Axiomatic definitions of sublanguages of Loglan'82: Różnice pomiędzy wersjami
(→Program) |
(→Characters) |
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'a' = 'a' | 'a' = 'a' | ||
| − | 'a' =/= 'a' | + | 'a' =/= 'a'<br /> |
| + | |||
The language <math>\mathcal{L}_{0.1} </math> allows to declare variables of type char and to assign values to the variables. Assignments | The language <math>\mathcal{L}_{0.1} </math> allows to declare variables of type char and to assign values to the variables. Assignments | ||
| + | Example<br /> | ||
| + | program characters; | ||
| + | var c1,c2:char | ||
| + | begin | ||
| + | c1:='k'; | ||
| + | c2:=c1; | ||
| + | writeln(c2) | ||
| + | end | ||
=== Declarations of variables. Assignment instructions === | === Declarations of variables. Assignment instructions === | ||
Wersja z 14:12, 25 lis 2014
On these pages we shall attempt to develop a sequence of algorithmic theories that correspond to a sequence of sublanguages of of Loglan'82 language.
Part II Axiomatic definitions of sublanguages of Loglan'82
Here we shall present an increasing sequence of sublanguages [math]\mathcal{L}_0\subset\mathcal{L}_1\subset\mathcal{L}_2\subset \mathcal{L}_3\subset\mathcal{L}_4\subset \dots[/math]Loglan'82. For each language [math]\mathcal{L}_i[/math] we shall present its grammar and some axioms and inference rules that define its semantics.
Spis treści
Program
Program in Loglan'82 has the following structure
| definiendum | definiens |
|---|---|
| program | program <name>;
begin
end |
where name is any identifier, i.e. a finite sequence of letters and digits beginning with a letter.
The declarations and instructions are finite sequences of declarations and instructions respectively, empty squence included.
This allow us to define the first sublanguage [math]\mathcal{L}_0[/math] of Loglan'82.
[math]\mathcal{L}_0 \stackrel{df}{=}\{p\in \mathcal{A}^*: p=\textbf{program}\ \textit{id}; \textbf{begin end} \}[/math]
Programs of the language [math]\mathcal{L}_0[/math] are empty programs, they posses just a name. Their list of instructions as well as list of declarations are empty. The effect of execution of such program is do nothing.
Now we shall define a new language [math]\mathcal{L}_{0.1}[/math]. First, we say that any expression of the form:
writeln;
write(integer);
write("here your text");
is an output instruction.
[math]\mathcal{L}_{0.1} \stackrel{df}{=}\{p\in \mathcal{A}^*: p=\textbf{program} \textit{ id}; \textbf{begin} \lt\textit{output instructions}\gt \textbf{end} \}[/math]
| program print; begin
end |
Primitive types
Characters
The type char is a finite set of characters. No operation is defined on charcters. However one can compare two characters.
'a' = 'a'
'a' =/= 'a'
The language [math]\mathcal{L}_{0.1} [/math] allows to declare variables of type char and to assign values to the variables. Assignments
Example
program characters;
var c1,c2:char
begin
c1:='k';
c2:=c1;
writeln(c2)
end
Declarations of variables. Assignment instructions
Example
program P2 ;
- var x,y: integer;
begin
- y:=74;
- x:= y+ 8;
end
Grammar
Context free grammar
Well formed expressions
Axiom
[math]\{x:=\tau\}( \alpha ) \Leftrightarrow \alpha(x/\tau)[/math]
