MathExpr.mesa
Carl Waldspurger, August 14, 1986 6:36:20 pm PDT
Definitions for Mathematics Expressions
DIRECTORY
MathRules USING [AtomBoxProc, AtomPaintProc, CompoundBoxProc, CompositionProc, AtomToRopeProc, Size],
MathBox USING [BOX],
MathTypes USING [Style, AtomValue, FormatClass],
ImagerFont USING [Extents],
Vector USING [VEC],
Rope USING [ROPE];
MathExpr: CEDAR DEFINITIONS ~
BEGIN
Abbreviations from Imported Interfaces
ROPE: TYPE ~ Rope.ROPE;
VEC: TYPE ~ Vector.VEC;
BOX: TYPE ~ MathBox.BOX;
Style: TYPE ~ MathTypes.Style;
FormatClass: TYPE ~ MathTypes.FormatClass;
AtomValue: TYPE ~ MathTypes.AtomValue;
AtomBoxProc: TYPE ~ MathRules.AtomBoxProc;
AtomPaintProc: TYPE ~ MathRules.AtomPaintProc;
CompoundBoxProc: TYPE ~ MathRules.CompoundBoxProc;
CompositionProc: TYPE ~ MathRules.CompositionProc;
AtomToRopeProc: TYPE ~ MathRules.AtomToRopeProc;
Size: TYPE ~ MathRules.Size;
Mathematics Expressions
An EXPR is an IMMUTABLE mathematical expression with formatting information.
EXPR: TYPE ~ REF MathExprRep; -- external abstract type
MathExprRep: TYPE; -- internal concrete rep
AtomEXPR: TYPE ~ REF AtomExprRep; -- abstract
AtomExprRep: TYPE; -- concrete
CompoundEXPR: TYPE ~ REF CompoundExprRep; -- abstract
CompoundExprRep: TYPE; -- concrete
MatrixEXPR: TYPE ~ REF MatrixExprRep; -- abstract
MatrixExprRep: TYPE; -- concrete
ExprFlavors: TYPE ~ {atom, compound, matrix};
TaggedMathExpr: TYPE ~
RECORD [
id: ATOM,
expression: EXPR
];
Expression Class Type Definitions
AtomFlavor: TYPE ~ {symbol, argument, placeholder};
AtomClass: TYPE ~ REF AtomClassRep;
AtomClassRep: TYPE ~
RECORD [
name: ATOM, -- class identifier, e.g. $integer
formatClass: FormatClass, -- e.g. atom
flavor: AtomFlavor, -- type of atom: symbol, argument, placeholder
style: Style, -- font info
boxRule: MathRules.AtomBoxProc, -- returns info about atom size
paintRule: MathRules.AtomPaintProc, -- paints atom onto imager context
cvtRope: MathRules.AtomToRopeProc -- returns value as rope
];
CompoundClass: TYPE ~ REF CompoundClassRep;
CompoundClassRep: TYPE ~
RECORD [
name: ATOM, -- class identifier, e.g. $product
formatClass: FormatClass, -- e.g. binaryOp
description: ROPE, -- for menu buttons, etc. to describe how expr looks, e.g. "a + b"
arguments: LIST OF Argument,
symbols: LIST OF Symbol,
boxRule: MathRules.CompoundBoxProc,
compBox: MathRules.CompositionProc,
cvtAS: ROPENIL -- conversion specification to Dennis Arnon's AlgebraSystem
];
MatrixFlavor: TYPE ~ RECORD [
class: ATOM, -- type of matrix expr, e.g. matrix or determinant
formatClass: FormatClass -- e.g. matrix
];
Other Types
Argument: TYPE ~ RECORD [
name: ATOM, -- unique (within enclosing class) identifier for argument
aliases: LIST OF ATOM, -- aliases for name using convention $aliasFoo, $aliasBar
size: Size -- relative sizing information (big, script, etc.)
];
Symbol: TYPE ~ RECORD[
name: ATOM, -- unique (within enclosing class) identifier for symbol
aliases: LIST OF ATOM, -- aliases for name using convention $aliasFoo, $aliasBar
size: Size, -- relative sizing information (big, script, etc.)
value: EXPR -- a symbol is an expression
];
Constructors
Primitive Constructors
MakeArgument: PROC[name: ATOM, aliases: LIST OF ATOM, size: Size] RETURNS[Argument];
effects: constructs and returns an argument object
MakeSymbol: PROC[name: ATOM, aliases: LIST OF ATOM, size: Size, value: EXPR] RETURNS[Symbol];
effects: constructs and returns a symbol object
MakeAtomClass: PROC[name: ATOM, formatClass: FormatClass, flavor: AtomFlavor, style: Style, boxRule: AtomBoxProc, paintRule: AtomPaintProc, cvtRope: AtomToRopeProc] RETURNS[AtomClass];
effects: constructs and returns a new atom class object
MakeCompoundClass: PROC[name: ATOM, formatClass: FormatClass, description: ROPE, args: LIST OF Argument, syms: LIST OF Symbol, boxRule: CompoundBoxProc, compBox: CompositionProc, cvtAS: ROPENIL] RETURNS[CompoundClass];
effects: constructs and returns a new compound class object
MakeAtomChar: PROC[c: CHAR] RETURNS[AtomValue];
effects: Constructs and returns a new atom value of type char
MakeAtomRope: PROC[r: ROPE] RETURNS[AtomValue];
effects: Constructs and returns a new atom value of type rope
MakeAtomBox: PROC[b: ImagerFont.Extents] RETURNS[AtomValue];
effects: Constructs and returns a new atom value of type box.
MakeAtomOther: PROC[other: REF ANY] RETURNS[AtomValue];
effects: COnstructs and returns a new atom value of type other
Math Expression Constructors
MakeAtomicExpr: PROC[class: ATOM, value: AtomValue] RETURNS[EXPR];
effects: constructs and returns a new atomic expression object
SIGNALS badAtomClass if class is unrecognized
MakeCompoundExpr: PROC[class: ATOM, args: LIST OF TaggedMathExpr] RETURNS[EXPR];
effects: constructs and returns a new compound expression object
SIGNALS badCompoundClass if class is unrecognized
SIGNALS badExprs if exprs has the wrong number or wrong type of elements
MakeMatrixExpr: PROC[flavor: MatrixFlavor, nRows, nCols: NAT, elements: LIST OF TaggedMathExpr, openSym, closeSym, space: EXPR] RETURNS[EXPR];
effects: constructs and returns a new matrix expression object
SIGNALS badMatrixSize if nRows or nCols is invalid
SIGNALS badMatrix if rows has the wrong number or wrong type of elements
Selectors
GetType: PROC[expr: EXPR] RETURNS[ExprFlavors];
effect: Returns atom if expr is an AtomEXPR,
Returns compound if expr is a CompoundEXPR
GetAtomClass: PROC[expr: AtomEXPR] RETURNS[AtomClass];
effects: Returns the class of atomic expression expr.
GetAtomExpr: PROC[expr: EXPR] RETURNS[AtomEXPR];
effects: If expr.Type = atom, returns atomic expression.
Otherwise SIGNALS wrongExprType
GetValue: PROC[expr: AtomEXPR] RETURNS[AtomValue];
effects: Returns the value of atomic expression expr.
GetCompoundClass: PROC[expr: CompoundEXPR] RETURNS[CompoundClass];
effects: Returns the class of compound expression expr.
GetCompoundExpr: PROC[expr: EXPR] RETURNS[CompoundEXPR];
effects: If expr.Type = compound, returns compound expression.
Otherwise SIGNALS wrongExprType
GetMatrixExpr: PROC[expr: EXPR] RETURNS[MatrixEXPR];
effects: IF expr.Type[] = matrix, returns matrix expression
Otherwise SIGNALS wrongExprType
GetSubExprs: PROC[expr: CompoundEXPR] RETURNS[LIST OF TaggedMathExpr];
effects: Returns the subexpressions for compound expression expr.
GetMatrixElements: PROC[expr: MatrixEXPR] RETURNS[LIST OF TaggedMathExpr];
effects: Returns the rows of expression for matrix expression expr.
GetMatrixSize: PROC[expr: MatrixEXPR] RETURNS[NAT, NAT];
effects: Returns the size (dimensions) of expr as [nRows, nCols]
GetMatrixFlavor: PROC[expr: MatrixEXPR] RETURNS[MatrixFlavor];
effects: Returns the flavor of expr.
GetMatrixOpenSym: PROC[expr: MatrixEXPR] RETURNS[EXPR];
effects: Returns open symbol expression of expr
GetMatrixCloseSym: PROC[expr: MatrixEXPR] RETURNS[EXPR];
effects: Returns close symbol expression of expr
GetMatrixSpace: PROC[expr: MatrixEXPR] RETURNS[EXPR];
effects: Returns space expression of expr
List Selectors
GetTaggedExpr: PROC[tag: ATOM, exprs: LIST OF TaggedMathExpr] RETURNS[TaggedMathExpr];
effects: Returns the TaggedMathExpr in exprs associated with tag.
SIGNALS exprNotFound if no association exists.
Signals & Errors
badAtomClass: ERROR;
badCompoundClass: ERROR;
badExprs: ERROR[reason: ATOM];
exprNotFound: ERROR;
wrongExprType: ERROR;
invalidReplacement: ERROR;
END.