sunterlib/s48/sequences -- Finite Sequences

A sequence library in various structures dealing with
* abstract sequences defined by their behaviour
* general sequences or a union type of built-in and abstract sequences
* vectors in particular
  [ for list and string libraries ,open srfi-1 resp. srfi-13 ]

The library comes in three structures:
* ABSEQUENCES  -- basic procedures for abstract sequences, contained in
* SEQUENCE-LIB -- procedures for general (and abstract) sequences
* VECTOR-LIB   -- procedures for vectors

The VECTOR-LIB exports some SCHEME bindings such as VECTOR-REF, redefines
some SCHEME procedures such as VECTOR-FILL! (to accept optional [start:end)
parameters) and consists mainly of generic sequence code compiled with
the basic sequence operation names bound to the corresponding vector
procedures.  The library is neither complete nor tweaked nor tested
sytematically.  (The idea to recycle parts of the srfi-13 code came
too late.)  It contains the folllowing procedures, arranged in
columns=structures and `* categories' from SRFI-13 and -1.


VECTOR-LIB            SEQUENCE-LIB             ABSEQUENCES, also SL
* Predicates or so
vector?               sequence?                absequence?
                                               sequence-behavior?
[ versions with 1 sequence and optional start & end parameters ]
vector-every          sequence-every
vector-any            sequence-any
[ versions with >1 sequence but no optional start & end parameters ]
vectors-every         sequences-every
vectors-any           sequences-any
[ 2 seq. args and opt. start & end parms for both seqs ]
vector=               sequence=
[ >=0 sequence args, no start & end parameters ]
vectors=              sequences=

* Constructors
make-vector           make-another-sequence    make-absequence/behavior
vector                                         absequence/behavior
                                               make-sequence-behavior
                                               make-absequence-record

* List & Sequence Conversion
list->vector                                   list->absequence/behavior
vector->list          sequence->list

* Selection
vector-length         sequence-length          absequence-length
vector-ref            sequence-ref             absequence-ref
                                               absequence:behavior
vector-copy           sequence-copy
                      sequence-copy/maker
subvector             subsequence

* Modification
vector-set!           sequence-set!            absequence-set!
sequence-fill!        vector-fill!             absequence-fill!

* Reverse & Append
vector-append         sequence-append

* Fold, Unfold & Map
[ versions with 1 sequence and optional start & end parameters ]
vector-map            sequence-map
                      sequence-map/maker
vector-for-each       sequence-for-each
vector-fold           sequence-fold
vector-fold-right     sequence-fold-right
[ versions with >1 sequence but no start & end parameters ]
vectors-map           sequences-map
                      sequences-map/maker
vectors-for-each      sequences-for-each
vectors-fold          sequences-fold
vectors-fold-right    sequences-fold-right

                                  *

Prelude

For our purposes, (each valid state of) a sequence with length n maps a
bounded segment of integers [0:n) into a set of Scheme values, typically
Anything or Character.  Any kind Sq of sequences with elements in T
supports the following basic operations, whatever the names, with the
obvious jobs:
                 maker :     (make-sq n [e]) --> s
                 predicate : (sq? x) --> b
                 getter :    (sq-ref s k) --> s[k]
                 setter :    (sq-set! s k x) --> unspec
                 meter :     (sq-length s) --> n


The following kinds of sequences are supported by this facility:

  Vector
  Absequence := a record type (record packages data + behaviour)
  Sequence := Vector | Byte-Vector | String | Proper-List | Absequence

Absequences carry a SEQUENCE-BEHAVIOR record that contains MAKER,
PREDICATE, etc. procedures.  They are the official backdoor where
user-defined sequence types enter the general sequence lib.  There are
Examples.

                                    *

The Procedures

Optional [START END] (abbreviating [START [END]]) parameters default to 0
resp. the sequence length.  An optional MAKER parameter defaults to
the maker of the actual type of the (first) sequence argument.
Sequence arguments of vector and absequence procedures must be vectors
resp. absequences, notwithstanding the generic parameter name S used below.
Sequence arguments of general sequence procedures may have different
actual sequence types, e.g. (SEQUENCES-EVERY CHAR=? "abc" '#(#\a)) is
ok since both String and Vector <= Sequence.

Equivalences
  as far as the specs go, that is: the equivalences don't extend to
unspecified behaviour but I didn't bother to spell this out in detail.
The stated equivalences may have to suffer from exceptions as the
library grows, but please report deviations anyway.

* (sequences-foo x ...) = (sequence-foo x ...) and
  (vectors-foo x ...) = (vector-foo x ...)
  if the arg.list is admissible for both procedures.
  [ SEQUENCES-procedures don't support optional [start:end)
  parameters;  SEQUENCE-procedures don't support an arbitrary number
  of sequence arguments.  Same for vectors. ]

* if all sequence arguments to a general sequence procedure are
  vectors the result is that of the corresponding vector procedure.
  E.g. ``sequence-map = vector-map'' on vectors.

* if all sequence arguments to a general sequence procedure are lists
  (strings) and there is a corresponding list (string) procedure in
  the respective srfi, the result complies with the srfi spec.
  E.g. ``sequences-fold = fold'' on lists,
       ``sequence-fold = string-fold'' on strings.
  Exception:  SEQUENCE= vs. STRING= -- parameter lists don't match (ELT=)


* Predicates

(vector? x) --> b0
(sequence? x) --> b1
(absequence? x) --> b2
(sequence-behavior? x) --> b

Synopsis:  The obvious type predicates.  Note that by the type
inclusions the boolean B0 ==> B1 and B2 ==> B1.

                                    *

(vector-every foo? s [start end]) --> x
(sequence-every foo? s [start end]) --> x

Synopsis:  Return the value x of (and (foo? s[start]) ... (foo? s[end-1])).

                                    *

(vector-any foo? s [start end]) --> x
(sequence-any foo? s [start end]) --> x

Synopsis:  Return the value x of (or (foo? s[start]) ... (foo? s[end-1])).

                                   *

(vectors-every foo? s0 s1 ...) --> b
(sequences-every foo? s0 s1 ...) --> b

Synopsis:  Return the value x of (and[0<=i<n] (foo? s0[i] s1[i] ...)) with
n := min.k sequence-length sk.

                                   *

(vectors-any foo? s0 s1 ...) --> b
(sequences-any foo? s0 s1 ...) --> b

Synopsis:  Return the value x of (or[0<=i<n] (foo? s0[i] s1[i] ...)) with
n := min.k sequence-length sk.

                                  *

(vector= elt= s0 s1 [start0 end0 start1 end1]) --> b
(sequence= elt= s0 s1 [start0 end0 start1 end1]) --> b

Synopsis:  Return boolean(S0 and S1 represent the same sequence), i.e.
B = (and (elt= s0[start0] s1[start1]) ...)
[ deviates from STRING= in SRFI-13 due to ELT= parameter ]

                                  *

(vectors= elt= s0 ...) --> b
(sequences= elt= s0 ...) --> b

Synopsis:  Return B = boolean(S0, ... represent the same sequence), i.e.
B = #t given <2 sequence args, and
  = (and[k=0,...) (sequence= elt= s(k) s(k+1))) otherwise.

                                  *

Constructors

(make-vector len [fill]) --> s
(make-absequence/behavior sb len [fill]) --> s

Synopsis:  Make a fresh vector resp. absequence S (with sequence-behavior
SB) of length LEN (and all elements = FILL).

                                  *

(vector x0 ...) --> s
(absequence/behavior sb x0 ...) --> s

Synopsis:  Make a fresh vector (absequence with sequence-behavior SB)
of minimal length with the elements S[0] = X0, ...

                                  *

(make-sequence-behavior maker predicate getter setter meter) --> sb

Synopsis: Package the concrete sequence behaviour (basic procedures
listed in the prelude) in the sequence-behavior record SB.

(make-absequence-record sb data) --> abs
Synopsis:  Package the sequence-behavior SB and the concrete sequence DATA
in the absequence record ABS.

                                  *

List & Sequence Conversion

(list->vector xs [sbart end]) --> s
(list->absequence/behavior sb xs [start end]) --> s

Synopsis:  Make a new vector (absequence with sequence-behavior SB) S
representing the sequence xs[start],..,xs[end-1].

                                 *

(vector->list s [start end]) --> xs
(sequence->list s [start end]) --> xs

Synopsis:  Return xs = (list s[start] ... s[end-1]).

                                 *

(vector-length s) --> n
(sequence-length s) --> n
(absequence-length s) --> n

Synopsis:  Return length N of vector / sequence / absequence S.

                                 *

(vector-ref v k) --> v[k]
(sequence-ref s k) --> s[k]
(absequence-ref abs k) --> abs[k]

                                 *

(absequence:behavior abs) --> sb

Synopsis:  Return sequence-behavior SB for the concrete sequence
packaged in absequence ABS.

                                 *

(vector-copy s0 [start end]) --> s1
(sequence-copy s0 [start end]) --> s1
(sequence-copy/maker maker s0 [start end]) -- s1

Synopsis:  Make new vector resp. sequence (with MAKER)
S1 = < s0[start+i] : i in [0:end-start) >.
[ MAKER intentionally not made third optional arg. ]

                                 *

(subvector s0 start end) --> s1
(subsequence s0 start end) --> s1

Synopsis:  s1 := (sequence-copy s0 start end)

                                *

Modification

(vector-set! s i x) --> unspec
(sequence-set! s i x) --> unspec
(absequence-set! s i x) --> unspec

Synopsis:  Set s[i] := x.

                                *

(vector-fill! s x [start end]) --> unspec
(sequence-fill! s x [start end]]) --> unspec
(absequence-fill! s x [start end]) --> unspec

Synopsis:  Set s[i] := x for all i in [start:end) etc.

                                *

Reverse & Append

(vector-append s0 ...) --> s
(sequence-append s0 ...) --> s

Synoposis:  Make a new vector resp. sequence S = `s0 o ...'.  If there
is no argument, make S a vector, otherwise type(S) = type(S0).  [ You
can force the result type by choosing a suitable empty sequence S0.
E.g. (sequence-append (vector) "sloty" '(5 5)) works.
Of course, VECTOR-APPEND always produces vectors from vectors. ]

                                *

Fold, Unfold & Map

(vector-map f s [start end]) --> fs
(vectors-map f s0 ...) --> fs
(sequence-map f s [start end]) --> fs
(sequence-map/maker maker f s [start end]) --> fs
(sequences-map f s0 s1 ...) --> fs
(sequences-map/maker maker f s0 s1 ...) --> fs

Synopsis:  Make new vector / sequence FS representing the sequence
f(s[start]),...,f(s[end-1])  resp.
(f(s0[i],...) : 0<=i<n)      with n = min.k sequence-length sk.
Use the MAKER, if supplied, otherwise the maker of the first sequence
arg's concrete type.  [ MAKER intentionally not made third optional
arg. ]

                                *

(vector-for-each proc s [start end]) --> unspec
(vectors-for-each f s0 s1 ...) --> unspec
(sequence-for-each proc s [start end]) --> unspec
(sequences-for-each proc s0 s1 ...) --> unspec

Synopsis:  Call (proc v[i]) for all i in [start:end) in some order, resp.
call (proc v0[i] v1[i] ...) for all i in [0:n) in some order with
n = min.k sequence-length sk.

                                *

(vector-fold kons nil s [start end]) --> sq
(vectors-fold kons nil s0 s1 ...) --> sq
(sequence-fold kons nil s0 [start end]) --> sq
(sequences-fold kons nil s0 s1 ...) --> sq

Synopsis:  Let  y o x             := (kons x      y)  resp.
                y o (x0, x1, ...) := (kons x0 ... y),

and let o be left-associative (so that we can spare us the brackets).
Compute
        sq = nil o s[start]          o ... o s[end-1],       resp.
        sq = nil o (s0[0],s1[0],...) o ... o (s0[n-1],s1[n-1],...)
with
        n := min.k sequence-length sk.

                               *

(vector-fold-right kons nil s [start end]) --> sq
(vectors-fold-right kons nil s0 s1 ...) --> sq
(sequence-fold-right kons nil s [start end]) --> sq
(sequences-fold-right kons nil s0 s1 ...) --> sq

Synopsis:  Let  x o y := (kons x      y)       resp.
      (x0,x1,...) o y := (kons x0 ... y),

and let o be right-associative (so that we can spare us the brackets).
Compute
        sq = s[start]    o ... o s[end-1]      o nil,  resp.
        sq = (s0[0] ...) o ... o (s0[n-1] ...) o nil
with
        n := min.k sequence-length sk.

                                 *

Examples:
; Demo implementation of partial sequences
; ,open sequence-lib srfi-9 krims

(define-record-type :shaseq
  (make-shaseq-record sequence start end)
  shaseq?
  (sequence shaseq:sequence)
  (start shaseq:start)
  (end shaseq:end))


(define (share-sequence s start end)
  (assert (<= 0 start end (sequence-length s)))
  (make-shaseq-record s start end))


(define (displace-index shas k)
  (let ((start (shaseq:start shas)))
    (+ start k)))


;; maker -- dummyish
(define (make-shaseq len . maybe-fill)
  (make-shaseq-record (apply make-vector len maybe-fill)
                      0 len))
;; getter
(define (shaseq-ref shas k)
  (sequence-ref (shaseq:sequence shas)
                (displace-index shas k)))
;; setter
(define (shaseq-set! shas k x)
  (sequence-set! (shaseq:sequence shas)
                 (displace-index shas k)
                 x))
;; meter
(define (shaseq-length shas)
  (- (shaseq:end shas)
     (shaseq:start shas)))


(define shaseq-behavior
  (make-sequence-behavior make-shaseq shaseq?
                          shaseq-ref shaseq-set!
                          shaseq-length))

(define a-string (string-copy "brachman foo gratz bladotzky"))
(define an-abs (make-absequence-record shaseq-behavior
                                       (share-sequence a-string 3 11)))

;; prints ``(c h m a n   f o)''
(display (sequence-fold-right cons '() an-abs))

;; prints ``>>> chman fo <<<''
(display (sequence-append ">>> " an-abs '#(#\ #\< #\< #\<)))

(sequence-fill! an-abs #\X 4)
;; prints ``brachmaXXXXo gratz bladotzky''
(display a-string)

; EOF
                                 *

Sela (for now).

                                oOo