sbv-8.7: SMT Based Verification: Symbolic Haskell theorem prover using SMT solving.

Copyright | (c) Levent Erkok
License | BSD3
Maintainer | erkokl@gmail.com
Stability | experimental
Safe Haskell | None
Language | Haskell2010

Data.SBV.RegExp

Contents

- Regular expressions
- Matching
- Constructing regular expressions
  - Literals
  - A class of characters
  - Spaces
  - Separators
  - Letters
  - Digits
  - Numbers
  - Identifiers

Description

A collection of regular-expression related utilities. The recommended workflow is to import this module qualified as the names of the functions are specificly chosen to be common identifiers. Also, it is recommended you use the `OverloadedStrings` extension to allow literal strings to be used as symbolic-strings and regular-expressions when working with this module.

Synopsis

- data RegExp
  - = Literal String
  - | All
  - | None
  - | Range Char Char
  - | Conc [RegExp]
  - | KStar RegExp
  - | KPlus RegExp
  - | Opt RegExp
  - | Loop Int Int RegExp
  - | Union [RegExp]
  - | Inter RegExp RegExp
- class RegExpMatchable a where
  - match :: a -> RegExp -> SBool
- exactly :: String -> RegExp
- oneOf :: String -> RegExp
- newline :: RegExp
- whiteSpaceNoNewLine :: RegExp
- whiteSpace :: RegExp
- tab :: RegExp
- punctuation :: RegExp
- asciiLetter :: RegExp
- asciiLower :: RegExp
- asciiUpper :: RegExp
- digit :: RegExp
- octDigit :: RegExp
- hexDigit :: RegExp
- decimal :: RegExp
- octal :: RegExp
- hexadecimal :: RegExp
- floating :: RegExp
- identifier :: RegExp

# Regular expressions

data RegExp Source #

Regular expressions. Note that regular expressions themselves are concrete, but the `match` function from the `RegExpMatchable` class can check membership against a symbolic string/character. Also, we are preferring a datatype approach here, as opposed to coming up with some string-representation; there are way too many alternatives already so inventing one isn't a priority. Please get in touch if you would like a parser for this type as it might be easier to use.

Constructors

Literal String | Precisely match the given string
All | Accept every string
None | Accept no strings
Range Char Char | Accept range of characters
Conc [RegExp] | Concatenation
KStar RegExp | Kleene Star: Zero or more
KPlus RegExp | Kleene Plus: One or more
Opt RegExp | Zero or one
Loop Int Int RegExp | From `n` repetitions to `m` repetitions
Union [RegExp] | Union of regular expressions
Inter RegExp RegExp | Intersection of regular expressions

#### Instances

Instances details

Eq RegExp Source # |
Instance details Defined in Data.SBV.Core.Symbolic Methods (==) :: RegExp -> RegExp -> Bool (/=) :: RegExp -> RegExp -> Bool
Num RegExp Source # | Regular expressions as a `Num` instance. Note that only `+` (union) and `*` (concatenation) make sense.
Instance details Defined in Data.SBV.Core.Symbolic Methods (+) :: RegExp -> RegExp -> RegExp (-) :: RegExp -> RegExp -> RegExp (*) :: RegExp -> RegExp -> RegExp negate :: RegExp -> RegExp abs :: RegExp -> RegExp signum :: RegExp -> RegExp fromInteger :: Integer -> RegExp
Ord RegExp Source # |
Instance details Defined in Data.SBV.Core.Symbolic Methods compare :: RegExp -> RegExp -> Ordering (<) :: RegExp -> RegExp -> Bool (<=) :: RegExp -> RegExp -> Bool (>) :: RegExp -> RegExp -> Bool (>=) :: RegExp -> RegExp -> Bool max :: RegExp -> RegExp -> RegExp min :: RegExp -> RegExp -> RegExp
Show RegExp Source # | Show instance for `RegExp`. The mapping is done so the outcome matches the SMTLib string reg-exp operations
Instance details Defined in Data.SBV.Core.Symbolic Methods showsPrec :: Int -> RegExp -> ShowS show :: RegExp -> String showList :: [RegExp] -> ShowS
IsString RegExp Source # | With overloaded strings, we can have direct literal regular expressions.
Instance details Defined in Data.SBV.Core.Symbolic Methods fromString :: String -> RegExp

# Matching

A symbolic string or a character (`SString` or `SChar`) can be matched against a regular-expression. Note that the regular-expression itself is not a symbolic object: It's a fully concrete representation, as captured by the `RegExp` class. The `RegExp` class is an instance of the `IsString` class, which makes writing literal matches easier. The `RegExp` type also has a (somewhat degenerate) `Num` instance: Concatenation corresponds to multiplication, union corresponds to addition, and `0` corresponds to the empty language.

Note that since `match` is a method of `RegExpMatchable` class, both `SChar` and `SString` can be used as an argument for matching. In practice, this means you might have to disambiguate with a type-ascription if it is not deducible from context.

    >>> prove $ \s -> (s :: SString) `match` "hello" .<=> s .== "hello"
    Q.E.D.
    >>> prove $ \s -> s `match` Loop 2 5 "xyz" .=> length s .>= 6
    Q.E.D.
    >>> prove $ \s -> s `match` Loop 2 5 "xyz" .=> length s .<= 15
    Q.E.D.
    >>> prove $ \s -> match s (Loop 2 5 "xyz") .=> length s .>= 7
    Falsifiable. Counter-example:
      s0 = "xyzxyz" :: String
    >>> prove $ \s -> (s :: SString) `match` "hello" .=> s `match` ("hello" + "world")
    Q.E.D.
    >>> prove $ \s -> sNot $ (s::SString) `match` ("so close" * 0)
    Q.E.D.
    >>> prove $ \c -> (c :: SChar) `match` oneOf "abcd" .=> ord c .>= ord (literal 'a') .&& ord c .<= ord (literal 'd')
    Q.E.D.

class RegExpMatchable a where Source #

Matchable class. Things we can match against a `RegExp`. (TODO: Currently SBV does *not* optimize this call if the input is a concrete string or a character, but rather directly calls down to the solver. We might want to perform the operation on the Haskell side for performance reasons, should this become important.)

For instance, you can generate valid-looking phone numbers like this:

    >>> :set -XOverloadedStrings
    >>> let dig09 = Range '0' '9'
    >>> let dig19 = Range '1' '9'
    >>> let pre   = dig19 * Loop 2 2 dig09
    >>> let post  = dig19 * Loop 3 3 dig09
    >>> let phone = pre * "-" * post
    >>> sat $ \s -> (s :: SString) `match` phone
    Satisfiable. Model:
      s0 = "100-1000" :: String

Methods

match :: a -> RegExp -> SBool Source #

``match` s r` checks whether `s` is in the language generated by `r`.

#### Instances

Instances details

RegExpMatchable SString Source # | Matching symbolic strings.
Instance details Defined in Data.SBV.RegExp Methods match :: SString -> RegExp -> SBool Source #
RegExpMatchable SChar Source # | Matching a character simply means the singleton string matches the regex.
Instance details Defined in Data.SBV.RegExp Methods match :: SChar -> RegExp -> SBool Source #

# Constructing regular expressions

## Literals

exactly :: String -> RegExp Source #

A literal regular-expression, matching the given string exactly. Note that with `OverloadedStrings` extension, you can simply use a Haskell string to mean the same thing, so this function is rarely needed.

    >>> prove $ \(s :: SString) -> s `match` exactly "LITERAL" .<=> s .== "LITERAL"
    Q.E.D.

## A class of characters

oneOf :: String -> RegExp Source #

Helper to define a character class.

    >>> prove $ \(c :: SChar) -> c `match` oneOf "ABCD" .<=> sAny (c .==) (map literal "ABCD")
    Q.E.D.

## Spaces

newline :: RegExp Source #

Recognize a newline. Also includes carriage-return and form-feed.

    >>> newline
    (re.union (str.to.re "\n") (str.to.re "\r") (str.to.re "\f"))
    >>> prove $ \c -> c `match` newline .=> isSpace c
    Q.E.D.

whiteSpaceNoNewLine :: RegExp Source #

Recognize white-space, but without a new line.

    >>> whiteSpaceNoNewLine
    (re.union (str.to.re "\x09") (re.union (str.to.re "\v") (str.to.re "\xa0") (str.to.re " ")))
    >>> prove $ \c -> c `match` whiteSpaceNoNewLine .=> c `match` whiteSpace .&& c ./= literal '\n'
    Q.E.D.

whiteSpace :: RegExp Source #

Recognize white space.

    >>> prove $ \c -> c `match` whiteSpace .=> isSpace c
    Q.E.D.

## Separators

tab :: RegExp Source #

Recognize a tab.

    >>> tab
    (str.to.re "\x09")
    >>> prove $ \c -> c `match` tab .=> c .== literal '\t'
    Q.E.D.

punctuation :: RegExp Source #

Recognize a punctuation character. Anything that satisfies the predicate `isPunctuation` will be accepted. (TODO: Will need modification when we move to unicode.)

    >>> prove $ \c -> c `match` punctuation .=> isPunctuation c
    Q.E.D.

## Letters

asciiLetter :: RegExp Source #

Recognize an alphabet letter, i.e., `A`..`Z`, `a`..`z`.

    >>> asciiLetter
    (re.union (re.range "a" "z") (re.range "A" "Z"))
    >>> prove $ \c -> c `match` asciiLetter .<=> toUpper c `match` asciiLetter
    Q.E.D.
    >>> prove $ \c -> c `match` asciiLetter .<=> toLower c `match` asciiLetter
    Q.E.D.

asciiLower :: RegExp Source #

Recognize an ASCII lower case letter

    >>> asciiLower
    (re.range "a" "z")
    >>> prove $ \c -> (c :: SChar) `match` asciiLower  .=> c `match` asciiLetter
    Q.E.D.
    >>> prove $ \c -> c `match` asciiLower  .=> toUpper c `match` asciiUpper
    Q.E.D.
    >>> prove $ \c -> c `match` asciiLetter .=> toLower c `match` asciiLower
    Q.E.D.

asciiUpper :: RegExp Source #

Recognize an upper case letter

    >>> asciiUpper
    (re.range "A" "Z")
    >>> prove $ \c -> (c :: SChar) `match` asciiUpper  .=> c `match` asciiLetter
    Q.E.D.
    >>> prove $ \c -> c `match` asciiUpper  .=> toLower c `match` asciiLower
    Q.E.D.
    >>> prove $ \c -> c `match` asciiLetter .=> toUpper c `match` asciiUpper
    Q.E.D.

## Digits

digit :: RegExp Source #

Recognize a digit. One of `0`..`9`.

    >>> digit
    (re.range "0" "9")
    >>> prove $ \c -> c `match` digit .<=> let v = digitToInt c in 0 .<= v .&& v .< 10
    Q.E.D.

octDigit :: RegExp Source #

Recognize an octal digit. One of `0`..`7`.

    >>> octDigit
    (re.range "0" "7")
    >>> prove $ \c -> c `match` octDigit .<=> let v = digitToInt c in 0 .<= v .&& v .< 8
    Q.E.D.
    >>> prove $ \(c :: SChar) -> c `match` octDigit .=> c `match` digit
    Q.E.D.

hexDigit :: RegExp Source #

Recognize a hexadecimal digit. One of `0`..`9`, `a`..`f`, `A`..`F`.

    >>> hexDigit
    (re.union (re.range "0" "9") (re.range "a" "f") (re.range "A" "F"))
    >>> prove $ \c -> c `match` hexDigit .<=> let v = digitToInt c in 0 .<= v .&& v .< 16
    Q.E.D.
    >>> prove $ \(c :: SChar) -> c `match` digit .=> c `match` hexDigit
    Q.E.D.

## Numbers

decimal :: RegExp Source #

Recognize a decimal number.

    >>> decimal
    (re.+ (re.range "0" "9"))
    >>> prove $ \s -> (s::SString) `match` decimal .=> sNot (s `match` KStar asciiLetter)
    Q.E.D.

octal :: RegExp Source #

Recognize an octal number. Must have a prefix of the form `0o`/`0O`.

    >>> octal
    (re.++ (re.union (str.to.re "0o") (str.to.re "0O")) (re.+ (re.range "0" "7")))
    >>> prove $ \s -> s `match` octal .=> sAny (.== take 2 s) ["0o", "0O"]
    Q.E.D.

hexadecimal :: RegExp Source #

Recognize a hexadecimal number. Must have a prefix of the form `0x`/`0X`.

    >>> hexadecimal
    (re.++ (re.union (str.to.re "0x") (str.to.re "0X")) (re.+ (re.union (re.range "0" "9") (re.range "a" "f") (re.range "A" "F"))))
    >>> prove $ \s -> s `match` hexadecimal .=> sAny (.== take 2 s) ["0x", "0X"]
    Q.E.D.

floating :: RegExp Source #

Recognize a floating point number. The exponent part is optional if a fraction is present. The exponent may or may not have a sign.

    >>> prove $ \s -> s `match` floating .=> length s .>= 3
    Q.E.D.

## Identifiers

identifier :: RegExp Source #

For the purposes of this regular expression, an identifier consists of a letter followed by zero or more letters, digits, underscores, and single quotes. The first letter must be lowercase.

    >>> prove $ \s -> s `match` identifier .=> isAsciiLower (head s)
    Q.E.D.
    >>> prove $ \s -> s `match` identifier .=> length s .>= 1
    Q.E.D.