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355 lines
10 KiB
Markdown
355 lines
10 KiB
Markdown
% Cryptol version 2 Syntax
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Layout
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======
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Groups of declarations are organized based on indentation.
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Declarations with the same indentation belong to the same group.
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Lines of text that are indented more than the beginning of a
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declaration belong to that declaration, while lines of text that are
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indented less terminate a group of declarations. Groups of
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declarations appear at the top level of a Cryptol file, and inside
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`where` blocks in expressions. For example, consider the following
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declaration group
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f x = x + y + z
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where
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y = x * x
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z = x + y
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g y = y
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This group has two declaration, one for `f` and one for `g`. All the
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lines between `f` and `g` that are indented more then `f` belong to
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`f`.
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This example also illustrates how groups of declarations may be nested
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within each other. For example, the `where` expression in the
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definition of `f` starts another group of declarations, containing `y`
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and `z`. This group ends just before `g`, because `g` is indented
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less than `y` and `z`.
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Comments
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========
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Cryptol supports block comments, which start with `/*` and end with
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`*/`, and line comments, which start with `//` and terminate at the
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end of the line. Block comments may be nested arbitrarily.
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Examples:
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/* This is a block comment */
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// This is a line comment
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/* This is a /* Nested */ block comment */
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Identifiers
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===========
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Cryptol identifiers consist of one or more characters. The first
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character must be either an English letter or underscore (`_`). The
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following characters may be an English letter, a decimal digit,
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underscore (`_`), or a prime (`'`). Some identifiers have special
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meaning in the language, so they may not be used in programmer-defined
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names (see [Keywords](#keywords-and-built-in-operators)).
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Examples:
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name name1 name' longer_name
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Name Name2 Name'' longerName
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Keywords and Built-in Operators
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===============================
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The following identifiers have special meanings in Cryptol, and may
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not be used for programmer defined names:
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<!--- The table below can be generated by running `chop.hs` on this list:
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Arith
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Bit
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Cmp
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False
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Inf
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True
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else
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export
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extern
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fin
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if
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import
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inf
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lg2
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max
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min
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module
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newtype
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pragma
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property
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then
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type
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where
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width
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--->
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Arith Inf extern inf module then
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Bit True fin lg2 newtype type
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Cmp else if max pragma where
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False export import min property width
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The following table contains Cryptol's operators and their
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associativity with lowest precedence operators first, and highest
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precedence last.
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Operator Associativity
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--------------- -------------
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`||` left
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`^` left
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`&&` left
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`->` (types) right
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`!=` `==` not associative
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`>` `<` `<=` `>=` not associative
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`#` right
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`>>` `<<` `>>>` `<<<` left
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`+` `-` left
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`*` `/` `%` left
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`^^` right
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`!` `!!` `@` `@@` left
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(unary) `-` `~` right
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Table: Operator precedences.
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Numeric Literals
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================
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Numeric literals may be written in binary, octal, decimal, or
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hexadecimal notation. The base of a literal is determined by its
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prefix: `0b` for binary, `0o` for octal, no special prefix for
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decimal, and `0x` for hexadecimal.
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Examples:
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254 // Decimal literal
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0254 // Decimal literal
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0b11111110 // Binary literal
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0o376 // Octal literal
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0xFE // Hexadecimal literal
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0xfe // Hexadecimal literal
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Numeric literals represent finite bit sequences (i.e., they have type
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`[n]`). Using binary, octal, and hexadecimal notation results in bit
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sequences of a fixed length, depending on the number of digits in the
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literal. Decimal literals are overloaded, and so the length of the
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sequence is inferred from context in which the literal is used.
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Examples:
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0b1010 // : [4], 1 * number of digits
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0o1234 // : [12], 3 * number of digits
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0x1234 // : [16], 4 * number of digits
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10 // : {n}. (fin n, n >= 4) => [n]
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// (need at least 4 bits)
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0 // : {n}. (fin n) => [n]
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Bits
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====
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The type `Bit` has two inhabitants: `True` and `False`. These values
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may be combined using various logical operators, or constructed as
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results of comparisons.
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Operator Associativity Description
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--------------------- ------------- -----------
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`||` left Logical or
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`^` left Exclusive-or
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`&&` left Logical and
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`!=` `==` none Not equals, equals
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`>` `<` `<=` `>=` none Comparisons
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`~` right Logical negation
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Table: Bit operations.
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If Then Else with Multiway
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==========================
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`If then else` has been extended to support multi-way
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conditionals. Examples:
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x = if y % 2 == 0 then 22 else 33
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x = if y % 2 == 0 then 1
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| y % 3 == 0 then 2
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| y % 5 == 0 then 3
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else 7
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Tuples and Records
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==================
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Tuples and records are used for packaging multiples values together.
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Tuples are enclosed in parenthesis, while records are enclosed in
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braces. The components of both tuples and records are separated by
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commas. The components of tuples are expressions, while the
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components of records are a label and a value separated by an equal
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sign. Examples:
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(1,2,3) // A tuple with 3 component
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() // A tuple with no components
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{ x = 1, y = 2 } // A record with two fields, `x` and `y`
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{} // A record with no fields
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The components of tuples are identified by position, while the
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components of records are identified by their label, and so the
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ordering of record components is not important. Examples:
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(1,2) == (1,2) // True
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(1,2) == (2,1) // False
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{ x = 1, y = 2 } == { x = 1, y = 2 } // True
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{ x = 1, y = 2 } == { y = 2, x = 1 } // True
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The components of a record or a tuple may be accessed in two ways: via
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pattern matching or by using explicit component selectors. Explicit
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component selectors are written as follows:
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(15, 20).0 == 15
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(15, 20).1 == 20
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{ x = 15, y = 20 }.x == 15
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Explicit record selectors may be used only if the program contains
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sufficient type information to determine the shape of the tuple or
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record. For example:
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type T = { sign : Bit, number : [15] }
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// Valid definition:
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// the type of the record is known.
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isPositive : T -> Bit
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isPositive x = x.sign
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// Invalid definition:
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// insufficient type information.
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badDef x = x.f
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The components of a tuple or a record may also be accessed using
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pattern matching. Patterns for tuples and records mirror the syntax
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for constructing values: tuple patterns use parenthesis, while record
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patterns use braces. Examples:
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getFst (x,_) = x
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distance2 { x = xPos, y = yPos } = xPos ^^ 2 + yPos ^^ 2
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f p = x + y where
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(x, y) = p
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Sequences
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=========
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A sequence is a fixed-length collection of elements of the same type.
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The type of a finite sequence of length `n`, with elements of type `a`
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is `[n] a`. Often, a finite sequence of bits, `[n] Bit`, is called a
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_word_. We may abbreviate the type `[n] Bit` as `[n]`. An infinite
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sequence with elements of type `a` has type `[inf] a`, and `[inf]` is
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an infinite stream of bits.
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[e1,e2,e3] // A sequence with three elements
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[t .. ] // Sequence enumerations
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[t1, t2 .. ] // Step by t2 - t1
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[t1 .. t3 ]
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[t1, t2 .. t3 ]
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[e1 ... ] // Infinite sequence starting at e1
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[e1, e2 ... ] // Infinite sequence stepping by e2-e1
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[ e | p11 <- e11, p12 <- e12 // Sequence comprehensions
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| p21 <- e21, p22 <- e22 ]
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Note: the bounds in finite unbounded (those with ..) sequences are
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type expressions, while the bounds in bounded-finite and infinite
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sequences are value expressions.
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Operator Description
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--------------------------- -----------
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`#` Sequence concatenation
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`>>` `<<` Shift (right,left)
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`>>>` `<<<` Rotate (right,left)
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`@` `!` Access elements (front,back)
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`@@` `!!` Access sub-sequence (front,back)
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`update` `updateEnd` Update the value of a sequence at a location (front,back)
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`updates` `updatesEnd` Update multiple values of a sequence (front,back)
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Table: Sequence operations.
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There are also lifted point-wise operations.
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[p1, p2, p3, p4] // Sequence pattern
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p1 # p2 // Split sequence pattern
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Functions
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=========
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\p1 p2 -> e // Lambda expression
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f p1 p2 = e // Function definition
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Local Declarations
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==================
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e where ds
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Note that by default, any local declarations without type signatures
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are monomorphized. If you need a local declaration to be polymorphic,
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use an explicit type signature.
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Explicit Type Instantiation
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===========================
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If `f` is a polymorphic value with type:
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f : { tyParam }
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f = zero
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you can evaluate `f`, passing it a type parameter:
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f `{ tyParam = 13 }
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Demoting Numeric Types to Values
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================================
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The value corresponding to a numeric type may be accessed using the
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following notation:
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`{t}
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Here `t` should be a type expression with numeric kind. The resulting
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expression is a finite word, which is sufficiently large to accommodate
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the value of the type:
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`{t} : {w >= width t}. [w]
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Explicit Type Annotations
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=========================
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Explicit type annotations may be added on expressions, patterns, and
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in argument definitions.
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e : t
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p : t
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f (x : t) = ...
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Type Signatures
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===============
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f,g : {a,b} (fin a) => [a] b
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Type Synonym Declarations
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=========================
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type T a b = [a] b
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