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• A radix specifier consists of an underscore immediately followed either by a sequence of one or more digits or by the English name in all uppercase ASCII letters of an integer from 2 to 16. • A simple numeral base is a word that consists only of letters and digits immediately followed by a radix specifier. The radix of a simple numeral base is the value corresponding to the sequence of digits in radix specifier interpreted in base ten, or the value of the integer whose English name is spelled out by the radix specifier. It is a static error if the radix is 0 or 1. • A compound numeral base is a word that consists only of letters and digits immediately followed by a ‘ . ’ character immediately followed by a simple numeral base. • A numeral in a Fortress program is a maximal contiguous subsequence that is either a numeral base (simple or compound), a numeral prefix or a numeral prefix immediately followed by a space immediately followed by a numeral base (simple or compound). A numeral is simple if it does not contain a ‘.’ character; otherwise, the number is compound. It is a static error if a numeral contains more than one ‘.’ character. Here are some examples of numerals, shown in unformatted form: 17 7fff_16 0fff_SIXTEEN 1fab 10101101_2 3.14159265 0.a FF_EIGHT k12.52_24 P_50 DEAD.BEEF_16 PI_FIFTEEN 5.14 Operator Tokens In this section, we describe how to determine the operator tokens of a program. Because operator tokens do not occur within comments, string literals and character literals, we henceforth in this section consider only characters that are outside these constructs. An operator word of a program is a word that is not reserved, consists only of uppercase letters and underscores (no digits or non-uppercase letters), does not begin or end with an underscore, and has at least two different letters. A base operator is an ordinary operator character, 6 the two-character sequence “ ** ”, an operator word, a (contiguous) sequence of two or more vertical-line characters (U+007C), or a multicharacter enclosing operator, as defined in Section 5.14.1. A base operator is maximal of a program if it is not contained within any other base operator of that program. It is a static error if two maximal base operators overlap (which is only possible if both are multicharacter enclosing operators). A simple operator is a maximal base operator that is an operator character, the two-character sequence “ ** ”, or an operator word. A maximal base operator is an operator token unless it is a simple operator other than an enclosing or vertical-line operator character, and it is immediately preceded by ‘ˆ’ or immediately followed by ‘=’. Such an operator is an enclosing operator if it is an enclosing operator character (see Section F.1) or a multicharacter enclosing operator; it is a vertical-line operator if it has only vertical-line operator characters (see Section F.2); otherwise, it is an ordinary operator. If a simple operator is immediately preceded by ‘ˆ’ then the ‘ˆ’ followed by the simple operator is an operator token; such an operator token is called a superscripted postfix operator. In addition, “ ˆT ” is also a superscripted postfix operator provided that it is not immediately followed by a word character. It is a static error for a superscripted postfix operator to be immediately followed by a word character other than apostrophe. Finally, if a simple operator is not immediately preceded by ‘ˆ’ and is immediately followed by ‘=’ then the simple operator followed by the ‘=’ is an operator token; such an operator token is called a compound assignment operator. 6 The operator characters are enumerated in Appendix F, less the special operator characters listed in Section 5.1. 50
5.14.1 Multicharacter Enclosing Operators The following multicharacter sequences (in which there must be no other characters, and particularly no whitespace) can be used as brackets as described below: 1. Any contiguous nonempty sequence of vertical-line characters is a vertical-line operator. Such an operator can be used in an enclosing pair matching itself. 2. Any of ‘(’ or ‘[’ or ‘{’ may be immediately followed by any number of ‘/’ characters or by any number of ‘\’ characters. Such a token is a left bracket, and it is matched by the multicharacter token consisting of the same number and kind of ‘/’ or ‘\’ characters followed immediately by a matching ‘)’ or ‘]’ or ‘}’, as appropriate. Thus, for example, “(////” and “////)” are matching left and right brackets respectively. (In the future, we may allow tokens with mixtures of ‘/’ and ‘\’, in which case the left and right brackets should match from outside in. But for now, such tokens are simply illegal.) 3. One or more ‘’ characters as there are ‘
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 and 10: IV Fortress for Library Writers 214
Page 11 and 12: 40.10The Trait Fortress.Core.Binary
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: escape sequences are useful for ASC
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
Page 61 and 62: Chapter 7 Names Names are used to r
Page 63 and 64: 7.3 Qualified Names Fortress provid
Page 65 and 66: Fortress also allows coercion betwe
Page 67 and 68: • element types of a tuple type c
Page 69 and 70: TypeAlias ::= type Id [StaticParams
Page 71 and 72: ‘}’. If such a clause contains
Page 73 and 74: Note that a trait declaration inher
Page 75 and 76: the parametric trait WrappedDiction
Page 77 and 78: Chapter 10 Objects An object is a v
Page 79 and 80: FldDef ::= FldMod ∗ Id [IsType] (
Page 81 and 82: Chapter 11 Static Parameters Trait,
Page 83 and 84: 11.5 Operator and Identifier Parame
Page 85 and 86: Chapter 12 Functions Functions are
Page 87 and 88: swap(x :Object, y : Object) = (y, x
Page 89 and 90: A function declaration may be separ
Page 91 and 92: Chapter 13 Expressions Fortress is
Page 93 and 94: Negating the literal 0 produces a s
Page 95 and 96: the function is evaluated with the
Page 97 and 98: 13.10 Assignments Syntax: Expr ::=
Page 99 and 100: 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
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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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