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Appendix D Rendering of Fortress Identifiers In order to more closely approximate mathematical notation, Fortress mandates standard rendering for various input elements, particularly for numerals and identifiers, as specified in Section 5.17. In this Appendix, we describe the detailed rules for rendering an identifier. If an identifier consists of letters and possibly digits, but no underscores or other connecting punctuation, prime marks, or apostrophes, then the rules are fairly simple: (a) If the identifier consists of two ASCII capital letters that are the same, possibly followed by digits, then a single capital letter is rendered double-struck, followed by full-sized (not subscripted) digits in roman font. QQ is rendered as Q RR64 is rendered as R64 ZZ is rendered as Z ZZ512 is rendered as Z512 (b) Otherwise, if the identifier has more than two characters and begins with a capital letter, then it is rendered in roman font. (Such names are typically used as names of types in Fortress. Note that an identifier cannot consist entirely of capital letters, because such a token is considered to be an operator.) Integer is rendered as Integer Matrix is rendered as Matrix TotalOrder is rendered as TotalOrder BooleanAlgebra is rendered as BooleanAlgebra Fred17 is rendered as Fred17 R2D2 is rendered as R2D2 (c) Otherwise, if the identifier consists of one or more letters followed by one or more digits, then the letters are rendered in italic and the digits are rendered as roman subscripts. a3 is rendered as a 3 foo7 is rendered as foo 7 M1 is rendered as M 1 z128 is rendered as z 128 Ω13 is rendered as Ω 13 myFavoriteThings1625 is rendered as myFavoriteThings 1625 (d) The following names are always rendered in roman type out of respect for tradition: sin cos tan cot sec csc sinh cosh tanh coth sech csch arcsin arccos arctan arccot arcsec arccsc arsinh arcosh artanh arcoth arsech arcsch arg deg det exp inf sup lg ln log gcd max min (e) Otherwise the identifier is simply rendered entirely in italic type. 342
a is rendered as a foobar is rendered as foobar length is rendered as length isInstanceOf is rendered as isInstanceOf foo7a is rendered as foo7a l33tsp33k is rendered as l33tsp33k If the identifier begins or ends with an underscore, or both, but has no other underscores or other connecting punctuation, or prime marks, or apostrophes: (f) If the identifier, ignoring its underscores, consists of two ASCII capital letters that are the same, possibly followed by one or more digits, then a single capital letter is rendered in sans-serif (for a leading underscore), script (for a trailing underscore), or italic san-serif (for both a leading and a trailing underscore), and any digits are rendered as roman subscripts. (g) Otherwise, the identifier without its underscores is rendered in boldface (for a leading underscore), roman (for a trailing underscore), or bold italic (for both a leading and a trailing underscore); except that if the identifier, ignoring its underscores, consists of one or more letters followed by one or more digits, then the digits are rendered as roman subscripts regardless of the underscores. m is rendered as m s is rendered as s km is rendered as km kg is rendered as kg V is rendered as V kW is rendered as kW v is rendered as v foo13 is rendered as foo 13 (Roman identifiers are typically used for names of SI dimensional units. See sections 6.1.1 and 6.2.1 of [24] for style questions with respect to dimensions and units.) These last two rules are actually special cases of the following general rules that apply whenever an identifier contains at least one underscore, other connecting punctuation, prime mark, or apostrophe: An identifier containing underscores is divided into portions by its underscores; in addition, any apostrophe, prime, or double prime character separates portions and is also itself a portion. (h) If any portion is empty other than the first or last, then the entire identifier is rendered in italics, underscores and all. Otherwise, the portions are rendered as follows. The idea is that there is a principal portion that may be preceded and/or followed by modifiers, and there may also be a face portion: • If the first portion is not empty, script, fraktur, sansserif, or monospace, then the principal portion is the first portion and there is no face portion. • If the first portion is script, fraktur, sansserif, or monospace, then the principal portion is the second portion and the face portion is the first portion. • If the first portion is empty and the second portion is not script, fraktur, sansserif, or monospace, then the principal portion is the second portion and there is no face portion. • Otherwise the principal portion is the third portion and the face portion is the second portion. If there is no face portion, the principal portion will be rendered in ordinary italics. However, if the first portion is empty (that is, the identifier begins with a leading underscore), then the principal portion is to be rendered in roman boldface. If the last portion is empty (that is, the identifier ends with a trailing underscore), then the principal portion will be roman rather than italic, or bold italic rather than bold. If there is a face portion, then that describes an alternate typeface to be used in rendering the principal portion. If there is no face portion, but the principal portion consists of two copies of the same letter, then it is rendered as a single letter in a double-struck face (also known as “blackboard bold”), sans-serif, script, or italic sans-serif font according to whether the first and last portions are (not empty, not empty), (empty, not empty), (not empty, empty), or (empty, empty), respectively. Otherwise, if the first portion is empty (that is, the identifier begins with a leading underscore), then the principal portion is to be rendered in a bold version of the selected face, and if the last portion is empty (that 343
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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
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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
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
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: Upgrade A predicate upg? takes two
Page 345 and 346: • If a portion is sub and another
Page 347 and 348: supercalifragilisticexpialidocious
Page 349 and 350: any alternative names, with undersc
Page 351 and 352: Appendix F Operator Precedence, Cha
Page 353 and 354: U+007C VERTICAL LINE | | U+2016 DOU
Page 355 and 356: The following two operators have th
Page 357 and 358: U+003D EQUALS SIGN = = EQ U+2243 AS
Page 359 and 360: U+22DD EQUAL TO OR GREATER-THAN U+2
Page 361 and 362: U+2289 NEITHER A SUPERSET OF NOR EQ
Page 363 and 364: F.4.8 Miscellaneous Relational Oper
Page 365 and 366: U+21A5 UPWARDS ARROW FROM BAR U+21A
Page 367 and 368: U+2224 DOES NOT DIVIDE ∤ U+2225 P
Page 369 and 370: U+27F8 LONG LEFTWARDS DOUBLE ARROW
Page 371 and 372: U+2960 UPWARDS HARPOON WITH BARB LE
Page 373 and 374: U+29ED BLACK CIRCLE WITH DOWN ARROW
Page 375 and 376: Appendix G Concrete Syntax In this
Page 377 and 378: Extends ::= extends TraitTypes Excl
Page 379 and 380: StaticParam ::= Id [Extends] [absor
Page 381 and 382: Value ::= Literal | fn ValParam [Is
Page 383 and 384: Appendix H Generated Concrete Synta
Page 385 and 386: -> fn_decl -> object_decl -> var_de
Page 387 and 388: -> id extends_opt absorbs_opt -> "n
Page 389 and 390: -> w "excludes" w type_ref_list com
Page 391 and 392: -> 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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