NIAL

1. Nested Interactive Array Language Dennis Brown Northern Kentucky University CSC 507 – November 2005 NIAL

2. Origins of NIAL • Based on nested array theory developed by Dr. Trenchard More, Jr. • Invented in 1981 by Michael Jenkins of Queen’s University in Kingston, Ontario • Influenced by APL and Lisp • NIAL is an acronym for Nested Interactive Array Language, but is also a reference to Njal’s Saga (a Nordic legend)

3. APL vs. NIAL • APL was invented in 1962 • Very efficient for some types of calculation, but required a special character set:

4. APL vs. NIAL (cont.) • NIAL uses keywords instead of symbols, so no custom keyboard is required • For example, ρ (rho) in APL becomes “reshape” in NIAL • NIAL also adds control structures (from imperative languages) that APL did not have • The original version of APL did not support nested arrays

5. Strings ‘abc’ `a `b `c Phrases “dog phrase ‘dog’ Faults ‘?conform’ NIAL Data Types • Numbers • integers • floating points • booleans (l, o, True, False) • Characters • `X, `v, `3 • Lists • 3 `C 5 (strand notation) • [3 `C 5] • [] (empty list)

6. Strings vs. Phrases A string is a list: first ‘abc’  `a last ‘abc’  `c A phrase is atomic: first “abc  “abc last “abc  “abc

7. x y z := 5 6 7 assigns 5 to x, 6 to y, 7 to z [1 2 3] * 2 [2 4 6] [1 2 3] * [3 2 1] [3 4 3] [1 2 3] * 3 2 1 [3 6 9] [2 4 6] [1 2 3] Lists – Examples • sum 2 3 4 • 9 • sum [2 3 4] • [2 3 4] • sum (2 3 4) (1 2 3) • 3 5 7 • each sum (2 3 4) (1 2 3) • 9 6

8. first 1 2 3 1 rest 1 2 3 2 3 hitch 1 (2 3) 1 2 3 Lisp vs. NIAL • (car 1 2 3) 1 • (cdr 1 2 3) (2 3) • (cons 1 (2 3)) (1 2 3)

9. Tables • A table is a multi-dimensional list • The reshape function can be used to create a table with a specified number of rows and columns • 2 3 reshape 1 2 3 4 5 6 7 8 1 2 3 4 5 6 • 2 3 reshape 1 2 3 4 1 2 3 4 1 2

10. post 1 2 3 1 2 3 Tables – Continued • x := 3 3 reshape count 9 1 2 3 4 5 6 7 8 9 • x | [2,] (row slice) 7 8 9 • x | [,2] (col. slice) 3 6 9 • x @ (1 2) 6

11. Functions • Functions are defined using the syntax “is operation,” followed by the formal parameters, and then the function body enclosed in braces • Functions are evaluated using right associativity Examples: • factorial IS OPERATION x { * count x } • nthroot IS OPERATION x n { power x ( reciprocal n ) }

12. Transformers • A transformer changes how functions are applied • “each” is a built-in transformer that applies a function to each value of a list • each first (“abc “def) (3 7 8) (`z `x `q) • “abc 3 `z • New transformers can be created using IS TRANSFORMER • Transformers were a novel feature in NIAL, and allow the language to support parallel architectures efficiently

13. Atlases • An atlas is a list of functions that can be applied to a data item, producing a list of results • [first, last, reverse] `a `b `c • [`a `c ‘cba’] brackets are used because ‘cba’ is a list! • [+, -, *, /, quotient] 12 7 • 19 5 84 1.71 1

14. x := `a `e `i `o `u x := l x gets 3 plus 4 x gets plus 3 4 x := 3 times prod 4 5 [0 3] choose x x | [0, 3] Different Ways of Saying the Same Thing • x := ‘aeiou’ • x := True • x := 3 + 4 • x := 3 + 4 • x gets 3 * 4 * 5 • x @ (0 3) • x @ (0 3)

15. IF Statements • IF, ELSE, ELSEIF, and ENDIF are supported • Comparison operators and boolean operations are available IF (x >= 3.4) and (y < 7) THEN out_of_range := True ELSE out_of_range := False ENDIF

16. CASE Statements • CASE statements allow selection based on a value (not necessarily an integer) • An optional ELSE clause handles the default case • Each non-default case must end with END – there is no fall-through like in C and Java CASE n FROM 1: value := ‘one’ END 2: value := ‘two’ END ELSE value := ‘unknown’ ENDCASE

17. Loops • NIAL supports the three usual types of loops: • WHILE {condition} DO {expressions} ENDWHILE • REPEAT {expressions} UNTIL {condition} ENDREPEAT • FOR {variable} WITH {range} DO {expressions} ENDFOR • The count function is useful with FOR loops • FOR i WITH count 10 DO write(i) ENDFOR • It is better to use the EACH transformer, however • The EXIT statement can be used to force a loop to terminate

18. Q’Nial Interpreter • Q’Nial allows NIAL statements to be entered and interpreted dynamically • Windows version is now available free from NIAL Systems (www.nial.com) • C++ source code for Q’Nial is also available free of charge

19. Q’Nial in Action

20. The Future of NIAL • NIAL has been used in academic research (particularly in AI) and at some insurance companies, but has declined in popularity since the 1980s • Newer languages in its niche can do the same tasks just as well or better • APL version 2 • J and its successors • J is available for free; NIAL was very expensive until recently • NIAL is not easy to integrate with native C libraries • Best use of NIAL is as a prototyping language

21. References • Nial Systems Limited http://www.nial.com • Q’nial Research Project http://www.qnial.net • “A Quick Look at Nial,” Journal of J/APL http://www.apl.demon.co.uk/aplandj/qnial.html • Comparison of array languages, Keith Smillie http://www.cs.ualberta.ca/~smillie/ComputerAndMe/Part23.html • “APL programming language,” Wikipedia http://en.wikipedia.org/wiki/APL_programming_language

22. Questions?