If you look back on early computers like ENIAC,
reprogramming meant rewiring the machine.
So a programming language gives us a notation
for us to tell a computer what to do without having
to re-wire.
For this to work, the programmer needs to
understand what is being told to the computer and
the the computer needs to be able to understand
what it is supposed to do.
Hence, a programming language is a notation
system for describing computation in both a
machine readable and human readable format.
What is a computation?
This was a question that was studied in the 1930 and
1940s.
Turing, Church and others defined different models of
computation based on things such as physical
implementability, operations from mathematics, linguistic
manipulation, etc.
Each of these definitions turned out to be equivalent to
each other.
So for our purposes a computation is what can be done a
computer with as much memory as we need and with as
time as we need.
A language which can allow us to will be called Turing complete.
Machine Readable.
Since computers understand machine code
instructions like:
cmp eax, ebx.
jne do_something.
or the bits that correspond to them.
We need to have some way to translate from a
programming language to machine code.
So that this always works we need a step by step
procedure (an algorithm) which will work for all
programs written in our language.
For languages which are specified using certain
kinds of context-free grammars such algorithms
exist.
Human Readable.
This is a harder to define thing than machine
readable.
Basically, though it amounts to the programming
language to provide abstractions which are close
to how a human would think about solving a
problem.
Next day, we will talk about the basic kinds of
abstractions people have considered.
