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40.10 <strong>The</strong> Trait <strong>Fortress</strong>.Core.BinaryEndianLinearEndianSequence trait BinaryEndianLinearEndianSequencenat b,bool bigEndianBytes,bool bigEndianBits, nat n,bool bigEndianSequence extends { BasicBinaryOperations BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,bigEndianSequence } where { b ≤ maxBinaryWordBitLog } coercion nat b ′ ,bool bigEndianBytes,bool bigEndianBits (x:BinaryEndianWordb ′ ,bigEndianBytes,bigEndianBits) where {bigEndianBytes = bigEndianSequence, 2 b′ = n · 2 b } coercion nat m,nat radix,nat q,nat k,nat v(x:NaturalNumeralm,radix, v) where {radix = 2 q , q · m = n · 2 bk } opr [j: IndexInt] : BinaryEndianWordb,bigEndianBytes,bigEndianBits throws { IndexOutOfBoundsException } opr nat k[j: IntegerStatick] : BinaryWordb,bigEndianBytes,bigEndianBits where { k < n } opr nat m[r: RangeOfStaticSizeIndexInt, m] : BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, m,bigEndianSequence throws { IndexOutOfBoundsException } where { m ≤ n } opr int a,nat m,int c[r:StaticRangea, m, c] : BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, m,bigEndianSequence where { 0 ≤ a < n, 0 ≤ a + m · c < n } opr [j: IndexInt] := (v: BinaryEndianWordb,bigEndianBytes,bigEndianBits): BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,bigEndianSequence throws { IndexOutOfBoundsException } opr nat k[j: IntegerStatick] := (v: BinaryEndianWordb,bigEndianBytes,bigEndianBits): BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,bigEndianSequence where { k < n } opr nat m[r: RangeOfStaticSizeIndexInt, m] := (v: BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, m,bigEndianSequence): BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,bigEndianSequence throws { IndexOutOfBoundsException } opr int a,nat m,int c[r:StaticRangea, m, c] := (v: BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, k,bigEndianSequence): BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,bigEndianSequence where { 0 ≤ a < n, 0 ≤ a + m · c < n } update(j:IndexInt, v: BinaryEndianWordb,bigEndianBytes,bigEndianBits): BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,bigEndianSequence throws { IndexOutOfBoundsException } updatenat k(j: IntegerStatick, 298
v: BinaryEndianWordb,bigEndianBytes,bigEndianBits): BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,bigEndianSequence where { k < n } updatenat m(r:RangeOfStaticSizeIndexInt, m, v: BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, m,bigEndianSequence): BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,bigEndianSequence throws { IndexOutOfBoundsException } updateint a,nat m,int c (r:StaticRangea, m, c, v: BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, m,bigEndianSequence): BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,bigEndianSequence where { 0 ≤ a < n, 0 ≤ a + m · c < n } opr ‖ nat m(self,other: BinaryEndianLinearEndianSequence b,bigEndianBytes,bigEndianBits, m,bigEndianSequence): BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n + m,bigEndianSequence opr ‖ nat m,nat radix,nat q,nat k,nat v(self,other: NaturalNumeralm,radix, v): LinearSequenceT, n + k where {radix = 2 q , q · m = k · 2 b } opr ‖ nat m,nat radix,nat q,nat k,nat v(other: NaturalNumeralm,radix, v,self): LinearSequenceT, n + k where {radix = 2 q , q · m = k · 2 b } littleEndian():BinaryEndianLinearEndianSequenceb,false,false, n,bigEndianSequence bigEndian():BinaryEndianLinearEndianSequenceb,true,true, n,bigEndianSequence littleEndianBits():BinaryEndianLinearEndianSequenceb,bigEndianBytes,false, n,bigEndianSequence bigEndianBits():BinaryEndianLinearEndianSequenceb,bigEndianBytes,true, n,bigEndianSequence littleEndianSequence():BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,false bigEndianSequence():BinaryEndianLinearEndianSequenceb,bigEndianBytes,bigEndianBits, n,true splitnat b ′ () : BinaryEndianLinearEndianSequenceb ′ ,bigEndianBytes,bigEndianBits, n · 2 b−b′ ,bigEndianSequence where { b ′ ≤ b } end 40.10.1 coercion nat b ′ ,bool bigEndianBytes,bool bigEndianBits (x:BinaryEndianWordb ′ ,bigEndianBytes,bigEndianBits) where {bigEndianBytes = bigEndianSequence, 2 b′ = n · 2 b } [Description to be supplied.] 299
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
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Chapter 33 Overloaded Functional De
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coercions: T U ⇐⇒ T ♦ U ∧
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The More Specific Rule for Function
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An infix/multifix operator declarat
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may be so defined except ordinary p
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and here some of these computed dim
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unit name 1 name 2 name 3 : . . . u
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Chapter 36 Support for Domain-Speci
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Because syntax expanders are define
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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
Page 277 and 278: 40.3.2 opr nat m[r:RangeOfStaticSiz
Page 279 and 280: 40.5 The Trait Fortress.Core.Binary
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
Page 287 and 288: 40.6.16 opr ‖ nat m,bool bigEndia
Page 289 and 290: countLeadingZeroBits():IndexInt cou
Page 291 and 292: 40.7.41 signedShift(j:IndexInt):T 4
Page 293 and 294: 40.8.6 signedDivide(other: T,overfl
Page 295 and 296: littleEndian():BinaryEndianLinearEn
Page 297: 40.9.16 opr ‖ nat m,nat radix,nat
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
Page 327 and 328: Values, evaluation contexts, and re
Page 329 and 330: Valid function declarations: p ⊢
Page 331 and 332: Method definition lookup: visible p
Page 333 and 334: Values, intermediate expressions, e
Page 335 and 336: Field typing: p; ∆; Γ ⊢ vd ok
Page 337 and 338: Appendix B Overloaded Functional De
Page 339 and 340: Proof. We prove this for δ, but th
Page 341 and 342: Upgrade A predicate upg? takes two
Page 343 and 344: a is rendered as a foobar is render
Page 345 and 346: • If a portion is sub and another
Page 347 and 348: 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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