8.16.0.4
2.5 Prisms
| (require ocular-patdown/optics/prism) | |
| package: ocular-patdown | |
A prism is an optic that is like an isomorphism, but can be partial in one direction. In terms of foci, it can have zero or one. It is useful for dealing with subtypes, or situations where you can convert from A to B, but not always from B to A.
Examples:
> (prism-project string-number-prism "1") 1
> (prism-inject string-number-prism 1) "1"
> (prism-project string-number-prism "one" #f) #f
All isomorphisms are prisms, but not all prisms are isomorphisms.
All prisms are traversals, but not all traversals are prisms.
Predicate for prisms. Recognizes implementers of gen:prism.
Examples:
> (prism? string-number-prism) #t
> (prism? symbol<->string) #t
> (prism? car-lens) #f
> (prism? list-traversal) #f
procedure
(make-prism project inject) → prism?
project : (-> any/c (or/c any/c prism-absent?) any/c) inject : (-> any/c any/c)
Constructor for prisms. project takes in a target and returns the focus if there is one, or (prism-absent) otherwise.
inject takes in a focus and returns a target.
Example:
> (define my-string-number-prism (make-prism (lambda (str) (or (string->number str) (prism-absent))) number->string))
There are a few laws that prisms should obey:
These laws are the same as the isomorphism laws (see make-iso) when there is a focus.
In other words, project and inject must be inverse functions of each other when there is a focus.
procedure
Constructs a value representing the absence of a focus in a prism.
procedure
(prism-absent? val) → boolean?
val : any/c
Predicate for prism-absent.
2.5.1 Prism Operations
procedure
(prism-project prism target [failure-result]) → any/c
prism : prism? target : any/c
failure-result : (or/c any/c (-> any/c)) = (lambda () (error ...))
Get the focus of target under prism if there is one, and use failure-result otherwise.
failure-result is either a value or a zero-argument procedure that returns a value.
Examples:
> (prism-project string-number-prism "1") 1
> (prism-project string-number-prism "one" #f) #f
procedure
(prism-inject prism focus) → any/c
prism : prism? focus : any/c
Get the target from focus under prism.
Example:
> (prism-inject string-number-prism 1) "1"
procedure
(prism-compose prism ...) → prism?
prism : prism?
Like optic-compose, but for prisms.
Example:
> (prism-inject (prism-compose symbol<->string string-number-prism) 1) '|1|
2.5.2 Library Prisms
value
Prism between strings and numbers.
Examples:
> (prism-project string-number-prism "1") 1
> (prism-project string-number-prism "one" #f) #f
> (prism-inject string-number-prism 1) "1"
procedure
(guard-prism predicate) → prism?
predicate : (-> any/c boolean?)
Prism that has a focus if (predicate target) is true.
Examples:
> (prism-project (guard-prism number?) 1) 1
> (prism-project (guard-prism number?) "one" #f) #f
> (prism-inject (guard-prism number?) 1) 1
2.5.3 Prism Generic Interface
syntax
Generic interface for prisms.
Example:
> (struct make-prism (project inject) #:methods gen:prism [(define (prism-project prism target [failure-result default-failure-result]) (let ([focus ((make-prism-project prism) target)]) (if (prism-absent? focus) (if (procedure? failure-result) (failure-result) failure-result) focus))) (define (prism-inject prism focus) ((make-prism-inject prism) focus))])