SHARP APL

SHARP APL
Developer	I.P. Sharp Associates
Released	around 1979
Array model	flat with boxes
Index origin	0 or 1
Function styles	defined functions, some tacit capabilities
Numeric types	64-bit float, complex
Unicode support	none
Influenced by	APL\360
Influenced	J, A+, K, Dyalog APL

SHARP APL (later SAX: SHARP APL for UNIX) was a standalone version of APL offered by I.P. Sharp Associates (IPSA), who had previously offered APL interpretation as a timesharing service. IPSA employed many notable APL designers including Ken Iverson, and SHARP APL was the source of many developments in flat array theory. Notable features of SHARP APL include function rank, the Rank operator, and leading axis theory, as well as relative comparison tolerance and close composition operators including Under.

Primitive functions

Arithmetic

Scalar

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

Non-scalar

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

Relational

Glyph	Rank	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

Indexing

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

Structural

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

Miscellaneous

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

Primitive Operators

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
¨	f	n	mf		With
.	f	g	2	∞ ∞	Alternant	Inner-product
.	m	g		∞ ∞		Tie, Outer-product
.	f	m	mf		Ply

Implementation

Numeric types

SHARP originally supported only real numbers using double (8-byte) precision. Numbers were stored in one of three types:

• Boolean, with one bit per value
• Integer, with four bytes per value
• Floating, with eight bytes per value

SATN-40 describes the addition of complex numbers to SHARP APL.

External links

Wikipedia