diff --git a/doc/userdoc.org b/doc/userdoc.org
index d6d9c3fb02bee372bcb29fbc941cab376ec19c19..4c2bc135225e2603707dfc7114360ad284c8d5fc 100644
--- a/doc/userdoc.org
+++ b/doc/userdoc.org
@@ -617,6 +617,45 @@ This may sound strange but there are few reasons for that.
nature in some sense .
#+END_note
+**** Expression types
+
+The interpreter gives type to some special expressions.
+- special boolean (type ~B~) expressions. Two *keywords* allow to define
+ boolean values: ~true~ and ~false~.
+- Integers (type ~Z~) are defined as a contiguous list of digits.
+ - For instance, the code ~0123~ is interpreted as the integer $123$.
+ - However the sequence ~123 456~ is *not interpreted* as $123456$ but as
+ the two integers $123$ and $456$.
+- Real values (type ~R~) use the same syntax as in ~C++~. For instance,
+ the following expressions are accepted to define the number $1.23$.
+#+BEGIN_SRC pugs :exports both
+ 1.23;
+ 0.123E1;
+ .123e+1;
+ 123e-2;
+ 12.3E-1;
+#+END_SRC
+- ~string~ values are defined as the set of characters enclosed between
+ two double quotes ( ~"~ ). The string /Hello world!/ would be simply
+ written as ~"Hello world!"~. Strings support the following escape
+ sequences (similarly to ~C++~):
+ | escape | meaning |
+ |--------+-----------------|
+ | ~\'~ | single quote |
+ | ~\"~ | double quote |
+ | ~\?~ | question mark |
+ | ~\\~ | backslash |
+ | ~\a~ | audible bell |
+ | ~\b~ | backspace |
+ | ~\f~ | new page |
+ | ~\n~ | new line |
+ | ~\r~ | carriage return |
+ | ~\t~ | horizontal tab |
+ | ~\v~ | vertical tab |
+ These special character are not interpreted by ~pugs~ itself but
+ interpreted by the system when an output is created. They are just
+ allowed in the definition of a ~string~.
+
**** Variables of basic types are stored by value
This means that each variable of basic type allocates its own memory
@@ -721,6 +760,240 @@ affectations are /instructions/.
#+END_note
+***** List of defined operator ~=~ for basic types.
+
+As already mentioned, operator ~=~ is defined for *all* types in ~pugs~ if
+the right hand side expression has the *same* type as the left hand side
+variable. This is true for basic types as well as for high-level
+types. We now give the complete list of supported ~=~ affectations. The
+lists are sorted by type of left hand side variable.
+
+- ~B~: boolean left hand side variable. One is only allowed to affect boolean
+ values.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+
+- ~N~: natural integer ($\mathbb{N}$ or $\mathbb{Z}_{\ge0}$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ (for convenience) |
+
+- ~Z~: integer ($\mathbb{Z}$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+
+- ~R~: real ($\mathbb{R}$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^1~: vector of dimension 1 ($\mathbb{R}^1$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+ | ~R^1~ |
+
+- ~R^2~: vector of dimension 2 ($\mathbb{R}^2$) left hand side variable.
+ | allowed expression type |
+ |---------------------------------------------|
+ | ~R^2~ |
+ | ~0~ (special value) |
+ | list of 2 scalar (~B~, ~N~, ~Z~ or ~R~) expressions |
+ An example of initialization using a list or the special value ~0~ is
+ #+NAME: affectation-to-R2-from-list
+ #+BEGIN_SRC pugs :exports both :results output
+ let u:R^2, u = (-3, 2.5);
+ let z:R^2, z = 0;
+ cout << "u = " << u << "\n";
+ cout << "z = " << z << "\n";
+ #+END_SRC
+ which produces
+ #+RESULTS: affectation-to-R2-from-list
+ Observe that ~0~ is a special value and *treated as a keyword*. There is no conversion from
+ integer values. For instance:
+ #+NAME: R2-invalid-integer-affectation
+ #+BEGIN_SRC pugs-error :exports both :results output
+ let z:R^2, z = 1-1;
+ #+END_SRC
+ produces the compilation error
+ #+results: R2-invalid-integer-affectation
+
+- ~R^3~: vector of dimension 3 ($\mathbb{R}^3$) left hand side variable.
+ | allowed expression type |
+ |---------------------------------------------|
+ | ~R^3~ |
+ | ~0~ (special value) |
+ | list of 3 scalar (~B~, ~N~, ~Z~ or ~R~) expressions |
+ An example of initialization using a list is
+ #+NAME: affectation-to-R3-from-list
+ #+BEGIN_SRC pugs :exports both :results output
+ let u:R^3, u = (-3, 2.5, 1E-2);
+ let z:R^3, z = 0;
+ cout << "u = " << u << "\n";
+ cout << "z = " << z << "\n";
+ #+END_SRC
+ the output is
+ #+RESULTS: affectation-to-R3-from-list
+
+- ~R^1x1~: matrix of dimensions $1\times1$ ($\mathbb{R}^1\times1$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+ | ~R^1x1~ |
+
+- ~R^2x2~: matrix of dimension $2\times2$ ($\mathbb{R}^2x2$) left hand side variable.
+ | allowed expression type |
+ |---------------------------------------------|
+ | ~R^2x2~ |
+ | ~0~ (special value) |
+ | list of 4 scalar (~B~, ~N~, ~Z~ or ~R~) expressions |
+ An example of initialization using a list or the special value ~0~ is
+ #+NAME: affectation-to-R2x2-from-list
+ #+BEGIN_SRC pugs :exports both :results output
+ let u:R^2x2, u = (-3, 2.5,
+ 4, 1.2);
+ let z:R^2x2, z = 0;
+ cout << "u = " << u << "\n";
+ cout << "z = " << z << "\n";
+ #+END_SRC
+ which produces
+ #+RESULTS: affectation-to-R2x2-from-list
+
+- ~R^3x3~: matrix of dimension $3\times3$ ($\mathbb{R}^3x3$) left hand side variable.
+ | allowed expression type |
+ |---------------------------------------------|
+ | ~R^3x3~ |
+ | ~0~ (special value) |
+ | list of 9 scalar (~B~, ~N~, ~Z~ or ~R~) expressions |
+ An example of initialization using a list is
+ #+NAME: affectation-to-R3x3-from-list
+ #+BEGIN_SRC pugs :exports both :results output
+ let u:R^3x3, u = (-3, 2.5, 1E-2,
+ 2, 1.7, -2,
+ 1.2, 4, 2.3);
+ let z:R^3x3, z = 0;
+ cout << "u = " << u << "\n";
+ cout << "z = " << z << "\n";
+ #+END_SRC
+ the output is
+ #+RESULTS: affectation-to-R3x3-from-list
+
+- ~string~ left hand side variable. Expressions of any basic types can
+ be used as the right hand side.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+ | ~R^1~ |
+ | ~R^2~ |
+ | ~R^3~ |
+ | ~R^1x1~ |
+ | ~R^2x2~ |
+ | ~R^3x3~ |
+ | ~string~ |
+
+***** List of defined operator ~+=~ for basic types.
+
+- ~B~: the ~+=~ operator is not defined for left hand side boolean
+ variables.
+
+- ~N~: natural integer ($\mathbb{N}$ or $\mathbb{Z}_{\ge0}$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ (for convenience) |
+
+- ~Z~: integer ($\mathbb{Z}$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+
+- ~R~: real ($\mathbb{R}$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^1~: vector of dimension 1 ($\mathbb{R}^1$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~R^1~ |
+
+- ~R^2~: vector of dimension 2 ($\mathbb{R}^2$) left hand side variable.
+ | allowed expression type |
+ |---------------------------------------------|
+ | ~R^2~ |
+
+- ~R^3~: vector of dimension 3 ($\mathbb{R}^3$) left hand side variable.
+ | allowed expression type |
+ |---------------------------------------------|
+ | ~R^3~ |
+
+- ~R^1x1~: matrix of dimensions $1\times1$ ($\mathbb{R}^1\times1$) left hand side variable.
+ | allowed expression type |
+ |-------------------------|
+ | ~R^1x1~ |
+
+- ~R^2x2~: matrix of dimension $2\times2$ ($\mathbb{R}^2x2$) left hand side variable.
+ | allowed expression type |
+ |---------------------------------------------|
+ | ~R^2x2~ |
+
+- ~R^3x3~: matrix of dimension $3\times3$ ($\mathbb{R}^3x3$) left hand side variable.
+ | allowed expression type |
+ |---------------------------------------------|
+ | ~R^3x3~ |
+
+- ~string~ left hand side variable. Expressions of any basic types can
+ be used as the right hand side.
+ | allowed expression type |
+ |-------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+ | ~R^1~ |
+ | ~R^2~ |
+ | ~R^3~ |
+ | ~R^1x1~ |
+ | ~R^2x2~ |
+ | ~R^3x3~ |
+ | ~string~ |
+
+***** TODO List of defined operator ~-=~ for basic types.
+
+- ~B~: the ~-=~ operator is not defined for left hand side boolean variables.
+
+***** TODO List of defined operator ~*=~ for basic types.
+
+- ~B~: the ~*=~ operator is not defined for left hand side boolean variables.
+
+***** TODO List of defined operator ~/=~ for basic types.
+
+- ~B~: the ~/=~ operator is not defined for left hand side boolean variables.
+
**** Unary operators
The ~pugs~ language allows the following tokens as unary operators
@@ -743,8 +1016,9 @@ 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.
+of the same type as the argument (except if the argument is a ~N~, then
+the result is a ~Z~). 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
@@ -771,7 +1045,7 @@ produces the compilation error
Again, this is done to simplify the syntax and to avoid weird
constructions.
-**** Binary operators
+**** TODO Binary operators
Syntax for binary operators follows again a classical structure if
~exp1~ and ~exp2~ denotes two expressions and if ~op~ denotes a binary
@@ -808,9 +1082,9 @@ they follow a few rules.
\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}
+ \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*}
@@ -844,10 +1118,10 @@ they follow a few rules.
\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}
+ \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*}