APL бағдарламалау тілінің символдары мен ережелері

Set of rules defining correctly structured programs

The programming language APL is distinctive in being symbolic rather than lexical: its primitives are denoted by symbols, not words. These symbols were originally devised as a mathematical notation to describe algorithms. APL programmers often assign informal names when discussing functions and operators (for example, "product" for ×/) but the core functions and operators provided by the language are denoted by non textual symbols.

Most symbols denote functions or operators. A monadic function takes as its argument the result of evaluating everything to its right. (Moderated in the usual way by parentheses.) A dyadic function has another argument, the first item of data on its left. Many symbols denote both monadic and dyadic functions, interpreted according to use. For example, ⌊3.2 gives 3, the largest integer not above the argument, and 3⌊2 gives 2, the lower of the two arguments.

Name(s) Notation Meaning Unicode code point Roll One integer selected randomly from the first B integers Ceiling Least integer greater than or equal to B Floor Greatest integer less than or equal to B Shape, Rho Number of components in each dimension of B Not, Tilde Logical: 1 is 0, 0 is 1 Absolute value Magnitude of B Index generator, Iota Vector of the first B integers Exponential e to the B power Negation Changes sign of B Conjugate The complex conjugate of B (real numbers are returned unchanged) Signum ¯1 if B<0; 0 if B=0; 1 if B>0 Reciprocal 1 divided by B Ravel, Catenate, Laminate Reshapes B into a vector Matrix inverse, Monadic Quad Divide Inverse of matrix B Pi times Multiply by π Logarithm Natural logarithm of B Reversal Reverse elements of B along last axis Reversal Reverse elements of B along first axis Grade up Indices of B which will arrange B in ascending order Grade down Indices of B which will arrange B in descending order Execute Execute an APL expression Monadic format A character representation of B Monadic transpose Reverse the axes of B Factorial Product of integers 1 to B Depth Nesting depth: 1 for un nested array Table Makes B into a table, a 2 dimensional array.

The Unicode Basic Multilingual Plane includes the APL symbols in the Miscellaneous Technical block, which are thus usually rendered accurately from the larger Unicode fonts installed with most modern operating systems. These fonts are rarely designed by typographers familiar with APL glyphs. So, while accurate, the glyphs may look unfamiliar to APL programmers or be difficult to distinguish from one another. Some Unicode fonts have been designed to display APL well: APLX Upright, APL385 Unicode, and SimPL. Before Unicode, APL interpreters were supplied with fonts in which APL characters were mapped to less commonly used positions in the ASCII character sets, usually in the upper 128 code points. These mappings (and their national variations) were sometimes unique to each APL vendor's interpreter, which made the display of APL programs on the Web, in text files and manuals frequently problematic.

Note the APL On/Off Key topmost rightmost key, just below. Also note the keyboard had some 55 unique (68 listed per tables above, including comparative symbols but several symbols appear in both monadic and dyadic tables) APL symbol keys (55 APL functions (operators) are listed in IBM's 5110 APL Reference Manual), thus with the use of alt, shift and ctrl keys it would theoretically have allowed a maximum of some 59 (keys) *4 (with 2 key pressing) *3 (with tri key pressing, e. g., ctrl alt del) or some 472 different maximum key combinations, approaching the 512 EBCDIC character max (256 chars times 2 codes for each keys combination). Again, in theory the keyboard pictured here would have allowed for about 472 different APL symbols/functions to be keyboard input, actively used. In practice, early versions were only using something roughly equivalent to 55 APL special symbols (excluding letters, numbers, punctuation, etc. keys). Thus, early APL was then only using about 11% (55/472) of a symbolic language's at that time utilization potential, based on keyboard # keys limits, again excluding numbers, letters, punctuation, etc. In another sense keyboard symbols utilization was closer to 100%, highly efficient, since EBCDIC only allowed 256 distinct chars, and ASCII only 128.

APL has proved to be extremely useful in solving mathematical puzzles, several of which are described below.