diff --git a/doc/userdoc.org b/doc/userdoc.org
index e53ebdf13b1b8d20812539db787f7f1bb0dad8ad..d6d9c3fb02bee372bcb29fbc941cab376ec19c19 100644
--- a/doc/userdoc.org
+++ b/doc/userdoc.org
@@ -585,7 +585,7 @@ It produces the following error
#+results: invalid-compound-definition
which is easy to fix.
-*** TODO Basic types<<basic-types>>
+*** Basic types<<basic-types>>
Basic types in ~pugs~ are boolean ~B~, natural integers ~N~, integers ~Z~,
real ~R~, small vectors ~R^1~, ~R^2~ and ~R^3~, small matrices ~R^1x1~, ~R^2x2~
@@ -670,13 +670,13 @@ This will be detailed in section [[functions]].
#+END_note
This means that all affectation, unary and binary operators are
-defined for all types.
+defined explicitly for supported types.
*** Operators
**** Affectation operators
-In the ~pugs~ language the affectation operators are the following.
+In the ~pugs~ language, the affectation operators are the following.
| operator | description |
|----------+----------------------|
| ~=~ | affectation operator |
@@ -700,7 +700,7 @@ but does not produce the expected result.
}
#+END_SRC
Obviously the mistake is that the test should have been ~(b==false)~,
-since otherwise, the following block is never executed (in ~C++~, the
+since otherwise, the conditional block is never executed (in ~C++~, the
result of an affectation is the value affected to the variable, which
is always false in that case.
@@ -716,18 +716,146 @@ This cannot happen with ~pugs~. A similar example
produces the following error
#+results: no-affectation-result
-#+END_note
-
-Here is the complete list of supported affectation operators according
-to left hand side variable type (/lvalue/ type) and right hand side
-expression type (/rvalue/ type).
-
+Actually, affectations are /expressions/ in ~C++~, in ~pugs~ language,
+affectations are /instructions/.
+#+END_note
**** Unary operators
+The ~pugs~ language allows the following tokens as unary operators
+| operator | description |
+|----------+----------------------|
+| ~not~ | not operator |
+| ~+~ | plus unary operator |
+| ~-~ | minus unary operator |
+|----------+----------------------|
+| ~++~ | increment operator |
+| ~--~ | decrement operator |
+
+The ~not~, ~+~ and ~-~ operators apply to the *expression* on their right. ~++~
+and ~--~ operators apply only to a *variable* that can be positioned
+before (post increment/decrement) or after the token (pre
+increment/decrement). These operators are also inspired from their ~C++~
+counterparts for commodity.
+
+The ~+~ unary operator is a convenient operator that is *elided* when
+parsing the script.
+
+For basic types, when these operators are defined, they return a value
+of the same type as the argument. These operators can be defined for
+high-level types.
+- The ~not~ operator is only defined for boolean values (~B~)
+- the ~-~ unary operator is defined for numeric basic types: ~B~,
+ ~N~, ~Z~, ~R~, ~R^1~, ~R^2~, ~R^3~, ~R^1x1~, ~R^2x2~ and ~R^3x3~. It is not defined
+ for ~string~ variables.
+- pre and post increment operators, ~--~ and ~++~, are defined for all
+ scalar basic types: ~N~, ~Z~ and ~R~. They are not defined for ~B~, ~R^1~,
+ ~R^2~, ~R^3~, ~R^1x1~, ~R^2x2~, ~R^3x3~ and ~string~ variables.
+
+Note that the pre increment/decrement operators behave slightly
+differently than their ~C++~ counterparts since they are not allowed to
+be chained. In ~C++~, the following code is allowed
+#+BEGIN_SRC C++ :exports source
+ int i = 0;
+ int j = ++ ++i;
+#+END_SRC
+In ~pugs~, it is forbidden:
+#+NAME: double-pre-incr-result
+#+BEGIN_SRC pugs-error :exports both :results output
+ let i:N, i=0;
+ let j:N, j = ++ ++i;
+#+END_SRC
+produces the compilation error
+#+results: double-pre-incr-result
+Again, this is done to simplify the syntax and to avoid weird
+constructions.
+
**** Binary operators
+Syntax for binary operators follows again a classical structure if
+~exp1~ and ~exp2~ denotes two expressions and if ~op~ denotes a binary
+operator, one writes simply ~exp1 op exp2~.
+
+Here is the list of binary operators
+| keyword | operator |
+|---------+-----------------------|
+| ~and~ | logic and |
+| ~or~ | logic and |
+| ~xor~ | logic exclusive or |
+|---------+-----------------------|
+| ~==~ | equality |
+| ~!=~ | non-equality |
+| ~<~ | lower than |
+| ~<=~ | lower than or equal |
+| ~>~ | greater than |
+| ~>=~ | greater than or equal |
+|---------+-----------------------|
+| ~<<~ | shift left |
+| ~>>~ | shift right |
+|---------+-----------------------|
+| ~+~ | sum |
+| ~-~ | difference |
+| ~*~ | product |
+| ~/~ | division |
+
+Binary operators can be defined for high-level types. For basic types,
+they follow a few rules.
+
+- Logical operators ~and~, ~or~ and ~xor~ are defined for boolean operands
+ (type is ~B~) only. The result of the expression is a boolean.
+ #+begin_src latex :results drawer :exports results
+ \begin{equation*}
+ \left|
+ \begin{array}{rl}
+ \mathtt{and}:&\quad \mathbb{B}\times \mathbb{B} \to \mathbb{B}\\
+ \mathtt{or}:& \quad\mathbb{B}\times \mathbb{B} \to \mathbb{B}\\
+ \mathtt{xor}:& \quad \mathbb{B}\times \mathbb{B} \to \mathbb{B}
+ \end{array}
+ \right.
+ \end{equation*}
+ #+end_src
+- Comparison operators ~==~, ~!=~, ~<~, ~<=~, ~>~ and ~>=~ are defined for all
+ basic scalar type and return a boolean value.
+ #+begin_src latex :results drawer :exports results
+ \begin{equation*}
+ \forall \mathbb{S}_1, \mathbb{S}_2 \in \{\mathbb{B},\mathbb{N},\mathbb{Z},\mathbb{R}\},
+ \quad
+ \left|
+ \begin{array}{rl}
+ \mathtt{==}:& \mathbb{S}_1 \times \mathbb{S}_2 \to \mathbb{B}\\
+ \mathtt{!=}:& \mathbb{S}_1 \times \mathbb{S}_2 \to \mathbb{B}\\
+ \mathtt{<}: & \mathbb{S}_1 \times \mathbb{S}_2 \to \mathbb{B}\\
+ \mathtt{<=}:& \mathbb{S}_1 \times \mathbb{S}_2 \to \mathbb{B}\\
+ \mathtt{>}: & \mathbb{S}_1 \times \mathbb{S}_2 \to \mathbb{B}\\
+ \mathtt{>=}:& \mathbb{S}_1 \times \mathbb{S}_2 \to \mathbb{B}
+ \end{array}
+ \right.
+ \end{equation*}
+ #+end_src
+ When comparing a boolean value (type ~B~) with another scalar value
+ type (~N~, ~Z~ or ~R~), the value ~true~ is interpreted as $1$ and the value
+ ~false~ as $0$.
+\\
+ For vector and matrix basic types, the only allowed operators are ~==~
+ and ~!=~.
+ #+begin_src latex :results drawer :exports results
+ \begin{equation*}
+ \forall d \in \{1,2,3\},\quad
+ \left|
+ \begin{array}{rl}
+ \mathtt{==}:& \mathbb{R}^d\times \mathbb{R}^d \to \mathbb{B}\\
+ \mathtt{==}:& \mathbb{R}^{d\times d} \times \mathbb{R}^{d\times d} \to \mathbb{B}\\
+ \mathtt{!=}:& \mathbb{R}^d\times \mathbb{R}^d \to \mathbb{B}\\
+ \mathtt{!=}:& \mathbb{R}^{d\times d} \times \mathbb{R}^{d\times d} \to \mathbb{B}
+ \end{array}
+ \right.
+ \end{equation*}
+ #+end_src
+- Shift operators ~<<~ and ~>>~ are not used to define binary operators
+ between two basic types
+- Arithmetic operators are defined
+
*** TODO High-level types<<high-level-types>>
*** TODO Lists