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## levenshtein

Levenshtein edit distance

## Documentation

Levenshtein is a collection of procedures providing various forms of the Levenshtein edit distance calculation.

The Levenshtein edit distance has been used for areas as diverse as soil sample and language dialect analysis. Not just for text strings.

### 8-bit Values Only

Performs edit distance calculation for byte strings & blobs. All return the total edit cost.

#### levenshtein-distance/byte

##### Usage

(use levenshtein-byte)

*[procedure]*

`(levenshtein-distance/byte SOURCE TARGET)`

Calculates the edit distance from the `SOURCE` to the `TARGET`. All costs are unitary.

#### levenshtein-distance/transpose-byte

##### Usage

(use levenshtein-transpose-byte)

*[procedure]*

`(levenshtein-distance/transpose-byte SOURCE TARGET)`

Calculates the edit distance from the `SOURCE` to the `TARGET`, taking into account the Transpose operation. All costs are unitary.

By using the Transpose operation the total edit cost is not at least the difference of the sizes of the two strings.

### Any "Sequence"

A functor implementing an edit distance algorithm parameterized by a cost and sequence operation modules.

See Examples for Usage

#### levenshtein-distance/sequence

*[procedure]*

`(levenshtein-distance/sequence SOURCE TARGET [:insert-cost INSERT-COST] [#:delete-cost DELETE-COST] [#:substitute-cost SUBSTITUTE-COST] (#:get-work-vector GET-WORK-VECTOR) [#:elm-eql ELM-EQL] [#:limit-cost LIMIT-COST])`

`SOURCE``string`.`TARGET``string`.`INSERT-COST``number`, default`1`.`DELETE-COST``number`, default`1`.`SUBSTITUTE-COST``number`, default`1`.`ELM-EQL``procedure`;`(-> object object boolean)`, default`eqv?`. The equality predicate.`GET-WORK-VECTOR``procedure`, default`make-vector`.`LIMIT-COST``number`or`#f`, default`#f`. Quit when cost over limit.

The `SOURCE` & `TARGET` must be the same type, which the instantiating sequence module supports.

**Note** that the element comparison procedure is passed via the argument list, and not via the sequence implementation module. Annoying when using strings but useful when using vectors.

### Only Vector - Baroque & Slow

A functor implementing an edit distance algorithm parameterized by a cost operation module.

Performs edit distance calculation for vectors. Allows definition of new edit operations. Will keep track of edit operations performed. Primarily a toy.

See Examples for Usage

#### levenshtein-distance/vector*

*[procedure]*

`(levenshtein-distance/vector* SOURCE TARGET [EDIT-OPER ...] [#:elm-eql ELM-EQL] [#:operations? OPERATIONS])`

Calculates the edit distance from the source vector `SOURCE` to the target vector `TARGET`. Returns the total edit cost or (values <total edit cost> <performed operations matrix>).

`SOURCE``vector`.`TARGET``vector`.`EDIT-OPER``levenshtein-operator`. Edit operation definitions to apply. Defaults are the basic Insert, Delete, and Substitute.`ELM-EQL``procedure`;`(-> object object boolean)`, default`char=?`. The equality predicate.`OPERATIONS``boolean`. Include the matrix of edit operations performed? Default`#f`.

### Interface Implementation Modules

levenshtein-cost-fixnum.scm levenshtein-cost-generic.scm levenshtein-cost-numbers.scm

levenshtein-sequence-string.scm levenshtein-sequence-utf8.scm levenshtein-sequence-vector.scm

### Edit Operators

Edit operation specification. A set of base operations is predefined, but may be overridden. The base set is identified by the keys Insert, Delete, Substitute, and Transpose. A printer and reader are provided for edit operations.

#### Usage

(use levenshtein-operators)

#### levenshtein-operator

*[record]*

`levenshtein-operator`

*[procedure]*

`(levenshtein-operator-key OPER) -> {{symbol}}`

*[procedure]*

`(levenshtein-operator-name OPER) -> {{string}}`

*[procedure]*

`(levenshtein-operator-cost OPER) -> {{number}}`

*[procedure]*

`(levenshtein-operator-above OPER) -> {{fixnum}}`

*[procedure]*

`(levenshtein-operator-left OPER) -> {{fixnum}}`

#### make-levenshtein-operator

*[procedure]*

`(make-levenshtein-operator KEY NAME COST ABOVE LEFT)`

Returns a new edit operator.

`KEY``symbol`. Key for the operation.`NAME``string`. Describes the operation.`COST``number`. The cost of the operation.`ABOVE``non-negative-fixnum`. How far back in the source.`LEFT``non-negative-fixnum`. How far back in the target.

#### levenshtein-operator?

*[procedure]*

`(levenshtein-operator? OBJECT)`

Is the `OBJECT` a levenshtein operator?

#### clone-levenshtein-operator

*[procedure]*

`(clone-levenshtein-operator EDIT-OPERATION [#:key KEY] [#:name NAME] [#:cost COST] [#:above ABOVE] [#:left LEFT])`

Returns a duplicate of the `EDIT-OPERATION`, with field values provided by the optional keyword arguments. `EDIT-OPERATION` may be the key of the already defined edit operation.

#### levenshtein-operator-ref

*[procedure]*

`(levenshtein-operator-ref KEY)`

Get the definition of an edit operation.

#### levenshtein-operator-set!

*[procedure]*

`(levenshtein-operator-set! EDIT-OPERATION)`

Define an edit operation.

#### levenshtein-operator-delete!

*[procedure]*

`(levenshtein-operator-delete! EDIT-OPERATION)`

Removes the `EDIT-OPERATION` definition. `EDIT-OPERATION` may be the `KEY` of the already defined edit operation.

#### levenshtein-operator-reset

*[procedure]*

`(levenshtein-operator-reset)`

Restore defined edit operations to the base set.

#### levenshtein-operator=?

*[procedure]*

`(levenshtein-operator=? A B)`

Are the `levenshtein-operator` `A` & `levenshtein-operator` `B` equal for all fields?

### Path Iterator

#### Usage

(use levenshtein-path-iterator)

#### levenshtein-path-iterator

*[procedure]*

`(levenshtein-path-iterator PATH-MATRIX)`

Creates an optimal edit distance operation path iterator over the performed operations matrix `PATH-MATRIX`. The matrix is usually the result of an invocation of `(levenshtein-distance/vector* ... operations: #t)`.

Each invocation of the iterator will generate a list of the form: `((cost source-index target-index levenshtein-operator) ...)`. The last invocation will return `#f`.

### Path Matrix Print

#### Usage

(use levenshtein-print)

#### print-levenshtein-matrix

*[procedure]*

`(print-levenshtein-matrix PATH-MATRIX)`

Displays a readable representation of the `PATH-MATRIX` on the `current-output-port`.

## Notes

- The functors are not available before Chicken 4.7.2, and so all support modules are also unavailable.
- To instantiate any of the functors the implementation module(s) must be included. Since the modules are installed in Chicken Repository, and the repository is not usually along the include path, the repository must be added to the include path. Using the environment variable CHICKEN_INCLUDE_PATH is convenient.

## Bugs & Limitations

`levenshtein-print`assumes a`levenshtein-operator-key`print-name is <= 15 characters and that the cost prints in <= 2 characters.

## Examples

(use levenshtein-byte) (use levenshtein-transpose-byte) (levenshtein-distance/byte "ctas" "cats") ;=> 2 (levenshtein-distance/transpose-byte "ctas" "cats") ;=> 1 ;cause of transpose

; Instantiate the distance measure algorithm (use levenshtein-path-iterator) (import levenshtein-vector-functor) (include "levenshtein-cost-fixnum") (module levenshtein-vector-fixnum = (levenshtein-vector-functor levenshtein-cost-fixnum)) (import (prefix levenshtein-vector-fixnum fx:)) (defineiter (levenshtein-path-iterator (fx:levenshtein-distance/vector* "YWCQPGK" "LAWYQQKPGKA" operations: #t)) ; ignoring interpreter feedback & we know the distance is 6 (definer0 (iter)) (definet0 r0) (definer1 (iter)) (definer2 (iter)) (definer3 (iter)) (definer4 (iter)) (definer5 (iter)) (iter) ; r0 now has #f, since the iterator finishes by returning to the initial caller, ; which is the body of '(define r0 (iter))', thus re-binding r0. However, t0 has ; the original returned value.

(import levenshtein-sequence-functor) (include "levenshtein-cost-fixnum") (include "levenshtein-sequence-vector") (module levenshtein-sequence-fixnum-vector = (levenshtein-sequence-functor levenshtein-cost-fixnum levenshtein-sequence-vector)) (import (prefix levenshtein-sequence-fixnum-vector fxvc:)) ; Now have 'fxvc:levenshtein-distance/sequence', be sure to verify the #:elm-eql ; keyword parameter default is what is wanted (include "levenshtein-cost-numbers") (include "levenshtein-sequence-utf8") (module levenshtein-sequence-numbers-utf8 = (levenshtein-sequence-functor levenshtein-cost-numbers levenshtein-sequence-utf8)) (import (prefix levenshtein-sequence-numbers-utf8 fnu8:)) ; Now have 'fnu8:levenshtein-distance/sequence', be sure to pass the #:elm-eql ; keyword parameter char=?

## Requirements

check-errors vector-lib srfi-63 numbers utf8 miscmacros moremacros setup-helper

## Author

## Version history

- 1.0.1
- Drop "format-compiler".
- 1.0.0
- Chicken 4 release.

## License

Copyright (c) 2012, Kon Lovett. All rights reserved.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the Software), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED ASIS, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.