[Indigo]<AlgebraStructures>MathExprClassesObject.mesa!9

MathExprClassesObject.mesa

Carl Waldspurger, August 30, 1986 7:12:37 pm PDT

Bier, November 20, 1986 2:02:38 pm PST

Arnon, March 24, 1987 4:15:31 pm PST

Mcisaac, August 19, 1987 5:33:35 pm PDT

DIRECTORY

MathExpr,

MathRules,

MathDB,

MathTypes,

MathBox,

ImagerFont,

ImagerTransformation,

Imager,

Rope,

Real,

Vector,

Convert,

MathConstructors;

MathExprClassesObject: CEDAR PROGRAM

IMPORTS MathBox, MathRules, ImagerFont, Imager, ImagerTransformation, MathExpr,

MathDB, Convert, Rope, Real, MathConstructors

BEGIN

Type Abbreviations from Imported Interfaces

EXPR: TYPE ~ MathExpr.EXPR;

BOX: TYPE ~ MathBox.BOX;

ROPE: TYPE ~ Rope.ROPE;

VEC: TYPE ~ Vector.VEC;

AtomBoxProc: TYPE ~ MathRules.AtomBoxProc;

AtomPaintProc: TYPE ~ MathRules.AtomPaintProc;

AtomToASRopeProc: TYPE ~ MathRules.AtomToASRopeProc;

AtomClass: TYPE ~ MathExpr.AtomClass;

AtomFlavor: TYPE ~ MathExpr.AtomFlavor;

FormatClass: TYPE ~ MathTypes.FormatClass;

MatrixClass: TYPE ~ MathExpr.MatrixClass;

Style: TYPE ~ MathTypes.Style;

CompoundBoxProc: TYPE ~ MathRules.CompoundBoxProc;

CompositionProc: TYPE ~ MathRules.CompositionProc;

Alignment2D: TYPE ~ MathRules.Alignment2D;

Offset: TYPE ~ MathRules.Offset;

Size: TYPE ~ MathRules.Size;

Argument: TYPE ~ MathExpr.Argument;

Symbol: TYPE ~ MathExpr.Symbol;

CompoundClass: TYPE ~ MathExpr.CompoundClass;

Procedure Abbreviations from Imported Interfaces

MakeAtomClass: PROC[name: ATOM, formatClass: FormatClass, flavor: AtomFlavor, style: Style, boxRule: AtomBoxProc, paintRule: AtomPaintProc, cvtASRule, cvtReduceRule, cvtSMPRule, cvtOtherRule: AtomToASRopeProc ← NIL] RETURNS[AtomClass] ~ MathExpr.MakeAtomClass;

MakeArgument: PROC[name: ATOM, aliases: LIST OF ATOM, size: Size] RETURNS[Argument] ~ MathExpr.MakeArgument;

MakeSymbol: PROC[name: ATOM, aliases: LIST OF ATOM, size: Size, value: EXPR] RETURNS[Symbol] ~ MathExpr.MakeSymbol;

MakeCompoundClass: PROC[name: ATOM, formatClass: FormatClass, description: ROPE, args: LIST OF Argument, syms: LIST OF Symbol, boxRule: CompoundBoxProc, compBox: CompositionProc, cvtAS, cvtReduce, cvtSMP, cvtOther: ROPE ← NIL] RETURNS[CompoundClass] ~ MathExpr.MakeCompoundClass;

Constants

smallGap: REAL = 0.05;

medGap: REAL = 0.10;

bigGap: REAL = 0.25;

Common AtomToASRope Procs

GreekVarToASRope: AtomToASRopeProc ~ {

IF value.Length[] < 1 THEN RETURN["unknown"]

ELSE RETURN[MathConstructors.CharToGreekName[value.Fetch[0]]];

};

UnknownToASRope: AtomToASRopeProc ~ {

RETURN["?"];

};

InfinityToASRope: AtomToASRopeProc ~ {

RETURN["infinity"];

};

rightArrowToASRope: AtomToASRopeProc ~ {

RETURN["rightArrow"];

};

barToASRope: AtomToASRopeProc ~ {

RETURN["bar"];

};

perpToASRope: AtomToASRopeProc ~ {

RETURN["perp"];

};

Common Atom Box Procs

LineBox: AtomBoxProc ~ {

effects: Returns a bounding box for a line

Note that this is always a dummy value (dsa - because lines will always occur as part of a CompoundExpr, and the line will then be scaled appropriately by the CompoundExpr's BoxProc.)

don't really need any data from value; always returns protoypical line size

RETURN[[leftExtent: 0.0, rightExtent: 1.0, descent: 0.0, ascent: 0.03]];

};

CharBox: AtomBoxProc ~ {

effects: Returns a bounding box for value

font: ImagerFont.Font ← ImagerFont.Scale[ImagerFont.Find[style.font], style.scale];

RETURN[ImagerFont.RopeBoundingBox[font, value]];

};

OverlayBox: AtomBoxProc ~ {

effects: Returns a bounding box for value as a sequence of overlayed chars

font: ImagerFont.Font ← ImagerFont.Scale[ImagerFont.Find[style.font], style.scale];

farLeft, farRight, farUp, farDown: REAL ← 0.0; -- extreme edges of overlayed extents

FOR i:INT IN [0..value.Length[]-1] DO

box: ImagerFont.Extents ← ImagerFont.RopeBoundingBox[font, value.Substr[i, 1]];

farLeft ← MAX[farLeft, box.leftExtent];

farRight ← MAX[farRight, box.rightExtent];

farUp ← MAX[farUp, box.ascent];

farDown ← MAX[farDown, box.descent];

ENDLOOP;

RETURN[[leftExtent: farLeft, rightExtent: farRight, descent: farDown, ascent: farUp]];

};

RopeBox: AtomBoxProc ~ {

effects: Returns a bounding box for value

font: ImagerFont.Font ← ImagerFont.Scale[ImagerFont.Find[style.font], style.scale];

RETURN[ImagerFont.RopeBoundingBox[font, value]];

};

SpaceBox: AtomBoxProc ~ {

effects: Returns a bounding box for value (dsa - style appears irrelevant for this one).

size: ATOM ← Convert.AtomFromRope[value];

RETURN[

SELECT size FROM

$null => [leftExtent: 0.0, rightExtent: 0.001, descent: 0.0, ascent: 0.001],

$thin => [leftExtent: 0.0, rightExtent: 0.05, ascent: 0.05, descent: 0.0],

$medium => [leftExtent: 0.0, rightExtent: 0.12, ascent: 0.12, descent: 0.0],

$thick => [leftExtent: 0.0, rightExtent: 0.25, ascent: 0.25, descent: 0.0],

$veryThick => [leftExtent: 0.0, rightExtent: 0.4, ascent: 0.4, descent: 0.0],

$matrix => [leftExtent: 0.0, rightExtent: 0.9, ascent: 0.65, descent: 0.0],

$limit => [leftExtent: 0.0, rightExtent: 0.25, ascent: 0.12, descent: 0.0],

$product => [leftExtent: 0.0, rightExtent: 0.001, ascent: 0.21, descent: -0.19]

default to $thin

ENDCASE => [leftExtent: 0.0, rightExtent: 0.05, ascent: 0.05, descent: 0.0]

];

};

Common Atom Paint Procs

PaintChar: AtomPaintProc ~ {

effects: Paints value onto context in absBox

check type

IF (absBox.Type[] # absolute) THEN ERROR wrongBoxType

ELSE {

font: ImagerFont.Font ← ImagerFont.Find[style.font];

extents: ImagerFont.Extents ← ImagerFont.RopeBoundingBox[font, value];

xFactor: REAL ← Real.Float[Real.Fix[100*absBox.Width[] / (extents.rightExtent + extents.leftExtent)]]/100;

yFactor: REAL ← Real.Float[Real.Fix[100*absBox.Height[] / (extents.ascent + extents.descent)]]/100;

Imager.SetXY[context, absBox.Offset[]];

Imager.SetFont[context,
ImagerFont.Modify[font, ImagerTransformation.Scale2[[xFactor, yFactor]]]];

Imager.ShowRope[context, value];

};

PaintOverlay: AtomPaintProc ~ {

effects: Paints value as a sequence of centered superimposed characters.

This is useful for things like negated symbols (/ slashed through)...

check types

IF (absBox.Type[] # absolute) THEN ERROR wrongBoxType

ELSE {

font: ImagerFont.Font ← ImagerFont.Find[style.font];

extents: ImagerFont.Extents ← OverlayBox[value, style];

xFactor: REAL ← Real.Float[Real.Fix[100*absBox.Width[] / (extents.rightExtent + extents.leftExtent)]]/100;

yFactor: REAL ← Real.Float[Real.Fix[100*absBox.Height[] / (extents.ascent + extents.descent)]]/100;

scale Font

font ← ImagerFont.Modify[font, ImagerTransformation.Scale2[[xFactor, yFactor]]];

paint chars, one by one, on ope of each other

FOR i:INT IN [0..value.Length[]-1] DO

char: ROPE ← value.Substr[i, 1];

box: ImagerFont.Extents ← ImagerFont.RopeBoundingBox[font, char];

position: VEC ← [MathRules.AlignHorizontal[box, [center], absBox, [center]],

MathRules.AlignVertical[box, [center], absBox, [center]]];

Imager.SetXY[context, position];

Imager.SetFont[context, font];

Imager.ShowRope[context, char];

ENDLOOP;

};

PaintRope: AtomPaintProc ~ {

effects: Paints value onto context in absBox

check types

IF (absBox.Type[] # absolute) THEN ERROR wrongBoxType

ELSE {

font: ImagerFont.Font ← ImagerFont.Find[style.font];

extents: ImagerFont.Extents ← ImagerFont.RopeBoundingBox[font, value];

xFactor: REAL ← Real.Float[Real.Fix[100*absBox.Width[] / (extents.rightExtent + extents.leftExtent)]]/100;

yFactor: REAL ← Real.Float[Real.Fix[100*absBox.Height[] / (extents.ascent + extents.descent)]]/100;

Imager.SetXY[context, absBox.Offset[]];

Imager.SetFont[context,
ImagerFont.Modify[font, ImagerTransformation.Scale2[[xFactor, yFactor]]]];

Imager.ShowRope[context, value];

};

PaintLine: AtomPaintProc ~ {

effects: Paints a line onto context filling absBox

caveats: Ignores value & style

r: Imager.Rectangle ← [x: absBox.Offset[].x + absBox.Extents[].leftExtent, y: absBox.Offset[].y + absBox.Extents[].descent, w: absBox.Width[], h: absBox.Height[]]; -- dsa 4/14/87: claim the + signs here should be - signs

r: Imager.Rectangle ← [x: absBox.Offset[].x - absBox.Extents[].leftExtent, y: absBox.Offset[].y - absBox.Extents[].descent, w: absBox.Width[], h: absBox.Height[]];

Imager.MaskRectangle[context, r];

};

PaintSpace: AtomPaintProc ~ {

effects: none

RETURN;

};

Procs for installing Atom Expression Classes

InstallAtomClasses: PROC [] ~ {

xcs, xci: Style;

integerClass, boolClass, realClass, variableClass, plainSymClass, overlaySymClass, smallMathSymClass, bigMathSymClass, italSymClass, mathItalSymClass, lineClass, placeholderClass, spaceClass, greekVarClass, infinityClass, rightArrowClass, barClass, perpClass: AtomClass;

xerox standard character set

xcs ← [font: "Xerox/XC1-2-2/Classic"];

xci ← [font: "Xerox/XC1-2-2/Classic-italic"];

define Atom Classes

integerClass ← MakeAtomClass[$integer, atom, argument, xcs, RopeBox, PaintRope];

boolClass ← MakeAtomClass[$bool, atom, argument, xcs, RopeBox, PaintRope];

realClass ← MakeAtomClass[$real, atom, argument, xcs, RopeBox, PaintRope];

variableClass ← MakeAtomClass[$variable, atom, argument, xci, RopeBox, PaintRope];

greekVarClass ← MakeAtomClass[$greekVar, atom, argument, xcs, RopeBox, PaintRope, GreekVarToASRope];

plainSymClass ← MakeAtomClass[$plainSym, atom, symbol, xcs, RopeBox, PaintRope]; -- MathConstructors.MakePlainSym

overlaySymClass ← MakeAtomClass[$overlaySym, atom, symbol, xcs, OverlayBox, PaintOverlay]; -- MathConstructors.MakeOverlaySym

bigMathSymClass ← MakeAtomClass[$bigMathSym, atom, symbol, xcs, RopeBox, PaintRope, UnknownToASRope]; -- MathConstructors.MakeBigMathSym

smallMathSymClass ← MakeAtomClass[$smallMathSym, atom, symbol, xcs, RopeBox, PaintRope, UnknownToASRope]; -- MathConstructors.MakeSmallMathSym

mathItalSymClass ← MakeAtomClass[$mathItalicSym, atom, symbol, xci, RopeBox, PaintRope, UnknownToASRope]; -- MathConstructors.MakeMathItalSym

italSymClass ← MakeAtomClass[$italicSym, atom, symbol, xci, RopeBox, PaintRope, UnknownToASRope]; -- MathConstructors.MakeItalSym

lineClass ← MakeAtomClass[$line, atom, symbol, xcs, LineBox, PaintLine];

placeholderClass ← MakeAtomClass[$placeholder, atom, placeholder, xcs, RopeBox, PaintRope, UnknownToASRope];

spaceClass ← MakeAtomClass[$space, atom, symbol, xcs, SpaceBox, PaintSpace];

infinityClass ← MakeAtomClass[$infinity, atom, argument, xcs, RopeBox, PaintRope, InfinityToASRope];

rightArrowClass ← MakeAtomClass[$rightArrow, atom, argument, xcs, RopeBox, PaintRope, rightArrowToASRope];

barClass ← MakeAtomClass[$bar, atom, argument, xcs, RopeBox, PaintRope, barToASRope];

perpClass ← MakeAtomClass[$perp, atom, argument, xcs, RopeBox, PaintRope, barToASRope];

register atom classes

MathDB.InstallAtomClass[integerClass];

MathDB.InstallAtomClass[boolClass];

MathDB.InstallAtomClass[realClass];

MathDB.InstallAtomClass[variableClass];

MathDB.InstallAtomClass[greekVarClass];

MathDB.InstallAtomClass[plainSymClass];

MathDB.InstallAtomClass[overlaySymClass];

MathDB.InstallAtomClass[italSymClass];

MathDB.InstallAtomClass[smallMathSymClass];

MathDB.InstallAtomClass[bigMathSymClass];

MathDB.InstallAtomClass[mathItalSymClass];

MathDB.InstallAtomClass[lineClass];

MathDB.InstallAtomClass[placeholderClass];

MathDB.InstallAtomClass[spaceClass];

MathDB.InstallAtomClass[infinityClass];

MathDB.InstallAtomClass[rightArrowClass];

MathDB.InstallAtomClass[barClass];

MathDB.InstallAtomClass[perpClass];

};

Box Procs for Compound Expr Classes

FixedSizeBoxRule: CompoundBoxProc ~ {

effects: Returns unaltered boxes (i.e. no resizing takes place)

RETURN[boxes];

};

Composition Procs for Compound Expr Classes

ComplexCompRule: CompositionProc ~ {

effects: Composes layout for expr of form ($complex $a $b)

tempBox: BOX;

tempBoxes: LIST OF BOX;

alignments: LIST OF Alignment2D ←

LIST[

[$a, [$plus, [right], [left, -medGap]],

[$plus, [origin], [origin]]],

[$leftParen, [$a, [right], [left, -medGap]],

[$plus, [origin], [origin]]],

[$b, [$plus, [left], [right, medGap]],

[$plus, [origin], [origin]]],

[$i, [$b, [left], [right, medGap]],

[$b, [origin], [origin]]],

[$rightParen, [$i, [left], [right, medGap]],

[$plus, [origin], [origin]]]

];

[tempBox, tempBoxes] ←
MathRules.Compose[boxes, alignments, [$a, [origin]], [$plus, [origin]]];

RETURN[tempBox, tempBoxes];

};

Procs for installing Compound Expression Classes

InstallCompoundClasses: PROC [] ~ {

local declarations

complexClass: CompoundClass;

realPartArg, imaginaryPartArg: Argument;

plusSym, iSym, funLParenSym, funRParenSym: Symbol;

define info for "complex a b" (a + bi)

realPartArg ← MakeArgument[$a, LIST[$aliasA, $aliasHot], normal];

imaginaryPartArg ← MakeArgument[$b, LIST[$aliasB], normal];

iSym ← MakeSymbol[$i, NIL, normal, MathConstructors.MakeItalSym['i]];

plusSym ← MakeSymbol[$plus, LIST[$aliasBinOp], normal, MathConstructors.MakePlainSym['+]];

define info for functions (parens also used by complex)

funLParenSym ← MakeSymbol[$leftParen, NIL, normal, MathConstructors.MakePlainSym['[]];

funRParenSym ← MakeSymbol[$rightParen, NIL, normal, MathConstructors.MakePlainSym[']]];

altFunLP ← MakeSymbol[$leftParen, NIL, normal, MathConstructors.MakeSpace[$null]];

altFunRP ← MakeSymbol[$rightParen, NIL, normal, MathConstructors.MakeSpace[$null]];

complexClass ← MakeCompoundClass[$complex, other, "a + bi", LIST[realPartArg, imaginaryPartArg], LIST[funLParenSym, plusSym, iSym, funRParenSym], FixedSizeBoxRule, ComplexCompRule, "($a + $bi)"];

MathDB.InstallCompoundClass[complexClass];

};

Procs for installing Matrix Expression Classes

InstallMatrixClasses: PROC [] ~ {

setClass, pointClass, sequenceClass, vectorClass, matrixClass: MatrixClass;

setClass ← MathExpr.MakeMatrixClass[$set, matrix, MathConstructors.MakePlainSym['{], MathConstructors.MakePlainSym['}], MathConstructors.MakeSpace[$matrix]]; -- brackets are { }

pointClass ← MathExpr.MakeMatrixClass[$point, matrix, MathConstructors.MakePlainSym[')], MathConstructors.MakePlainSym[')], MathConstructors.MakeSpace[$matrix]]; -- brackets are ( )

sequenceClass ← MathExpr.MakeMatrixClass[$sequence, matrix, MathConstructors.MakePlainSym['<], MathConstructors.MakePlainSym['>], MathConstructors.MakeSpace[$matrix]]; -- brackets are < >

vectorClass ← MathExpr.MakeMatrixClass[$vector, matrix, MathConstructors.MakePlainSym[']], MathConstructors.MakePlainSym[']], MathConstructors.MakeSpace[$matrix]]; -- brackets are [ ]

matrixClass ← MathExpr.MakeMatrixClass[$matrix, matrix, MathConstructors.MakePlainSym['[], MathConstructors.MakePlainSym[']], MathConstructors.MakeSpace[$matrix]]; -- brackets are [ ]

MathDB.InstallMatrixClass[setClass];

MathDB.InstallMatrixClass[pointClass];

MathDB.InstallMatrixClass[sequenceClass];

MathDB.InstallMatrixClass[vectorClass];

MathDB.InstallMatrixClass[matrixClass];

};

Signals & Errors

wrongAtomValueType: PUBLIC ERROR = CODE;

wrongBoxType: PUBLIC ERROR = CODE;

Install Atom and Matrix Classes (Start Code)

InstallAtomClasses[];

InstallCompoundClasses[];

InstallMatrixClasses[];

END.