From ff9258fb22e0f29f0c3ab5c3d081822830908a4e Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 15 Jul 2026 10:52:50 +0200 Subject: [PATCH] [FMFP] Notes on LTL --- semester4/fmfp/code/promela/00_basics.pml | 7 +++++ ...methods-functional-programming-summary.pdf | Bin 736490 -> 739936 bytes .../01_linear-temporal-logic.tex | 1 + .../parts/06_exercises/02_fm/03_modelling.tex | 14 ++++++++-- .../fmfp/parts/06_exercises/02_fm/04_ltl.tex | 25 ++++++++++++++++++ 5 files changed, 45 insertions(+), 2 deletions(-) diff --git a/semester4/fmfp/code/promela/00_basics.pml b/semester4/fmfp/code/promela/00_basics.pml index 77ebe2c..0387346 100644 --- a/semester4/fmfp/code/promela/00_basics.pml +++ b/semester4/fmfp/code/promela/00_basics.pml @@ -34,6 +34,13 @@ vector v; // using the custom vector type mtype msg = ack; // Using the symbolic constant +// --- Functions ----------------------------------------------- +// Note that these are not full functions and recursion is not supported! +inline fun() { + // function body goes here +} + + // --- Processes ----------------------------------------------- // Process declarations proctype myProc(int p) { diff --git a/semester4/fmfp/formal-methods-functional-programming-summary.pdf b/semester4/fmfp/formal-methods-functional-programming-summary.pdf index f8f924aaf56d86feb6454f224a6c7615379bcc96..c44b9e54dd2436ea901d846185b69bfb9e1f9341 100644 GIT binary patch delta 89078 zcmX7uQ*>orvxbu$+fK)}ZJQn2HagyM(qYFoI<{@wwr%6|f4++~))?=2)~uR0vu3@k z&R*$u66tGlQ2@nL_4z3Lpx^@t@&xt!s3NBXw+^h6=&JXaa4Fn@PnoRw#T#&{5%n1@ z9}wAsoMQ>IU}*K~A0mi9K7M5cLX-3*??9}m^rh_Bbz3woLmGlC00YFs@=`!|K+&2< zU_n`-L2pw&P(ks)bnXWKQ|Zw_@v%WwQ)FoWsd(N&=0R8CiN#vF{|Ga)6Jhq4L)4!b{7S2eyL?`G+Ows)`vxr&$A@YDm#sBC zpjafu?gA7ST#n|5?!WJ|FF;{YK{r!Mzd-T8ulQ~hQf8$9XwB?59WQf24jJt>F?|-lY3*Z2n2>SgJGs3E30ER2qO&DCRL<@#9Y8nC0!Z+<3D!%=f#DAQ7EK)erEK=* zA(?dkLk$03%gVgH6fVZy6(QW)_KmwM>kAw12R_jdHh76KIL^qu@E`c0W@NdQPCO8V z@#mh-9y#n{6QN<_eQY1R4|f0ZK4w0O-(hqNnGgum;yr^g0db5W{i*Zj;U3~}CO^`U 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b/semester4/fmfp/parts/05_modelling/02_linear-temporal-logic/01_linear-temporal-logic.tex @@ -1,4 +1,5 @@ \subsubsection{Linear Temporal Logic} +\label{sec:ltl-details} This is used to formalize LT-properties of traces. \paragraph{Operators} diff --git a/semester4/fmfp/parts/06_exercises/02_fm/03_modelling.tex b/semester4/fmfp/parts/06_exercises/02_fm/03_modelling.tex index 5f181b4..0c195e7 100644 --- a/semester4/fmfp/parts/06_exercises/02_fm/03_modelling.tex +++ b/semester4/fmfp/parts/06_exercises/02_fm/03_modelling.tex @@ -4,9 +4,19 @@ and putting an \texttt{assert} (or more) into the \texttt{init} block, to check Note that for non-determinism, we use Promela conditionals without conditions. -For parallelism, we can use the \texttt{run} keyword for a \texttt{proctype}, then we wait for the processes to terminate using -\texttt{\_nr\_pr == 1} and do our assertion. +For parallelism, we can use the \texttt{run} keyword for a \texttt{proctype} (rest of syntax is just as with a function in most C-like programming languages), +then we wait for the processes to terminate using \texttt{\_nr\_pr == 1} and do our assertion. + +We can use an \texttt{atomic} block to ensure atomicity. + +Promela \bi{does not} support functions, instead, the \texttt{inline} keyword works similarly to macros in \texttt{C}, +they are simply substituted into the code at compile time. +In some solutions, they use double-dash arrows (\verb|-->|). From testing, it seems that it is also fine to use normal arrows (\verb|->|) and it will still work. +For completeness, the double-dash arrows are used in if statements with conjuncts or disjuncts. If we are given a text description only however, things get more challenging, as we need to model the properties given there. A possible simplification of the process may be to model things one property at a time, then combine them as needed. + +To check if something is achievable (i.e. there is a solution to the task), we can use an \texttt{assert false} on the case where we have success +If there is a way, then the assertion will fail (because it will always fail and is only called if \texttt{success} is true) diff --git a/semester4/fmfp/parts/06_exercises/02_fm/04_ltl.tex b/semester4/fmfp/parts/06_exercises/02_fm/04_ltl.tex index 6d43903..19cbc5d 100644 --- a/semester4/fmfp/parts/06_exercises/02_fm/04_ltl.tex +++ b/semester4/fmfp/parts/06_exercises/02_fm/04_ltl.tex @@ -1,2 +1,27 @@ \subsubsection{Linear Time Properties (LTL)} We refer to Section~\ref{sec:ltl} for intuition, as these tend to mostly be intuition exercises. + +For doing verification of liveness / safety properties using \texttt{spin} and Promela, +the operators are translated to Promela as follows: +\verb+[] <> ! && || -> U+ for $\square \Diamond \neg \land \lor \Rightarrow U$, respectively. +In addition, we have the equality operator as a primitive propositional formula. We have \texttt{p == true} for $p$ in the operators. + +Execute \texttt{spin -a file.pml}, followed by \texttt{gcc pan.c} and \texttt{./a.out}. + +As a reminder, these are the operators (details in Section~\ref{sec:ltl-details}): +\begin{itemize} + \item Now: $p$ states that the proposition is true ``\textit{now}'' + \item Holds until: $\Phi U \Psi$ states that $\Phi$ holds (with no other valid proposition holding between) until $\Psi$ holds. + \item Next: $\bigcirc \Phi$ states that $\Phi$ holds for the ``next'' + \item Eventually: $\Diamond \Phi$ states that $\Phi$ holds \textit{eventually}, $\Diamond \Phi \equiv (\texttt{true} U \Phi)$ + \item Always (from now on): $\square \Phi$ states that from now on, $\Phi$ will always hold, $\square \Phi \equiv \neg \Diamond \neg \Phi$ +\end{itemize} +For the implication (where the left hand side is called the \textit{antecedent}, right hand side is called the \textit{consequent}), +remember to show the case where the antecedent is true and state that for antecedent false, it is trivially true + +Another important remark is that you can't just write $\Diamond \neg s_1$, where $s_1$ is a state, you need to specify the propositions. + + +\subparagraph{Liveness and Safety Properties} +Proofs here run using the definitions directly, either by showing a counter example (for disproving) or showing that, in fact, the definition holds. +Indirect proofs may also come in handy, because it is typically easier to show that something is not a safety property (or liveness property) that to show that it is.