8.16.0.4
2.4 Isomorphisms
| (require ocular-patdown/optics/isomorphism) | |
| package: ocular-patdown | |
An isomorphism is an optic whose focus is "equivalent" (isomorphic) to its target. An isomorphism can be used when two data types can be converted back and forth between each other. Isomorphisms are useful for treating one data type as another.
Examples:
> (optic-modify symbol<->string 'foo string-upcase) 'FOO
> (optic-get symbol<->string 'foo) "foo"
> (iso-forward symbol<->string 'foo) "foo"
> (iso-backward symbol<->string "foo") 'foo
All isomorphisms are lenses, but not all lenses are isomorphisms.
Predicate for isomorphisms. Recognizes implementers of gen:iso.
Examples:
> (iso? symbol<->string) #t
> (iso? car-lens) #f
Constructor for isomorphisms.
Example:
> (define my-symbol<->string (make-iso symbol->string string->symbol))
forward and backward must be inverses of each other:
2.4.1 Isomorphism operations
procedure
(iso-forward iso target) → any/c
iso : iso? target : any/c
Convert target to its equivalent focus.
Example:
> (iso-forward symbol<->string 'foo) "foo"
procedure
(iso-backward iso focus) → any/c
iso : iso? focus : any/c
Convert focus to its equivalent target.
Example:
> (iso-backward symbol<->string "foo") 'foo
Modify target with proc as if it was its focus under iso.
proc must accept and return a focus.
Example:
> (iso-modify symbol<->string 'foo string-upcase) 'FOO
procedure
(iso-reverse iso) → iso?
iso : iso?
Reverse/invert iso such that it works in the opposite direction.
Examples:
> (iso-forward symbol<->string 'foo) "foo"
> (iso-forward (iso-reverse symbol<->string) "foo") 'foo
procedure
(iso-compose iso ...) → iso?
iso : iso?
Like optic-compose, but for isomorphisms.
Examples:
> (iso-forward (iso-compose vector<->list list-reverse-iso) #(1 2 3)) '(3 2 1)
> (iso-backward (iso-compose vector<->list list-reverse-iso) '(3 2 1)) '#(1 2 3)
2.4.2 Library Isomorphisms
value
Isomorphism between symbols and strings.
Example:
> (iso-modify symbol<->string 'foo string-upcase) 'FOO
value
Isomorphism between vectors and lists.
Example:
> (iso-modify vector<->list #(1 2 3) reverse) '#(3 2 1)
value
Isomorphism between lists and reversed lists. Useful for folding over a traversal
in reverse.
Examples:
> (iso-forward list-reverse-iso (list 1 2 3)) '(3 2 1)
> (iso-backward list-reverse-iso (list 3 2 1)) '(1 2 3)
> (traversal-foldl (optic-compose vector<->list list-reverse-iso list-traversal) #("a" "b" "c") string-append "") "abc"
value
Isomorphism between values and themselves. The identity of optic-compose.
Examples:
> (iso-forward identity-iso 1) 1
> (iso-backward identity-iso 1) 1
2.4.3 Isomorphism Generic Interface
syntax
A generic interface for isomorphisms.
Example:
> (struct make-iso [forward backward] #:methods gen:iso [(define (iso-forward iso target) ((make-iso-forward iso) target)) (define (iso-backward iso focus) ((make-iso-backward iso) focus))])