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U+227B SUCCEEDS ≻ SUCC U+227D SUCCEEDS OR EQUAL TO SUCCEQ U+227F SUCCEEDS OR EQUIVALENT TO SUCCSIM U+22B1 SUCCEEDS UNDER RELATION U+22DF EQUAL TO OR SUCCEEDS EQSUCC U+22E9 SUCCEEDS BUT NOT EQUIVALENT TO SUCCNSIM U+2AB0 SUCCEEDS ABOVE SINGLE-LINE EQUALS SIGN U+2AB2 SUCCEEDS ABOVE SINGLE-LINE NOT EQUAL TO U+2AB4 SUCCEEDS ABOVE EQUALS SIGN U+2AB6 SUCCEEDS ABOVE NOT EQUAL TO U+2AB8 SUCCEEDS ABOVE ALMOST EQUAL TO U+2ABA SUCCEEDS ABOVE NOT ALMOST EQUAL TO U+2ABC DOUBLE SUCCEEDS The following are miscellaneous curly comparison operators. They may not be mixed or chained. U+2280 DOES NOT PRECEDE ⊀ NPREC U+2281 DOES NOT SUCCEED ⊁ NSUCC U+22E0 DOES NOT PRECEDE OR EQUAL ̸ U+22E1 DOES NOT SUCCEED OR EQUAL ̸ F.4.6 Triangular Comparison Operators The following are triangular “subgroup” comparison operators. They may be mixed and chained with each other and with equivalence operators (see Section F.4.1). U+22B2 NORMAL SUBGROUP OF U+22B4 NORMAL SUBGROUP OF OR EQUAL TO The following are triangular “contains as subgroup” comparison operators. They may be mixed and chained with each other and with equivalence operators (see Section F.4.1). U+22B3 CONTAINS AS NORMAL SUBGROUP U+22B5 CONTAINS AS NORMAL SUBGROUP OR EQUAL TO The following are miscellaneous triangular comparison operators. They may not be mixed or chained. U+22EA NOT NORMAL SUBGROUP OF U+22EB DOES NOT CONTAIN AS NORMAL SUBGROUP U+22EC NOT NORMAL SUBGROUP OF OR EQUAL TO U+22ED DOES NOT CONTAIN AS NORMAL SUBGROUP OR EQUAL ⊳ ⊲ ⋪ ⋫ F.4.7 Chickenfoot Comparison Operators The following are chickenfoot “smaller than” comparison operators. They may be mixed and chained with each other and with equivalence operators (see Section F.4.1). U+2AAA SMALLER THAN LARGER U+2AAD LARGER THAN OR EQUAL TO −≥ LARGEREQ 362
F.4.8 Miscellaneous Relational Operators The following operators are considered to be relational operators, having higher precedence than certain boolean operators, as described in a later section. ∌ U+2208 ELEMENT OF ∈ IN U+2209 NOT AN ELEMENT OF /∈ NOTIN U+220A SMALL ELEMENT OF ∈ U+220B CONTAINS AS MEMBER ∋ CONTAINS U+220C DOES NOT CONTAIN AS MEMBER U+220D SMALL CONTAINS AS MEMBER ∋ U+22F2 ELEMENT OF WITH LONG HORIZONTAL STROKE U+22F3 ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE U+22F4 SMALL ELEMENT OF WITH VERTICAL BAR AT END OF HORIZONTAL STROKE U+22F5 ELEMENT OF WITH DOT ABOVE ˙∈ U+22F6 ELEMENT OF WITH OVERBAR ∈ U+22F7 SMALL ELEMENT OF WITH OVERBAR ∈ U+22F8 ELEMENT OF WITH UNDERBAR ∈ U+22F9 ELEMENT OF WITH TWO HORIZONTAL STROKES U+22FA CONTAINS WITH LONG HORIZONTAL STROKE U+22FB CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE U+22FC SMALL CONTAINS WITH VERTICAL BAR AT END OF HORIZONTAL STROKE U+22FD CONTAINS WITH OVERBAR ∋ U+22FE SMALL CONTAINS WITH OVERBAR ∋ U+22FF Z NOTATION BAG MEMBERSHIP F.5 Boolean Operators Every operator listed in this section has lower precedence than any operator listed in Section F.4. The following are the Boolean conjunction operators: U+2227 LOGICAL AND ∧ AND U+27D1 AND WITH DOT U+2A51 LOGICAL AND WITH DOT ABOVE ˙∧ U+2A53 DOUBLE LOGICAL AND U+2A55 TWO INTERSECTING LOGICAL AND ∧ U+2A5A LOGICAL AND WITH MIDDLE STEM U+2A5C LOGICAL AND WITH HORIZONTAL DASH U+2A5E LOGICAL AND WITH DOUBLE OVERBAR U+2A60 LOGICAL AND WITH DOUBLE UNDERBAR The following are the Boolean disjunction operators: U+2228 LOGICAL OR ∨ OR U+2A52 LOGICAL OR WITH DOT ABOVE ˙∨ U+2A54 DOUBLE LOGICAL OR U+2A56 TWO INTERSECTING LOGICAL OR ∨ U+2A5B LOGICAL OR WITH MIDDLE STEM U+2A5D LOGICAL OR WITH HORIZONTAL DASH U+2A62 LOGICAL OR WITH DOUBLE OVERBAR U+2A63 LOGICAL OR WITH DOUBLE UNDERBAR 363
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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
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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
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
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: U+2289 NEITHER A SUPERSET OF NOR EQ
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
Page 393 and 394: -> op wr op_follows_op_w -> op wr e
Page 395 and 396: -> no_space_op_expr_result no_space
Page 397 and 398: id_opt -> -> w id with_opt -> -> w
Page 399 and 400: -> unpasting_elem rect_separator un
Page 401 and 402: -> "}" comprehension -> set_compreh
Page 403: -> do_expr -> for_expr -> spawn_exp
Page 406 and 407: -> type_ref -> "(" w type_ref w ","
Page 408 and 409: enc -> enc_literal op_or_enc -> op
Page 410 and 411: Bibliography [1] O. Agesen, L. Bak,
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