9.6 KiB
% Cryptol version 2 Syntax % %
Layout
Groups of declarations are organized based on indentation.
Declarations with the same indentation belong to the same group.
Lines of text that are indented more than the beginning of a
declaration belong to that declaration, while lines of text that are
indented less terminate a group of declaration. Groups of
declarations appear at the top level of a Cryptol file, and inside
where blocks in expressions. For example, consider the following
declaration group
f x = x + y + z
where
y = x * x
z = x + y
g y = y
This group has two declaration, one for f and one for g. All the
lines between f and g that are indented more then f belong to
f.
This example also illustrates how groups of declarations may be nested
within each other. For example, the where expression in the
definition of f starts another group of declarations, containing y
and z. This group ends just before g, because g is indented
less than y and z.
Comments
Cryptol supports block comments, which start with /* and end with
*/, and line comments, which start with // and terminate at the
end of the line. Block comments may be nested arbitrarily.
Examples:
/* This is a block comment */
// This is a line comment
/* This is a /* Nested */ block comment */
Identifiers
Cryptol identifiers consist of one or more characters. The first
character must be either an English letter or underscore (_). The
following characters may be an English letter, a decimal digit,
underscore (_), or a prime ('). Some identifiers have special
meaning in the language, so they may not be used in programmer-defined
names (see Keywords).
Examples:
name name1 name' longer_name
Name Name2 Name'' longerName
Keywords and Built-in Operators
The following identifiers have special meanings in Cryptol, and may not be used for programmer defined names:
Arith Inf extern inf module then
Bit True fin lg2 newtype type
Cmp else if max pragma where
False export import min property width
The following table contains Cryptol's operators and their associativity with lowest precedence operators first, and highest precedence last.
Operator Associativity
|| left
^ left
&& left
-> (types) right
!= == not associative
> < <= >= not associative
# right
>> << >>> <<< left
+ - left
* / % left
^^ right
! !! @ @@ left
(unary) - ~ right
Table: Operator precedences.
Numeric Literals
Numeric literals may be written in binary, octal, decimal, or
hexadecimal notation. The base of a literal is determined by its
prefix: 0b for binary, 0o for octal, no special prefix for
decimal, and 0x for hexadecimal.
Examples:
254 // Decimal literal
0254 // Decimal literal
0b11111110 // Binary literal
0o376 // Octal literal
0xFE // Hexadecimal literal
0xfe // Hexadecimal literal
Numeric literals represent finite bit sequences (i.e., they have type
[n]). Using binary, octal, and hexadecimal notation results in bit
sequences of a fixed length, depending on the number of digits in the
literal. Decimal literals are overloaded, and so the length of the
sequence is inferred from context in which the literal is used.
Examples:
0b1010 // : [4], 1 * number of digits
0o1234 // : [12], 3 * number of digits
0x1234 // : [16], 4 * number of digits
10 // : {n}. (fin n, n >= 4) => [n]
// (need at least 4 bits)
0 // : {n}. (fin n) => [n]
Bits
The type Bit has two inhabitants: True and False. These values
may be combined using various logical operators, or constructed as
results of comparisons.
Operator Associativity Description
|| left Logical or
^ left Exclusive-or
&& left Logical and
!= == none Not equals, equals
> < <= >= none Comparisons
~ right Logical negation
Table: Bit operations.
If Then Else with Multiway
If then else has been extended to support multi-way
conditionals. Examples:
x = if y % 2 == 0 then 22 else 33
x = if y % 2 == 0 then 1
| y % 3 == 0 then 2
| y % 5 == 0 then 3
else 7
Tuples and Records
Tuples and records are used for packaging multiples values together. Tuples are enclosed in parenthesis, while records are enclosed in braces. The components of both tuples and records are separated by commas. The components of tuples are expressions, while the components of records are a label and a value separated by an equal sign. Examples:
(1,2,3) // A tuple with 3 component
() // A tuple with no components
{ x = 1, y = 2 } // A record with two fields, `x` and `y`
{} // A record with no fileds
The components of tuples are identified by position, while the components of records are identified by their label, and so the ordering of record components is not important. Examples:
(1,2) == (1,2) // True
(1,2) == (2,1) // False
{ x = 1, y = 2 } == { x = 1, y = 2 } // True
{ x = 1, y = 2 } == { y = 2, x = 1 } // True
The components of a record or a tuple may be accessed in two ways: via pattern matching or by using explicit component selectors. Explicit component selectors are written as follows:
(15, 20).1 == 15
(15, 20).2 == 20
{ x = 15, y = 20 }.x == 15
Explicit record selectors may be used only if the program contains sufficient type information to determine the shape of the tuple or record. For example:
type T = { sign :: Bit, number :: [15] }
// Valid defintion:
// the type of the record is known.
isPositive : T -> Bit
isPositive x = x.sign
// Invalid defintion:
// insufficient type information.
badDef x = x.f
The components of a tuple or a record may also be access by using pattern matching. Patterns for tuples and records mirror the syntax for constructing values: tuple patterns use parenthesis, while record patterns use braces. Examples:
getFst (x,_) = x
distance2 { x = xPos, y = yPos } = xPos ^^ 2 + yPos ^^ 2
f x = fst + snd where
Sequences
A sequence is a fixed-length collection of element of the same type.
The type of a finite sequence of length n, with elements of type a
is [n] a. Often, a finite sequence of bits, [n] Bit, is called a
word. We may abbreviate the type [n] Bit as [n]. An infinite
sequence with elements of type a has type [inf] a, and [inf] is
an infinite stream of bits.
[e1,e2,e3] // A sequence with three elements
[t .. ] // Sequence enumerations
[t1, t2 .. ] // Step by t2 - t1
[t1 .. t3 ]
[t1, t2 .. t3 ]
[e1 ... ] // Infinite sequence starting at e1
[e1, e2 ... ] // Infinite sequence stepping by e2-e1
[ e | p11 <- e11, p12 <- e12 // Sequence comprehensions
| p21 <- e21, p22 <- e22 ]
Note: the bounds in finite unbounded (those with ..) sequences are type expressions, while the bounds in bounded-finite and infinite sequences are value expressions.
Operator Description
# Sequence concatenation
>> << Shift (right,left)
>>> <<< Rotate (right,left)
@ ! Access elements (front,back)
@@ !! Access sub-sequence (front,back)
Table: Sequence operations.
There are also lifted point-wise operations.
[p1, p2, p3, p4] // Sequence pattern
p1 # p2 // Split sequence pattern
Functions
\p1 p2 -> e // Lambda expression
f p1 p2 = e // Function definition
Local Declarations
e where ds
Explicit Type Instantiation
If f is a polymorphic value with type:
f : { tyParam }
f `{ tyParam = t }
Demoting Numeric Types to Values
The value corresponding to a numeric type may be accessed using the following notation:
`{t}
Here t should be a type expression with numeric kind. The resulting
expression is a finite word, which is sufficiently large to accomodate
the value of the type:
`{t} :: {w >= width t}. [w]
Explicit Type Annotations
Explicit type annotations may be added on expressions, patterns, and in argument definitions.
e : t
p : t
f (x : t) = ...
Type Signatures
f,g : {a,b} (fin a) => [a] b
Type Synonym Declarations
type T a b = [a] b