The Fortress Language Specification - CiteSeerX

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40.4 Constructing Heap Sequences 40.4.1 makeHeapSequenceT extends Object(n:IndexInt,item: T):HeapSequenceT throws { NegativeLengthException } A new heap sequence of length n is allocated and returned. A NegativeLengthException is thrown if n < 0 . Every element of the heap sequence is initialized to be the same as the given item . 40.4.2 computeHeapSequenceT extends Object(n:IndexInt, f: IndexInt → T): HeapSequenceT throws { NegativeLengthException } A new heap sequence of length n is allocated and returned. A NegativeLengthException is thrown if n < 0 . Element j of the new heap sequence is initialized to a value computed by calling the given function f with argument j . 278
40.5 The Trait Fortress.Core.BinaryWord A value of type BinaryWordb is a binary word of 2 b bits; b may be any natural number, so BinaryWord0 is a bit, BinaryWord3 is a byte, BinaryWord6 is a 64-bit word, and BinaryWord10 is a 1024-bit word. In fact, for convenience, the type abbreviations Bit and Byte are defined: type Bit = BinaryWord0 type Byte = BinaryWord3 The type BinaryWordb has 2 (2b) distinct values. When the binary word is regarded as an unsigned integer, these values are identified with the nonnegative integers that are less than 2 (2b) . A binary word may also be regarded as a signed integer: a value that, when regarded as an unsigned integer, is identified with an integer less than 2 (2b −1) , is identified with that same integer when regarded as a signed integer; but a value that, when regarded as an unsigned integer, is identified with an integer not less than 2 (2b −1) , is identified with that same integer less 2 (2b) . (This is the standard “two’s complement” representation for signed integers.) A binary word of one bit can have one of two values, 0 or 1. A binary word of more than one bit has two halves, a high half and a low half, which are binary words of half the size. If v is the unsigned integer value of a binary word of 2 b bits, b ≥ 1 , h is the unsigned integer value of its high half, and l is the unsigned integer value of its low half, then v = h · 2 2b−1 + l . Operations on binary words include bitwise boolean operations, arithmetic operations, shifts and rotates, population count, and counting of leading and trailing zeros. The type BinaryWordb is not “endian” and has no operations that depend on endianness. However, if w is binary word, then w.littleEndian is a little-endian version of w and w.bigEndian is a big-endian version of w ; for example, if w is of type BinaryWord6 , then w.littleEndian 63 is the most significant bit (the sign bit if the word is regarded as a two’s-complement integer), and w.bigEndian 0 is that same bit. trait BinaryWordnat b extends { BasicBinaryWordOperationsBinaryWordb } comprises {} where { b ≤ maxBinaryWordBitLog } coercion int r(x:IntegerStaticr) where { −2 b−1 ≤ r < 2 b } coercion bool bigEndianBytes,bool bigEndianBits (x:BinaryEndianWordb,bigEndianBytes,bigEndianBits) coercion nat b ′ ,nat n,bool bigEndianSequence (x:BinaryLinearEndianSequenceb ′ , n,bigEndianSequence) where { 2 b = n · 2 b′ } coercion nat b ′ ,bool bigEndianBytes,bool bigEndianBits,nat n,bool bigEndianSequence (x:BinaryEndianLinearEndianSequenceb ′ ,bigEndianBytes,bigEndianBits, n,bigEndianSequence) where { 2 b = n · 2 b′ } bit(m:IndexInt):Bit getter lowHalf ():BinaryWordb − 1 where { b > 0 } getter highHalf ():BinaryWordb − 1 where { b > 0 } opr ‖ nat m(self,other: BinaryWordb): BinaryWordb + 1 where { b < maxBinaryWordBitLog } bitShuffle(other: BinaryWordb):BinaryWordb + 1 where { b < maxBinaryWordBitLog } bitUnshuffle():(BinaryWordb − 1, BinaryWordb − 1) where { b > 0 } end 279
Page 1 and 2:
The Fortress Language Specification
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4 Evaluation 36 4.1 Values . . . .
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12 Functions 85 12.1 Function Decla
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17.7 Coercions for Tuple and Arrow
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IV Fortress for Library Writers 214
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40.10The Trait Fortress.Core.Binary
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Chapter 1 Introduction The Fortress
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A note on the presented libraries i
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component HelloWorld export Executa
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foo:String → () baz: String → S
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fortress upgrade Gary with Ralph No
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halve(x : R64) : R64 = x/2 Predicta
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while x < 10 do print x x += 1 end
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It is also possible to convert a me
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factorial(n) = ∏ i←1:n i This f
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In both methods cons and append , t
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default distributions will provide
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Chapter 3 Programs A program consis
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Chapter 10), a literal (see Section
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(discussed in Section 13.13) to a s
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Chapter 5 Lexical Structure A Fortr
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U+0021 EXCLAMATION MARK ! U+0023 NU
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If a character (or any other syntac
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BIG SI unit absorbs abstract also a
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escape sequences are useful for ASC
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5.14.1 Multicharacter Enclosing Ope
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Note: the elegant way to write Avog
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• top-level variable declarations
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declares id to be a mutable variabl
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several new variables. This syntax
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Chapter 7 Names Names are used to r
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7.3 Qualified Names Fortress provid
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Fortress also allows coercion betwe
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• element types of a tuple type c
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TypeAlias ::= type Id [StaticParams
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‘}’. If such a clause contains
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Note that a trait declaration inher
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the parametric trait WrappedDiction
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Chapter 10 Objects An object is a v
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FldDef ::= FldMod ∗ Id [IsType] (
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Chapter 11 Static Parameters Trait,
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11.5 Operator and Identifier Parame
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Chapter 12 Functions Functions are
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swap(x :Object, y : Object) = (y, x
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A function declaration may be separ
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Chapter 13 Expressions Fortress is
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Negating the literal 0 produces a s
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the function is evaluated with the
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13.10 Assignments Syntax: Expr ::=
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treeSum(t : TreeLeaf) = 0 treeSum(t
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Several common mathematical operato
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The body of each iteration is run i
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to the value of the condition expre
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An atomic expression consists of th
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13.26 Try Expressions Syntax: Flow
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13.27.2 Static Expressions and Valu
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A = [1 2 3; 4 5 6; 7 8 9] then A 1,
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evaluates to the set {0, 4, 16} Map
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ignore(f x) is equivalent to: f x;
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trait CheckedException extends { Ex
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Chapter 15 Overloading and Multiple
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e called with. In other words, we e
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Chapter 16 Operators Operators are
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• “ordinary” operators: + −
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left context whitespace operator fi
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The rules below are designed to for
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16.8.3 Enclosing Operators When use
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16.8.9 Intersection, Union, and Set
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Chapter 17 Conversions and Coercion
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17.3 Coercion Invocations One may i
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arguments nor with variable number
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trait B extends A end trait C exten
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a new coercion in a subexpression
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for tokens. For readability, plural
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Chapter 19 Tests and Properties For
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19.5 Test Suites In order to allow
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Chapter 20 Type Inference Type infe
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3. If a i is a functional applicati
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21.2 Programming Discipline If Fort
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Here the call f(a, a) ends up setti
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2. Ancestors, dynamically ordered b
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The ways in which fortresses are ac
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Component equivalence is determined
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22.5 Type Inference for Components
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Fortress.IO Fortress.Crypto IronLin
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execute(componentName:String, args:
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3. If the replacement does not expo
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This method runs all test functions
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Fortress.IO Fortress.Crypto Fortres
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Part III Fortress APIs and Document
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23.1.3 hash(maxval: N64): N64 23.1.
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opr =(self,other: Boolean):Boolean
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24.1.20 getter hashCode(): N64 24.1
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False: BooleanInterval Uncertain: B
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24.2.11 opr ∧(self,other: Boolean
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24.2.19 possibly(self): Boolean 24.
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Chapter 25 Numbers 25.1 Rational Nu
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opr ⌈self ⌉: N realpart(self):
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25.1.11 opr (self,other: Q):Boolean
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25.1.26 floor(self): Z 25.1.27 opr
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Chapter 26 Negated Relational Opera
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26.1.26 opr ⊀T extends BinaryPred
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27.3 The Trait Fortress.Standard.Un
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Chapter 29 Dimensions and Units 29.
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unit secondOfAngle secondsOfAngle:
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Chapter 30 Tests 30.1 The Object Fo
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31.2 Convenience Types An optional
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Chapter 32 Parallelism and Locality
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y evaluating the two elements of th
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There is a DefaultDistribution whic
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v = spawn at a.region(i) do a i end
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expr ∑ type wrapper ∑ body R,
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32.8.3 Using Overloading to Adapt G
Page 227 and 228: Chapter 33 Overloaded Functional De
Page 229 and 230: coercions: T U ⇐⇒ T ♦ U ∧
Page 231 and 232: The More Specific Rule for Function
Page 233 and 234: An infix/multifix operator declarat
Page 235 and 236: may be so defined except ordinary p
Page 237 and 238: and here some of these computed dim
Page 239 and 240: unit name 1 name 2 name 3 : . . . u
Page 241 and 242: Chapter 36 Support for Domain-Speci
Page 243 and 244: Because syntax expanders are define
Page 245 and 246: Part V Fortress APIs and Documentat
Page 247 and 248: property ∀(a:T) ¬(a ∼ a) end A
Page 249 and 250: trait PartialOrderOperatorsT extend
Page 251 and 252: The HasMinimalElement trait specifi
Page 253 and 254: The trait Commutative requires the
Page 255 and 256: A value e is a left identity for a
Page 257 and 258: trait ApproximatelyHasInverses T ex
Page 259 and 260: end extends { ApproximateCommutativ
Page 261 and 262: A default definition is provided fo
Page 263 and 264: trait RationalQuantityunit U absorb
Page 265 and 266: (self,other:RationalQuantityU,ninf
Page 267 and 268: 38.2.4 getter hashCode(): Z64 38.2.
Page 269 and 270: Chapter 39 Components and APIs We d
Page 271 and 272: Chapter 40 Memory Sequences and Bin
Page 273 and 274: updatenat k(j: IntegerStatick, v: T
Page 275 and 276: 40.1.12 update(j:IndexInt, v: T): L
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Page 281 and 282: 40.5.5 bit(m:IndexInt): Bit The res
Page 283 and 284: 40.6 The Trait Fortress.Core.Binary
Page 285 and 286: 40.6.4 opr nat m[r:RangeOfStaticSiz
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Page 291 and 292: 40.7.41 signedShift(j:IndexInt):T 4
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Page 295 and 296: littleEndian():BinaryEndianLinearEn
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Page 301 and 302: 40.10.9 opr nat m[r:RangeOfStaticSi
Page 303 and 304: 40.10.24 splitnat b ′ () : Binary
Page 305 and 306: itAnd(selfStart: IndexInt,source:T,
Page 307 and 308: 40.13.2 wrappingAdd(selfStart: Inde
Page 309 and 310: 40.13.30 unsignedMax(selfStart: Ind
Page 311 and 312: 40.13.55 gatherBits(selfStart:Index
Page 313 and 314: Appendix A Fortress Calculi A.1 Bas
Page 315 and 316: Values, evaluation contexts, redexe
Page 317 and 318: Expression typing: p; ∆; Γ ⊢ e
Page 319 and 320: α, β type variables f method name
Page 321 and 322: Function/method name lookup: Fname(
Page 323 and 324: One owner for all the visible metho
Page 325 and 326: Traits defining a method: defining
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Valid function declarations: p ⊢
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Method definition lookup: visible p
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Values, intermediate expressions, e
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Field typing: p; ∆; Γ ⊢ vd ok
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Appendix B Overloaded Functional De
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Proof. We prove this for δ, but th
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Upgrade A predicate upg? takes two
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a is rendered as a foobar is render
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• If a portion is sub and another
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supercalifragilisticexpialidocious
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any alternative names, with undersc
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Appendix F Operator Precedence, Cha
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U+007C VERTICAL LINE | | U+2016 DOU
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The following two operators have th
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U+003D EQUALS SIGN = = EQ U+2243 AS
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U+22DD EQUAL TO OR GREATER-THAN U+2
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U+2289 NEITHER A SUPERSET OF NOR EQ
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F.4.8 Miscellaneous Relational Oper
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U+21A5 UPWARDS ARROW FROM BAR U+21A
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U+2224 DOES NOT DIVIDE ∤ U+2225 P
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U+27F8 LONG LEFTWARDS DOUBLE ARROW
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U+2960 UPWARDS HARPOON WITH BARB LE
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U+29ED BLACK CIRCLE WITH DOWN ARROW
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Appendix G Concrete Syntax In this
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Extends ::= extends TraitTypes Excl
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StaticParam ::= Id [Extends] [absor
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Value ::= Literal | fn ValParam [Is
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Appendix H Generated Concrete Synta
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-> fn_decl -> object_decl -> var_de
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-> id extends_opt absorbs_opt -> "n
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-> w "excludes" w type_ref_list com
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-> obj_decl_body_elem br obj_decl_b
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-> op wr op_follows_op_w -> op wr e
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-> no_space_op_expr_result no_space
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id_opt -> -> w id with_opt -> -> w
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-> unpasting_elem rect_separator un
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-> "}" comprehension -> set_compreh
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-> do_expr -> for_expr -> spawn_exp
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-> type_ref -> "(" w type_ref w ","
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enc -> enc_literal op_or_enc -> op
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Bibliography [1] O. Agesen, L. Bak,
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