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36 Support for Domain-Specific Languages 241 36.1 Definitions of Syntax Expanders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 36.2 Declarations of Syntax Expanders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 36.3 Restrictions on Delimiters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 36.4 Processing Syntax Expanders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 36.5 Expanders for Fortress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 V Fortress APIs and Documentation for Library Writers 245 37 Algebraic Constraints 246 37.1 Predicates and Equivalence Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 37.2 Partial and Total Orders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 37.3 Operators and Their Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 37.4 Monoids, Groups, Rings, and Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 37.5 Boolean Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 38 Numbers 262 38.1 The Trait Fortress.Standard.RationalQuantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 38.2 The Trait Fortress.Standard.TotalComparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 38.3 Top-level Total Comparison Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 38.4 The Trait Fortress.Standard.Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 38.5 Top-level Comparison Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 39 Components and APIs 269 40 Memory Sequences and Binary Words 271 40.1 The Trait Fortress.Core.LinearSequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 40.2 Constructing Linear Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 40.3 The Trait Fortress.Core.HeapSequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 40.4 Constructing Heap Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 40.5 The Trait Fortress.Core.BinaryWord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 40.6 The Trait Fortress.Core.BinaryEndianWord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 40.7 The Trait Fortress.Core.BasicBinaryOperations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 40.8 The Trait Fortress.Core.BasicBinaryWordOperations . . . . . . . . . . . . . . . . . . . . . . . . . . 292 40.9 The Trait Fortress.Core.BinaryLinearEndianSequence . . . . . . . . . . . . . . . . . . . . . . . . . . 294 10
40.10The Trait Fortress.Core.BinaryEndianLinearEndianSequence . . . . . . . . . . . . . . . . . . . . . . 298 40.11The Trait Fortress.Core.BinaryHeapEndianSequence . . . . . . . . . . . . . . . . . . . . . . . . . . 303 40.12The Trait Fortress.Core.BinaryEndianHeapEndianSequence . . . . . . . . . . . . . . . . . . . . . . . 303 40.13The Trait Fortress.Core.BasicBinaryHeapSubsequenceOperations . . . . . . . . . . . . . . . . . . . 304 VI Appendices 312 A Fortress Calculi 313 A.1 Basic Core Fortress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 A.2 Core Fortress with Where Clauses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 A.3 Core Fortress with Overloading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 A.4 Acyclic Core Fortress with Field Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 B Overloaded Functional Declarations 337 B.1 Proof of Coercion Resolution for Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 B.2 Proof of Overloading Resolution for Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 C Components and APIs 340 D Rendering of Fortress Identifiers 342 E Support for Unicode Input in ASCII 346 E.1 Word Pasting across Line Breaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 E.2 Preprocessing of Names of Unicode Characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 F Operator Precedence, Chaining, and Enclosure 351 F.1 Bracket Pairs for Enclosing Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 F.2 Vertical-Line Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 F.3 Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 F.4 Relational Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 F.5 Boolean Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 F.6 Other Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 G Concrete Syntax 375 H Generated Concrete Syntax 383 11
Page 1 and 2: The Fortress Language Specification
Page 3 and 4: 4 Evaluation 36 4.1 Values . . . .
Page 5 and 6: 12 Functions 85 12.1 Function Decla
Page 7 and 8: 17.7 Coercions for Tuple and Arrow
Page 9: IV Fortress for Library Writers 214
Page 13 and 14: Chapter 1 Introduction The Fortress
Page 15 and 16: A note on the presented libraries i
Page 17 and 18: component HelloWorld export Executa
Page 19 and 20: foo:String → () baz: String → S
Page 21 and 22: fortress upgrade Gary with Ralph No
Page 23 and 24: halve(x : R64) : R64 = x/2 Predicta
Page 25 and 26: while x < 10 do print x x += 1 end
Page 27 and 28: It is also possible to convert a me
Page 29 and 30: factorial(n) = ∏ i←1:n i This f
Page 31 and 32: In both methods cons and append , t
Page 33 and 34: default distributions will provide
Page 35 and 36: Chapter 3 Programs A program consis
Page 37 and 38: Chapter 10), a literal (see Section
Page 39 and 40: (discussed in Section 13.13) to a s
Page 41 and 42: Chapter 5 Lexical Structure A Fortr
Page 43 and 44: U+0021 EXCLAMATION MARK ! U+0023 NU
Page 45 and 46: If a character (or any other syntac
Page 47 and 48: BIG SI unit absorbs abstract also a
Page 49 and 50: escape sequences are useful for ASC
Page 51 and 52: 5.14.1 Multicharacter Enclosing Ope
Page 53 and 54: Note: the elegant way to write Avog
Page 55 and 56: • top-level variable declarations
Page 57 and 58: declares id to be a mutable variabl
Page 59 and 60: 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
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property ∀(a:T) ¬(a ∼ a) end A
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trait PartialOrderOperatorsT extend
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The HasMinimalElement trait specifi
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The trait Commutative requires the
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A value e is a left identity for a
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trait ApproximatelyHasInverses T ex
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end extends { ApproximateCommutativ
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A default definition is provided fo
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trait RationalQuantityunit U absorb
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(self,other:RationalQuantityU,ninf
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38.2.4 getter hashCode(): Z64 38.2.
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Chapter 39 Components and APIs We d
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Chapter 40 Memory Sequences and Bin
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updatenat k(j: IntegerStatick, v: T
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40.1.12 update(j:IndexInt, v: T): L
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40.3.2 opr nat m[r:RangeOfStaticSiz
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40.5 The Trait Fortress.Core.Binary
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40.5.5 bit(m:IndexInt): Bit The res
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40.6 The Trait Fortress.Core.Binary
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40.6.4 opr nat m[r:RangeOfStaticSiz
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40.6.16 opr ‖ nat m,bool bigEndia
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countLeadingZeroBits():IndexInt cou
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40.7.41 signedShift(j:IndexInt):T 4
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40.8.6 signedDivide(other: T,overfl
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littleEndian():BinaryEndianLinearEn
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40.9.16 opr ‖ nat m,nat radix,nat
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v: BinaryEndianWordb,bigEndianBytes
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40.10.9 opr nat m[r:RangeOfStaticSi
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40.10.24 splitnat b ′ () : Binary
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itAnd(selfStart: IndexInt,source:T,
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40.13.2 wrappingAdd(selfStart: Inde
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40.13.30 unsignedMax(selfStart: Ind
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40.13.55 gatherBits(selfStart:Index
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Appendix A Fortress Calculi A.1 Bas
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Values, evaluation contexts, redexe
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Expression typing: p; ∆; Γ ⊢ e
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α, β type variables f method name
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Function/method name lookup: Fname(
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One owner for all the visible metho
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Traits defining a method: defining
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Values, evaluation contexts, and re
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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
Page 337 and 338:
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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