diff options
| author | Marshall Lochbaum <mwlochbaum@gmail.com> | 2020-09-05 10:39:41 -0400 |
|---|---|---|
| committer | Marshall Lochbaum <mwlochbaum@gmail.com> | 2020-09-05 10:39:41 -0400 |
| commit | f0e089208e22236483747360394155dc76cf7e48 (patch) | |
| tree | 6f7f782ca939ca38e93eb262c9fe19da9b5c14d6 | |
| parent | cea2d535ba34acc17568004be9f87a145fd64616 (diff) | |
Show source of errors (primitive or compiler)
| -rw-r--r-- | docs/bqn.js | 22 | ||||
| -rw-r--r-- | src/r.bqn | 132 |
2 files changed, 77 insertions, 77 deletions
diff --git a/docs/bqn.js b/docs/bqn.js index ebf4a92f..813f4bd0 100644 --- a/docs/bqn.js +++ b/docs/bqn.js @@ -79,7 +79,7 @@ let run = (B,O,S) => { // Bytecode, Objects, Sections/blocks // Runtime let assertFn = pre => (x,w) => { - if (x!==1) throw Error(pre + (has(w)?": "+w.join(""):"")); + if (x!==1) throw Error(pre + (has(w)?(pre?": ":"")+w.join(""):"")); return x; } let arr = (r,sh) => {r.sh=sh;return r;} @@ -94,19 +94,19 @@ let plus = (x,w) => { if (s==="number" && t==="number") return w+x; if (s==="number" && t==="string") return ctrans(x,w); if (s==="string" && t==="number") return ctrans(w,x); - if (s==="string" && t==="string") throw Error("Cannot add two characters"); - throw Error("Cannot add non-data values"); + if (s==="string" && t==="string") throw Error("+: Cannot add two characters"); + throw Error("+: Cannot add non-data values"); } let minus = (x,w) => { if (typeof x!=="number") { if (has(w)&&typeof w==="string") return w.codePointAt(0)-x.codePointAt(0); - throw Error("Can only negate numbers"); + throw Error("-: Can only negate numbers"); } if (!has(w)) return -x; let s=typeof w; if (s==="number") return w-x; if (s==="string") return ctrans(w,-x); - throw Error("Cannot subtract from non-data value"); + throw Error("-: Cannot subtract from non-data value"); } let lesseq = (x,w) => { let s=typeof w, t=typeof x; @@ -145,7 +145,7 @@ let provide = [ ,(x,w) => has(w)?Math.log(x)/Math.log(w):Math.log(x) // Log ,group_len // GroupLen ,group_ord // GroupOrd - ,assertFn("Primitive failed") // ! + ,assertFn("") // ! ,plus // + ,minus // - ,(x,w) => w*x // × @@ -164,19 +164,19 @@ let provide = [ ]; let runtime = run( - new 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- ,provide.concat([0,1,2,32,3,8,-1,Infinity,-Infinity,4,str("Argument to fold must be a list"),str("Equal-rank argument shapes don\'t agree"),str("Argument shape prefixes don\'t agree"),str("Grade argument must have rank at least 1"),str("Replication argument in Indices or Replicate must have rank 1"),str("Amounts to replicate must be natural numbers"),str("Right argument to Select must be an array"),str("Indices in Select must be integers"),str("Select indices out of range"),str("Reverse argument must have rank at least 1"),str("Amount to rotate must be an integer"),str("First-axis function right argument must have rank at least 1"),str("Left argument must have rank at most 1"),str("Left argument length must be at most right argument rank"),str("Elements in Merge argument must have matching shapes"),str("No monadic form: ≥"),str("No monadic form: ≤"),str("Identity not found"),str("Shape argument to Reshape must have rank at most 1"),str("Shape in Reshape must consist of natural numbers"),str("Can\'t compute axis length in Reshape when rest of shape is empty"),str("Shape in Reshape must be a natural number or ∘ ⌊ ⌽ ↑"),str("Shape must be exact when reshaping with ∘"),str("Range argument must consist of natural numbers"),str("Range argument must be a number or list"),str("Insert argument must have rank at least 1"),str("Rank of joined arguments must differ by at most 1"),str("Cell shapes of joined arguments must match"),str("Left argument to Take or Drop must be an integer"),str("Prefixes argument must have rank at least 1"),str("Suffixes argument must have rank at least 1"),str("Windows right argument must be an array"),str("Windows left argument must have rank at most 1"),str("Windows left argument length must be at most right argument rank"),str("Windows left argument must consist of natural numbers"),str("Window length must be at most axis length plus one"),str("Replicate argument lengths must match"),str("Join argument must be an array"),str("Join argument elements must all have the same rank"),str("Join argument element rank must be at least argument rank"),str("Join argument element shapes must be compatible"),str("Grouping argument must consist of integers"),str("Grouping argument values cannot be less than ¯1"),str("Group Indices argument must be a list"),str("Group right argument must be an array"),str("Compound group left argument must be a list"),str("Group left argument total rank must be at most right argument rank"),str("Group argument lengths must be compatible"),str("Indices in compound Pick must be lists"),str("Pick index length must match right argument rank"),str("Pick indices must consist of integers"),str("Pick index out of range"),str("Bins argument must have rank at least 1"),str("Bins right argument rank is too small"),str("Bins left argument must be sorted"),str("Search principal argument must have rank at least 1"),str("Unique mask argument must have rank at least 1"),str("Find left argument rank cannot exceed right argument rank"),str("Left argument to Reorder Axes must have rank at most 1"),str("Reorder Axes left argument length must not exceed right argument rank"),str("Reorder Axes left argument must consist of natural numbers"),str("No such axis in Reorder Axes"),str("Inverse failed"),str("Inverse does not exist"),str("Inverse not found"),str("Repetition numbers must be integers")]) - 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3,8,21,0,2,17,21,2,55,16,22,0,3,11,14,21,0,1,21,2,58,21,2,6,21,2,51,8,21,0,2,17,22,0,4,11,14,21,0,1,15,145,1,21,2,7,21,2,58,21,2,62,21,0,4,21,2,89,16,21,2,62,0,22,17,21,2,63,16,19,8,21,2,6,15,146,1,8,21,0,2,17,22,0,5,11,14,21,0,5,21,0,3,3,2,25,21,0,2,22,0,3,11,14,21,0,1,22,0,4,11,14,15,147,1,21,1,7,3,2,21,2,0,21,2,59,21,2,7,21,1,6,8,8,22,0,5,11,14,0,21,21,0,5,16,25,15,148,1,22,0,3,11,14,0,27,21,0,3,0,22,21,2,62,21,0,1,17,17,21,2,62,0,22,17,25,21,0,2,21,2,103,21,0,1,21,2,8,21,1,13,8,7,16,25,21,0,2,21,2,59,16,21,2,4,21,2,63,7,0,22,17,22,0,3,11,14,21,0,3,21,2,61,0,21,17,0,5,0,86,17,14,21,0,1,21,2,20,16,21,2,1,21,2,5,21,0,3,21,2,76,0,21,8,8,21,2,1,21,0,3,21,2,76,21,2,56,8,3,2,21,2,0,21,0,3,21,2,56,0,21,17,8,21,2,6,0,18,21,2,40,7,8,21,1,3,9,3,2,21,2,0,21,0,2,21,2,58,16,21,2,56,0,21,17,8,15,149,1,3,2,21,2,0,21,2,68,21,2,5,21,2,58,8,21,2,56,0,26,19,21,2,6,21,2,53,8,8,21,0,2,17,25,21,0,1,25,21,0,1,21,2,10,16,0,5,0,96,17,14,21,0,1,21,2,51,21,1,8,17,22,1,8,12,14,21,0,1,21,2,52,21,1,7,17,22,1,7,12,25,21,0,1,21,2,62,0,21,17,21,2,89,16,21,2,96,21,1,9,3,1,17,0,19,21,2,2,21,2,5,21,0,4,8,7,16,25,21,0,1,21,2,2,21,0,4,17,25,21,0,4,21,2,2,21,0,1,17,25,21,0,2,22,0,3,11,0,7,16,22,0,4,11,14,0,21,22,0,5,11,22,0,6,11,22,0,7,11,14,0,25,22,0,8,11,14,21,0,1,0,22,0,12,21,2,7,17,0,7,0,22,17,21,3,9,0,18,0,8,21,3,7,21,2,7,8,7,8,16,21,3,8,0,16,8,21,3,6,21,1,5,8,22,0,9,11,14,21,0,9,0,21,0,22,0,23,3,4,22,0,10,11,14,0,6,15,150,1,3,2,0,16,21,0,3,0,13,0,26,17,17,22,0,11,11,14,15,151,1,22,0,12,11,14,15,152,1,15,153,1,21,0,12,3,3,21,3,0,15,154,1,8,22,0,13,11,14,21,0,1,0,18,21,0,1,21,3,8,15,155,1,8,7,16,25,21,1,6,21,1,7,0,12,21,0,1,17,21,3,9,15,156,1,8,16,25,21,0,1,0,22,0,7,21,1,3,17,21,3,13,21,0,2,17,21,3,9,21,3,41,21,0,0,21,3,7,21,0,2,0,6,0,22,17,8,7,8,16,21,2,3,21,0,2,21,1,4,16,17,25,21,2,7,21,3,63,21,0,1,17,0,17,16,0,18,21,2,6,0,1,16,7,16,21,3,22,22,2,6,13,14,21,2,7,25,21,0,1,21,3,50,21,2,7,17,0,18,21,2,6,21,3,8,0,16,8,7,16,25,21,0,2,21,3,21,0,22,17,22,0,3,11,21,3,22,22,1,7,13,14,21,0,3,21,3,19,21,3,55,7,16,22,1,8,12,21,3,1,21,3,5,0,17,8,0,18,21,3,62,7,21,3,55,19,21,0,1,17,25,21,1,6,21,3,63,21,1,5,17,21,3,55,21,1,8,17,0,17,16,0,18,21,0,4,0,1,16,21,3,68,16,0,16,0,21,17,7,16,21,3,22,21,3,4,21,3,22,7,3,2,21,3,0,21,1,4,8,21,0,1,21,3,68,16,17,25,21,0,1,22,2,4,12,21,3,4,0,16,7,21,2,6,17,22,2,5,12,14,0,27,22,2,3,12,25,21,0,2,0,18,21,0,1,21,3,8,0,16,8,7,16,25,21,0,1,21,3,59,21,0,2,17,0,19,21,3,53,7,16,21,3,19,21,3,62,7,16,22,0,3,11,14,21,0,3,21,3,89,16,0,18,21,0,2,21,3,8,0,16,8,7,16,21,3,19,21,3,55,7,16,22,0,4,11,14,21,0,3,21,3,57,21,3,7,21,1,4,8,21,3,9,21,0,2,21,0,1,3,2,21,3,8,21,3,36,0,16,7,8,21,3,5,15,157,1,8,8,16,14,21,0,4,25,21,1,4,21,3,62,21,3,7,21,0,1,8,21,3,6,21,2,5,8,21,1,3,17,21,3,59,21,3,7,0,21,8,21,3,9,21,0,1,21,3,62,0,22,17,21,3,5,21,1,5,8,8,16,25,21,0,1,0,22,21,3,8,21,3,57,8,21,3,9,15,158,1,8,21,0,2,17,25,21,0,2,21,3,106,16,21,3,90,16,22,0,3,11,14,21,0,1,21,3,105,21,0,2,21,3,44,21,0,3,17,17,21,3,4,21,3,63,7,0,22,17,21,3,52,0,21,17,21,3,4,21,3,44,7,21,0,3,17,22,0,4,11,14,21,0,1,21,1,3,21,3,76,21,3,39,8,21,0,2,21,3,44,21,0,4,17,17,21,2,2,21,3,9,21,3,55,21,3,7,21,3,63,21,3,7,21,0,4,8,8,21,3,62,21,3,2,19,8,21,0,2,21,3,58,16,17,25,21,0,1,21,1,8,0,7,0,22,17,21,4,9,21,1,9,0,7,0,22,19,21,4,9,15,159,1,8,8,0,22,0,7,21,0,1,17,17,25,21,0,2,0,6,21,1,3,17,22,1,4,12,14,21,0,1,0,6,21,1,3,17,22,1,7,12,21,2,6,16,22,1,6,12,0,6,21,1,3,17,21,2,6,16,22,1,5,12,14,21,1,7,0,13,21,3,6,17,22,1,8,12,14,21,1,6,21,1,11,16,14,21,1,7,21,1,13,21,1,4,17,25,21,0,2,0,6,0,22,17,22,1,4,12,0,12,21,1,6,17,0,8,0,23,17,0,6,22,1,8,13,14,21,0,2,25,21,0,1,0,6,0,22,17,22,1,7,12,0,12,21,1,5,17,0,6,22,1,8,13,14,21,0,1,25,21,0,1,21,1,10,21,4,0,21,1,8,8,21,0,2,17,25,21,0,1,0,16,21,1,7,21,1,13,21,1,4,17,17,25,0,22,0,6,21,0,1,17,21,2,4,16,22,2,6,12,21,2,5,16,22,2,7,12,14,21,2,6,25,21,0,1,21,4,19,21,4,63,7,16,21,4,55,16,22,2,3,12,14,21,0,1,21,4,19,21,4,51,7,16,21,4,55,21,1,4,17,22,1,4,12,25,0,23,21,4,47,21,0,2,17,21,4,51,16,22,0,3,11,21,4,62,21,0,1,17,22,0,4,11,21,3,2,16,22,0,5,11,14,21,0,1,21,0,4,3,2,0,16,21,0,5,17,21,2,3,21,0,2,21,4,50,0,23,17,21,4,55,21,0,5,17,21,4,62,21,0,3,17,17,25,21,0,1,14,0,23,22,2,8,12,14,21,2,4,22,2,7,12,14,21,0,1,22,2,4,12,25]) + ,provide.concat([0,1,2,32,3,8,-1,Infinity,-Infinity,4,str("´: 𝕩 must be a list"),str("Mapping: Equal-rank argument shapes don\'t agree"),str("Mapping: Argument shape prefixes don\'t agree"),str("⍋𝕩: 𝕩 must have rank at least 1"),str("/: Replication argument must have rank 1"),str("/: Amounts to replicate must be natural numbers"),str("𝕨⊏𝕩: 𝕩 must be an array"),str("𝕨⊏𝕩: Indices in 𝕨 must be integers"),str("𝕨⊏𝕩: Indices out of range"),str("⌽𝕩: 𝕩 must have rank at least 1"),str("𝕨⌽𝕩: 𝕨 must consist of integers"),str("First-axis primitive: 𝕩 must have rank at least 1"),str("Multi-axis primitive: 𝕨 must have rank at most 1"),str("Multi-axis primitive: length of 𝕨 must be at most rank of 𝕩"),str(">𝕩: Elements of 𝕩 must have matching shapes"),str("≥: No monadic form"),str("≤: No monadic form"),str("´: Identity not found"),str("𝕨⥊𝕩: 𝕨 must have rank at most 1"),str("𝕨⥊𝕩: 𝕨 must consist of natural numbers"),str("𝕨⥊𝕩: Can\'t compute axis length when rest of shape is empty"),str("𝕨⥊𝕩: 𝕨 must consist of natural numbers or ∘ ⌊ ⌽ ↑"),str("𝕨⥊𝕩: Shape must be exact when reshaping with ∘"),str("↕𝕩: 𝕩 must consist of natural numbers"),str("↕𝕩: 𝕩 must be a number or list"),str("˝: 𝕩 must have rank at least 1"),str("𝕨∾𝕩: Rank of 𝕨 and 𝕩 must differ by at most 1"),str("𝕨∾𝕩: Cell shapes of 𝕨 and 𝕩 must match"),str("↑ or ↓: 𝕨 must be an integer"),str("↑𝕩: 𝕩 must have rank at least 1"),str("↓𝕩: 𝕩 must have rank at least 1"),str("𝕨↕𝕩: 𝕩 must be an array"),str("𝕨↕𝕩: 𝕨 must have rank at most 1"),str("𝕨↕𝕩: length of 𝕨 must be at most rank of 𝕩"),str("𝕨↕𝕩: 𝕨 must consist of natural numbers"),str("𝕨↕𝕩: Window length 𝕨 must be at most axis length plus one"),str("𝕨/𝕩: lengths of components of 𝕨 must match 𝕩"),str("∾𝕩: 𝕩 must be an array"),str("∾𝕩: elements of 𝕩 must all have the same rank"),str("∾𝕩: 𝕩 element rank must be at least argument rank"),str("∾𝕩: 𝕩 element shapes must be compatible"),str("⊔: Grouping argument must consist of integers"),str("⊔: Grouping argument values cannot be less than ¯1"),str("⊔𝕩: 𝕩 must be a list"),str("𝕨⊔𝕩: 𝕩 must be an array"),str("𝕨⊔𝕩: Compound 𝕨 must be a list"),str("𝕨⊔𝕩: Total rank of 𝕨 must be at most rank of 𝕩"),str("𝕨⊔𝕩: Lengths of components of 𝕨 must be compatible with 𝕩"),str("𝕨⊑𝕩: Indices in compound 𝕨 must be lists"),str("𝕨⊑𝕩: Index length in 𝕨 must match rank of 𝕩"),str("𝕨⊑𝕩: Indices in 𝕨 must consist of integers"),str("𝕨⊑𝕩: Index out of range"),str("⍋ or ⍒: Rank of 𝕨 must be at least 1"),str("⍋ or ⍒: Rank of 𝕩 must be at least cell rank of 𝕨"),str("⍋ or ⍒: 𝕨 must be sorted"),str("p⊐𝕩 or 𝕨∊p: p must have rank at least 1"),str("∊𝕩 or ⊐𝕩: 𝕩 must have rank at least 1"),str("⍷𝕩: Rank of 𝕨 cannot exceed rank of 𝕩"),str("𝕨⍉𝕩: 𝕨 must have rank at most 1"),str("𝕨⍉𝕩: Length of 𝕨 must not exceed rank of 𝕩"),str("𝕨⍉𝕩: 𝕨 must consist of natural numbers"),str("𝕨⍉𝕩: Skipped result axis"),str("⁼: Inverse failed"),str("⁼: Inverse does not exist"),str("⁼: Inverse not found"),str("⍟: Repetition numbers in 𝕨 must be integers")]) + ,[[0,1,0,138],[2,0,2935,6],[0,0,2962,3],[0,0,2966,3],[0,0,2970,3],[1,0,2974,5],[1,0,2982,5],[2,0,3000,6],[2,0,3015,6],[2,0,3034,6],[2,0,3056,6],[2,0,3078,6],[0,0,3110,3],[0,0,3121,3],[0,0,3130,3],[1,0,3139,9],[0,0,3252,3],[0,0,3292,4],[1,1,3368,4],[1,1,3441,3],[0,0,3505,3],[0,0,3516,5],[2,0,3600,12],[0,0,3806,4],[0,0,3855,6],[0,0,3945,7],[0,0,4074,4],[0,0,4230,4],[0,0,4291,4],[2,0,4393,16],[1,1,4623,2],[0,0,4647,3],[0,0,4674,3],[0,0,4700,3],[1,1,4739,2],[2,1,4749,4],[0,0,4785,4],[1,1,4882,2],[0,0,4915,3],[0,0,4942,3],[0,0,4964,3],[0,0,4986,3],[0,0,4997,3],[0,0,5026,3],[0,0,5032,9],[0,0,5183,5],[0,0,5216,3],[0,0,5225,3],[1,1,5231,2],[2,0,5300,10],[2,0,5359,8],[1,0,5552,5],[0,0,5594,8],[0,0,5830,4],[0,0,5911,3],[0,0,5961,4],[0,0,6082,3],[0,0,6132,4],[0,0,6298,3],[0,0,6317,3],[0,0,6351,3],[0,0,6365,7],[0,0,6412,11],[1,0,6677,8],[0,0,6776,4],[0,0,6859,6],[0,0,7190,4],[0,0,7403,3],[0,0,7421,4],[1,0,7493,9],[1,1,7563,3],[1,0,7588,14],[1,1,8023,4],[1,0,8073,6],[0,0,8212,4],[0,0,8280,3],[0,0,8354,3],[0,0,8409,4],[0,0,8538,4],[0,0,8658,3],[2,0,8698,6],[2,0,8727,7],[0,0,8768,6],[0,0,8918,3],[0,0,8988,3],[0,0,9025,5],[0,0,9169,3],[0,0,9216,3],[0,0,9242,3],[0,0,9329,3],[1,1,9384,2],[2,0,9393,13],[1,1,9547,2],[1,1,9561,2],[1,1,9565,2],[0,0,9569,3],[0,0,9581,3],[0,0,9604,3],[1,0,9625,6],[1,0,9742,11],[1,0,9963,5],[0,0,9978,3],[0,0,9993,3],[0,0,10008,3],[1,0,10053,8],[0,0,10192,8],[0,0,10360,5],[0,0,10435,3],[0,0,10452,3],[0,0,10458,4],[0,0,10507,3],[0,0,10517,3],[0,0,10545,5],[1,0,10641,5],[0,0,10652,8],[0,0,10909,3],[0,0,10950,3],[0,0,10970,3],[1,0,11024,6],[0,0,11177,6],[0,0,11305,10],[0,0,11490,3],[0,0,11590,3],[0,0,11632,3],[0,0,11685,4],[0,0,11745,3],[0,0,11776,3],[0,0,11814,6],[0,0,11921,6],[0,0,11971,4],[0,0,12001,3],[0,0,12020,4],[1,1,12178,2],[0,0,12182,3],[1,0,12225,5],[1,0,12262,5],[1,0,12273,5],[0,0,12284,14],[0,0,12460,3],[0,0,12481,3],[0,0,12535,3],[0,0,12570,3],[0,0,12594,4],[1,0,12654,5],[0,0,12721,3],[0,0,12750,3],[0,0,12767,5],[0,0,12878,3],[0,0,12933,3],[0,0,12957,5],[0,0,13086,3],[0,0,13126,3],[0,0,13209,3],[0,0,13243,3],[0,0,13272,3],[0,0,13290,3],[0,0,13307,3],[0,0,13336,3],[0,0,13379,6],[0,0,13458,3]] ); // Compiler -runtime[40] = assertFn("Compilation failed"); +runtime[40] = assertFn("Compiler"); let compile = run( new 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,[runtime[0],runtime[1],runtime[2],runtime[3],runtime[4],runtime[6],runtime[7],runtime[8],runtime[9],runtime[10],runtime[11],runtime[12],runtime[13],runtime[14],runtime[15],runtime[16],runtime[17],runtime[19],runtime[20],runtime[21],runtime[22],runtime[23],runtime[24],runtime[25],runtime[26],runtime[27],runtime[28],runtime[30],runtime[31],runtime[33],runtime[34],runtime[35],runtime[36],runtime[37],runtime[38],runtime[39],runtime[40],runtime[42],runtime[43],runtime[44],runtime[45],runtime[46],runtime[47],runtime[48],runtime[49],runtime[50],runtime[51],runtime[52],runtime[53],runtime[54],runtime[56],runtime[59],' ,[[0,1,0,34],[0,0,475,3],[1,1,541,4],[0,0,634,34],[0,0,1945,13],[0,0,2267,6],[0,0,2373,6],[0,0,2486,3],[0,0,2516,77],[0,0,5808,11],[0,0,5931,3],[0,0,5946,3],[0,0,5986,4],[0,0,6072,3],[2,1,6107,3]] ); -runtime[40] = assertFn("Assertion failed"); +runtime[40] = assertFn("!"); runtime.map((r,i) => { let prims = "+-×÷⋆√⌊⌈|¬∧∨<>≠=≤≥≡≢⊣⊢⥊∾≍↑↓↕⌽⍉/⍋⍒⊏⊑⊐⊒∊⍷⊔!˙˜˘¨⌜⁼´˝`∘○⊸⟜⌾⊘◶⎉⚇⍟"; r.glyph = prims.charAt(i); // Used to format @@ -24,7 +24,7 @@ Nat←IsArray◶⟨0⊸≤×⌊⊸=,0⟩ ≠ ← (0<=)◶⟨1⋄0⊑≢⟩ # LIMITED to monadic case _fold←{ - "Argument to fold must be a list" ! 1==𝕩 + "´: 𝕩 must be a list" ! 1==𝕩 l←≠v←𝕩 ⋄ F←𝔽 r←𝕨 (0<l)◶{𝕩⋄Identity f}‿{l↩l-1⋄l⊑𝕩}⊘⊣ 𝕩 {r↩(𝕩⊑v)F r}⌜(l-1)⊸-⌜↕l @@ -40,12 +40,12 @@ Cell←{(𝕨⊸+⊑𝕩˜)⌜↕(≠𝕩)-𝕨}⟜≢ _eachd←{ _d←{ # Equal ranks p←≢𝕨 - "Equal-rank argument shapes don't agree" ! 1(⊑⟜p=⊑⟜(≢𝕩))⊸×´↕=𝕨 + "Mapping: Equal-rank argument shapes don't agree" ! 1(⊑⟜p=⊑⟜(≢𝕩))⊸×´↕=𝕨 p⥊ (⊑⟜(⥊𝕨)𝔽⊑⟜(⥊𝕩))⌜↕1×´p } _e←{ # 𝕨 has smaller or equal rank p←≢𝕨 ⋄ k←=𝕨 ⋄ q←≢𝕩 - "Argument shape prefixes don't agree" ! 1(⊑⟜p=⊑⟜q)⊸×´↕k + "Mapping: Argument shape prefixes don't agree" ! 1(⊑⟜p=⊑⟜q)⊸×´↕k l←1(q⊑˜k⊸+)⊸×´↕(=𝕩)-k a←⥊𝕨 ⋄ b←⥊𝕩 q⥊⥊(≠a) (⊑⟜a𝔽l⊸×⊸+⊑b˜)⌜○↕ l @@ -70,7 +70,7 @@ Cmp ← +○IsArray◶⟨ } ⟩ _grade_←{ - "Grade argument must have rank at least 1" ! 1≤=𝕩 + "⍋𝕩: 𝕩 must have rank at least 1" ! 1≤=𝕩 l←≠𝕩 m←1×´1 Cell 𝕩 d←⥊𝕩 @@ -92,10 +92,10 @@ _grade_←{ } Indices←{ - "Replication argument in Indices or Replicate must have rank 1" ! 1==𝕩 + "/: Replication argument must have rank 1" ! 1==𝕩 l←≠𝕩 { - "Amounts to replicate must be natural numbers" ! 1×´Nat⌜𝕩 + "/: Amounts to replicate must be natural numbers" ! 1×´Nat⌜𝕩 k←l-1 N ← ((⊢+-×0=𝕩⊑˜⊢)`k⊸-⌜↕l)⊑˜k-⊢ # Next nonzero E ← ⊑⟜(+`𝕩) @@ -114,10 +114,10 @@ TransposeInv←{ }⍟(0<=) SelSub←{ - "Right argument to Select must be an array" ! IsArray 𝕨 - "Indices in Select must be integers" ! 1×´⥊Int⌜ 𝕨 + "𝕨⊏𝕩: 𝕩 must be an array" ! IsArray 𝕨 + "𝕨⊏𝕩: Indices in 𝕨 must be integers" ! 1×´⥊Int⌜ 𝕨 l←≠𝕩 - "Select indices out of range" ! 1×´⥊ ((-l)⊸≤×l⊸>)⌜ 𝕨 + "𝕨⊏𝕩: Indices out of range" ! 1×´⥊ ((-l)⊸≤×l⊸>)⌜ 𝕨 ((⊢+l×0>⊢)⌜𝕨)(1==𝕩)◶{ c←1×´s←1 Cell 𝕩 𝕨((⥊𝕩)⊑˜c⊸×⊸+)⌜s⥊↕c @@ -127,12 +127,12 @@ SelSub←{ } Reverse ← { - "Reverse argument must have rank at least 1" ! 1≤=𝕩 + "⌽𝕩: 𝕩 must have rank at least 1" ! 1≤=𝕩 l←≠𝕩 ((l-1)⊸-⌜↕l) Select 𝕩 } Rot ← { - "Amount to rotate must be an integer" ! Int𝕨 + "𝕨⌽𝕩: 𝕨 must consist of integers" ! Int𝕨 l←≠𝕩 ⋄ 𝕨-↩l×⌊𝕨÷l ⋄ ((𝕨+⊢-l×(l-𝕨)≤⊢)⌜↕l) Select 𝕩 } @@ -164,11 +164,11 @@ Depth←IsArray◶0‿{1+0(⊣-≤×-)´Depth⌜⥊𝕩} _onAxes_←{ F←𝔽 (𝔾<≡)∘⊣◶{ # One axis - "First-axis function right argument must have rank at least 1" ! 1≤=𝕩 + "First-axis primitive: 𝕩 must have rank at least 1" ! 1≤=𝕩 𝕨F𝕩 }‿{ # Multiple axes - "Left argument must have rank at most 1" ! 1≥=𝕨 - "Left argument length must be at most right argument rank" ! 𝕨≤○≠≢𝕩 + "Multi-axis primitive: 𝕨 must have rank at most 1" ! 1≥=𝕨 + "Multi-axis primitive: length of 𝕨 must be at most rank of 𝕩" ! 𝕨≤○≠≢𝕩 l←≠𝕨 ⋄ W←⊑⟜(⥊𝕨) 0{(W𝕨)F(1+𝕨)⊸𝕊˘⍟(𝕨<l-1)𝕩}⍟(0<l)𝕩 } @@ -179,7 +179,7 @@ Select←ToArray⊸(SelSub _onAxes_ 1) Merge←{ c←≢0⊑⥊𝕩 - "Elements in Merge argument must have matching shapes" ! 1×´(c≡≢)⌜⥊𝕩 + ">𝕩: Elements of 𝕩 must have matching shapes" ! 1×´(c≡≢)⌜⥊𝕩 𝕩⊑⟜Deshape˜⌜c⥊↕1×´c }⍟(0<≠∘⥊)⍟IsArray @@ -198,27 +198,27 @@ _sort ← {(𝕗⊑⟨Cmp,Cmp˜⟩)_grade_𝕗 ⊸ Select} > ↩ Merge ⊘ ((1-≤) _perv) ≠ ↩ ≠ ⊘ ((1-=) _perv) = ↩ = ⊘ (= _perv) -≥ ← ("No monadic form: ≥"!0˜) ⊘ (≥ _perv) -≤ ↩ ("No monadic form: ≤"!0˜) ⊘ (≤ _perv) +≥ ← ("≥: No monadic form"!0˜) ⊘ (≥ _perv) +≤ ↩ ("≤: No monadic form"!0˜) ⊘ (≤ _perv) + ↩ + _perv - ↩ - _perv ¬ ← 1+- -identity ← (0⊑⟨"Identity not found"!0˜⟩) {(0⊑𝕨){𝕗=𝕩}◶𝕩‿(1⊑𝕨)}´ ⟨+‿0,-‿0,×‿1,÷‿1,⋆‿1,√‿1,∧‿1,∨‿0,¬‿1,|‿0,⌊‿∞,⌈‿¯∞,<‿0,≤‿1,=‿1,≥‿1,>‿0,≠‿0⟩ +identity ← (0⊑⟨"´: Identity not found"!0˜⟩) {(0⊑𝕨){𝕗=𝕩}◶𝕩‿(1⊑𝕨)}´ ⟨+‿0,-‿0,×‿1,÷‿1,⋆‿1,√‿1,∧‿1,∨‿0,¬‿1,|‿0,⌊‿∞,⌈‿¯∞,<‿0,≤‿1,=‿1,≥‿1,>‿0,≠‿0⟩ Deshape←IsArray◶{⟨𝕩⟩}‿⥊ Reshape←{ - "Shape argument to Reshape must have rank at most 1" ! 1≥=𝕨 + "𝕨⥊𝕩: 𝕨 must have rank at most 1" ! 1≥=𝕨 s←Deshape 𝕨 sp←+´p←¬Nat⌜s - "Shape in Reshape must consist of natural numbers" ! 1≥sp + "𝕨⥊𝕩: 𝕨 must consist of natural numbers" ! 1≥sp n←≠d←Deshape 𝕩 l←sp◶(×´)‿{ lp←×´p⊣◶⊢‿1¨𝕩 - "Can't compute axis length in Reshape when rest of shape is empty" ! 0<lp + "𝕨⥊𝕩: Can't compute axis length when rest of shape is empty" ! 0<lp i←+´p×↕≠p t←ReshapeT i⊑s - "Shape in Reshape must be a natural number or ∘ ⌊ ⌽ ↑" ! t<4 - Chk ← ⊢ ⊣ "Shape must be exact when reshaping with ∘" ! ⌊⊸= + "𝕨⥊𝕩: 𝕨 must consist of natural numbers or ∘ ⌊ ⌽ ↑" ! t<4 + Chk ← ⊢ ⊣ "𝕨⥊𝕩: Shape must be exact when reshaping with ∘" ! ⌊⊸= a←(2⌊t)◶⟨Chk,⌊,⌈⟩n÷lp s↩p⊣◶⊢‿a¨s {d∾↩(Type d)⌜↕𝕩-n⋄n}⍟(n⊸<)⍟(3=t)lp×a @@ -230,8 +230,8 @@ Reshape←{ ⥊ ↩ Deshape ⊘ ⥊ Range←{ - I←{"Range argument must consist of natural numbers"!Nat𝕩⋄↕𝕩} - M←{"Range argument must be a number or list"!1==𝕩⋄(<⟨⟩)⥊⊸∾⌜´I⌜𝕩} + I←{"↕𝕩: 𝕩 must consist of natural numbers"!Nat𝕩⋄↕𝕩} + M←{"↕𝕩: 𝕩 must be a number or list"!1==𝕩⋄(<⟨⟩)⥊⊸∾⌜´I⌜𝕩} IsArray◶I‿M 𝕩 } @@ -261,7 +261,7 @@ _rankOp_←{ } ⎉ ← _rankOp_ _insert←{ - "Insert argument must have rank at least 1" ! 1≤=𝕩 + "˝: 𝕩 must have rank at least 1" ! 1≤=𝕩 𝕨 𝔽´ <˘𝕩 } ˝ ← _insert @@ -270,43 +270,43 @@ _insert←{ JoinTo←∨○(1<=)◶(∾○⥊)‿{ s←𝕨Pair○≢𝕩 a←1⌈´k←≠⌜s - "Rank of joined arguments must differ by at most 1" ! ∧´1≥a-k + "𝕨∾𝕩: Rank of 𝕨 and 𝕩 must differ by at most 1" ! ∧´1≥a-k c←(k¬a)+⟜(↕a-1)⊸⊏¨s - "Cell shapes of joined arguments must match" ! ≡´c + "𝕨∾𝕩: Cell shapes of 𝕨 and 𝕩 must match" ! ≡´c l←+´(a=k)⊣◶1‿(0⊑⊢)¨s (⟨l⟩∾0⊑c)⥊𝕨∾○⥊𝕩 } Take←{ T←{ - "Left argument to Take or Drop must be an integer" ! Int 𝕨 + "↑ or ↓: 𝕨 must be an integer" ! Int 𝕨 l←≠𝕩 ⋄ n←𝕨<0 ⋄ e←l⌊r←|𝕨 ⋄ s←⟨r⟩ ⋄ m←1 i ← 𝕩{s∾↩c←1 Cell 𝕨⋄𝕩(×+⌜↕∘⊢)m↩×´c}⍟(1≠=𝕩) (l-e)+⍟n ↕e s⥊𝕩{(⥊𝕩)n◶⟨∾,∾˜⟩(0⊑⥊Type𝕗)⌜↕m×r-e}⍟(l<r) ⊑⟜(⥊𝕩)⌜i } 𝕨 T _onAxes_ 0 ((1⌜∘↕0⌈𝕨-○≠⊢)⊸∾∘≢⥊⥊) 𝕩 } -Prefixes ← {"Prefixes argument must have rank at least 1"!1≤=𝕩 ⋄ Take⟜𝕩⌜↕1+≠𝕩} +Prefixes ← {"↑𝕩: 𝕩 must have rank at least 1"!1≤=𝕩 ⋄ Take⟜𝕩⌜↕1+≠𝕩} ↑ ← Prefixes ⊘ Take Drop←{ s←(≠𝕨)(⊣↑⊢∾˜·1⌜∘↕0⌈-⟜≠)≢𝕩 ((sׯ1⋆𝕨>0)+(-s)⌈s⌊𝕨)↑𝕩 } -Suffixes ← {"Suffixes argument must have rank at least 1"!1≤=𝕩 ⋄ Drop⟜𝕩⌜↕1+≠𝕩} +Suffixes ← {"↓𝕩: 𝕩 must have rank at least 1"!1≤=𝕩 ⋄ Drop⟜𝕩⌜↕1+≠𝕩} ↓ ← Suffixes ⊘ Drop Windows←{ - "Windows right argument must be an array" ! IsArray 𝕩 - "Windows left argument must have rank at most 1" ! 1≥=𝕨 - "Windows left argument length must be at most right argument rank" ! 𝕨≤○≠≢𝕩 - "Windows left argument must consist of natural numbers" ! ∧´Nat⌜⥊𝕨 + "𝕨↕𝕩: 𝕩 must be an array" ! IsArray 𝕩 + "𝕨↕𝕩: 𝕨 must have rank at most 1" ! 1≥=𝕨 + "𝕨↕𝕩: length of 𝕨 must be at most rank of 𝕩" ! 𝕨≤○≠≢𝕩 + "𝕨↕𝕩: 𝕨 must consist of natural numbers" ! ∧´Nat⌜⥊𝕨 s←(≠𝕨)↑≢𝕩 - "Window length must be at most axis length plus one" ! ∧´𝕨≤1+s + "𝕨↕𝕩: Window length 𝕨 must be at most axis length plus one" ! ∧´𝕨≤1+s 𝕨{(∾⟜(𝕨≠⊸↓≢𝕩)∘≢⥊>)<⌜⊸⊏⟜𝕩¨s(¬+⌜○Range⊢)⥊𝕨}⍟(0<≠𝕨)𝕩 } Rep ← Indices⊸⊏ -Replicate ← {0<=𝕨}◶{𝕨˘⊸Rep𝕩}‿{"Replicate argument lengths must match"!𝕨=○≠𝕩⋄𝕨Rep𝕩} _onAxes_ (1-0=≠) +Replicate ← {0<=𝕨}◶{𝕨˘⊸Rep𝕩}‿{"𝕨/𝕩: lengths of components of 𝕨 must match 𝕩"!𝕨=○≠𝕩⋄𝕨Rep𝕩} _onAxes_ (1-0=≠) ↕ ↩ Range ⊘ Windows ⌽ ← Reverse ⊘ (Rot _onAxes_ 0) @@ -319,35 +319,35 @@ Join←(1≠=)◶⟨∨´1≠=⌜,1⟩◶{ }‿{ # Multidimensional C←(<⟨⟩)⥊⊸∾⌜´⊢ # Cartesian array product - "Join argument must be an array" ! IsArray 𝕩 + "∾𝕩: 𝕩 must be an array" ! IsArray 𝕩 s←≢⌜𝕩 d←≠0⊑⥊s - "Join argument elements must all have the same rank" ! ∧´⥊d=≠⌜s - "Join argument element rank must be at least argument rank" ! d≥=𝕩 + "∾𝕩: elements of 𝕩 must all have the same rank" ! ∧´⥊d=≠⌜s + "∾𝕩: 𝕩 element rank must be at least argument rank" ! d≥=𝕩 l←(≢𝕩){(𝕩⊑⟜≢a Pick1˜(j=𝕩)⊸×)⌜↕𝕨}¨j←↕r←=a←𝕩 - "Join argument element shapes must be compatible" ! (r⊸↑⌜s)≡C l + "∾𝕩: 𝕩 element shapes must be compatible" ! (r⊸↑⌜s)≡C l i←C{p←+´⌜↑𝕩⋄(↕0⊑⌽p)-𝕩/¯1↓p}⌜l >i<⌜⊸⊏¨l/𝕩 }⍟(0<≠∘⥊) _group←{ - "Grouping argument must consist of integers" ! ∧´Int⌜𝕩 - "Grouping argument values cannot be less than ¯1" ! ∧´¯1≤𝕩 + "⊔: Grouping argument must consist of integers" ! ∧´Int⌜𝕩 + "⊔: Grouping argument values cannot be less than ¯1" ! ∧´¯1≤𝕩 d←(l←GroupLen𝕩)GroupOrd𝕩 i←0⋄(𝔽{𝕩⋄(i↩i+1)⊢i⊑d}⌜∘↕)⌜l } GroupInds←{ - "Group Indices argument must be a list" ! 1==𝕩 + "⊔𝕩: 𝕩 must be a list" ! 1==𝕩 G←⊢_group (1<≡)◶⟨G , (<<⟨⟩) ∾⌜⌜´ {⊏⟜(⥊↕≢𝕩)⌜ G⥊𝕩}⌜⟩ 𝕩 } GroupGen←{ - "Group right argument must be an array" ! IsArray 𝕩 + "𝕨⊔𝕩: 𝕩 must be an array" ! IsArray 𝕩 𝕨↩Pair∘ToArray⍟(2>≡)𝕨 - "Compound group left argument must be a list" ! 1==𝕨 + "𝕨⊔𝕩: Compound 𝕨 must be a list" ! 1==𝕨 n←+´=⌜𝕨 - "Group left argument total rank must be at most right argument rank" ! n≤=𝕩 - "Group argument lengths must be compatible" ! ∧´(Join≢⌜𝕨)=n↑≢𝕩 + "𝕨⊔𝕩: Total rank of 𝕨 must be at most rank of 𝕩" ! n≤=𝕩 + "𝕨⊔𝕩: Lengths of components of 𝕨 must be compatible with 𝕩" ! ∧´(Join≢⌜𝕨)=n↑≢𝕩 l←≠⌜𝕨↩⥊⌜𝕨 S←⊏⟜(𝕩⥊˜⟨×´l⟩∾n Cell 𝕩) (1≠≠)◶(S _group 0⊸⊑)‿(S⌜ ·+⌜⌜´ (⌽×`⟨1⟩∾⌽1↓l) × ⊢_group⌜) 𝕨 @@ -357,10 +357,10 @@ GroupGen←{ ⊔ ← GroupInds ⊘ GroupGen Pick1←{ - "Indices in compound Pick must be lists" ! 1==𝕨 - "Pick index length must match right argument rank" ! 𝕨=○≠s←≢𝕩 - "Pick indices must consist of integers" ! ∧´Int⌜𝕨 - "Pick index out of range" ! ∧´𝕨(≥⟜-∧<)s + "𝕨⊑𝕩: Indices in compound 𝕨 must be lists" ! 1==𝕨 + "𝕨⊑𝕩: Index length in 𝕨 must match rank of 𝕩" ! 𝕨=○≠s←≢𝕩 + "𝕨⊑𝕩: Indices in 𝕨 must consist of integers" ! ∧´Int⌜𝕨 + "𝕨⊑𝕩: Index out of range" ! ∧´𝕨(≥⟜-∧<)s 𝕨↩𝕨+s×𝕨<0 (⥊𝕩)⊑˜0(⊑⟜𝕨+⊑⟜s×⊢)´-↕⊸¬≠𝕨 } @@ -401,11 +401,11 @@ _binSearch ← { } _bins←{ c←1-˜=𝕨 - "Bins argument must have rank at least 1" ! 0≤c - "Bins right argument rank is too small" ! c≤=𝕩 + "⍋ or ⍒: Rank of 𝕨 must be at least 1" ! 0≤c + "⍋ or ⍒: Rank of 𝕩 must be at least cell rank of 𝕨" ! c≤=𝕩 lw←×´sw←1 Cell 𝕨 cw←lw 𝔽○(⊑⟜(⥊𝕨)) _getCellCmp 0 - "Bins left argument must be sorted" ! 0⊸<◶⟨1,∧´0≤˜·cw⟜(lw⊸+)⌜lw×↕∘-⟜1⟩≠𝕨 + "⍋ or ⍒: 𝕨 must be sorted" ! 0⊸<◶⟨1,∧´0≤˜·cw⟜(lw⊸+)⌜lw×↕∘-⟜1⟩≠𝕨 cx←c-˜=𝕩 sx←cx Cell 𝕩 ⋄ lc←sw CmpLen sx cc ← (⊑⟜(⥊𝕨))⊸𝔽⟜(⊑⟜(⥊𝕩)) _getCellCmp´ lc @@ -422,7 +422,7 @@ _search←{ # 0 for ∊˜, 1 for ⊐ red ← 𝕗⊑⟨¬∧˝,+˝∧`⟩ { c←1-˜=𝕨 - "Search principal argument must have rank at least 1" ! 0≤c + "p⊐𝕩 or 𝕨∊p: p must have rank at least 1" ! 0≤c 𝕨 ∧○(8<≠∘⥊)◶⟨ (0<≠𝕨)◶⟨0⎉c∘⊢, Red≢⌜○((0<c)◶⟨⊢,<⎉c⟩)⟩ { g←⌽⍒𝕨 ⋄ i←g⊏˜0⌈1-˜(g⊏𝕨)⍋𝕩 ⋄ (≠𝕨)(⊣+i⊸-⊸×)⍟ind(i⊏𝕨)≡⎉c𝕩 } @@ -431,14 +431,14 @@ _search←{ # 0 for ∊˜, 1 for ⊐ } PermInv ← 1¨⊸GroupOrd _self←{ - "Unique mask argument must have rank at least 1" ! 1≤=𝕩 + "∊𝕩 or ⊐𝕩: 𝕩 must have rank at least 1" ! 1≤=𝕩 g←⍋𝕩 (PermInv g) ⊏ g 𝔽 0⊸<◶⟨1,-⟜1≢○(⊑⟜(g⊏<˘⍟(1<=)𝕩))⊢⟩⌜↕≠𝕩 } SelfClas ← (PermInv∘⍋∘/˜⊏˜1-˜+`∘⊢) _self Find←{ r←=𝕨 - "Find left argument rank cannot exceed right argument rank" ! r≤=𝕩 + "⍷𝕩: Rank of 𝕨 cannot exceed rank of 𝕩" ! r≤=𝕩 𝕨 ≡⎉r (≢𝕨) ↕⎉r 𝕩 } @@ -447,9 +447,9 @@ Find←{ ⍷ ← ∊⊸/ ⊘ Find ReorderChk←{ - "Left argument to Reorder Axes must have rank at most 1" ! 1≥=𝕨 - "Reorder Axes left argument length must not exceed right argument rank" ! 𝕨≤○≠≢𝕩 - "Reorder Axes left argument must consist of natural numbers" ! ∧´Nat⌜⥊𝕨 + "𝕨⍉𝕩: 𝕨 must have rank at most 1" ! 1≥=𝕨 + "𝕨⍉𝕩: Length of 𝕨 must not exceed rank of 𝕩" ! 𝕨≤○≠≢𝕩 + "𝕨⍉𝕩: 𝕨 must consist of natural numbers" ! ∧´Nat⌜⥊𝕨 } ReorderAxesSub←{ (𝕨⊸⊏Pick𝕩˜)⌜↕⌊´⌜𝕨⊔≢𝕩 @@ -458,7 +458,7 @@ ReorderAxes←{ 𝕨 ReorderChk 𝕩 𝕨↩⥊𝕨 r←(=𝕩)-+´¬∊𝕨 - "No such axis in Reorder Axes" ! ∧´𝕨<r + "𝕨⍉𝕩: Skipped result axis" ! ∧´𝕨<r (𝕨∾𝕨(¬∘∊˜/⊢)↕r) ReorderAxesSub 𝕩 } ReorderAxesInv←{ @@ -477,8 +477,8 @@ ProgressiveIndexOf ← {𝕨⊐○(≍˘⟜OccurrenceCount𝕨⊸⊐)𝕩} ⊑ ↩ (0⊑⥊) ⊘ Pick ◶ ↩ {𝕨((𝕨𝔽𝕩)⊑𝕘){𝔽}𝕩} # Same definition, new Pick -IA ← "Inverse failed"⊸! -IX ← "Inverse does not exist"⊸! +IA ← "⁼: Inverse failed"⊸! +IX ← "⁼: Inverse does not exist"⊸! _invChk_ ← {i←𝕨𝔽𝕩⋄IX 𝕩≡𝕨𝔾i⋄i} GroupIndsInv ← { IA 1==𝕩 @@ -494,7 +494,7 @@ GroupInv ← { IA ∧´Nat⌜𝕨 (⊔𝕨) ⍋⊸⊏○∾ 𝕩 } -inverse ← {(⊑(0⊏𝕩)⊐<) ⊑ ((1⊏𝕩)∾⟨"Inverse not found"!0˜⟩)˜} ⍉ (2∾˜2÷˜≠)⊸⥊ ⟨ +inverse ← {(⊑(0⊏𝕩)⊐<) ⊑ ((1⊏𝕩)∾⟨"⁼: Inverse not found"!0˜⟩)˜} ⍉ (2∾˜2÷˜≠)⊸⥊ ⟨ +, +⊘(-˜) -, - ×, ⊢⊘(÷˜) @@ -522,7 +522,7 @@ inverse ← {(⊑(0⊏𝕩)⊐<) ⊑ ((1⊏𝕩)∾⟨"Inverse not found"!0˜⟩ _repeat_←{ n←𝕨𝔾𝕩 l←u←0 - {"Repetition numbers must be integers"!Int𝕩⋄l↩l⌊𝕩⋄u↩u⌈𝕩}⚇0 n + {"⍟: Repetition numbers in 𝕨 must be integers"!Int𝕩⋄l↩l⌊𝕩⋄u↩u⌈𝕩}⚇0 n a←𝕩⋄_p←{𝔽∘⊣`⟨a⟩∾↕0+𝕩} pos←(𝕨𝔽 ⊢)_p u neg←(𝕨𝔽⁼⊢)_p-l |