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Let's build a computer language

Notation-like languages

Example:(ABC) There is a music language called ABC. A program in this language is basically a text file containing a piece of music. The following ABC program is a sample. X: 1 T: Hindu Spiritual Hymn C: Trad. M: 2/4 K: Cmaj L: 1/4 GD|EF/F/|ED/C/|B,2|G,B,|C/D/E/F/|EC/B,/|C2| CD/D/-|D/D/D/E/|FG/F/|G2|DG|FF/F/|E/D/E/D/|C2| FG/G/|B/B/B/B/|cd/B/|c2|de/f/|e/e/d/d/|cd/B/|c2| dc|BA/G/|AG/F/|ED/D/|DG|FF|E/D/E/D/|C2| DD|DD/E/|FG/G/|G2|DG|FF/F/|E/D/E/D/|C2| This is part of a Hindu scriptural hymn. There is a free software called abc2midi that converts (or compiles) this into an audio midi file: ram1.mid. To understand the ABC language you need to know a few simple facts about music. Any musical piece is basically a sequence of notes. In Indian music, these are called Sa, Re, Ga, Ma etc. The corresponding Western names are Do, Re, Mi etc. Another Western notation is to use the letters of the alphabet: a,b,c etc. The notes correspond to the (white) keys of the keyboard instruments. The names of the white keys in a keyboard Now that we know this much about music, let's take a look at the ABC program. The first 6 lines specify various things about the piece. The first line, for instance, says that it is piece 1 in the file. The second line gives the name. The third line gives the name of the composer (here it is Trad. meaning that it is a traditional tune of unknown origin.) The next three lines are more technical: they specify the scale and tempo of the piece. We do not need these details here. The actual music starts from the 7-th line. It is basically a list of key names separated by vertical bars. (The vertical bars mark a musical time block.) The first block is GD, which means ``Press the G key, hold it down for a second, release it, then press the D key, hold it down for a second, and then release it." The next block is EF/F/, which has similar interpretation. The slashes after the F's mean you have to hold the F key down for only half a second. There are many other features of the ABC language that are given at here.

Example:(TeX) Typesetting a complicated mathematical formula elegantly is not always easy. Consider the formula A complicated math formula The main difficulty here is that a mathematical formula is not exactly like a left-to-right text. A popular language to specify these is TeX. Here is a TeX program to produce the above formula: $$\Phi(u;\mu,\sigma) = \int_{-\infty}^{u} {1 \over \sigma\sqrt{2\pi}} e^{-{(x-\mu)^2\over 2\sigma^2}} dx.$$ \bye At a first glance this program may appear too complicated. But like most programs this is actually made of simpler building blocks. The greek letters are written as \Phi, \mu etc. The integral sign is produced by \int_{...}^{...}. The lower limit is written inside the first set of curly brackets. The upper limit goes inside the second set of curly brackets. Fractions are written as {... \over ...}, the numerator and denominator are written before and after the \over. Notice one little point: the caret (^) is used whenever some text needs to be raised, e.g., the exponent of a power, the upper limit of an integral. The amounts of raising are different in these two cases. TeX figures out the correct amount from the context. TeX also lets you abbreviate frequently used parts of a program as templates. For instance, if we need the above formula many times, but each time with different upper and lower limits for the integral, then we can define the following template. \def\myint#1#2{ \int_{#1}^{#2} {1 \over \sigma\sqrt{2\pi}} e^{-{(x-\mu)^2\over 2\sigma^2}} dx. } Now you can write $$\myint{-2}{3} = \myint{-2}{0} + \myint{0}{3}.$$ to produce

Script-like languages

Example:(POV-Ray) Consider the following image. Computer-generated photo-realistic image This was created in a wonderful language called POV-Ray. Here is the program that created it. POV-Ray is freely available in the web and this program comes with the POV-Ray software. // Persistence Of Vision raytracer version 3.5 sample file. // File by Alexander Enzmann (modified by Dieter Bayer) // // -w320 -h240 // -w800 -h600 +a0.3 global_settings { assumed_gamma 2.2 } camera { location <0, 8, -15> look_at <0, 0, 0> angle 46 } light_source { <10, 30, -20> color red 1 green 1 blue 1 } blob { threshold 0.5 cylinder { <-7, 0, 0>, <7, 0, 0>, 4, 2 } cylinder { <0, 0, -7>, <0, 0, 7>, 4, 2 } sphere { <0, 3, 0>, 2.5, -4 } pigment { color red 1 green 0 blue 0 } finish { ambient 0.2 diffuse 0.8 phong 1 } rotate <-30, 0, 0> } POV-Ray takes the above program as input, and produces the image shown earlier. The meaning of the above program is pretty self-evident. The lines starting with // are comments. The global_settings command sets some parameter values. Then we specify the position of the camera and the light source. Finally, we describe the object itself as a blob, which is POV-Ray's term for an object of non-standard geometry. It is described in terms of standard geometric shapes like cylinders and spheres. In fact, the object is made by intersecting two cylinders, and then denting out a spherical cap. After describing the shape of the object, the program specifies the colour and texture of the material. Finally, it rotates the object for better viewing. In the language of compilers we would say that the POV-Ray software is a compiler for the POV-Ray language. It converts the description of a scene to an image of the scene. If you want to know more about POV-Ray, click here.

Example: (Virtual Reality Modelling Language) This is another script-like language to describe 3-dimensional scenes. However, unlike POV-Ray, here the generated scene is not just a static image. It is an interactive world of virtual reality that you can manipulate with your mouse. For instance, you can walk around an object and look at it from different directions. It is somewhat difficult to understand what I mean here unless you experience virtual reality yourself. For this you may download and install a VRML viewer like Cosmoplayer. Here is a sample program #VRML V2.0 utf8 # A Cylinder Shape { appearance Appearance { material Material { } } geometry Cylinder { height 2.0 radius 1.5 } } The program is not difficult to understand. It defines a cylinder of some unspecified material. If you have a VRML-aware browser (e.g., Internet Explorer after installing Cosmoplayer) then click here to see the above code in action. If you do not have a VRML-aware browser, then you have to be satisfied with the following screenshot. Screenshot Rather complicated virtual worlds may be made using VRML, including animation and interactivity.

Example: (Prolog) A completely different type of language is Prolog. This is a script-like language to describe facts and to pose questions. Here is an example. Consider the two facts: If one studies math then one will pass the math exam. Rita studies all subjects. Based on these two facts, we want to answer the question: Will Rita pass in math? We represent the facts as the following Prolog program: passes(Student,math) :- studies(Student,math). studies(rita, _). To make sense of this read ":-" as "if." The "_" stands for "everything." We feed this program into a Prolog system. The system processes these and asks for queries answerable based on these facts. We wanted to know if Rita will pass in the math. So we type ?- passes(rita, math). Prolog consults the facts, and answers "Yes."

C-like languages

What's common in all these?

Each language has its own application area. The application domain of the ABC language is music. The person who wrote the compiler for this language obviously had to know about music and the midi format. Similarly, the domain of POV-Ray consists of techniques to render 3-dimensional photo-realistic images. For general purpose C-like languages, the domain consists of the details of the machine language into which the program is translated by the compiler.
In each of the examples above, we have the concept of a low level implementation. For ABC it is the midi format. The abc2midi software is just a compiler that translates an ABC program to midi format. Similarly, POV-Ray relies on standard computer graphics tools at the low level to draw lines, curves and points. Prolog turns everything into trees, and manipulates the trees using low level tools possibly written as a set of functions in C.
In all the examples, the domain knowlege is built into the compiler. A program itself is just a description of a problem in that domain. The job of the compiler is to apply the domain knowledge to solve the problem, and to produce a low level implementation of the solution. For instance, suppose that a music book contains a piece of music written in tems of notations. You know the notations theretically, but not how to play the piece based on them. Thus, the notations for the music is just a description of the music. In order to listen to the actual music, you may take the book to an expert pianist, who can play the piece for you on the piano, record it, and hand you the CD. The abc2midi compiler plays the role of this expert.

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