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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.
 
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.
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Part II Axiomatic definitions of sublanguages of Loglan'82
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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.
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=== Program ===
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Program in Loglan'82 has the following structure<br />
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{| class="wikitable"
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|+ Program
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!definiendum!! definiens
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|-
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| style="background-color:palegreen" | ''program''
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| style="background-color:GoldenRod" | '''program''' <''name''>;<br />
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:<''declarations''><br />
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'''begin'''<br />
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:<''instructions''><br />
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'''end'''
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|}
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where ''name'' is any identifier, i.e. a finite sequence of letters and digits beginning with a letter.
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The ''declarations'' and ''instructions'' are  finite sequences of declarations and instructions respectively, empty squence included.
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This allow us to define the first sublanguage <math>\mathcal{L}_0</math> of Loglan'82.
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<math>\mathcal{L}_0 \stackrel{df}{=}\{p\in \mathcal{A}^*: p=\textbf{program}\ \textit{id}; \textbf{begin end}  \}</math>
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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''.
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Now we shall define a new language <math>\mathcal{L}_{0.1}</math>. First, we say that any expression of the form:<br />
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writeln;  <br />
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write(''integer''); <br />
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write("here your text"); <br />
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is an output instruction.
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<math>\mathcal{L}_{0.1} \stackrel{df}{=}\{p\in \mathcal{A}^*: p=\textbf{program} \textit{ id}; \textbf{begin} <\textit{output instructions}> \textbf{end}  \}</math>
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{| class="wikitable"
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|+ style="text-align:left" | '''Example 0.1''' <br />
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|-
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| program print; <br />
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begin <br />
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:write("hallo world!"); writeln; <br />
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:write("Today is: May"); write(22); write(2014); writeln <br />
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end <br/>
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|}
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=== Declarations of variables. Assignment instructions ===
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'''Example'''<br />
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'''program'''  P2 ;<br />
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:'''var''' x,y: integer;<br />
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'''begin'''<br />
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:y:=74;<br />
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:x:= y+ 8;<br />
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'''end'''<br />
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'''Grammar'''<br />
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Context free grammar
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Well formed expressions
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'''Axiom'''<br />
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<math>\{x:=\tau\}( \alpha ) \Leftrightarrow \alpha(x/\tau)</math>

Wersja z 12:48, 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.

Program

Program in Loglan'82 has the following structure

Program
definiendum definiens
program program <name>;
<declarations>

begin

<instructions>

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]

Example 0.1
program print;

begin

write("hallo world!"); writeln;
write("Today is: May"); write(22); write(2014); writeln

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]

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