tl: fix the definition of ##[i:j]

Reported by Victor Khomenko.

* NEWS, doc/tl/tl.tex, spot/tl/formula.cc: Fix the definition.
* tests/core/ltl2tgba.test: Add some test cases.

NEWS

@@ -60,10 +60,11 @@ New in spot 2.7.4.dev (not yet released)
 
   - The parser for SERE learned to recognize the ##n and ##[i:j]
     operators from SVA.  So {##2 a ##0 b[+] ##1 c ##2 e} is another
-    way to write {[*2];a:b[+];c;1;e}, and {a ##[i:j] b} is parsed as
+    way to write {[*2];a:b[+];c;1;e}.  The syntax {a ##[i:j] b} is
-    {a:{[*i..j];b}}.  The formula::sugar_delay() function implement
+    replaced in different ways depending on the values of i, a, and b.
-    this SVA operator in terms of the existing PSL operators.
+    The formula::sugar_delay() function implement this SVA operator in
-    ##[+] and ##[*] are sugar for ##[1:$] and ##[0:$].
+    terms of the existing PSL operators.  ##[+] and ##[*] are sugar
+    for ##[1:$] and ##[0:$].
 
   - spot::relabel_apply() make it easier to reverse the effect
     of spot::relabel() or spot::relabel_bse() on formula.

doc/tl/tl.tex

@@ -775,16 +775,23 @@ $f \CONCAT \1\CONCAT g$, but the delay can be a range, and $f$ can be
 omitted.
 
 \begin{align*}
-  f\DELAY{\mvar{i}} g &\equiv f\DELAYR{\mvar{i}..\mvar{i}} g & {}\DELAY{\mvar{i}} g &\equiv {}\DELAYR{\mvar{i}..\mvar{i}} g\\
+  f\DELAYR{\mvar{i}..\mvar{j}}g & \equiv f\CONCAT{}\1\STAR{\mvar{i-1}..\mvar{j-1}}\CONCAT{}g\quad\text{if~}i>0                                                    \\
-  f\DELAYR{..} g &\equiv f\FUSION\{\STAR{}\CONCAT g\} & f\DELAYR{\mvar{i}..} g &\equiv f\FUSION\{\STAR{\mvar{i}..}\CONCAT g\} \\
+  f\DELAYR{0..\mvar{j}}g        & \equiv f\FUSION(\1\STAR{0..\mvar{j}}\CONCAT{}g)\quad\text{if~}\varepsilon\nVDash f                                              \\
-  f\DELAYR{..\mvar{j}} g &\equiv f\FUSION\{\STAR{0..\mvar{j}}\CONCAT g\} &
+  f\DELAYR{0..\mvar{j}}g        & \equiv (f\CONCAT{}\1\STAR{0..\mvar{j}})\FUSION{}g)\quad\text{if~}\varepsilon\VDash f \land \varepsilon\nVDash g                 \\
-  f\DELAYR{\mvar{i}..\mvar{j}} g &\equiv f\FUSION\{\STAR{\mvar{i}..\mvar{j}}\CONCAT g\} \\
+  f\DELAYR{0..\mvar{j}}g        & \equiv (f\FUSION{}g)\OR(f\CONCAT{}\1\STAR{0..\mvar{j-1}}\CONCAT{}g)\quad\text{if~}\varepsilon\VDash f \land \varepsilon\VDash g \\
-  {}\DELAYR{..} g &\equiv \STAR{}\CONCAT g & {}\DELAYR{\mvar{i}..} g &\equiv \STAR{\mvar{i}..}\CONCAT g \\
+  f\DELAYR{\mvar{i}..}g         & \equiv f\CONCAT{}\1\STAR{\mvar{i-1}..}\CONCAT{}g\quad\text{if~}i>0                                                              \\
-  {}\DELAYR{..\mvar{j}} g &\equiv \STAR{0..\mvar{j}}\CONCAT g &
+  f\DELAYR{0..}g                & \equiv f\FUSION(\1\STAR{}\CONCAT{}g)\quad\text{if~}\varepsilon\nVDash f                                                         \\
-                                                                {}\DELAYR{\mvar{i}..\mvar{j}} g &\equiv \STAR{\mvar{i}..\mvar{j}}\CONCAT g \\
+  f\DELAYR{0..}g                & \equiv (f\CONCAT{}\1\STAR{})\FUSION{}g)\quad\text{if~}\varepsilon\VDash f \land \varepsilon\nVDash g                            \\
-  f \DELAYP{} g & \equiv f \DELAYR{1..} g & f \DELAYS{} g & \equiv f \DELAYR{0..} g \\
+  f\DELAYR{0..}g                & \equiv (f\FUSION{}g)\OR(f\CONCAT{}\1\STAR{}\CONCAT{}g)\quad\text{if~}\varepsilon\VDash f \land \varepsilon\VDash g
-   \DELAYP{} g & \equiv  \DELAYR{1..} g &  \DELAYS{} g & \equiv \DELAYR{0..} g
 \end{align*}
+\begin{align*}
+  f\DELAY{\mvar{i}} g           & \equiv f\DELAYR{\mvar{i}..\mvar{i}} g & {}\DELAY{\mvar{i}} g  & \equiv \1\DELAYR{\mvar{i}..\mvar{i}} g                          \\
+  f\DELAYP{}g                   & \equiv f\DELAYR{1..}g                 & \DELAYP{} g           & \equiv\DELAYR{1..}g                                             \\
+  f\DELAYS{}g                   & \equiv f\DELAYR{0..}g                 & \DELAYS{} g           & \equiv\DELAYR{0..}g
+  f\DELAYR{..\mvar{j}} g        & \equiv f\DELAYR{0..\mvar{j}} g\}      & \DELAYR{..\mvar{j}} g & \equiv \1\DELAYR{0..\mvar{j}} g\}                               \\
+  f\DELAYR{..} g                & \equiv f\DELAYR{0..} f g\}            & \DELAYR{..} g         & \equiv \1\DELAYR{0..} g\}                                       \\
+\end{align*}
+
 \subsection{Trivial Identities (Occur Automatically)}
 
 The following identities also hold if $j$ or $l$ are missing (assuming

spot/tl/formula.cc

@@ -1776,16 +1776,29 @@ namespace spot
   formula formula::sugar_delay(const formula& a, const formula& b,
                                unsigned min, unsigned max)
   {
-    // In general
+    // If min>=1
-    //   a ##[min:max] b  = a:(1[*min:max];b)
-    // however if min>=1 we prefer the following rule
     //   a ##[min:max] b  = a;1[*min-1:max-1];b
-    if (min == 0)
+    // If min==0 we can use
-      return Fusion({a, Concat({Star(tt(), min, max), b})});
+    //   a ##[min:max] b = a:(1[*0:max];b)  if a rejects [*0]
-    --min;
+    //   a ##[min:max] b = (a;1[*0:max]):b  if b rejects [*0]
+    //   a ##[min:max] b = (a:b)|(a;[*0:max-1];b)  else
+    if (min > 0)
+      {
+        --min;
+        if (max != unbounded())
+          --max;
+        return Concat({a, Star(tt(), min, max), b});
+      }
+    if (!a.accepts_eword())
+      return Fusion({a, Concat({Star(tt(), 0, max), b})});
+    if (!b.accepts_eword())
+      return Fusion({Concat({a, Star(tt(), 0, max)}), b});
+
     if (max != unbounded())
       --max;
-    return Concat({a, Star(tt(), min, max), b});
+    formula left = Fusion({a, b});
+    formula right = Concat({a, Star(tt(), 0, max), b});
+    return OrRat({left, right});
   }
 
   int atomic_prop_cmp(const fnode* f, const fnode* g)

tests/core/ltl2tgba.test

@@ -1,6 +1,6 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2009-2018 Laboratoire de Recherche et Développement de
+# Copyright (C) 2009-2019 Laboratoire de Recherche et Développement de
 # l'Epita (LRDE).
 # Copyright (C) 2003-2004 Laboratoire d'Informatique de Paris 6
 # (LIP6), département Systèmes Répartis Coopératifs (SRC), Université
@@ -218,6 +218,17 @@ ltlfilt -q -r -f '{{a*}[:+];c}' --equivalent-to 'Xc R a'
 ltlfilt -q    -f '{c && {b | [*0]}[:+]}' --equivalent-to 'c & b'
 ltlfilt -q -r -f '{c && {b | [*0]}[:+]}' --equivalent-to 'c & b'
 
+
+# The ##[i:j] operator introduced in 2.8 has four different rewritings
+# depending on whether a or b accepts [*0].
+
+for a in 'a1;a2' 'a1[*];a2[*]'; do
+    for b in 'b1;b2' 'b1[*];b2[*]'; do
+        ltlfilt -q -f "{($a) ##[0:8] ($b)}[]->c" \
+          --equivalent-to "{(($a):($b))|(($a);[*0:7];($b))}[]->c" || exit 1
+    done
+done
+
 # test unknown dot options
 ltl2tgba --dot=@ a 2>stderr && exit 1
 grep 'ltl2tgba: unknown option.*@' stderr