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/* String manipulation functions. */
{ lib }:
let
inherit (builtins) length;
in
rec {
inherit (builtins)
compareVersions
elem
elemAt
filter
fromJSON
head
isInt
isList
isAttrs
isString
match
parseDrvName
readFile
replaceStrings
split
storeDir
stringLength
substring
tail
toJSON
typeOf
unsafeDiscardStringContext
;
/* Concatenate a list of strings.
Type: concatStrings :: [string] -> string
Example:
concatStrings ["foo" "bar"]
=> "foobar"
*/
concatStrings = builtins.concatStringsSep "";
/* Map a function over a list and concatenate the resulting strings.
Type: concatMapStrings :: (a -> string) -> [a] -> string
Example:
concatMapStrings (x: "a" + x) ["foo" "bar"]
=> "afooabar"
*/
concatMapStrings = f: list: concatStrings (map f list);
/* Like `concatMapStrings` except that the f functions also gets the
position as a parameter.
Type: concatImapStrings :: (int -> a -> string) -> [a] -> string
Example:
concatImapStrings (pos: x: "${toString pos}-${x}") ["foo" "bar"]
=> "1-foo2-bar"
*/
concatImapStrings = f: list: concatStrings (lib.imap1 f list);
/* Place an element between each element of a list
Type: intersperse :: a -> [a] -> [a]
Example:
intersperse "/" ["usr" "local" "bin"]
=> ["usr" "/" "local" "/" "bin"].
*/
intersperse =
# Separator to add between elements
separator:
# Input list
list:
if list == [] || length list == 1
then list
else tail (lib.concatMap (x: [separator x]) list);
/* Concatenate a list of strings with a separator between each element
Type: concatStringsSep :: string -> [string] -> string
Example:
concatStringsSep "/" ["usr" "local" "bin"]
=> "usr/local/bin"
*/
concatStringsSep = builtins.concatStringsSep or (separator: list:
lib.foldl' (x: y: x + y) "" (intersperse separator list));
/* Maps a function over a list of strings and then concatenates the
result with the specified separator interspersed between
elements.
Type: concatMapStringsSep :: string -> (a -> string) -> [a] -> string
Example:
concatMapStringsSep "-" (x: toUpper x) ["foo" "bar" "baz"]
=> "FOO-BAR-BAZ"
*/
concatMapStringsSep =
# Separator to add between elements
sep:
# Function to map over the list
f:
# List of input strings
list: concatStringsSep sep (map f list);
/* Same as `concatMapStringsSep`, but the mapping function
additionally receives the position of its argument.
Type: concatIMapStringsSep :: string -> (int -> a -> string) -> [a] -> string
Example:
concatImapStringsSep "-" (pos: x: toString (x / pos)) [ 6 6 6 ]
=> "6-3-2"
*/
concatImapStringsSep =
# Separator to add between elements
sep:
# Function that receives elements and their positions
f:
# List of input strings
list: concatStringsSep sep (lib.imap1 f list);
/* Construct a Unix-style, colon-separated search path consisting of
the given `subDir` appended to each of the given paths.
Type: makeSearchPath :: string -> [string] -> string
Example:
makeSearchPath "bin" ["/root" "/usr" "/usr/local"]
=> "/root/bin:/usr/bin:/usr/local/bin"
makeSearchPath "bin" [""]
=> "/bin"
*/
makeSearchPath =
# Directory name to append
subDir:
# List of base paths
paths:
concatStringsSep ":" (map (path: path + "/" + subDir) (filter (x: x != null) paths));
/* Construct a Unix-style search path by appending the given
`subDir` to the specified `output` of each of the packages. If no
output by the given name is found, fallback to `.out` and then to
the default.
Type: string -> string -> [package] -> string
Example:
makeSearchPathOutput "dev" "bin" [ pkgs.openssl pkgs.zlib ]
=> "/nix/store/9rz8gxhzf8sw4kf2j2f1grr49w8zx5vj-openssl-1.0.1r-dev/bin:/nix/store/wwh7mhwh269sfjkm6k5665b5kgp7jrk2-zlib-1.2.8/bin"
*/
makeSearchPathOutput =
# Package output to use
output:
# Directory name to append
subDir:
# List of packages
pkgs: makeSearchPath subDir (map (lib.getOutput output) pkgs);
/* Construct a library search path (such as RPATH) containing the
libraries for a set of packages
Example:
makeLibraryPath [ "/usr" "/usr/local" ]
=> "/usr/lib:/usr/local/lib"
pkgs = import <nixpkgs> { }
makeLibraryPath [ pkgs.openssl pkgs.zlib ]
=> "/nix/store/9rz8gxhzf8sw4kf2j2f1grr49w8zx5vj-openssl-1.0.1r/lib:/nix/store/wwh7mhwh269sfjkm6k5665b5kgp7jrk2-zlib-1.2.8/lib"
*/
makeLibraryPath = makeSearchPathOutput "lib" "lib";
/* Construct a binary search path (such as $PATH) containing the
binaries for a set of packages.
Example:
makeBinPath ["/root" "/usr" "/usr/local"]
=> "/root/bin:/usr/bin:/usr/local/bin"
*/
makeBinPath = makeSearchPathOutput "bin" "bin";
/* Depending on the boolean `cond', return either the given string
or the empty string. Useful to concatenate against a bigger string.
Type: optionalString :: bool -> string -> string
Example:
optionalString true "some-string"
=> "some-string"
optionalString false "some-string"
=> ""
*/
optionalString =
# Condition
cond:
# String to return if condition is true
string: if cond then string else "";
/* Determine whether a string has given prefix.
Type: hasPrefix :: string -> string -> bool
Example:
hasPrefix "foo" "foobar"
=> true
hasPrefix "foo" "barfoo"
=> false
*/
hasPrefix =
# Prefix to check for
pref:
# Input string
str: substring 0 (stringLength pref) str == pref;
/* Determine whether a string has given suffix.
Type: hasSuffix :: string -> string -> bool
Example:
hasSuffix "foo" "foobar"
=> false
hasSuffix "foo" "barfoo"
=> true
*/
hasSuffix =
# Suffix to check for
suffix:
# Input string
content:
let
lenContent = stringLength content;
lenSuffix = stringLength suffix;
in lenContent >= lenSuffix &&
substring (lenContent - lenSuffix) lenContent content == suffix;
/* Determine whether a string contains the given infix
Type: hasInfix :: string -> string -> bool
Example:
hasInfix "bc" "abcd"
=> true
hasInfix "ab" "abcd"
=> true
hasInfix "cd" "abcd"
=> true
hasInfix "foo" "abcd"
=> false
*/
hasInfix = infix: content:
builtins.match ".*${escapeRegex infix}.*" "${content}" != null;
/* Convert a string to a list of characters (i.e. singleton strings).
This allows you to, e.g., map a function over each character. However,
note that this will likely be horribly inefficient; Nix is not a
general purpose programming language. Complex string manipulations
should, if appropriate, be done in a derivation.
Also note that Nix treats strings as a list of bytes and thus doesn't
handle unicode.
Type: stringToCharacters :: string -> [string]
Example:
stringToCharacters ""
=> [ ]
stringToCharacters "abc"
=> [ "a" "b" "c" ]
stringToCharacters "💩"
=> [ "�" "�" "�" "�" ]
*/
stringToCharacters = s:
map (p: substring p 1 s) (lib.range 0 (stringLength s - 1));
/* Manipulate a string character by character and replace them by
strings before concatenating the results.
Type: stringAsChars :: (string -> string) -> string -> string
Example:
stringAsChars (x: if x == "a" then "i" else x) "nax"
=> "nix"
*/
stringAsChars =
# Function to map over each individual character
f:
# Input string
s: concatStrings (
map f (stringToCharacters s)
);
/* Escape occurrence of the elements of `list` in `string` by
prefixing it with a backslash.
Type: escape :: [string] -> string -> string
Example:
escape ["(" ")"] "(foo)"
=> "\\(foo\\)"
*/
escape = list: replaceChars list (map (c: "\\${c}") list);
/* Quote string to be used safely within the Bourne shell.
Type: escapeShellArg :: string -> string
Example:
escapeShellArg "esc'ape\nme"
=> "'esc'\\''ape\nme'"
*/
escapeShellArg = arg: "'${replaceStrings ["'"] ["'\\''"] (toString arg)}'";
/* Quote all arguments to be safely passed to the Bourne shell.
Type: escapeShellArgs :: [string] -> string
Example:
escapeShellArgs ["one" "two three" "four'five"]
=> "'one' 'two three' 'four'\\''five'"
*/
escapeShellArgs = concatMapStringsSep " " escapeShellArg;
/* Test whether the given name is a valid POSIX shell variable name.
Type: string -> bool
Example:
isValidPosixName "foo_bar000"
=> true
isValidPosixName "0-bad.jpg"
=> false
*/
isValidPosixName = name: match "[a-zA-Z_][a-zA-Z0-9_]*" name != null;
/* Translate a Nix value into a shell variable declaration, with proper escaping.
The value can be a string (mapped to a regular variable), a list of strings
(mapped to a Bash-style array) or an attribute set of strings (mapped to a
Bash-style associative array). Note that "string" includes string-coercible
values like paths or derivations.
Strings are translated into POSIX sh-compatible code; lists and attribute sets
assume a shell that understands Bash syntax (e.g. Bash or ZSH).
Type: string -> (string | listOf string | attrsOf string) -> string
Example:
''
${toShellVar "foo" "some string"}
[[ "$foo" == "some string" ]]
''
*/
toShellVar = name: value:
lib.throwIfNot (isValidPosixName name) "toShellVar: ${name} is not a valid shell variable name" (
if isAttrs value && ! isCoercibleToString value then
"declare -A ${name}=(${
concatStringsSep " " (lib.mapAttrsToList (n: v:
"[${escapeShellArg n}]=${escapeShellArg v}"
) value)
})"
else if isList value then
"declare -a ${name}=(${escapeShellArgs value})"
else
"${name}=${escapeShellArg value}"
);
/* Translate an attribute set into corresponding shell variable declarations
using `toShellVar`.
Type: attrsOf (string | listOf string | attrsOf string) -> string
Example:
let
foo = "value";
bar = foo;
in ''
${toShellVars { inherit foo bar; }}
[[ "$foo" == "$bar" ]]
''
*/
toShellVars = vars: concatStringsSep "\n" (lib.mapAttrsToList toShellVar vars);
/* Turn a string into a Nix expression representing that string
Type: string -> string
Example:
escapeNixString "hello\${}\n"
=> "\"hello\\\${}\\n\""
*/
escapeNixString = s: escape ["$"] (toJSON s);
/* Turn a string into an exact regular expression
Type: string -> string
Example:
escapeRegex "[^a-z]*"
=> "\\[\\^a-z]\\*"
*/
escapeRegex = escape (stringToCharacters "\\[{()^$?*+|.");
/* Quotes a string if it can't be used as an identifier directly.
Type: string -> string
Example:
escapeNixIdentifier "hello"
=> "hello"
escapeNixIdentifier "0abc"
=> "\"0abc\""
*/
escapeNixIdentifier = s:
# Regex from https://github.com/NixOS/nix/blob/d048577909e383439c2549e849c5c2f2016c997e/src/libexpr/lexer.l#L91
if match "[a-zA-Z_][a-zA-Z0-9_'-]*" s != null
then s else escapeNixString s;
/* Escapes a string such that it is safe to include verbatim in an XML
document.
Type: string -> string
Example:
escapeXML ''"test" 'test' < & >''
=> "&quot;test&quot; &apos;test&apos; &lt; &amp; &gt;"
*/
escapeXML = builtins.replaceStrings
["\"" "'" "<" ">" "&"]
["&quot;" "&apos;" "&lt;" "&gt;" "&amp;"];
# Obsolete - use replaceStrings instead.
replaceChars = builtins.replaceStrings or (
del: new: s:
let
substList = lib.zipLists del new;
subst = c:
let found = lib.findFirst (sub: sub.fst == c) null substList; in
if found == null then
c
else
found.snd;
in
stringAsChars subst s);
# Case conversion utilities.
lowerChars = stringToCharacters "abcdefghijklmnopqrstuvwxyz";
upperChars = stringToCharacters "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
/* Converts an ASCII string to lower-case.
Type: toLower :: string -> string
Example:
toLower "HOME"
=> "home"
*/
toLower = replaceChars upperChars lowerChars;
/* Converts an ASCII string to upper-case.
Type: toUpper :: string -> string
Example:
toUpper "home"
=> "HOME"
*/
toUpper = replaceChars lowerChars upperChars;
/* Appends string context from another string. This is an implementation
detail of Nix.
Strings in Nix carry an invisible `context` which is a list of strings
representing store paths. If the string is later used in a derivation
attribute, the derivation will properly populate the inputDrvs and
inputSrcs.
Example:
pkgs = import <nixpkgs> { };
addContextFrom pkgs.coreutils "bar"
=> "bar"
*/
addContextFrom = a: b: substring 0 0 a + b;
/* Cut a string with a separator and produces a list of strings which
were separated by this separator.
Example:
splitString "." "foo.bar.baz"
=> [ "foo" "bar" "baz" ]
splitString "/" "/usr/local/bin"
=> [ "" "usr" "local" "bin" ]
*/
splitString = _sep: _s:
let
sep = builtins.unsafeDiscardStringContext _sep;
s = builtins.unsafeDiscardStringContext _s;
splits = builtins.filter builtins.isString (builtins.split (escapeRegex sep) s);
in
map (v: addContextFrom _sep (addContextFrom _s v)) splits;
/* Return a string without the specified prefix, if the prefix matches.
Type: string -> string -> string
Example:
removePrefix "foo." "foo.bar.baz"
=> "bar.baz"
removePrefix "xxx" "foo.bar.baz"
=> "foo.bar.baz"
*/
removePrefix =
# Prefix to remove if it matches
prefix:
# Input string
str:
let
preLen = stringLength prefix;
sLen = stringLength str;
in
if hasPrefix prefix str then
substring preLen (sLen - preLen) str
else
str;
/* Return a string without the specified suffix, if the suffix matches.
Type: string -> string -> string
Example:
removeSuffix "front" "homefront"
=> "home"
removeSuffix "xxx" "homefront"
=> "homefront"
*/
removeSuffix =
# Suffix to remove if it matches
suffix:
# Input string
str:
let
sufLen = stringLength suffix;
sLen = stringLength str;
in
if sufLen <= sLen && suffix == substring (sLen - sufLen) sufLen str then
substring 0 (sLen - sufLen) str
else
str;
/* Return true if string v1 denotes a version older than v2.
Example:
versionOlder "1.1" "1.2"
=> true
versionOlder "1.1" "1.1"
=> false
*/
versionOlder = v1: v2: compareVersions v2 v1 == 1;
/* Return true if string v1 denotes a version equal to or newer than v2.
Example:
versionAtLeast "1.1" "1.0"
=> true
versionAtLeast "1.1" "1.1"
=> true
versionAtLeast "1.1" "1.2"
=> false
*/
versionAtLeast = v1: v2: !versionOlder v1 v2;
/* This function takes an argument that's either a derivation or a
derivation's "name" attribute and extracts the name part from that
argument.
Example:
getName "youtube-dl-2016.01.01"
=> "youtube-dl"
getName pkgs.youtube-dl
=> "youtube-dl"
*/
getName = x:
let
parse = drv: (parseDrvName drv).name;
in if isString x
then parse x
else x.pname or (parse x.name);
/* This function takes an argument that's either a derivation or a
derivation's "name" attribute and extracts the version part from that
argument.
Example:
getVersion "youtube-dl-2016.01.01"
=> "2016.01.01"
getVersion pkgs.youtube-dl
=> "2016.01.01"
*/
getVersion = x:
let
parse = drv: (parseDrvName drv).version;
in if isString x
then parse x
else x.version or (parse x.name);
/* Extract name with version from URL. Ask for separator which is
supposed to start extension.
Example:
nameFromURL "https://nixos.org/releases/nix/nix-1.7/nix-1.7-x86_64-linux.tar.bz2" "-"
=> "nix"
nameFromURL "https://nixos.org/releases/nix/nix-1.7/nix-1.7-x86_64-linux.tar.bz2" "_"
=> "nix-1.7-x86"
*/
nameFromURL = url: sep:
let
components = splitString "/" url;
filename = lib.last components;
name = head (splitString sep filename);
in assert name != filename; name;
/* Create an --{enable,disable}-<feat> string that can be passed to
standard GNU Autoconf scripts.
Example:
enableFeature true "shared"
=> "--enable-shared"
enableFeature false "shared"
=> "--disable-shared"
*/
enableFeature = enable: feat:
assert isString feat; # e.g. passing openssl instead of "openssl"
"--${if enable then "enable" else "disable"}-${feat}";
/* Create an --{enable-<feat>=<value>,disable-<feat>} string that can be passed to
standard GNU Autoconf scripts.
Example:
enableFeatureAs true "shared" "foo"
=> "--enable-shared=foo"
enableFeatureAs false "shared" (throw "ignored")
=> "--disable-shared"
*/
enableFeatureAs = enable: feat: value: enableFeature enable feat + optionalString enable "=${value}";
/* Create an --{with,without}-<feat> string that can be passed to
standard GNU Autoconf scripts.
Example:
withFeature true "shared"
=> "--with-shared"
withFeature false "shared"
=> "--without-shared"
*/
withFeature = with_: feat:
assert isString feat; # e.g. passing openssl instead of "openssl"
"--${if with_ then "with" else "without"}-${feat}";
/* Create an --{with-<feat>=<value>,without-<feat>} string that can be passed to
standard GNU Autoconf scripts.
Example:
withFeatureAs true "shared" "foo"
=> "--with-shared=foo"
withFeatureAs false "shared" (throw "ignored")
=> "--without-shared"
*/
withFeatureAs = with_: feat: value: withFeature with_ feat + optionalString with_ "=${value}";
/* Create a fixed width string with additional prefix to match
required width.
This function will fail if the input string is longer than the
requested length.
Type: fixedWidthString :: int -> string -> string -> string
Example:
fixedWidthString 5 "0" (toString 15)
=> "00015"
*/
fixedWidthString = width: filler: str:
let
strw = lib.stringLength str;
reqWidth = width - (lib.stringLength filler);
in
assert lib.assertMsg (strw <= width)
"fixedWidthString: requested string length (${
toString width}) must not be shorter than actual length (${
toString strw})";
if strw == width then str else filler + fixedWidthString reqWidth filler str;
/* Format a number adding leading zeroes up to fixed width.
Example:
fixedWidthNumber 5 15
=> "00015"
*/
fixedWidthNumber = width: n: fixedWidthString width "0" (toString n);
/* Convert a float to a string, but emit a warning when precision is lost
during the conversion
Example:
floatToString 0.000001
=> "0.000001"
floatToString 0.0000001
=> trace: warning: Imprecise conversion from float to string 0.000000
"0.000000"
*/
floatToString = float: let
result = toString float;
precise = float == fromJSON result;
in lib.warnIf (!precise) "Imprecise conversion from float to string ${result}"
result;
/* Check whether a value can be coerced to a string */
isCoercibleToString = x:
elem (typeOf x) [ "path" "string" "null" "int" "float" "bool" ] ||
(isList x && lib.all isCoercibleToString x) ||
x ? outPath ||
x ? __toString;
/* Check whether a value is a store path.
Example:
isStorePath "/nix/store/d945ibfx9x185xf04b890y4f9g3cbb63-python-2.7.11/bin/python"
=> false
isStorePath "/nix/store/d945ibfx9x185xf04b890y4f9g3cbb63-python-2.7.11"
=> true
isStorePath pkgs.python
=> true
isStorePath [] || isStorePath 42 || isStorePath {} || …
=> false
*/
isStorePath = x:
if !(isList x) && isCoercibleToString x then
let str = toString x; in
substring 0 1 str == "/"
&& dirOf str == storeDir
else
false;
/* Parse a string as an int.
Type: string -> int
Example:
toInt "1337"
=> 1337
toInt "-4"
=> -4
toInt "3.14"
=> error: floating point JSON numbers are not supported
*/
# Obviously, it is a bit hacky to use fromJSON this way.
toInt = str:
let may_be_int = fromJSON str; in
if isInt may_be_int
then may_be_int
else throw "Could not convert ${str} to int.";
/* Read a list of paths from `file`, relative to the `rootPath`.
Lines beginning with `#` are treated as comments and ignored.
Whitespace is significant.
NOTE: This function is not performant and should be avoided.
Example:
readPathsFromFile /prefix
./pkgs/development/libraries/qt-5/5.4/qtbase/series
=> [ "/prefix/dlopen-resolv.patch" "/prefix/tzdir.patch"
"/prefix/dlopen-libXcursor.patch" "/prefix/dlopen-openssl.patch"
"/prefix/dlopen-dbus.patch" "/prefix/xdg-config-dirs.patch"
"/prefix/nix-profiles-library-paths.patch"
"/prefix/compose-search-path.patch" ]
*/
readPathsFromFile = lib.warn "lib.readPathsFromFile is deprecated, use a list instead"
(rootPath: file:
let
lines = lib.splitString "\n" (readFile file);
removeComments = lib.filter (line: line != "" && !(lib.hasPrefix "#" line));
relativePaths = removeComments lines;
absolutePaths = map (path: rootPath + "/${path}") relativePaths;
in
absolutePaths);
/* Read the contents of a file removing the trailing \n
Type: fileContents :: path -> string
Example:
$ echo "1.0" > ./version
fileContents ./version
=> "1.0"
*/
fileContents = file: removeSuffix "\n" (readFile file);
/* Creates a valid derivation name from a potentially invalid one.
Type: sanitizeDerivationName :: String -> String
Example:
sanitizeDerivationName "../hello.bar # foo"
=> "-hello.bar-foo"
sanitizeDerivationName ""
=> "unknown"
sanitizeDerivationName pkgs.hello
=> "-nix-store-2g75chlbpxlrqn15zlby2dfh8hr9qwbk-hello-2.10"
*/
sanitizeDerivationName =
let okRegex = match "[[:alnum:]+_?=-][[:alnum:]+._?=-]*";
in
string:
# First detect the common case of already valid strings, to speed those up
if stringLength string <= 207 && okRegex string != null
then unsafeDiscardStringContext string
else lib.pipe string [
# Get rid of string context. This is safe under the assumption that the
# resulting string is only used as a derivation name
unsafeDiscardStringContext
# Strip all leading "."
(x: elemAt (match "\\.*(.*)" x) 0)
# Split out all invalid characters
# https://github.com/NixOS/nix/blob/2.3.2/src/libstore/store-api.cc#L85-L112
# https://github.com/NixOS/nix/blob/2242be83c61788b9c0736a92bb0b5c7bbfc40803/nix-rust/src/store/path.rs#L100-L125
(split "[^[:alnum:]+._?=-]+")
# Replace invalid character ranges with a "-"
(concatMapStrings (s: if lib.isList s then "-" else s))
# Limit to 211 characters (minus 4 chars for ".drv")
(x: substring (lib.max (stringLength x - 207) 0) (-1) x)
# If the result is empty, replace it with "unknown"
(x: if stringLength x == 0 then "unknown" else x)
];
/* Computes the Levenshtein distance between two strings.
Complexity O(n*m) where n and m are the lengths of the strings.
Algorithm adjusted from https://stackoverflow.com/a/9750974/6605742
Type: levenshtein :: string -> string -> int
Example:
levenshtein "foo" "foo"
=> 0
levenshtein "book" "hook"
=> 1
levenshtein "hello" "Heyo"
=> 3
*/
levenshtein = a: b: let
# Two dimensional array with dimensions (stringLength a + 1, stringLength b + 1)
arr = lib.genList (i:
lib.genList (j:
dist i j
) (stringLength b + 1)
) (stringLength a + 1);
d = x: y: lib.elemAt (lib.elemAt arr x) y;
dist = i: j:
let c = if substring (i - 1) 1 a == substring (j - 1) 1 b
then 0 else 1;
in
if j == 0 then i
else if i == 0 then j
else lib.min
( lib.min (d (i - 1) j + 1) (d i (j - 1) + 1))
( d (i - 1) (j - 1) + c );
in d (stringLength a) (stringLength b);
/* Returns the length of the prefix common to both strings.
*/
commonPrefixLength = a: b:
let
m = lib.min (stringLength a) (stringLength b);
go = i: if i >= m then m else if substring i 1 a == substring i 1 b then go (i + 1) else i;
in go 0;
/* Returns the length of the suffix common to both strings.
*/
commonSuffixLength = a: b:
let
m = lib.min (stringLength a) (stringLength b);
go = i: if i >= m then m else if substring (stringLength a - i - 1) 1 a == substring (stringLength b - i - 1) 1 b then go (i + 1) else i;
in go 0;
/* Returns whether the levenshtein distance between two strings is at most some value
Complexity is O(min(n,m)) for k <= 2 and O(n*m) otherwise
Type: levenshteinAtMost :: int -> string -> string -> bool
Example:
levenshteinAtMost 0 "foo" "foo"
=> true
levenshteinAtMost 1 "foo" "boa"
=> false
levenshteinAtMost 2 "foo" "boa"
=> true
levenshteinAtMost 2 "This is a sentence" "this is a sentense."
=> false
levenshteinAtMost 3 "This is a sentence" "this is a sentense."
=> true
*/
levenshteinAtMost = let
infixDifferAtMost1 = x: y: stringLength x <= 1 && stringLength y <= 1;
# This function takes two strings stripped by their common pre and suffix,
# and returns whether they differ by at most two by Levenshtein distance.
# Because of this stripping, if they do indeed differ by at most two edits,
# we know that those edits were (if at all) done at the start or the end,
# while the middle has to have stayed the same. This fact is used in the
# implementation.
infixDifferAtMost2 = x: y:
let
xlen = stringLength x;
ylen = stringLength y;
# This function is only called with |x| >= |y| and |x| - |y| <= 2, so
# diff is one of 0, 1 or 2
diff = xlen - ylen;
# Infix of x and y, stripped by the left and right most character
xinfix = substring 1 (xlen - 2) x;
yinfix = substring 1 (ylen - 2) y;
# x and y but a character deleted at the left or right
xdelr = substring 0 (xlen - 1) x;
xdell = substring 1 (xlen - 1) x;
ydelr = substring 0 (ylen - 1) y;
ydell = substring 1 (ylen - 1) y;
in
# A length difference of 2 can only be gotten with 2 delete edits,
# which have to have happened at the start and end of x
# Example: "abcdef" -> "bcde"
if diff == 2 then xinfix == y
# A length difference of 1 can only be gotten with a deletion on the
# right and a replacement on the left or vice versa.
# Example: "abcdef" -> "bcdez" or "zbcde"
else if diff == 1 then xinfix == ydelr || xinfix == ydell
# No length difference can either happen through replacements on both
# sides, or a deletion on the left and an insertion on the right or
# vice versa
# Example: "abcdef" -> "zbcdez" or "bcdefz" or "zabcde"
else xinfix == yinfix || xdelr == ydell || xdell == ydelr;
in k: if k <= 0 then a: b: a == b else
let f = a: b:
let
alen = stringLength a;
blen = stringLength b;
prelen = commonPrefixLength a b;
suflen = commonSuffixLength a b;
presuflen = prelen + suflen;
ainfix = substring prelen (alen - presuflen) a;
binfix = substring prelen (blen - presuflen) b;
in
# Make a be the bigger string
if alen < blen then f b a
# If a has over k more characters than b, even with k deletes on a, b can't be reached
else if alen - blen > k then false
else if k == 1 then infixDifferAtMost1 ainfix binfix
else if k == 2 then infixDifferAtMost2 ainfix binfix
else levenshtein ainfix binfix <= k;
in f;
}