This article recalls groundwork for programming language theory. There was defined a
little programming language and introduced Floyd-Hoare Logic as an instrument for proving
program in this language. Definitely it is also possible to use Floyd-Hoare Logic for proving
other program languages but it is necessary to adapt used rules for commands of these
languages. Proving programs correct is useful because it is important not only for life critical
system to work correct. Next there was introduced l-calculus as one possible way to represent
universal computing system. There was shown its notation and operations with l-expressions.
Also there was demonstrated how it is possible to represent various data objects and how can
be defined functions by recursion. At the end there was shown which classes of function can
be represented in l-calculus.