Introduction to Programming Languages

CS152

Chris Pollett

Aug 23, 2021

What is a Programming Language?

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 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 that allow one to define complicated functions based on a fixed set of simpler functions that came from physical processes, operations from mathematics, linguistic manipulation, etc.
Each of these definitions turned out to be equivalent to each other in terms of what complicated functions that could be defined.
A computation is essentially the steps involved in how the simpler functions are used in one of these models to compute a give complicated function.
One such model called, a random access machine (RAM), runs programs written in a fixed instructions set on inputs to produce outputs just like a modern computer.
Unlike a modern computer though it has as much memory and time as need to carry out its computation from inputs to outputs.
A programming language PL that for any (RAM) program `P` we can find a program `P'` in PL that produces the same input output map as `P` we will call Turing complete.
PL being Turing complete shows that PL can describe at the least the RAM functions.
Usually, we will be interested in translating the reverse direction, mapping a high level programming language program to a low level RAM like program.

Machine Readable.

Computers understand machine code instruction programs like:

55 89 e5 53 83 ec 04 83 e4 f0 e8 31 00 00 00 89 
c3 e8 2a 00 00 00 39 c3 74 10 8d b6 00 00 00 00
39 c3 7e 13 29 c3 39 c3 75 f6 89 1c 24 e8 6e 00
00 00 8b 5d fc c9 c3 29 d8 eb eb 90

which might be stored in computer memory.

The above is a sequence of bytes written in hexadecimal for an 80x86 machine code GCD program. There are only a fixed number of different kinds of instructions in 80x86, the 80x86 instruction set.
A computer has circuitry that fetches the next instruction from memory to be processed based on a program counter, decodes the instruction, executes it potentially accessing other memory locations, and writes back values into memory, including the location of where the next instruction to process is.
When the circuits to do the above are "run" is controlled by an electronic clock.
The above byte sequence specifies a sequence of instructions and their arguments which can be written using a more human readable assembly language in a more or less 1 to 1 way:

For example, the pushl %ebp corresponds to the hex number 55 above.
We need to have some way to translate from a higher level programming language to machine code to avoid pulling out what little remains of our hair trying to code using these low level instructions.
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.