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{{Infobox array language
{{Infobox array language
| logo                    = [[File:Sharp APL logo.png]]
| array model              = [[Flat array model|flat]] with [[Box|boxes]]
| array model              = [[Flat array model|flat]] with [[Box|boxes]]
| index origin            = 0 or 1
| index origin            = 0 or 1
Line 7: Line 8:
| released                = 1993  
| released                = 1993  
| withdrawn                = around 2017
| withdrawn                = around 2017
| latest release           = 6.0 / 2000
| latest release version  = 6.0 / 2000
| platforms                = S/390, x86
| platforms                = S/390, x86
| operating systems        = UNIX (AIX, Solaris), Linux
| operating systems        = UNIX (AIX, Solaris), Linux
| implementation language  = [[wikipedia:C (programming language)|C]]
| license                  = Free for personal use / Proprietary commercial software
| license                  = Free for personal use / Proprietary commercial software
| download                = [https://github.com/abrudz/sax GitHub]
| developer                = [[Soliton Associates]]
| developer                = [[Soliton Associates]]
| influenced by            = [[APL*PLUS]]
| influenced by            = [[SHARP APL]]
| influenced              = [[Dyalog APL]]
| influenced              = [[J]]
| documentation            = [https://abrudz.github.io/SAX2/SAX61.pdf PDF]
| documentation            = [https://abrudz.github.io/SAX2/SAX61.pdf PDF]
| file ext                = .sw, .sf
| file ext                = .sw, .sf
}}
}}
'''SAX''' ('''S'''HARP '''A'''PL for UNI'''X''') 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]].
'''SAX''' ('''S'''HARP '''A'''PL for UNI'''X''') was a version of [[SHARP APL]]. Developed and sold initially by [[IPSA]], it was later offered by [[Soliton Associates]], and eventually became the last active SHARP product. SAX supported most but not all features of the previous SHARP implementation for IBM platforms, with [[complex number]]s being a significant exception. It also included more features from [[A Dictionary of APL]] such as [[Swap]] (<syntaxhighlight lang=apl inline>⊃</syntaxhighlight>) and [[From]] (<syntaxhighlight lang=apl inline>{</syntaxhighlight>).<ref>[[Soliton Associates]]. "Platform Differences". 1993-06. Held in [https://museum.eecs.yorku.ca/collections/show/15 York University IPSA collection].</ref>


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


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! Glyph                          !! Rank !! Monadic              !! Ranks !! Dyadic
! Glyph                          !! Rank !! Monadic              !! Ranks !! Dyadic
|-
|-
| <source lang=apl inline>⌹</source> || 2 || [[Matrix inverse]]    || ∞ 2 || [[Matrix divide]]
| <syntaxhighlight lang=apl inline>⌹</syntaxhighlight> || 2 || [[Matrix inverse]]    || ∞ 2 || [[Matrix divide]]
|-
|-
| <source lang=apl inline>?</source> ||  || See [[#Scalar|Scalar]] || * * || [[Deal]]
| <syntaxhighlight lang=apl inline>?</syntaxhighlight> ||  || See [[#Scalar|Scalar]] || * * || [[Deal]]
|-
|-
| <source lang=apl inline>⊤</source> ||  ||                        || ∞ ∞ || [[Encode]]
| <syntaxhighlight lang=apl inline>⊤</syntaxhighlight> ||  ||                        || ∞ ∞ || [[Encode]]
|-
|-
| <source lang=apl inline>⊥</source> ||  ||                        || ∞ ∞ || [[Decode]]
| <syntaxhighlight lang=apl inline>⊥</syntaxhighlight> ||  ||                        || ∞ ∞ || [[Decode]]
|}
|}


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! Glyph                          !! Rank !! Monadic                            !! Ranks !! Dyadic
! Glyph                          !! Rank !! Monadic                            !! Ranks !! Dyadic
|-
|-
| <source lang=apl inline>=</source> ||  || See [[#Miscellaneous|Miscellaneous]] || 0 0 || [[Equals]]
| <syntaxhighlight lang=apl inline>=</syntaxhighlight> ||  || See [[#Miscellaneous|Miscellaneous]] || 0 0 || [[Equals]]
|-
|-
| <source lang=apl inline>≠</source> ||  || See [[#Miscellaneous|Miscellaneous]] || 0 0 || [[Not Equals]]
| <syntaxhighlight lang=apl inline>≠</syntaxhighlight> ||  || See [[#Miscellaneous|Miscellaneous]] || 0 0 || [[Not Equals]]
|-
|-
| <source lang=apl inline><</source> ||  || See [[#Structural|Structural]]      || 0 0 || [[Less Than]]
| <syntaxhighlight lang=apl inline><</syntaxhighlight> ||  || See [[#Structural|Structural]]      || 0 0 || [[Less Than]]
|-
|-
| <source lang=apl inline>≤</source> ||  ||                                      || 0 0 || [[Less Than or Equal]]
| <syntaxhighlight lang=apl inline>≤</syntaxhighlight> ||  ||                                      || 0 0 || [[Less Than or Equal]]
|-
|-
| <source lang=apl inline>≥</source> ||  ||                                      || 0 0 || [[Greater Than or Equal]]
| <syntaxhighlight lang=apl inline>≥</syntaxhighlight> ||  ||                                      || 0 0 || [[Greater Than or Equal]]
|-
|-
| <source lang=apl inline>></source> ||  || See [[#Structural|Structural]]      || 0 0 || [[Greater Than]]
| <syntaxhighlight lang=apl inline>></syntaxhighlight> ||  || See [[#Structural|Structural]]      || 0 0 || [[Greater Than]]
|-
|-
| <source lang=apl inline>≡</source> ||  ||                                      || ∞ ∞ || [[Match]]
| <syntaxhighlight lang=apl inline>≡</syntaxhighlight> ||  ||                                      || ∞ ∞ || [[Match]]
|-
|-
| <source lang=apl inline>∊</source> ||  ||                                      || 0 ∞ || [[Membership]]
| <syntaxhighlight lang=apl inline>∊</syntaxhighlight> ||  ||                                      || 0 ∞ || [[Membership]]
|-
|-
| <source lang=apl inline>⍷</source> ||  ||                                      || ∞ ∞ || [[Find]]
| <syntaxhighlight lang=apl inline>⍷</syntaxhighlight> ||  ||                                      || ∞ ∞ || [[Find]]
|}
|}


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! Glyph                          !! Rank !! Monadic                            !! Ranks !! Dyadic
! Glyph                          !! Rank !! Monadic                            !! Ranks !! Dyadic
|-
|-
| <source lang=apl inline>@</source> ||  || See [[#Miscellaneous|Miscellaneous]] || 0 ∞ || [[Squad Index|From]]
| <syntaxhighlight lang=apl inline>@</syntaxhighlight> ||  || See [[#Miscellaneous|Miscellaneous]] || 0 ∞ || [[Squad Index|From]]
|-
|-
| <source lang=apl inline>⍳</source> || 1 || [[Index Generator|Count]]            || 1 0 || [[Index Of]]
| <syntaxhighlight lang=apl inline>⍳</syntaxhighlight> || 1 || [[Index Generator|Count]]            || 1 0 || [[Index Of]]
|-
|-
| <source lang=apl inline>⍸</source> ||  ||                                      || ∞ ∞ || [[Indices of Match|Index]]
| <syntaxhighlight lang=apl inline>⍸</syntaxhighlight> ||  ||                                      || ∞ ∞ || [[Indices of Match|Index]]
|-
|-
| <source lang=apl inline>⍋</source> || ∞ || Numeric [[Grade up]]                || ∞ ∞ || Character [[Grade up]]
| <syntaxhighlight lang=apl inline>⍋</syntaxhighlight> || ∞ || Numeric [[Grade up]]                || ∞ ∞ || Character [[Grade up]]
|-
|-
| <source lang=apl inline>⍒</source> || ∞ || Numeric [[Grade down]]              || ∞ ∞ || Character [[Grade down]]
| <syntaxhighlight lang=apl inline>⍒</syntaxhighlight> || ∞ || Numeric [[Grade down]]              || ∞ ∞ || Character [[Grade down]]
|}
|}


Line 124: Line 127:
! Glyph                          !! Rank !! Monadic                                !! Ranks !! Dyadic
! Glyph                          !! Rank !! Monadic                                !! Ranks !! Dyadic
|-
|-
| <source lang=apl inline>⍴</source> || ∞ || [[Shape|Shape of]]                        || 1 ∞ || [[Reshape]]
| <syntaxhighlight lang=apl inline>⍴</syntaxhighlight> || ∞ || [[Shape|Shape of]]                        || 1 ∞ || [[Reshape]]
|-
|-
| <source lang=apl inline>↑</source> ||  || See [[#Miscellaneous|Miscellaneous]]      || 1 ∞ || [[Take]]
| <syntaxhighlight lang=apl inline>↑</syntaxhighlight> ||  || See [[#Miscellaneous|Miscellaneous]]      || 1 ∞ || [[Take]]
|-
|-
| <source lang=apl inline>↓</source> || ∞ || [[Raze]]                                  || 1 ∞ || [[Drop]]
| <syntaxhighlight lang=apl inline>↓</syntaxhighlight> || ∞ || [[Raze]]                                  || 1 ∞ || [[Drop]]
|-
|-
| <source lang=apl inline><</source> || ∞ || [[Enclose]]/Box                          ||    || See [[#Relational|Relational]]
| <syntaxhighlight lang=apl inline><</syntaxhighlight> || ∞ || [[Enclose]]/Box                          ||    || See [[#Relational|Relational]]
|-
|-
| <source lang=apl inline>⊃</source> || ∞ || [[Enclose if simple|Conditional Enclose]] || ∞ ∞ || [[Link]]
| <syntaxhighlight lang=apl inline>⊃</syntaxhighlight> || ∞ || [[Enclose if simple|Conditional Enclose]] || ∞ ∞ || [[Link]]
|-
|-
| <source lang=apl inline>></source> || 0 || [[Disclose]]/Open                        ||    || See [[#Relational|Relational]]
| <syntaxhighlight lang=apl inline>></syntaxhighlight> || 0 || [[Mix|Disclose]]/Open                        ||    || See [[#Relational|Relational]]
|-
|-
| <source lang=apl inline>,</source> || ∞ || [[Ravel]]                                || ∞ ∞ || [[Catenate]]
| <syntaxhighlight lang=apl inline>,</syntaxhighlight> || ∞ || [[Ravel]]                                || ∞ ∞ || [[Catenate]]
|-
|-
| <source lang=apl inline>⍪</source> || ∞ || [[Table]]                                || ∞ ∞ || [[Catenate First|Catenate-Down]]
| <syntaxhighlight lang=apl inline>⍪</syntaxhighlight> || ∞ || [[Table]]                                || ∞ ∞ || [[Catenate First|Catenate-Down]]
|-
|-
| <source lang=apl inline>⌽</source> || 1 || [[Reverse]]                              || 0 1 || [[Rotate]]
| <syntaxhighlight lang=apl inline>⌽</syntaxhighlight> || 1 || [[Reverse]]                              || 0 1 || [[Rotate]]
|-
|-
| <source lang=apl inline>⊖</source> || ∞ || [[Reverse First|Reverse-Down]]            || ∞ ∞ || [[Rotate First|Rotate-Down]]
| <syntaxhighlight lang=apl inline>⊖</syntaxhighlight> || ∞ || [[Reverse First|Reverse-Down]]            || ∞ ∞ || [[Rotate First|Rotate-Down]]
|-
|-
| <source lang=apl inline>⍉</source> || ∞ || Monadic [[Transpose]]                    || 0 ∞ || Dyadic [[Transpose]]
| <syntaxhighlight lang=apl inline>⍉</syntaxhighlight> || ∞ || Monadic [[Transpose]]                    || 0 ∞ || Dyadic [[Transpose]]
|}
|}


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! Glyph                          !! Rank !! Monadic                !! Ranks !! Dyadic
! Glyph                          !! Rank !! Monadic                !! Ranks !! Dyadic
|-
|-
| <source lang=apl inline>⊣</source> || ∞ || [[Stop]]                  || ∞ ∞ || [[Left Identity|Left]]
| <syntaxhighlight lang=apl inline>⊣</syntaxhighlight> || ∞ || [[Stop]]                  || ∞ ∞ || [[Left Identity|Left]]
|-
|-
| <source lang=apl inline>⊢</source> || ∞ || [[Identity|Pass]]        || ∞ ∞ || [[Right Identity|Right]]
| <syntaxhighlight lang=apl inline>⊢</syntaxhighlight> || ∞ || [[Identity|Pass]]        || ∞ ∞ || [[Right Identity|Right]]
|-
|-
| <source lang=apl inline>≠</source> || ∞ || [[Nubsieve]]              ||    || See [[#Relational|Relational]]
| <syntaxhighlight lang=apl inline>≠</syntaxhighlight> || ∞ || [[Nubsieve]]              ||    || See [[#Relational|Relational]]
|-
|-
| <source lang=apl inline>↑</source> || ∞ || [[Nub]]                  ||    || See [[#Structural|Structural]]
| <syntaxhighlight lang=apl inline>↑</syntaxhighlight> || ∞ || [[Nub]]                  ||    || See [[#Structural|Structural]]
|-
|-
| <source lang=apl inline>=</source> || ∞ || [[Nubin]]                ||    || See [[#Relational|Relational]]
| <syntaxhighlight lang=apl inline>=</syntaxhighlight> || ∞ || [[Nubin]]                ||    || See [[#Relational|Relational]]
|-
|-
| <source lang=apl inline>~</source> ||  || See [[#Scalar|Scalar]]    || ∞ ∞ || [[Without|Less]]
| <syntaxhighlight lang=apl inline>~</syntaxhighlight> ||  || See [[#Scalar|Scalar]]    || ∞ ∞ || [[Without|Less]]
|-
|-
| <source lang=apl inline>@</source> || 1 || [[Cartesian Product|All]] ||    || See [[#Indexing|Indexing]]
| <syntaxhighlight lang=apl inline>@</syntaxhighlight> || 1 || [[Cartesian Product|All]] ||    || See [[#Indexing|Indexing]]
|-
|-
| <source lang=apl inline>⍕</source> || ∞ || [[Monadic Format]]        || * ∞ || [[Dyadic Format]]
| <syntaxhighlight lang=apl inline>⍕</syntaxhighlight> || ∞ || [[Monadic Format]]        || * ∞ || [[Dyadic Format]]
|-
|-
| <source lang=apl inline>⍎</source> || * || [[Execute]]              ||    ||
| <syntaxhighlight lang=apl inline>⍎</syntaxhighlight> || * || [[Execute]]              ||    ||
|}
|}


Line 176: Line 179:
! Glyph !!colspan=2|Operands !!colspan=2|Ranks !! Monadic Call  !! Dyadic Call
! Glyph !!colspan=2|Operands !!colspan=2|Ranks !! Monadic Call  !! Dyadic Call
|-
|-
| <source lang=apl inline>/</source> ||                                    || <source lang=apl inline>f</source> || <source lang=apl inline>∞</source>  ||                                        || [[Reduce]]                      ||
| <syntaxhighlight lang=apl inline>/</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  ||                                        || [[Reduce]]                      ||
|-
|-
| <source lang=apl inline>⌿</source> ||                                    || <source lang=apl inline>f</source> || <source lang=apl inline>∞</source>  ||                                        || [[Reduce First|Reduce-down]]    ||
| <syntaxhighlight lang=apl inline>⌿</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  ||                                        || [[Reduce First|Reduce-down]]    ||
|-
|-
| <source lang=apl inline>\</source> ||                                    || <source lang=apl inline>f</source> || <source lang=apl inline>∞</source>  ||                                        || [[Scan]]                        ||
| <syntaxhighlight lang=apl inline>\</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  ||                                        || [[Scan]]                        ||
|-
|-
| <source lang=apl inline>⍀</source> ||                                    || <source lang=apl inline>f</source> || <source lang=apl inline>∞</source>  ||                                        || [[Scan First|Scan-down]]        ||
| <syntaxhighlight lang=apl inline>⍀</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  ||                                        || [[Scan First|Scan-down]]        ||
|-
|-
| <source lang=apl inline>/</source> ||                                    || <source lang=apl inline>m</source> || <source lang=apl inline>∞</source>  ||                                        || [[Replicate|Copy]]/[[Compress]] ||
| <syntaxhighlight lang=apl inline>/</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>m</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  ||                                        || [[Replicate|Copy]]/[[Compress]] ||
|-
|-
| <source lang=apl inline>⌿</source> ||                                    || <source lang=apl inline>m</source> || <source lang=apl inline>∞</source>  ||                                        || [[Replicate|Copy]]-down/[[Compress]]-down ||
| <syntaxhighlight lang=apl inline>⌿</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>m</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  ||                                        || [[Replicate|Copy]]-down/[[Compress]]-down ||
|-
|-
| <source lang=apl inline>\</source> ||                                    || <source lang=apl inline>m</source> || <source lang=apl inline>∞</source>  ||                                        || [[Expand]]                      ||
| <syntaxhighlight lang=apl inline>\</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>m</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  ||                                        || [[Expand]]                      ||
|-
|-
| <source lang=apl inline>⍀</source> ||                                    || <source lang=apl inline>m</source> || <source lang=apl inline>∞</source>  ||                                        || [[Expand First|Expand-down]]    ||
| <syntaxhighlight lang=apl inline>⍀</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>m</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  ||                                        || [[Expand First|Expand-down]]    ||
|-
|-
| <source lang=apl inline>⊂</source> ||                                    || <source lang=apl inline>f</source> || <source lang=apl inline>∞</source>  || <source lang=apl inline>rf lf</source> ||colspan=2| Swap
| <syntaxhighlight lang=apl inline>⊂</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  || <syntaxhighlight lang=apl inline>rf lf</syntaxhighlight> ||colspan=2| [[Swap]]
|-
|-
| <source lang=apl inline>&</source> ||                                    || <source lang=apl inline>f</source> || <source lang=apl inline>∞</source>  || <source lang=apl inline>∞  ∞</source>  ||colspan=2| Select
| <syntaxhighlight lang=apl inline>&</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>∞</syntaxhighlight>  || <syntaxhighlight lang=apl inline>∞  ∞</syntaxhighlight>  ||colspan=2| Select
|-
|-
| <source lang=apl inline>⍤</source> || <source lang=apl inline>f</source> || <source lang=apl inline>g</source> || <source lang=apl inline>mg</source> || <source lang=apl inline>mg mg</source> ||colspan=2| On ([[close Over]])
| <syntaxhighlight lang=apl inline>⍤</syntaxhighlight> || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>g</syntaxhighlight> || <syntaxhighlight lang=apl inline>mg</syntaxhighlight> || <syntaxhighlight lang=apl inline>mg mg</syntaxhighlight> ||colspan=2| On ([[close Over]])
|-
|-
| <source lang=apl inline>⍤</source> || <source lang=apl inline>f</source> || <source lang=apl inline>n</source> || <source lang=apl inline>n</source>  || <source lang=apl inline>n  n</source>  ||colspan=2| [[Rank operator|Rank]]
| <syntaxhighlight lang=apl inline>⍤</syntaxhighlight> || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>n</syntaxhighlight> || <syntaxhighlight lang=apl inline>n</syntaxhighlight>  || <syntaxhighlight lang=apl inline>n  n</syntaxhighlight>  ||colspan=2| [[Rank operator|Rank]]
|-
|-
| <source lang=apl inline>⍤</source> || <source lang=apl inline>m</source> || <source lang=apl inline>g</source> || <source lang=apl inline>mg</source> || <source lang=apl inline>mg mg</source> ||colspan=2| [[Cut operator|Cut]]
| <syntaxhighlight lang=apl inline>⍤</syntaxhighlight> || <syntaxhighlight lang=apl inline>m</syntaxhighlight> || <syntaxhighlight lang=apl inline>g</syntaxhighlight> || <syntaxhighlight lang=apl inline>mg</syntaxhighlight> || <syntaxhighlight lang=apl inline>mg mg</syntaxhighlight> ||colspan=2| [[Cut]]
|-
|-
| <source lang=apl inline>⍥</source> || <source lang=apl inline>f</source> || <source lang=apl inline>g</source> || <source lang=apl inline>mg</source> || <source lang=apl inline>mg mg</source> ||colspan=2| Upon ([[close Atop]])
| <syntaxhighlight lang=apl inline>⍥</syntaxhighlight> || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>g</syntaxhighlight> || <syntaxhighlight lang=apl inline>mg</syntaxhighlight> || <syntaxhighlight lang=apl inline>mg mg</syntaxhighlight> ||colspan=2| Upon ([[close Atop]])
|-
|-
| <source lang=apl inline>¨</source> || <source lang=apl inline>f</source> || <source lang=apl inline>g</source> || <source lang=apl inline>mg</source> || <source lang=apl inline>mg mg</source> ||colspan=2| [[close Under|Under]]
| <syntaxhighlight lang=apl inline>¨</syntaxhighlight> || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>g</syntaxhighlight> || <syntaxhighlight lang=apl inline>mg</syntaxhighlight> || <syntaxhighlight lang=apl inline>mg mg</syntaxhighlight> ||colspan=2| [[close Under|Under]]
|-
|-
| <source lang=apl inline>¨</source> || <source lang=apl inline>m</source> || <source lang=apl inline>g</source> || <source lang=apl inline>mg</source> ||                                        ||rowspan="2"|With ([[Bind]])    ||
| <syntaxhighlight lang=apl inline>¨</syntaxhighlight> || <syntaxhighlight lang=apl inline>m</syntaxhighlight> || <syntaxhighlight lang=apl inline>g</syntaxhighlight> || <syntaxhighlight lang=apl inline>mg</syntaxhighlight> ||                                        ||rowspan="2"|With ([[Bind]])    ||
|-
|-
| <source lang=apl inline>¨</source> || <source lang=apl inline>f</source> || <source lang=apl inline>n</source> || <source lang=apl inline>mf</source> ||                                        ||
| <syntaxhighlight lang=apl inline>¨</syntaxhighlight> || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>n</syntaxhighlight> || <syntaxhighlight lang=apl inline>mf</syntaxhighlight> ||                                        ||
|-
|-
| <source lang=apl inline>.</source> || <source lang=apl inline>f</source> || <source lang=apl inline>g</source> || <source lang=apl inline>2</source>  || <source lang=apl inline>∞  ∞</source>  || [[Alternant]]                  || [[Inner Product|Inner-product]]
| <syntaxhighlight lang=apl inline>.</syntaxhighlight> || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>g</syntaxhighlight> || <syntaxhighlight lang=apl inline>2</syntaxhighlight>  || <syntaxhighlight lang=apl inline>∞  ∞</syntaxhighlight>  || [[Alternant]]                  || [[Inner Product|Inner-product]]
|-
|-
| <source lang=apl inline>.</source> || <source lang=apl inline>m</source> || <source lang=apl inline>g</source> ||                                    || <source lang=apl inline>∞  ∞</source>  ||                                || [[Tie]], [[Outer Product|Outer-product]]
| <syntaxhighlight lang=apl inline>.</syntaxhighlight> || <syntaxhighlight lang=apl inline>m</syntaxhighlight> || <syntaxhighlight lang=apl inline>g</syntaxhighlight> ||                                    || <syntaxhighlight lang=apl inline>∞  ∞</syntaxhighlight>  ||                                || [[Tie]], [[Outer Product|Outer-product]]
|-
|-
| <source lang=apl inline>.</source> || <source lang=apl inline>f</source> || <source lang=apl inline>m</source> || <source lang=apl inline>mf</source> ||                                        || [[Ply]]                        ||
| <syntaxhighlight lang=apl inline>.</syntaxhighlight> || <syntaxhighlight lang=apl inline>f</syntaxhighlight> || <syntaxhighlight lang=apl inline>m</syntaxhighlight> || <syntaxhighlight lang=apl inline>mf</syntaxhighlight> ||                                        || [[Ply]]                        ||
|}
|}


== External links ==
== References ==
 
<references/>
[[wikipedia:I._P._Sharp_Associates|Wikipedia]]
{{APL dialects}}[[Category:APL dialects]][[Category:Flat array languages]][[Category:Leading axis languages]]
 
{{APL dialects}}[[Category:APL dialects]][[Category:Flat array languages]]

Latest revision as of 03:23, 11 May 2024

SAX (SHARP APL for UNIX) was a version of SHARP APL. Developed and sold initially by IPSA, it was later offered by Soliton Associates, and eventually became the last active SHARP product. SAX supported most but not all features of the previous SHARP implementation for IBM platforms, with complex numbers being a significant exception. It also included more features from A Dictionary of APL such as Swap (⊃) and From ({).[1]

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

References

  1. ↑ Soliton Associates. "Platform Differences". 1993-06. Held in York University IPSA collection.
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
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