A

abstract

~ class 11, 101

~ type 173

bounded ~ type

     see partially ~ type

partially ~ type 29, 173

abstraction

bounded type ~ 171

constructor ~ 288

operator ~ 288

type ~ 169, 243

application

constructor ~ 288

operator ~ 288

type ~ 169, 243

assumption (of rule)

see premise judgment

attribute (of object) 12

B

binary method 31, 208, 294

~ in O-1/2/3 157, 274, 308

bounded

~ abstract type

     see partially abstract type

~ existential quantifier 173

~ polymorphism 171

~ type abstraction 171

~ type parameterization 29

~ type variable 171

~ universal quantifier 171, 228, 243, 288

~ universal quantifier in O-2/3 274, 306

C

call-by-

~keyword 67

~name 65

~value 65

call-next-method 16

class 11

~ encoding 73, 100, 124, 144, 209, 214, 237, 295

~ in O-1/2/3 153, 274, 307

~ selection 155, 275, 307

~ type in O-1/2/3 153, 274, 306

abstract ~ 101

concrete ~ 102

leaf ~ 102

root ~ 155, 276, 307

class-based 1, 11, 155, 273, 305

cloning 36, 130

interpretation of ~ 260, 263, 271

closed term 61

closure 136, 147, 244

coalesced sum 186

complete metric space (of cupers) 188

complete uniform per 187

conclusion (of rule) 62, 79

concrete class 102

congruence rule 62

constructor 287

~ abstraction 288

~ application 288

context 62

contractiveness 185, 188, 194, 197

contravariance 21, 28, 94, 116, 178, 231

~ annotation 110, 223

~ of function types 21, 94, 112, 178

~ of universal quantifiers 171

covariance 20, 94, 116, 178, 231

~ annotation 110, 223

~ of existential quantifiers 174

~ of object types 109

~ of product types 20, 111, 179

~ of record types 106, 112, 179

~ requirement for Self types 202, 223

cuper (complete uniform per) 187

cyclic-record interpretation 262, 267

D

default parameters 67

delegation 13, 39, 42

dynamic ~ 46

static ~ 46

delegation-based 42

denotational semantics 185

derivation 63, 79

disjoint union type 122

dispatch

dynamic ~ 18

multiple ~ 53

single ~ 53

static ~ 18

distance (for cupers) 188

dynamic

~ dispatch 18

~ inheritance 46

~ typing 126

     see also typecase

E

elder 108

embedding 13, 39

embedding-based 40

embedding-retraction pair 186

environment (for judgments) 79

environment (semantic) 197

type ~ 197

equational theory 84

~ and self 90

~ for constructors 290

~ for existential quantifiers 174

~ for records 106

~ for recursive types 114

~ for Self quantifiers 181

~ for structural objects 217

~ for subtyping 98

~ for universal quantifiers 171

~ for -objects 203

first-order ~ 89

untyped ~ 62

error value 185

existential

~ quantifier 173

bounded ~ quantifier 173

F

F-bounded parameterization 33

field 12, 58

~ selection 52, 58, 130

~ update 52, 58, 130, 245

imperative ~s 130, 245

finiteness 187, 188

fixpoint

~ of a function on cupers 188

~ of an operator 295

~ operator 68, 92

formal system 79

fragment 79

equational ~ 84

free variable 61, 118, 176

fresh method 239

function 66

~ encoding 66, 91, 112, 115, 131, 178

function type 21, 83

~ encoding 91, 112, 115, 178

contravariance of ~s 21, 94, 112, 178

subtyping of ~s 21, 94

G

grammar notation 60

ground type 82

H

higher-order

~ bounded parameterization 33

~ subtyping 295

     see also subconstructor

host object 9, 38, 57

I

implementation

~ of abstract type 173

~ of inheritance 14

inclusion 287

inheritance 9, 38

~ in O-1/2/3 153, 273, 305

~ of binary methods 30, 297, 305

~-is-not-subtyping 30

dynamic ~ 46

encoding of ~ 74, 100, 209, 238, 295

encoding of multiple ~ 75, 101

explicit ~ 39

implementation of ~ 14

implicit ~ 39

mixin ~ 39

multiple ~ 14, 16, 44, 48

single ~ 16

single ~ in O-1/2/3 153, 273, 305

static ~ 46

inner 16

inspect 20

instance interface 102, 239

interface

~ of abstract type 173

instance ~ 102

subclass ~ 102, 239

interpretation

~ of objects 257

cyclic-record ~ 262, 267

recursive-record ~ 78, 260, 265

self-application ~ 76, 185, 259, 264, 271

split-method ~ 263, 268

state-application ~ 261, 266

invariance 21, 94, 116

~ annotation 110, 223

~ of object types 94

~ of recursive types 116

invariant

object shape ~ 215

recoup ~ 214

structural ~ 216

structural subtyping ~ 215

invocation 13, 18, 39, 42, 52, 58, 59, 129

J

judgment 62, 79

valid ~ 80

K

kind 287

L

leaf class 102

let 130, 245

lifting 186

location 136, 146, 242

M

match-bound

~ quantified type 306

~ type abstraction 306

~ type application 306

matching 33, 305

method 8, 57, 153, 274, 307

~ extraction 14, 93, 106

~ invocation 13, 18, 39, 42, 52, 58, 59, 129

~ lookup 13

~ override 9, 74

~ override in O-1/2/3 153, 273, 307

~ specialization 22, 28, 239, 273, 282

~ suite 13

~ type 146, 247

~ update 14, 37, 52, 58, 59, 129, 210, 224, 241

~ update in O-1/2/3 153, 275, 307

binary ~ 31, 208, 294

binary ~ in O-1/2/3 157, 274, 308

fresh ~ 239

imperative ~ update 129, 241

private ~ 102

protected ~ 102

public ~ 102

recoup ~ 212

virtual ~ 15

metric space

complete ~ (of cupers) 188

minimum types 95, 118

mode-switching 46, 49

multiple

~ dispatch 53

~ inheritance 14, 16, 44, 48

~ subtyping 27

encoding of ~ inheritance 75, 101

N

narrow 20

negative occurrence 177, 223

new 12

~ in O-1/2/3 155, 275, 307

see also class

nonexpansiveness 188, 194, 197

O

object 7, 57

~ extension 38, 60

~ in O-1/2/3 153, 273, 307

~ protocol 25

~ shape invariant 215

~ without class 35

~-orientation 7

donor ~ 38

host ~ 9, 38, 57

prototype ~ 47

structural ~ 216

trait ~ 47

-~ 201

object type 26, 35, 80, 189, 288

~ in O-1/2/3 153, 273, 305

~ with Self 201, 222

covariance of ~s 109

invariance of ~s 94

structural ~ 216

subtyping of ~s 94

-~ 201

object-based 1, 35, 155, 273, 305

occurrence

negative ~ 177, 223

positive ~ 177, 223

operational semantics 64, 86, 120, 127, 135, 224, 228, 242, 244, 289

operator

~ abstraction 288

~ application 288

fixpoint of an ~ 295

type ~ 287

override 9, 74

~ in O-1/2/3 153, 273, 307

P

parametric in Self 125, 211, 237, 274, 281

parent link 42

partial equivalence relation 187

partially abstract type 29, 173

per (partial equivalence relation) 187

polymorphism 169, 274

bounded ~ 171

subtype ~ 17

positive occurrence 177, 223

pre-method 23, 73, 100, 144, 209, 214, 237, 297

premise judgment 62, 79

primitive semantics 58

private method 102

product type 20

~ encoding 111

covariance of ~s 20, 111, 179

projection 186

protected method 102

protocol 32

prototype 36, 47

public method 102

Q

qua 16, 20

quantifier

bounded existential ~ 173

bounded universal ~ 171, 228, 243, 288

bounded universal ~ in O-2/3 274, 306

existential ~ 173

Self ~ 169, 179, 201, 269

universal ~ 170

R

rank 187, 188

record 76, 106, 259

~ encoding 112

record type 106, 179, 264

~ encoding 112, 179

covariance of ~s 106, 112, 179

subtyping of ~s 106

recoup 212

~ invariant 214

recursive type 113

invariance of ~s 116

recursive-record interpretation 78, 260, 265

reduction 61

weak ~ 64

reparent 47

representation type 173, 202

resend 16

result 64, 86, 120, 136, 242, 244, 289

~ typing 146, 248

root class 155, 276, 307

rule 79

~ naming 79

congruence ~ 62

structural ~ 172, 190, 216, 221, 243, 293

S

scoping 61, 118, 176

selection 52

selection (of field) 52, 58, 130

Self

~ quantifier 169, 179, 201, 269

~ type 24, 30, 125, 169, 201, 221, 242, 294

~ type in O-2/3 273, 305

~ type specialization 24

     see also method specialization

parametric in ~ 125, 211, 237, 274, 281

self 9, 57

self-application

~ interpretation 76, 185, 259, 264, 271

~ semantics 185

self-unfolding 202

semantics

denotational ~ 185

operational ~ 64, 86, 120, 127, 135, 224, 228, 242, 244, 289

self-application ~ 185

shallow copy

see cloning

single

~ dispatch 53

~ inheritance 16

~ inheritance in O-1/2/3 153, 273, 305

specialization

method ~ 22, 28, 239, 273, 282

Self type ~ 24

split-method interpretation 263, 268

stack 136, 242

~ type 247

~ typing 147, 248

state-application interpretation 261, 266

static dispatch 18

store 136, 242

~ typing 146, 248

structural

~ invariants 216

~ object 216

~ object type 216

~ rule 172, 190, 216, 221, 243, 293

~ subtyping 172, 190

~ subtyping invariant 215

~ update 172, 190, 222, 243, 293

stuck 87, 138, 152

subclass 15, 27, 30

~ in O-1/2/3 155, 273, 307

~ interface 102, 239

see also class, inheritance

subconstructor 287, 290

see also higher-order subtyping

subject reduction 86, 97, 121, 127, 146, 229, 247, 301

suboperator 295

subprotocol 32

substitution 59, 61, 113, 120

subsumption 18, 93

~ in O-1/2/3 154, 273, 305

subtype polymorphism 17

subtyping 18, 27, 30, 93

~ by type name 27

~ by type structure 27

~ for existential quantifiers 174

~ for function types 21, 94

~ for object types 94

~ for object types with primitive Self and variance 226

~ for object types with Self 204

~ for record types 106

~ for Self quantifiers 180

~ for universal quantifiers 171

~ for variance annotations 110

~ in O-1/2 153, 273

higher-order ~ 295

     see also subconstructor

multiple ~ 27

structural ~ 172, 190

sum, coalesced 186

super 15

~ encoding 74, 101

~ in O-1/2/3 156, 276, 307

syntax notation 60

T

trait 47, 144

~ encoding 73, 101

     see also class encoding

true type 18

type

~ abstraction 169, 243

~ application 169, 243

~ operator 287

~ parameter 28

~ variable 113, 171

abstract ~ 173

bounded ~ parameterization 29

bounded ~ variable 171

bounded abstract ~

     see partially abstract ~

disjoint union ~ 122

dynamic ~ 126

     see also typecase

environment (semantic) 197

function ~ 21, 83

method ~ 146, 247

minimum ~s 95, 118

object ~ 26, 35, 80, 189, 288

object ~ in O-1/2/3 153, 273, 305

object ~ with Self 201, 222

partially abstract ~ 29, 173

product ~ 20

record ~ 106, 179, 264

recursive ~ 113

representation ~ 173, 202

Self ~ 24, 30, 125, 169, 201, 221, 242, 294

Self ~ in O-2/3 273, 305

stack ~ 247

store ~ 146, 248

unique ~s 85

-object ~ 201

typecase 19, 23, 126

~ in O-1/2/3 156, 274, 311

typing environment 79

U

unfolding 202

union type, disjoint 122

unique types 85

unit 122

unit type 122

universal

~ quantifier 170

bounded ~ quantifier 171, 228, 243, 288

bounded ~ quantifier in O-2/3 274, 306

update

field ~ 52, 58, 130, 245

method ~ 14, 37, 52, 58, 59, 129, 210, 224, 241

method ~ in O-1/2/3 153, 275, 307

V

valid judgment 63, 80

variance

see co~, contra~, in~

variance annotations 110, 124, 222

~ in O-1/2/3 154, 274, 307

virtual method 15