.Open Language Reference Manual for the Language A . Context This document is an example and template for a language reference manual --(LRM). It defines a very simple programming language called A. The document defines the language piece by piece. For each part it defines the syntax and semantics. It also comments on the purpose for the part and gives examples of the code described. Good `LRM`s need examples, comments, syntax, and semantics. This manual was written using XBNF and translated to HTML by Dr. Botting's `mth2html` translator that added the contents list and inserted hyperlinks. These are also parts of good manuals. This is an example for a class and is the basis for project work, so I've not documented some of the options and issues that arise in the design languages. I've deliberately added one feature that is a bad idea. I wonder if you can spot the language that I ripped it from.... and added a perverse twist of my own. Finally I know of several typographical errors and many omissions. . Warning This is a bad language. Do not try it at home. If you feel like writing a compiler or interpreter don't -- it is not difficult BUT its better to fix the problems with `A` FIRST. Your first job is to spot the problems and omissions. . Historical Context `A` is not unlike half-a-dozen "autocodes" used in the 1960's in the United Kingdom. Real languages in this family include: Pegasus Autocode, Elliott 803 Autocode, Mercury Autocode, and K-code. All were compiled, targeted scientific computing, and are not mentioned in most text books. They did not survive competition from FORTRAN, COBOL, and Algol. However, they are small enough to be defined by a small LRM. `A` is slightly more complex than Pegasus Autocode, and definitely less complex than K-code. The big omission is any form data structure, and so, no indexing or subscripts. .Open The Language A . Programs Program written in A consists of a series of executable statements (each on one line), and terminated by an "END" statement: program::= #($statement $eoln) "END" $eoln. eoln::=`end of line`, any sequence of white space characters including at least one "Carriage Return" character. Here is an example of a program written in A: .As_is READ a .As_is b=a*a .As_is PRINT b .As_is END The above program reads a floating point decimal number (7.0 for example, and puts it into floating point location a. The next squares it, and stores the result in b. Then it prints out the result(49.0). A program in `A` starts by executing the the first statement and finishes when the END statement is executed. Normally each statement is taken in sequence, however, some statements can select a different successor statement that is before or after them in the sequence. For example to print the sum of the first `n` integers one writes: .As_is i=1 .As_is s=0 .As_is READ n .As_is j=i>=n .As_is SKIP 4*j .As_is s=s+i .As_is i=i+1 .As_is SKIP -4 .As_is PRINT s .As_is END The following program does the same thing using a formula (s = n(n+1)/2) instead of a `loop`. .As_is i=1 .As_is READ n .As_is s=n+1 .As_is s=s*n .As_is s=s/2 .As_is PRINT s .As_is END Notice how complex formulas must be written out as a series of simple calculations. . Statements There are four types of statement (other than the END statement): statement ::= $assignment | $input | $output | $skip. assignment::= $variable "=" $expression. .As_is d=b*b .As_is e=4*a .As_is e=e*c .As_is d=d-e An assignment evaluates the expression on the right hand side and places the value in the variable on the left hand side of the equals sign. input::= "READ" $variable. .As_is READ a .As_is READ n When an input statement is executed a number (in decimal notation) is taken from the user and placed in the variable. output::="PRINT" $expression | "OUT" $text. .As_is PRINT d .As_is OUT Real Roots A PRINT statement evaluates its expression and converts it to decimal notation before sending it the the user. The OUT statement takes the text, as is, and send that that to the user. skip::="SKIP" $O($sign) $expression. .As_is SKIP -12 .As_is SKIP +3 .As_is SKIP 0 .As_is SKIP +17*k SKIP statements are the only control statement. The break the flow of control. After a break statement control is passed to any statement before the or after the SKIP depending on the value of the expression in the SKIP. Notice that expressions can also evaluate simple tests by comparing values -- see $Relations later. The following indicates which statement is executed given the values 0, -1, -2, +1, and +2 in a SKIP: .As_is (-2) ... .As_is (-1)... .As_is SKIP ? .As_is (0) .... .As_is (+1) ... .As_is (+2) ... It is possible to could any control flow using SKIP -- but a wise programmer will draw a flowchart first. . Variables Variable are represented by the 26 lowercase letters. Letters `i` through `r` inclusive are for integer (fixed point ) numbers. The rest are hold floating point numbers. variable::="a" .. "z". integer_variable::="i".."r". real_variables::=variable ~ integer_variable. .As_is a .As_is i . Expressions An expression has at most one operator or a single function. expression::= $element $O( $operator $second_element ) | $function $element. element::= $variable | $constant. second_element::=$element. operator ::= "-" | "+" | "*" | "/" | $relation. relation::="<" | ">" | "<=" | ">=" | "<>" | "=". function::=$sign | "SQRT" | "ABS" | "LOG" | "COS" | "SIN" | "TAN" | "EXP". sign ::= "+" | "-". Examples .As_is x .As_is -x .As_is -i .As_is i+1 .As_is x+i .As_is x+1.234 .As_is x+y .As_is x*y .As_is x*y .As_is -3 .As_is SQRT 2 .As_is SQRT d In expressions the values are converted from integers to floating point as needed. . Relations The values of a relation are always either one(true) or zero(false). They are typically used in SKIP statements to choose different successors depending on the values of variable. For example the following code places the larger of `x` and `y` into `z`. .As_is j=x>y .As_is SKIP 2*j .As_is z=y .As_is SKIP 1 .As_is z=x exercise: can you write code to put the minimum of x, y into z? . Constants A constant is a number: fixed point integer or floating point number with a decimal point. Only decimal notation is used. constant::= $fixed | $floating. fixed::= $N($digit). .As_is 1234 floating::= $N($digit) "." $N($digit). .As_is 12.34 Notice that "1." and ".95" must be written as "1.0" and "0.95" respectively. . Longer Example: Solving a Quadratic (Untested) .As_is READ a .As_is READ b .As_is READ c .As_is d=b*b .As_is e=4*a .As_is e=e*c .As_is d=d-e .As_is e=2*a .As_is r=d<0 .As_is SKIP r*9 .As_is d=SQRT d .As_is s=d-b .As_is s=s/e .As_is t=-t .As_is t=t-d .As_is t=t/e .As_is PRINT s .As_is PRINT t .As_is SKIP 8 .As_is d=d-d .As_is d=SQRT d .As_is s=b/e .As_is s=-s .As_is t=d/e .As_is PRINT s .As_is OUT + or - i * .As_is PRINT t .As_is END Exercise: handle the case when a is zero. . Semantics Here is an outline of the semantic structure of the language A using the UML. .Image A.gif [UML semantics] . Note `A` is not the smallest possible programming language. .Close The Language A . Notation For X, N(X)::=`1 or more X's`, For X, O(X)::=`optional X`, 0..1, .See http://cse.csusb.edu/dick/cs320/cs320xbnf.htm digit::="0".."9", .See http://cse.csusb.edu/dick/cs320/cs320xbnf.htm .Close Language Reference Manual for the Language A