SAX

SAX (SHARP APL for UNIX) was a version of SHARP APL offered by Soliton Associates. Notable features of SAX include function rank, the Rank operator, and leading axis theory, as well as relative comparison tolerance and close composition operators including Under.

Primitive functions

All scalar functions have rank zero.

Glyph	Monadic	Dyadic
`+`	Conjugate/Identity	Addition
`-`	Negate	Subtraction
`×`	Signum	Multiplication
`÷`	Reciprocal	Division
`*`	Exponential	Power
`⍟`	Natural Logarithm	Base-⍺ Logarithm
`\|`	Magnitude	Residue
`!`	Factorial	Out-Of/Combinations
`⌊`	Floor	Minimum
`⌈`	Ceiling	Maximum
`○`	Pi Times	Circle functions
`∧`		And/Least Common Multiple (LCM)
`∨`		Or/Greatest Common Divisor (GCD)
`⍲`		Nand
`⍱`		Nor
`~`	Not	See Miscellaneous
`?`	Roll	See Non-scalar

Glyph	Rank	Monadic	Ranks	Dyadic
`⌹`	2	Matrix inverse	∞ 2	Matrix divide
`?`		See Scalar	* *	Deal
`⊤`			∞ ∞	Encode
`⊥`			∞ ∞	Decode

Glyph	Monadic	Ranks	Dyadic
`=`	See Miscellaneous	0 0	Equals
`≠`	See Miscellaneous	0 0	Not Equals
`<`	See Structural	0 0	Less Than
`≤`		0 0	Less Than or Equal
`≥`		0 0	Greater Than or Equal
`>`	See Structural	0 0	Greater Than
`≡`		∞ ∞	Match
`∊`		0 ∞	Membership
`⍷`		∞ ∞	Find

Glyph	Rank	Monadic	Ranks	Dyadic
`@`		See Miscellaneous	0 ∞	From
`⍳`	1	Count	1 0	Index Of
`⍸`			∞ ∞	Index
`⍋`	∞	Numeric Grade up	∞ ∞	Character Grade up
`⍒`	∞	Numeric Grade down	∞ ∞	Character Grade down

Glyph	Rank	Monadic	Ranks	Dyadic
`⍴`	∞	Shape of	1 ∞	Reshape
`↑`		See Miscellaneous	1 ∞	Take
`↓`	∞	Raze	1 ∞	Drop
`<`	∞	Enclose/Box		See Relational
`⊃`	∞	Conditional Enclose	∞ ∞	Link
`>`	0	Disclose/Open		See Relational
`,`	∞	Ravel	∞ ∞	Catenate
`⍪`	∞	Table	∞ ∞	Catenate-Down
`⌽`	1	Reverse	0 1	Rotate
`⊖`	∞	Reverse-Down	∞ ∞	Rotate-Down
`⍉`	∞	Monadic Transpose	0 ∞	Dyadic Transpose

Glyph	Rank	Monadic	Ranks	Dyadic
`⊣`	∞	Stop	∞ ∞	Left
`⊢`	∞	Pass	∞ ∞	Right
`≠`	∞	Nubsieve		See Relational
`↑`	∞	Nub		See Structural
`=`	∞	Nubin		See Relational
`~`		See Scalar	∞ ∞	Less
`@`	1	All		See Indexing
`⍕`	∞	Monadic Format	* ∞	Dyadic Format
`⍎`	*	Execute

Glyph	Operands		Ranks		Monadic Call	Dyadic Call
`/`		`f`	`∞`		Reduce
`⌿`		`f`	`∞`		Reduce-down
`\`		`f`	`∞`		Scan
`⍀`		`f`	`∞`		Scan-down
`/`		`m`	`∞`		Copy/Compress
`⌿`		`m`	`∞`		Copy-down/Compress-down
`\`		`m`	`∞`		Expand
`⍀`		`m`	`∞`		Expand-down
`⊂`		`f`	`∞`	`rf lf`	Swap
`&`		`f`	`∞`	`∞ ∞`	Select
`⍤`	`f`	`g`	`mg`	`mg mg`	On (close Over)
`⍤`	`f`	`n`	`n`	`n n`	Rank
`⍤`	`m`	`g`	`mg`	`mg mg`	Cut
`⍥`	`f`	`g`	`mg`	`mg mg`	Upon (close Atop)
`¨`	`f`	`g`	`mg`	`mg mg`	Under
`¨`	`m`	`g`	`mg`		With (Bind)
`¨`	`f`	`n`	`mf`		With (Bind)
`.`	`f`	`g`	`2`	`∞ ∞`	Alternant	Inner-product
`.`	`m`	`g`		`∞ ∞`		Tie, Outer-product
`.`	`f`	`m`	`mf`		Ply

APL dialects [edit]
Maintained	APL+Win ∙ APL2 ∙ APL64 ∙ APL\iv ∙ Aplette ∙ April ∙ Co-dfns ∙ Dyalog APL ∙ Dyalog APL Vision ∙ dzaima/APL ∙ GNU APL ∙ Kap ∙ NARS2000 ∙ Pometo ∙ TinyAPL
Historical	A Programming Language ∙ A+ (A) ∙ APL# ∙ APL2C ∙ APL\360 ∙ APL/700 ∙ APL\1130 ∙ APL\3000 ∙ APL.68000 ∙ APL*PLUS ∙ APL.jl ∙ APL.SV ∙ APLX ∙ Extended Dyalog APL ∙ Iverson notation ∙ IVSYS/7090 ∙ NARS ∙ ngn/apl ∙ openAPL ∙ Operators and Functions ∙ PAT ∙ Rowan ∙ SAX ∙ SHARP APL ∙ Rationalized APL ∙ VisualAPL (APLNext) ∙ VS APL ∙ York APL
Derivatives	AHPL ∙ BQN ∙ CoSy ∙ ELI ∙ Glee ∙ I ∙ Ivy ∙ J ∙ Jelly ∙ K (Goal, Klong, Q) ∙ KamilaLisp ∙ Lang5 ∙ Lil ∙ Nial ∙ RAD ∙ Uiua
Overviews	Comparison of APL dialects ∙ Timeline of array languages ∙ Timeline of influential array languages ∙ Family tree of array languages