lpsparunfold

The algorithm applies a transformation on data expressions of a linear process specification (LPS), by which other tools (such as lpsparelm, lpsconstelm) can apply their transformations more effectively. Concretely, this tool unfolds a sort with associated constructor functions to a set of process parameters in the LPS, in such a way that all behaviour is preserved.

Let’s consider an example LPS, saved in the file Turnonoff.mcrl2:

sort
  Sys = struct sys(status: Type, n:Nat);
  Type = struct p_on | p_off;
map
  set_status: Sys # Bool # Type -> Type;
  set_n: Sys # Nat -> Nat;
var
  s_Sys : Sys;
  p1,p2: Type;
  b:Bool;
  n2:Nat;
eqn
  set_status(sys(p1,n2), b, p2) = if(!b, p1, p2);
  set_n(s_Sys, n2) = n2;
act
  on, off;
proc
  P(s_Sys : Sys) =
    (status(s_Sys) == p_on && set_status(s_Sys, status(s_Sys) == p_on, p_off) == p_off)
      -> on . P(sys(set_status(s_Sys, status(s_Sys) == p_on, p_off), set_n(s_Sys, 0)))
    + sum n1: Nat . (status(s_Sys) == p_off && set_status(s_Sys, status(s_Sys) == p_off, p_on) == p_on)
      -> off . P(sys(set_status(s_Sys, status(s_Sys) == p_off, p_on), set_n(s_Sys, n1)));

init P(sys(p_off, 0));

If we execute txt2lps Turnonoff.mcrl2 | lpsparunfold --sort=Sys | lpspp, then we obtain an LPS that has the parameters P(s_Sys_pp: Sys1, s_Sys_pp1: Type, s_Sys_pp2: Nat). Here, the single parameter s_Sys has been replaced by three parameters as follows:

• s_Sys_pp indicates which constructor was stored in s_Sys. In this case, the sort Sys has just one constructor, which is now represented by the constructor c_sys of the new sort Sys1.

• s_Sys_pp1 and s_Sys_pp2 are the values of the status and n parameters that were originally stored inside the sys constructor.

• Additional mappings and rewrite rules are introduced to reconstruct the original value of s_Sys from the three new parameters (mapping C_Sys1) and to project out the constructor type (mapping Det_Sys1) and arguments (mappings pi_Sys and pi_Sys1). The expressions that occur in the LPS are manipulated to use these mappings. In the general case, the new rewrite rules are such that s == C_Sort(Det_Sort(s), c_1(pi_1(s),..,pi_n(s)), .., c_k(pi_1(s),..,pi_n(s))), where c_1,..,c_k are the constructors of the unfolded sort Sort.

Thus, the original parameter s_Sys is now effectively unfolded intro three parameters and its internal data is now stored in separate process parameters. This means they can be processed by tools such as lpsparelm, lpsconstelm and lpsstategraph.

Options

Selecting which parameter to unfold can be done with the –sort or –index options (exactly one should be given). Unfolding may be repeated with the –repeat option. For example, to unfold the first 4 elements of a list into process parameters, one may use lpsparunfold --sort=List(Nat) --repeat=4. The LPS is rewritten using the rewrite rules after every unfolding step (similar to using the tool lpsrewr).

There are also a few advanced options. First, there is –alt-case, which nests the newly introduced mapping C_Sort (where Sort is the sort to unfold) at a higher level, potentially allowing more rewriting. For example, when unfolding l : List(Nat), the expression l != [] becomes C_ListNat(stack_pp, false, true) instead of !(C_ListNat(stack_pp, [], stack_pp1 |> stack_pp2) == []). In some corner cases, this may create exponentially large expressions with the number of unfoldings.

Second, the option –no-pattern disables using rewrite rules defined with pattern matching to manipulate state update expressions. Using this option makes the state update expressions smaller, but reduces opportunity for rewriting and simplifying the LPS. Finally, there is the option –possibly-inconsistent, which adds an additional rewrite rule C_Sort(x, d_1, ..., d_n) = (d_1 && x == c_1) || (c_2 && x == c_2) || .... (d_n && x == c_n) (where d_1,..,d_n are of sort Bool) when unfolding Sort and rewrite rules for equality on the sort that is newly introduced. This can enable some simplifications, but may also make the data specification inconsistent, which means that it is possible to derive true == false.

Background

All theoretic background can be found in the paper

A. Stramaglia, J.J.A. Keiren, T. Neele. Simplifying Process Parameters by Unfolding Algebraic Data Types. ICTAC 2023. LNCS vol. 14446, pp. 399-416. (DOI)

Usage

lpsparunfold   [OPTION]... [INFILE [OUTFILE]]

Description

Unfolds a set of given process parameters of the linear process specification (LPS) in INFILE and writes the result to OUTFILE. If INFILE is not present, stdin is used. If OUTFILE is not present, stdout is used.

Command line options

-a , --alt-case

use an alternative placement method for case functions

-i[NUM] , --index=[NUM]

unfolds process parameters for comma separated indices

-x , --no-pattern

do not unfold pattern matching functions in state updates

-p , --possibly-inconsistent

add rewrite rules that can make a data specification inconsistent

-QNUM , --qlimit=NUM

limit enumeration of universal and existential quantifiers in data expressions to NUM iterations (default NUM=10, NUM=0 for unlimited).

-nNUM , --repeat=NUM

repeat unfold NUM times

-rNAME , --rewriter=NAME

use rewrite strategy NAME:

jitty

jitty rewriting

jittyc

compiled jitty rewriting

jittyp

jitty rewriting with prover

-sNAME , --sort=NAME

unfolds all process parameters of sort NAME

--timings[=FILE]

append timing measurements to FILE. Measurements are written to standard error if no FILE is provided

Standard options

-q , --quiet

do not display warning messages

-v , --verbose

display short log messages

-d , --debug

display detailed log messages

--log-level=LEVEL

display log messages up to and including level; either warn, verbose, debug or trace

-h , --help

display help information

--version

display version information

--help-all

display help information, including hidden and experimental options

Author

Frank Stappers, Jeroen Keiren, Thomas Neele