DIRECTORY
SafeStorage,
IO,
Atom,
Rope,
Basics,
Imager,
MathExpr;

MathObjects: CEDAR DEFINITIONS
 
= BEGIN

ROPE: TYPE = Rope.ROPE;
STREAM: TYPE = IO.STREAM;
Object: TYPE = REF ObjectRec;

ObjectRec: TYPE = RECORD [
class: Object _ NIL,
data: REF _ NIL
];
Class: TYPE = Object;

MethodType: TYPE = {Value, SideEffect, TrueNullaryOp, NullaryOp, UnaryOp, BinaryOp, BinaryMixedOp, TernaryOp, TernaryMixedOp, QuaternaryOp, LegalFirstCharOp, ReadOp, FromRopeOp, ToRopeOp, ToExprOp, FromExprOp, FromBOOLOp, FromINTOp, UnaryPredicate, BinaryPredicate, CompareToZeroOp, BinaryCompareOp, StructuredToGroundOp, ElementRankOp, UnaryImbedOp, BinaryImbedOp, ListImbedOp, MatrixImbedOp, StructureFromSetConstructor, VectorStructureConstructor, SequenceStructureConstructor, MatrixStructureConstructor, PolynomialStructureConstructor};

Method: TYPE = REF MethodRec;
MethodRec: TYPE = RECORD [
type: ATOM,
name of method's "signature", i.e. numbers and types of inputs and outputs;  used for "dispatch on signature" invocation via a global Alist of method types and applicator procs.  The actual ATOM here is a selector into that global AList.
ApplyToObject: PROC [method: REF, structure: Object, argList: LIST OF Object, recast: BOOL] RETURNS[value: Object];
m: Method;
ok: BOOL _ TRUE;
IF NARROW[method, Method] THEN m _ method ELSE m _ LookupMethodInStructure[method, structure];  -- FALSE => method is an ATOM methodSelector
IF recast THEN [ok, outArgs] _ RecastArgs[m, structure, argList] ELSE outArgs _ argList;
IF ok THEN
ELSE ERROR;
attributes: Atom.PropList, 

argTypes: REF UnaryToListOp _ NIL, -- Proc[Structure -> LIST OF Structure];
If output LIST has i < n = (# args this method) element Classes, then args i, i+1, ..., n expected to belong to last (ith) Class (useful e.g. for vector and matrix constructors).

value: REF -- REF Proc
The "impl" of the method

];

MethodDictionary: TYPE = Atom.PropList;
MakeMethod: PROC [type: MethodType, operator: BOOL, value: REF, desiredArgStructures: REF UnaryToListOp, doc: ROPE] RETURNS[Method];

DesiredArgStructures: PROC [methodSelector: ATOM, structure: Object] RETURNS[LIST OF Object];

DefaultDesiredArgStructures: UnaryToListOp;
GetMethodAndRecastArgs: PROC [methodSelector: ATOM, structure: Object, inArgs: LIST OF Object] RETURNS [ok: BOOL, method: Method, outArgs: LIST OF Object _ NIL];
RecastArgs: PROC [method: Method, structure: Object, inArgs: LIST OF Object] RETURNS [ok: BOOL, outArgs: LIST OF Object _ NIL];

ApplyLegalFirstCharMethod: PROC [method: Method, char: CHAR, structure: Object _ NIL] RETURNS[BOOL];

ApplyFromRopeMethod: PROC [method: Method, in: ROPE, structure: Object _ NIL] RETURNS[Object];

ApplyReadMethod: PROC [method: Method, in: STREAM, structure: Object _ NIL] RETURNS[Object];

ApplyFromExprMethod: PROC [method: Method, in: EXPR, structure: Object] RETURNS[Object];

ApplyCompareToZeroMethod: PROC [method: Method, arg: Object] RETURNS[Basics.Comparison];

ApplyBinaryCompareMethod: PROC [method: Method, firstArg, secondArg: Object] RETURNS[Basics.Comparison];

ApplyBinaryImbedMethod: PROC [method: Method, data1: Object, data2: REF, structure: Object] RETURNS[Object];

ApplyMixedMethod: PROC [method: Method, objectArgs: LIST OF Object, refArg: REF] RETURNS[Object];

ApplyPredNoLkpNoRecast: PROC [method: Method, argList: LIST OF Object] RETURNS[BOOL];

ApplyPredNoLkpRecast: PROC [method: Method, structure: Object, argList: LIST OF Object] RETURNS[BOOL];

ApplyPredLkpNoRecast: PROC [methodSelector: ATOM, structure: Object, argList: LIST OF Object] RETURNS[BOOL];

ApplyPredLkpRecast: PROC [methodSelector: ATOM, structure: Object, argList: LIST OF Object] RETURNS[BOOL];

ApplyNoLkpNoRecastRef: PROC [method: Method, argList: LIST OF Object] RETURNS[value: REF];

ApplyNoLkpRecastRef: PROC [method: Method, structure: Object, argList: LIST OF Object] RETURNS[value: REF];

ApplyLkpNoRecastRef: PROC [methodSelector: ATOM, structure: Object, argList: LIST OF Object] RETURNS[value: REF];

ApplyLkpRecastRef: PROC [methodSelector: ATOM, structure: Object, argList: LIST OF Object] RETURNS[value: REF];

ApplyNoLkpNoRecastObject: PROC [method: Method, argList: LIST OF Object] RETURNS[value: Object];

ApplyNoLkpRecastObject: PROC [method: Method, structure: Object, argList: LIST OF Object] RETURNS[value: Object];

ApplyLkpNoRecastObject: PROC [methodSelector: ATOM, structure: Object, argList: LIST OF Object] RETURNS[value: Object];
ApplyLkpRecastObject: PROC [methodSelector: ATOM, structure: Object, argList: LIST OF Object] RETURNS[value: Object];

ApplyNoLkpNoRecastExpr: PROC [method: Method, argList: LIST OF Object] RETURNS[value: EXPR];
ApplyNoLkpRecastExpr: PROC [method: Method, structure: Object, argList: LIST OF Object] RETURNS[value: EXPR];

ApplyLkpRecastExpr: PROC [methodSelector: ATOM, structure: Object, argList: LIST OF Object] RETURNS[value: EXPR];
ApplyLkpNoRecastExpr: PROC [methodSelector: ATOM, structure: Object, argList: LIST OF Object] RETURNS[value: EXPR];

SideEffect: TYPE = PROC [] RETURNS [];

TrueNullaryOp: TYPE = PROC [] RETURNS [result: Object];

UnaryOp: TYPE = PROC [arg: Object] RETURNS [result: Object];

UnaryPredicate: TYPE = PROC [arg: Object] RETURNS [BOOL];
UnaryInPlaceOp: TYPE = PROC [arg: Object];

UnaryToListOp: TYPE = PROC [arg: Object] RETURNS [result: LIST OF Object];

BinaryOp: TYPE = PROC [firstArg, secondArg: Object] RETURNS [result: Object];

BinaryPredicate: TYPE = PROC [firstArg, secondArg: Object] RETURNS [BOOL];

EqualityOp: TYPE = PROC [firstArg, secondArg: Object] RETURNS [BOOL]; -- redundant

BinaryInPlaceOp: TYPE = PROC [firstArg: Object, secondArg: REF];

BinaryMixedOp: TYPE = PROC [firstArg: Object, secondArg: REF] RETURNS [result: Object];

BinaryToPairOp: TYPE = PROC [firstArg: Object, secondArg: REF] RETURNS [firstResult, secondResult: Object];

TernaryOp: TYPE = PROC [firstArg, secondArg, thirdArg: Object] RETURNS [result: Object];

TernaryMixedOp: TYPE = PROC [firstArg, secondArg: Object, thirdArg: REF] RETURNS [result: Object];

QuaternaryOp: TYPE = PROC [firstArg, secondArg, thirdArg, fourthArg: Object] RETURNS [result: Object];
MakeClass: PROC [name: Rope.ROPE, superClass: Object, methodDictionary: MethodDictionary _ NIL] RETURNS[class: Object];

AddMethodToClass: PROC [methodSelector: ATOM, method: Method, class: Object];

SetSuperClass: PROC [object: Object, superClass: Object];
LookupMethodInClass: PROC [methodSelector: ATOM, class: Object] RETURNS[method: Method];
BuildClassOperators: PROC [class: Object] RETURNS[opNames: LIST OF ROPE, operators: LIST OF Method];
Category: TYPE ~  {set, lattice, group, ring, field, module, vectorSpace, algebra, divisionAlgebra};
PrintNameProc: TYPE = PROC [structure: Object] RETURNS [Rope.ROPE]; -- redundant with ToRopeOp

StructureToExprOp: TYPE = PROC [structure: Object] RETURNS [out: EXPR];

StructureEqualityTest: TYPE = PROC [thisStructure, otherStructure: Object] RETURNS [BOOL];

StructureRankOp: TYPE = PROC [structure: Object] RETURNS [CARDINAL];
ReportOpsProc: TYPE = PROC [structure: Object] RETURNS [opNames: LIST OF Rope.ROPE, refOps: LIST OF REF];
BinaryStructureLUBOp: TYPE = PROC [firstStructure, secondStructure: Object] RETURNS [LUBStructure: Object];
StructureFromSetConstructor: TYPE = PROC [set: Object] RETURNS [structure: Object];

VectorStructureConstructor: TYPE = PROC [coordinateStructure: Object, dimension: NAT, row: BOOL _ TRUE] RETURNS [vectorStructure: Object];

SequenceStructureConstructor: TYPE = PROC [elementStructure: Object, row: BOOL _ TRUE] RETURNS [sequenceStructure: Object];

MatrixStructureConstructor: TYPE = PROC [elementStructure: Object, nRows, nCols: NAT] RETURNS [matrixStructure: Object];

PolynomialStructureConstructor: TYPE = PROC [coeffRing, variableSeq: Object] RETURNS [polynomialStructure: Object];
IsCategory: PROC [structure: Object, category: Category] RETURNS [BOOL];

HasProperty: PROC [structure: Object, property: ATOM] RETURNS [BOOL];

MakeStructure: PROC [name: Rope.ROPE, class: Object, instanceData: REF] RETURNS[structure: Object];

StructureEqual: PROC [structure1, structure2: Object] RETURNS [BOOL];
LookupMethodInStructure: PROC [methodSelector: ATOM, structure: Object] RETURNS[Method];
LookupMethodInAllStructures: PROC [methodSelector: ATOM] RETURNS[method: Method, structure: Object];
ResetStructureRegistry: PROC[];

InstallStructure: PROC[structure: Object];

LookupStructure: PROC[name: ROPE] RETURNS[structure: Object];
KillStructure: PROC[name: ROPE];

LegalFirstCharOp: TYPE = PROC [char: CHAR, structure: Object] RETURNS [BOOL];
ReadOp: TYPE = PROC [in: IO.STREAM, structure: Object _ NIL] RETURNS [out: Object];

FromRopeOp: TYPE = PROC [in: Rope.ROPE, structure: Object _ NIL] RETURNS [out: Object];

ToRopeOp: TYPE = PROC [in: Object] RETURNS [out: Rope.ROPE];

WriteOp: TYPE = PROC [stream: IO.STREAM, in: Object];

FromExprOp: TYPE = PROC [in: EXPR, structure: Object] RETURNS [out: Object];

ToExprOp: TYPE = PROC [in: Object] RETURNS [out: EXPR];

FromBOOLOp: TYPE = PROC [in: BOOL, structure: Object _ NIL] RETURNS [out: Object];

FromINTOp: TYPE = PROC [in: INT, structure: Object _ NIL] RETURNS [out: Object];

NullaryOp: TYPE = PROC[structure: Object] RETURNS [result: Object];

CompareToZeroOp: TYPE = PROC [arg: Object] RETURNS [Basics.Comparison];

BinaryCompareOp: TYPE = PROC [firstArg, secondArg: Object] RETURNS [Basics.Comparison];

StructuredToGroundOp: TYPE = PROC [structuredElt: Object] RETURNS [groundElement: Object];
ElementRankOp: TYPE = PROC [arg: Object] RETURNS [CARDINAL];
Display2DOp: TYPE = PROC [object: Object, context: Imager.Context, dotWidth, segmentWidth: REAL];
Copy: UnaryOp;

ElementOf: PROC [object: Object, structure: Object] RETURNS [BOOL];
UnaryImbedOp: TYPE = PROC [in: Object, structure: Object] RETURNS [out: Object];
BinaryImbedOp: TYPE = PROC [data1: Object, data2: REF, structure: Object] RETURNS [out: Object];
ListImbedOp: TYPE = PROC [data: LIST OF Object, structure: Object] RETURNS [out: Object];
MatrixImbedOp: TYPE = PROC [elements: LIST OF Object, structure: Object] RETURNS [out: Object];

END.

,x
MathObjects.mesa
Copyright c 1989 by Xerox Corporation.  All rights reserved.
Arnon, August 28, 1989 1:42:36 pm PDT

Types From Imported Interfaces
Object Types
Class Type
We intentionally do not here specify the form of the .class or .data fields of classes.  We generally do expect, however, that the .data field of a class will contain a MethodDictionary as defined below.
Method Types
The following data gets moved into IMPL, to be stored in global AList of method types and applicator functions
Properties can be implemented as Methods of type "Value";  but really should be stored using fields or a property list in the class's .data

Should the system be able to "verbalize" the list of names and signature specs, so e.g. an external client can get the info?
Using m.type, search global AList of method types and applicator functions; when found, pass m and outArgs to applicator; it will make appropriate extracts from outArgs and pass to appropriate narrowing of m.value.

"constant" attributes stored e.g. as [$commutative, $commutative];  NIL value field would confuse with absence of attribute
Dynamic type checking of Object args to this method;  none done if = NIL
Construed as "desired" arg classes:  assume, for example, that the args of this method are expected to be Elements (and not Structures).  Here is the processing we will do to RecastArgs.  Consider arg A with Structure S (S is either a Domain or View).  If desired Structure Q is a Domain, and Q # S, we try to convert A into Q by first trying Q's Widen and Narrow procs (for direct Sub or Super Domain relations), then try to find a path from S to Q in the global Domain lattice.  We may fail and exit.  If Q is a Category, let C be S's Category.  First check Q = C, or Q is a superCategory of C via "basic" inheritance, or via the global Category lattice.  If success, create a (new Structure which is a) View V of S as Q, and create a new Object whose class is V and whose data is A.data.  Suppose Q is a View, with underlying Domain D.  Suppose S is a Domain.  Then, as above, see if S can be converted to D;  if so, then make the appropriate new Object in Q corresponding to A.  If S is a View, then let D' be its underlying Domain, see if D' can be converted to D as above; if so, make the appropriate new Object in Q corresponding to A.
Need some way to selectively turn off this type checking, e.g. if any Object ok, or if REF, ROPE, or INT args ok.  Perhaps can have notions of CedarType[INT], or CedarType[REF].
Should MethodDictionary's, or some portion of the info in them, be "externalizable" , or Objects, so that a domain or category can report info about itself?
A method's methodKey, i.e. methodSelector, should serve as the method's "name" for any external purpose, e.g. user menu entry, or "logging" of a method application;  should be identical to what some parser expects to be able to construct a MethodApplication object.
Note that we need to plan NOW for universal names, so we don't get into $sum, $Sum, $add confusions.

Method Operations
Does method lookup
RETURN[ LIST[structure] ];  (arg is expected to be a Structure)

Lookup method in structure, and recast args

Try to recast args
LookupMethodForStructure, RETURN[NARROW[ApplyNoLkpNoRecastRef]].
Error if anything at all goes wrong.
Apply method from structure.  It is assumed that method exists, and that correct number and types of args are supplied.
LookupMethodForStructure, RETURN[NARROW[ApplyNoLkpNoRecastRef]].
Error if anything at all goes wrong.
ApplyNoLkpNoRecastRef[GetMethodAndRecastArgs];  It is assumed that method exists, that correct number of args are supplied, and that args are recastable to desiredArgStructure. Error if anything at all goes wrong.
ERROR if method output type is not imbeddable as an Object
LookupMethodForStructure, RETURN[NARROW[ApplyNoLkpNoRecastRef]].
Error if anything at all goes wrong.


ApplyNoLkpNoRecastObject[GetMethodAndRecastArgs];  It is assumed that method exists, that correct number of args are supplied, and that args are recastable to desiredArgStructure. Error if anything at all goes wrong.
RETURN[NARROW[ApplyNoLkpNoRecastRef]].
Error if anything at all goes wrong.

LookupMethodForStructure, RETURN[NARROW[ApplyNoLkpNoRecastRef]].
Error if anything at all goes wrong.

LookupMethodForStructure, RETURN[NARROW[ApplyNoLkpNoRecastRef]].
Error if anything at all goes wrong.
Object (all Flavors) Operation Types

Class Operations
Typically a class is created with MethodDictionary = NIL, then MethodDictionary loaded with AddMethodToClass
Existing method, if any (generally there shouldn't be), is replaced
Sets class field of a Class, or class.class field of a Structure

Look up method in this class and its superclasses.

Structure Categories
Structure Operation Types
Identify the particular structure to the world.
Test whether some other structure is the same algebraic domain as this one
For things like ring characteristic (smallest positive integer k such that k*1 = 0;  0 if k infinite) and vector space dimension.

Report structure operations to outside world, e.g. a user interface
Should be made a concrete proc to be applied to method dictionaries

If either Structure NIL, return other
Structure Constructor Types
Make a Structure whose (finite) underlying set is the given argument.
A particular vector structure is defined by its coordinateStructure, which can be any Structure, its dimension, and whether its elements are displayed as rows or columns.
A particular sequence structure is defined by its elementStructure, which can be any Structure, and whether its elements are displayed as rows or columns.
A particular matrix structure is defined by its elementStructure and its nRows, nCols. elementStructure can be a ring, field, algebra, or divisionAlgebra.
A particular polynomial structure is defined by its coeffRing and its variables.
coeffRing can be a ring, field, algebra, or divisionAlgebra.
variableSeq is a sequence of any length, and the right thing happens.
Structure Operations
RETURN[structure1.name = structure2.name]

LookupMethodInClass[structure.class]

Linear search of StructureRegistry, LookupMethodForStructure until found or EOF.  If found, then structure is Structure where found.  Returns [NIL, NIL] if not found.
Structure Registry
Structures have nonNIL names. Mathematically different Structures have different names.

A central registry of Structures is kept, and we never have more than one instance of a given mathematical structure in existence. 

effects:  Installs structure in global StructureRegistry database. Replaces existing occurrence of a Structure with same name, if any, and otherwise places structure at the tail of StructureRegistry.   
effects:  Returns the Structure Object associated with name.
          returns NIL if not found

effects:  delete structure from global StructureRegistry DataBase, if present. Only needed when want to delete a given Structure name entirely, not if just want to replace.
StructureElement Operation Types
  True if char is legal first char in an external rep of a structure element.

Since no object arg, need a hook to structure
For things like determinant and coefficient extraction

For things like degree functions in euclidean domains, rank of matrices


Display an object in a 2D context.
StructureElement Operations
  True if object is an element of structure.  (check equality of its structure's name with this structure's name)

StructureElement Creation Types
Imbed in as an element of structure

Construct an element of structure from data1 and data2.
Sample use: constructing a term of a polynomial.

Construct an element of a point, sequence, or vector Structure from data

Construct an element of a matrix Structure from data.  Assumes that correct number of elements supplied, in correct order, and that each element supplied belongs to structure.elementStructure
*Old* Structure Class Record Defn
Category: TYPE = {set, lattice, group, ring, field, module, vectorSpace, algebra, divisionAlgebra};

ClassData: TYPE = REF ClassDataRec;
ClassDataRec: TYPE = RECORD [

Structure properties and operations
category: Category,

flavor: Rope.ROPE _ NIL,
Flavor identifies outermost constructor (if any) used to build objects of this structure.  Is a rope to allow expansion without interface changes. Examples:
"Ints"
"BigRats"
"Points"
"Polynomials"
"Matrices"
"Quotients"
"Structures"

printName: PrintNameProc,
longNameGenerator: PrintNameProc,
shortPrintName: PrintNameProc,  -- if none, should be set to printName
shortNameGenerator: PrintNameProc,  -- if none, should be set to printName
code: Rope.ROPE, -- for quick checks of structure equality
structureEqual: StructureEqualityTest, -- should use codes
characteristic: StructureRankOp _ NIL, -- rings, fields, modules, vector spaces, algebras, divisionAlgebras only
dimension: StructureRankOp _ NIL,-- modules, vector spaces, algebras, divisionAlgebras only
reportOps: ReportOpsProc _ NIL,


Test whether a given item belongs to this structure (run-time typechecking): check equality of its structure's code with this structure's code.
isElementOf: ElementOfProc,

I/O and Conversion of Structure elements
legalFirstChar: LegalFirstCharOp,
read: ReadOp,
fromRope: FromRopeOp,
toRope: ToRopeOp,
write: WriteOp,
fromExpr: FromExprOp _ NIL,
toExpr: ToExprOp _ NIL,
toIndexRope: ToRopeOp, -- print short object key (for use in sequences of objects)  
recast: UnaryImbedOp _ NIL, -- convert an element of a structure that conforms to this one (should be a noop on elements of this structure). Should use fastest available determination of structure, e.g. hashCode or shortPrintName.

Addition (lattices, rings, fields, vectorSpaces, algebras, divisionAlgebras only)
add: BinaryOp _ NIL,
negate: UnaryOp _ NIL,
subtract: BinaryOp _ NIL,
zero: NullaryOp _ NIL,

Multiplication (lattices, groups, rings, fields, algebras, divisionAlgebras only)
multiply: BinaryOp _ NIL, -- assumed associative; commutative or noncommutative ok
commutative: BOOL _ TRUE,
invert: UnaryOp _ NIL,
divide: BinaryOp _ NIL, -- (lattices only) set difference operation goes here if appropriate
one: NullaryOp,

Equality testing 
equal: EqualityOp _ NIL,  -- need not be present in sets and lattices

Module ops
rightModule: BOOL _ FALSE,  -- modules are left modules by default

Scalar multiplication (modules, vectorSpaces, algebras, divisionAlgebras only)
scalarMultiply: BinaryOp _ NIL, -- unless rightModule, this is left multiplication, i.e. scalar * vector. The underlying field of a vector space may be commutative or noncommutative.

Lattice ops
booleanAlgebra: BOOL _ FALSE,
complement: UnaryOp _ NIL,

Ordered structure ops (rings, fields, modules, vectorSpaces, algebras, divisionAlgebras only)
ordered: BOOL _ FALSE,
sign: CompareToZeroOp _ NIL,
abs: UnaryOp _ NIL,
compare: BinaryCompareOp _ NIL,

Common varieties of rings (and algebras) and their ops
integralDomain: BOOL _ FALSE,
gcdDomain: BOOL _ FALSE,
gcd: BinaryOp _ NIL, -- gcdDomains only
euclideanDomain: BOOL _ FALSE,
remainder: BinaryOp _ NIL, -- euclideanDomains only
degree: ElementRankOp _ NIL, -- euclideanDomains only

Common varieties of fields (and divisionAlgebras) and their ops
completeField: BOOL _ FALSE,
realField: BOOL _ FALSE,
realClosedField: BOOL _ FALSE,
algebraicallyClosedField: BOOL _ FALSE,

propList: Atom.PropList _ NIL
];
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