NIAL Nested Interactive Array Language Dennis Brown Northern

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

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)

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

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

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) • Strings – ‘abc’ – `a `b `c • Phrases – “dog – phrase ‘dog’ • Faults – ‘? conform’

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

Lists – Examples • sum 2 3 4 – 9 • sum [2 3 4] – [2 3 4] • sum (2 3 4) (1 2 3) – 357 • each sum (2 3 4) (1 2 3) – 96 • 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]

Lisp vs. NIAL • (car 1 2 3) 1 • (cdr 1 2 3) (2 3) • (cons 1 (2 3)) (1 2 3) • first 1 2 3 1 • rest 1 2 3 23 • hitch 1 (2 3) 123

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 8 123 456 • 2 3 reshape 1 2 3 4 123 412

Tables – Continued • x : = 3 3 reshape count 9 123 456 789 • x | [2, ] (row slice) 789 • x | [, 2] (col. slice) 369 • x @ (1 2) 6 • post 1 2 3

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 ) }

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

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

Different Ways of Saying the Same Thing • • x : = ‘aeiou’ x : = True x : = 3 + 4 x gets 3 * 4 * 5 x @ (0 3) • • 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]

IF Statements • IF, 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

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

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

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

Q’Nial in Action

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 1980 s • 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

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/Computer. And. Me/Part 23. html • “APL programming language, ” Wikipedia http: //en. wikipedia. org/wiki/APL_programming_language

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