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pugs
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72d24176
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72d24176
authored
3 years ago
by
Stéphane Del Pino
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Improve documentation of basic types and the associated operators
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72d24176
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@@ -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
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