"B"</span><span class="p">)))))</span>
<span class="p">(</span><span class="nf">check-liquid</span><span class="p">))</span>
</pre></div>
</div>
<p>Now the contract is liquid, and the toolchain confirms it.</p>
<div class="highlight-balzac notranslate"><div class="highlight"><pre><span></span><span class="cm">/*=============================================================================</span>
<span class="cm">Model checking result for (check-liquid)</span>
<span class="cm">Result: true</span>
<span class="cm">Model checking time: 322.0 ms</span>
<span class="cm">=============================================================================*/</span>
</pre></div>
</div>
</section>
<section id="liquidity-with-strategies">
<h2>Liquidity with strategies<a class="headerlink" href="#liquidity-with-strategies" title="Permalink to this headline">¶</a></h2>
<p>In the following contract, <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> can reveal her secret and redeem its deposit.
Otherwise, after a certain amount of time the block number 700000 will be appended to the blockchain,
<code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code> can redeem <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code>’s deposit, after providing his authorization to do so.</p>
<div class="highlight-bitml notranslate"><div class="highlight"><pre><span></span><span class="o">#</span><span class="nv">lang</span> <span class="nv">bitml</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"A"</span> <span class="s">"0339bd7fade9167e09681d68c5fc80b72166fe55bbb84211fd12bde1d57247fbe1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"B"</span> <span class="s">"034a7192e922118173906555a39f28fa1e0b65657fc7f403094da4f85701a5f809"</span><span class="p">)</span>
<span class="p">(</span><span class="nf">debug-mode</span><span class="p">)</span>
<span class="p">(</span><span class="nf">contract</span>
<span class="p">(</span><span class="nf">pre</span>
<span class="p">(</span><span class="k">deposit </span><span class="s">"A"</span> <span class="mi">1</span> <span class="s">"txid:2e647d8566f00a08d276488db4f4e2d9f82dd82ef161c2078963d8deb2965e35@1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">secret </span><span class="s">"A"</span> <span class="nv">a</span> <span class="s">"f9292914bfd27c426a23465fc122322abbdb63b7"</span><span class="p">))</span>
<span class="p">(</span><span class="nf">choice</span>
<span class="p">(</span><span class="k">reveal </span><span class="p">(</span><span class="nf">a</span><span class="p">)</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"A"</span><span class="p">))</span>
<span class="p">(</span><span class="k">auth </span><span class="s">"B"</span> <span class="p">(</span><span class="k">after </span><span class="mi">700000</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"B"</span><span class="p">))))</span>
<span class="p">(</span><span class="nf">check-liquid</span><span class="p">))</span>
</pre></div>
</div>
<p>We start by checking the strategy-less liquidity.
As the result of the verification shows, the contract is not liquid.
This is because if neither <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> reveals her secret nor <code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code> gives his authorization,
the funds will be stuck forever.</p>
<div class="highlight-balzac notranslate"><div class="highlight"><pre><span></span><span class="cm">/*=============================================================================</span>
<span class="cm">Model checking result for (check-liquid)</span>
<span class="cm">Result: false</span>
<span class="cm">Secrets: a:1</span>
<span class="cm">counterexample({[0 | 700000 | 'xconf U empty | B, A] < B : after 700000 : withdraw B + put empty reveal a if True . withdraw A, 100000000 satoshi > 'xconf | {A : a # 1},'C-LockAuthRev} {{A lock-reveal a}[0 | 700000 | 'xconf U empty | B, A] Lock({A : a # 1}) | < B : after 700000 : withdraw B + put empty reveal a if True . withdraw A, 100000000 satoshi > 'xconf,'Rifl} {{B lock after 700000 : withdraw B in 'xconf}[0 | 700000 | 'xconf U empty | B, A] Lock({A : a # 1}) | < Lock(B : after 700000 : withdraw B) + put empty reveal a if True . withdraw A, 100000000 satoshi > 'xconf,'Rifl} {{delta 700000}[700000 | nil | 'xconf U empty | B, A] Lock({A : a # 1}) | < Lock(B : after 700000 : withdraw B) + put empty reveal a if True . withdraw A, 100000000 satoshi > 'xconf,'Finalize}, {[700000 | nil | 'xconf U empty | B, A] Lock({A : a # 1}) | < Lock(B : after 700000 : withdraw B) + put empty reveal a if True . withdraw A, 100000000 satoshi > 'xconf,solution})</span>
<span class="cm">Model checking time: 104.0 ms</span>
<span class="cm">=============================================================================*/</span>
</pre></div>
</div>
<p>The BitML toolchain allows us to specify the intended behaviour of a participant, called <strong>strategy</strong>.
The security propriety is verified with respect to the specified strategies.</p>
<p>We check if the contract is liquid if the strategy of <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code>
consists in revealing her secret, expressed by <code class="code bitml docutils literal notranslate"><span class="pre">(strategy</span> <span class="pre">"A"</span> <span class="pre">(do-reveal</span> <span class="pre">a)))</span></code>
as parameter of <code class="code bitml docutils literal notranslate"><span class="pre">(check-liquid</span> <span class="pre">Strategy</span> <span class="pre">...)</span></code>.</p>
<p>We also check the liquidity if <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> authorizes the second branch of the contract,
with the strategy <code class="code bitml docutils literal notranslate"><span class="pre">(strategy</span> <span class="pre">"B"</span> <span class="pre">(do-auth</span> <span class="pre">(auth</span> <span class="pre">"B"(after</span> <span class="pre">700000</span> <span class="pre">(withdraw</span> <span class="pre">"B")))))</span></code>.</p>
<div class="highlight-bitml notranslate"><div class="highlight"><pre><span></span><span class="o">#</span><span class="nv">lang</span> <span class="nv">bitml</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"A"</span> <span class="s">"0339bd7fade9167e09681d68c5fc80b72166fe55bbb84211fd12bde1d57247fbe1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"B"</span> <span class="s">"034a7192e922118173906555a39f28fa1e0b65657fc7f403094da4f85701a5f809"</span><span class="p">)</span>
<span class="p">(</span><span class="nf">debug-mode</span><span class="p">)</span>
<span class="p">(</span><span class="nf">contract</span>
<span class="p">(</span><span class="nf">pre</span>
<span class="p">(</span><span class="k">deposit </span><span class="s">"A"</span> <span class="mi">1</span> <span class="s">"txid:2e647d8566f00a08d276488db4f4e2d9f82dd82ef161c2078963d8deb2965e35@1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">secret </span><span class="s">"A"</span> <span class="nv">a</span> <span class="s">"f9292914bfd27c426a23465fc122322abbdb63b7"</span><span class="p">))</span>
<span class="p">(</span><span class="nf">choice</span>
<span class="p">(</span><span class="k">reveal </span><span class="p">(</span><span class="nf">a</span><span class="p">)</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"A"</span><span class="p">))</span>
<span class="p">(</span><span class="k">auth </span><span class="s">"B"</span> <span class="p">(</span><span class="k">after </span><span class="mi">700000</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"B"</span><span class="p">))))</span>
<span class="p">(</span><span class="nf">check-liquid</span>
<span class="p">(</span><span class="k">strategy </span><span class="s">"A"</span> <span class="p">(</span><span class="k">do-reveal </span><span class="nv">a</span><span class="p">)))</span>
<span class="p">(</span><span class="nf">check-liquid</span>
<span class="p">(</span><span class="k">strategy </span><span class="s">"B"</span> <span class="p">(</span><span class="k">do-auth </span><span class="p">(</span><span class="k">auth </span><span class="s">"B"</span> <span class="p">(</span><span class="k">after </span><span class="mi">700000</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"B"</span><span class="p">)))))))</span>
</pre></div>
</div>
<p>For both strategies, the contract is liquid.</p>
<div class="highlight-balzac notranslate"><div class="highlight"><pre><span></span><span class="cm">/*=============================================================================</span>
<span class="cm">Model checking result for (check-liquid (strategy A (do-reveal a)))</span>
<span class="cm">Result: true</span>
<span class="cm">/*=============================================================================</span>
<span class="cm">Model checking result for (check-liquid (strategy B (do-auth (auth B (after 700000 (withdraw B))))))</span>
<span class="cm">Result: true</span>
<span class="cm">Model checking time: 270.0 ms</span>
<span class="cm">=============================================================================*/</span>
</pre></div>
</div>
</section>
<section id="quantitative-liquidity">
<h2>Quantitative liquidity<a class="headerlink" href="#quantitative-liquidity" title="Permalink to this headline">¶</a></h2>
<p>The previous flavours of liquidity require that no funds remain frozen
within the contract. However, in some cases a participant could accept the fact that a
portion of the funds remain frozen, especially when these funds would be ideally
assigned to other participants.</p>
<p>In the following contract, <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> and <code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code> put 1 BTC each.
Each of them will get their own BTC back if they reveal their secret.</p>
<div class="highlight-bitml notranslate"><div class="highlight"><pre><span></span><span class="o">#</span><span class="nv">lang</span> <span class="nv">bitml</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"A"</span> <span class="s">"0339bd7fade9167e09681d68c5fc80b72166fe55bbb84211fd12bde1d57247fbe1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"B"</span> <span class="s">"034a7192e922118173906555a39f28fa1e0b65657fc7f403094da4f85701a5f809"</span><span class="p">)</span>
<span class="p">(</span><span class="nf">debug-mode</span><span class="p">)</span>
<span class="p">(</span><span class="nf">contract</span>
<span class="p">(</span><span class="nf">pre</span>
<span class="p">(</span><span class="k">deposit </span><span class="s">"A"</span> <span class="mi">1</span> <span class="s">"txid:2e647d8566f00a08d276488db4f4e2d9f82dd82ef161c2078963d8deb2965e35@1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">deposit </span><span class="s">"B"</span> <span class="mi">1</span> <span class="s">"txid:0f795bda36ac661f2b9a626d46049bc14b95b2d0e69f5fb7ccc4c3d767db9f34@1"</span><span class="p">)</span>
<span class="p">(</span><span class="k">secret </span><span class="s">"A"</span> <span class="nv">a</span> <span class="s">"f9292914bfd27c426a23465fc122322abbdb63b7"</span><span class="p">)</span>
<span class="p">(</span><span class="k">secret </span><span class="s">"B"</span> <span class="nv">b</span> <span class="s">"9804ebb0fc4a8329981dd33aaff32b6cb579580a"</span><span class="p">))</span>
<span class="p">(</span><span class="nf">split</span>
<span class="p">(</span><span class="mi">1</span> <span class="k">-> </span><span class="p">(</span><span class="k">reveal </span><span class="p">(</span><span class="nf">a</span><span class="p">)</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"A"</span><span class="p">)))</span>
<span class="p">(</span><span class="mi">1</span> <span class="k">-> </span><span class="p">(</span><span class="k">reveal </span><span class="p">(</span><span class="nf">b</span><span class="p">)</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"B"</span><span class="p">))))</span>
<span class="p">(</span><span class="k">check </span><span class="s">"A"</span> <span class="k">has-more-than </span><span class="mi">1</span>
<span class="p">(</span><span class="k">strategy </span><span class="s">"A"</span> <span class="p">(</span><span class="k">do-reveal </span><span class="nv">a</span><span class="p">)))))</span>
</pre></div>
</div>
<p>In this setting, <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> is interested in checking if she will get back her bitcoin,
assuming that she reveals her secret. We check it using <code class="code bitml docutils literal notranslate"><span class="pre">(check</span> <span class="pre">"A"</span> <span class="pre">has-more-than</span> <span class="pre">1</span> <span class="pre">(strategy</span> <span class="pre">"A"</span> <span class="pre">(do-reveal</span> <span class="pre">a)))</span></code>.</p>
<div class="highlight-balzac notranslate"><div class="highlight"><pre><span></span><span class="cm">/*=============================================================================</span>
<span class="cm">Model checking result for (check A has-more-than 1 (strategy A (do-reveal a)))</span>
<span class="cm">Result: true</span>
<span class="cm">Model checking time: 134.0 ms</span>
<span class="cm">=============================================================================*/</span>
</pre></div>
</div>
</section>
<section id="custom-ltl-queries">
<h2>Custom LTL queries<a class="headerlink" href="#custom-ltl-queries" title="Permalink to this headline">¶</a></h2>
<p>The following contract is a <em>timed commitment</em>,
where <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> wants to choose a secret <code class="code balzac docutils literal notranslate"><span class="pre">a</span></code>,
and reveal it before the deadline <code class="code balzac docutils literal notranslate"><span class="pre">d</span></code>;
if <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> does not reveal the secret within <code class="code balzac docutils literal notranslate"><span class="pre">d</span></code>,
<code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code> can redeem the 1 BTC deposit as a compensation.</p>
<div class="highlight-bitml notranslate"><div class="highlight"><pre><span></span><span class="o">#</span><span class="nv">lang</span> <span class="nv">bitml</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"A"</span> <span class="s">"029c5f6f5ef0095f547799cb7861488b9f4282140d59a6289fbc90c70209c1cced"</span><span class="p">)</span>
<span class="p">(</span><span class="k">participant </span><span class="s">"B"</span> <span class="s">"022c3afb0b654d3c2b0e2ffdcf941eaf9b6c2f6fcf14672f86f7647fa7b817af30"</span><span class="p">)</span>
<span class="p">(</span><span class="nf">debug-mode</span><span class="p">)</span>
<span class="p">(</span><span class="nf">define</span> <span class="p">(</span><span class="nf">d</span><span class="p">)</span> <span class="mi">700000</span><span class="p">)</span>
<span class="p">(</span><span class="nf">contract</span>
<span class="p">(</span><span class="k">pre </span><span class="p">(</span><span class="k">deposit </span><span class="s">"A"</span> <span class="mi">1</span> <span class="s">"txA@0"</span><span class="p">)(</span><span class="k">secret </span><span class="s">"A"</span> <span class="nv">a</span> <span class="s">"f9292914bfd27c426a23465fc122322abbdb63b7"</span><span class="p">))</span>
<span class="p">(</span><span class="k">choice </span><span class="p">(</span><span class="k">reveal </span><span class="p">(</span><span class="nf">a</span><span class="p">)</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"A"</span><span class="p">))</span>
<span class="p">(</span><span class="k">after </span><span class="p">(</span><span class="k">ref </span><span class="p">(</span><span class="nf">d</span><span class="p">))</span> <span class="p">(</span><span class="k">withdraw </span><span class="s">"B"</span><span class="p">)))</span>
<span class="p">(</span><span class="k">check-query </span><span class="s">"[]<> (a revealed => A has-deposit>= 100000000 satoshi)"</span><span class="p">)</span>
<span class="p">(</span><span class="k">check-query </span><span class="s">"[]<> (a revealed \\/ B has-deposit>= 100000000 satoshi)"</span><span class="p">))</span>
</pre></div>
</div>
<p>The BitML toolchain allows us to check custom LTL properties,
tailored specifically for the contract being verified, using <code class="code bitml docutils literal notranslate"><span class="pre">(check-query</span> <span class="pre">"query")</span></code>.</p>
<p>In the timed commitment contract, we want the following two properties to be satisfied.</p>
<ul class="simple">
<li><p>If <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> reveal her secret, she will get back her deposit.
We check this property with <code class="code bitml docutils literal notranslate"><span class="pre">(check-query</span> <span class="pre">"[]<></span> <span class="pre">(a</span> <span class="pre">revealed</span> <span class="pre">=></span> <span class="pre">A</span> <span class="pre">has-deposit>=</span> <span class="pre">100000000</span> <span class="pre">satoshi)")</span></code>.</p></li>
<li><p>Either <code class="code bitml docutils literal notranslate"><span class="pre">"B"</span></code> gets to know the secret, or he will get the bitcoin as compensation.
We check this property with <code class="code bitml docutils literal notranslate"><span class="pre">(check-query</span> <span class="pre">"[]<></span> <span class="pre">(a</span> <span class="pre">revealed</span> <span class="pre">\/</span> <span class="pre">B</span> <span class="pre">has-deposit>=</span> <span class="pre">100000000</span> <span class="pre">satoshi)"))</span></code>.</p></li>
</ul>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Due to the internal representation of numbers in the model check, all BTC values have to be expressed in <strong>satoshi</strong> when checking custom LTL queries.</p>
</div>
<p>The result is true for both queries:</p>
<div class="highlight-balzac notranslate"><div class="highlight"><pre><span></span><span class="cm">/*=============================================================================</span>
<span class="cm">Model checking result for (check-query [] (a revealed => <> A has-deposit>= 100000000 satoshi))</span>
<span class="cm">Result: true</span>
<span class="cm">/*=============================================================================</span>
<span class="cm">Model checking result for (check-query []<> (a revealed \/ B has-deposit>= 100000000 satoshi))</span>
<span class="cm">Result: true</span>
<span class="cm">Model checking time: 408.0 ms</span>
<span class="cm">=============================================================================*/</span>
</pre></div>
</div>
<p>The first LTL property has the same semantic as checking the quantitative liquidity of 1 BTC
if the strategy of <code class="code bitml docutils literal notranslate"><span class="pre">"A"</span></code> is to reveal her secret, or
<code class="code bitml docutils literal notranslate"><span class="pre">(check</span> <span class="pre">"A"</span> <span class="pre">has-more-than</span> <span class="pre">1</span> <span class="pre">(strategy</span> <span class="pre">"A"</span> <span class="pre">(do-reveal</span> <span class="pre">a)))</span></code>.
Instead, the second LTL property cannot be expressed as a combination of liquidity and strategies.</p>
<p>Other that <code class="code balzac docutils literal notranslate"><span class="pre">revealed</span></code> and <code class="code balzac docutils literal notranslate"><span class="pre">has-deposit>=</span></code>, you can express your LTL properties with <code class="code balzac docutils literal notranslate"><span class="pre">has-deposit</span></code>, and <code class="code balzac docutils literal notranslate"><span class="pre">has-deposit<=</span></code>.</p>
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