The Fortress Language Specification - CiteSeerX

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40.5.10 bitUnshuffle():(BinaryWordb − 1, BinaryWordb − 1) where { b > 0 } This is the inverse of the bitShuffle method: the odd-numbered bits of this binary word are used to form a binary word of half the size, and likewise the even-numbered bits, and a tuple of the two binary words is returned. property ∀(v, w) v.bitShuffle(w).bitUnshuffle() = (v, w) 282
40.6 The Trait Fortress.Core.BinaryEndianWord The type BinaryEndianWordb,bigEndianBytes,bigEndianBits is exactly like BinaryWordb but bears two kinds of endianness information. A BinaryEndianWord may be split into a sequence of smaller words; the result is of type BinaryLinearEndianSequence. The flag bigEndianBytes indicates whether subword 0 is the most significant subword (if bigEndianBytes is true) or least significant subword (if bigEndianBytes is false) of the original binary word. A BinaryEndianWord may also be subscripted to extract a bit or a bit field; the flag bigEndianBits indicates whether bit 0 is the most significant bit (if bigEndianBits is true) or least significant bit (if bigEndianBits is false) of the original binary word. (Yes, it may seem strange for the bit ordering to differ from the subword ordering, but they do differ on a number of architectures, including SPARC.) Extracting a bit produces a Bit, that is, a BinaryWord0 . Extracting a bit field of width k produces a BinaryEndianLinearEndianSequence with n = k and b = 0 ; the endianness of the sequence matches the bit-endianness of the original BinaryEndianWord. trait BinaryEndianWordnat b,bool bigEndianBytes,bool bigEndianBits extends { BasicBinaryWordOperationsBinaryEndianWordb,bigEndianBytes,bigEndianBits, b} comprises {} where { b ≤ maxBinaryWordBitLog } coercion int r(x:IntegerStaticr) where { −2 b−1 ≤ r < 2 b } opr [j: IndexInt] : BinaryEndianWord1,bigEndianBytes,bigEndianBits throws { IndexOutOfBoundsException } opr nat k[j: IntegerStatick] : BinaryEndianWord1,bigEndianBytes,bigEndianBits where { k < 2 b } opr nat m[r: RangeOfStaticSizeIndexInt, m] : BinaryEndianLinearEndianSequence1,bigEndianBytes,bigEndianBits, m,bigEndianBits throws { IndexOutOfBoundsException } opr int a,nat m,int c[r:StaticRangea, m, c] : BinaryEndianLinearEndianSequence1,bigEndianBytes,bigEndianBits, m,bigEndianBits where { 0 ≤ a < 2 b , 0 ≤ a + m · c < 2 b } opr [j: IndexInt] := (v: Bit): BinaryEndianWordb,bigEndianBytes,bigEndianBits throws { IndexOutOfBoundsException } opr nat k[j: IntegerStatick] := (v: Bit): BinaryEndianWordb,bigEndianBytes,bigEndianBits where { k < 2 b } opr nat m[r: RangeOfStaticSizeIndexInt, m] := (v: BinaryLinearSequence1, m): BinaryEndianWordb,bigEndianBytes,bigEndianBits throws { IndexOutOfBoundsException } opr int a,nat m,int c[r:StaticRangea, m, c] := (v: BinaryLinearSequence1, k): BinaryEndianWordb,bigEndianBytes,bigEndianBits where { 0 ≤ a < 2 b , 0 ≤ a + m · c < 2 b } update(j:IndexInt, v: Bit): BinaryEndianWordb,bigEndianBytes,bigEndianBits throws { IndexOutOfBoundsException } updatenat k(j: IntegerStatick, v: Bit): BinaryEndianWordb,bigEndianBytes,bigEndianBits where { k < 2 b } updatenat m(r:RangeOfStaticSizeIndexInt, m, v: BinaryLinearSequence1, m): BinaryEndianWordb,bigEndianBytes,bigEndianBits throws { IndexOutOfBoundsException } updateint a,nat m,int c(r:StaticRangea, m, c, v:BinaryLinearSequence1, m): BinaryEndianWordb,bigEndianBytes,bigEndianBits where { 0 ≤ a < 2 b , 0 ≤ a + m · c < 2 b } 283
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 ∧
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
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: 40.5.5 bit(m:IndexInt): Bit The res
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 and 298: 40.9.16 opr ‖ nat m,nat radix,nat
Page 299 and 300: v: BinaryEndianWordb,bigEndianBytes
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
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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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