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SequenceIteration

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Editor: test1 Time: 2014/02/19 20:14:37 GMT+0
Note:

changed:
-
The following package demonstrate various form of iteration over
list and arrays, both using loops and using higher order functions.
Note that Spad loop

   for i in 0..5 for e in l repeat

is a parallel iteration, stepping i and e in sync stopping when one
of iterators runs out.

\begin{spad}
SI ==> SingleInteger
LSI ==> List SI
PSI ==> PrimitiveArray SI

)abbrev package TTT TTT
TTT : with (
   list_map1 : (LSI, SI -> SI) -> LSI;
     -- list_map1([e1, ..., en], f) returns
     -- \spad{[f(e1), ..., f(e_n)]}
   list_inc : LSI -> LSI;
     -- list_inc([e1,...,en]) returns \spad{[e1+1,...,en+1]}
     -- Note: we create a fresh list
   arr_inc : PSI -> PSI;
     -- arr_inc([e1,...,en]) returns \spad{[e1+1,...,en+1]}
     -- Note: we create a fresh array
   list_fill : (LSI, SI) -> LSI;
     -- list_fill(l, a) returns list having all elements equal
     -- to \spad{a} of the same length as \spad{l}
   list_map2: (LSI, LSI, (SI, SI) -> SI) -> LSI;
     -- list_map1(l1, l2, f) creates list from values obtained
     -- by applying f to corresponding elements of l1 and l2
     -- Note: we truncate result to length of shorter list,
     -- excess elements of l1 or l2 are ignored.
   list_add1 : (LSI, LSI) -> LSI;
     -- list_add1(l1, l2) returns list of sums of corresponding
     -- elements of l1 and l2 using list_map2 and a helper
     -- Note: we truncate result to length of shorter list,
     -- excess elements of l1 or l2 are ignored.
   list_add2 : (LSI, LSI) -> LSI;
     -- list_add2 is the same as list_add1 but using
     -- simple iteration
   list_add3 : (LSI, LSI) -> LSI;
     -- list_add2 is the same as list_add1 but uses anonymous
     -- function
   list_filter : (LSI, SI -> Boolean) -> LSI;
     -- list_filter(l, f) returns list of elements \spad{e} of
     -- \spad{l} for which \spad{f(e)} is true
   filter_pos1 : LSI -> LSI;
     -- filter_pos1(l) returns list of positive elements of l
     -- usinig simple iteration
   filter_pos2 : LSI -> LSI;
     -- filter_pos2(l) is like filter_pos1, but uses list_filter
   filter_pos3 : PSI -> PSI;
     -- filter_pos3(l) is like filter_pos1, but for arrays
   setelt3 : (PSI, LSI) -> Void
     -- setelt3(a, l) sets every third element of
     -- \spad{a} to appropriate element of \spad{l}
     -- Probably useless, but demonstrates itertion
 ) == add

    list_map1(l : LSI, f : SI -> SI) : LSI ==
        [f(el) for el in l]

    -- helper for list_inc
    inc_SI(el : SI) : SI == el + 1

    list_inc(l : LSI) : LSI ==
        list_map1(l, inc_SI)

    arr_inc(pa : PSI) : PSI ==
        [pa(i) + 1 for i in 0..(#pa - 1)]

    list_fill(l : LSI, x : SI) : LSI ==
        list_map1(l, (y : SI) : SI +-> x)

    list_map2(l1 : LSI, l2 : LSI, f : (SI, SI) -> SI) : LSI ==
        [f(el1, el2) for el1 in l1 for el2 in l2]

    -- helper for list_add1
    add_SI(x1 : SI, x2 : SI) : SI == x1 + x2

    list_add1(l1 : LSI, l2 : LSI) : LSI ==
       list_map2(l1, l2, add_SI)

    list_add2(l1 : LSI, l2 : LSI) : LSI ==
        [el1 + el2 for el1 in l1 for el2 in l2]

    list_add3(l1 : LSI, l2 : LSI) : LSI ==
        list_map2(l1, l2, (x1 : SI, x2 : SI) : SI +-> x1 + x2)

    list_filter(l : LSI, f : SI -> Boolean) : LSI ==
        [el for el in l | f(el)]

    filter_pos1(l : LSI) : LSI ==
        [el for el in l | 0 < el]

    pos_SI(x : SI) : Boolean == 0 < x

    filter_pos2(l : LSI) : LSI ==
        list_filter(l, pos_SI)

    filter_pos3(pa : PSI) : PSI ==
        [pa(i) for i in 0..(#pa - 1) | 0 < pa(i)]

    setelt3(pa : PSI, l : LSI) : Void ==
        for i in 0..(#pa - 1) by 3 for el in l repeat
            pa(i) := el
\end{spad}

Try it out:
\begin{axiom}
list_map1([-1, 2, 0], x +-> x*2)
list_inc([-1, 2, 0])
a := construct([-1, 2, 0])$PrimitiveArray(SingleInteger)
arr_inc(a)
list_fill([-1, 2, 0], 42)
list_map2([-1, 2, 0], [17, 1, 3], (x, y) +-> 42)
list_add1([-1, 2, 0], [17, 1, 3])
list_add2([-1, 2, 0], [17, 1, 3])
list_add3([-1, 2, 0], [17, 1, 3])
list_filter([17, 1, 3], x +-> x = 1)
filter_pos1([-1, 2, 0])
filter_pos2([-1, 2, 0])
filter_pos3(a)
b := construct([-1, 2, 0, 4])$PrimitiveArray(SingleInteger)
setelt3(b, [1, 2])
b
\end{axiom}

The following package demonstrate various form of iteration over list and arrays, both using loops and using higher order functions. Note that Spad loop

for i in 0..5 for e in l repeat

is a parallel iteration, stepping i and e in sync stopping when one of iterators runs out.

spad

SI ==> SingleInteger
LSI ==> List SI
PSI ==> PrimitiveArray SI

)abbrev package TTT TTT
TTT : with (
   list_map1 : (LSI, SI -> SI) -> LSI;
     -- list_map1([e1, ..., en], f) returns
     -- \spad{[f(e1), ..., f(e_n)]}
   list_inc : LSI -> LSI;
     -- list_inc([e1,...,en]) returns \spad{[e1+1,...,en+1]}
     -- Note: we create a fresh list
   arr_inc : PSI -> PSI;
     -- arr_inc([e1,...,en]) returns \spad{[e1+1,...,en+1]}
     -- Note: we create a fresh array
   list_fill : (LSI, SI) -> LSI;
     -- list_fill(l, a) returns list having all elements equal
     -- to \spad{a} of the same length as \spad{l}
   list_map2: (LSI, LSI, (SI, SI) -> SI) -> LSI;
     -- list_map1(l1, l2, f) creates list from values obtained
     -- by applying f to corresponding elements of l1 and l2
     -- Note: we truncate result to length of shorter list,
     -- excess elements of l1 or l2 are ignored.
   list_add1 : (LSI, LSI) -> LSI;
     -- list_add1(l1, l2) returns list of sums of corresponding
     -- elements of l1 and l2 using list_map2 and a helper
     -- Note: we truncate result to length of shorter list,
     -- excess elements of l1 or l2 are ignored.
   list_add2 : (LSI, LSI) -> LSI;
     -- list_add2 is the same as list_add1 but using
     -- simple iteration
   list_add3 : (LSI, LSI) -> LSI;
     -- list_add2 is the same as list_add1 but uses anonymous
     -- function
   list_filter : (LSI, SI -> Boolean) -> LSI;
     -- list_filter(l, f) returns list of elements \spad{e} of
     -- \spad{l} for which \spad{f(e)} is true
   filter_pos1 : LSI -> LSI;
     -- filter_pos1(l) returns list of positive elements of l
     -- usinig simple iteration
   filter_pos2 : LSI -> LSI;
     -- filter_pos2(l) is like filter_pos1, but uses list_filter
   filter_pos3 : PSI -> PSI;
     -- filter_pos3(l) is like filter_pos1, but for arrays
   setelt3 : (PSI, LSI) -> Void
     -- setelt3(a, l) sets every third element of
     -- \spad{a} to appropriate element of \spad{l}
     -- Probably useless, but demonstrates itertion
 ) == add

    list_map1(l : LSI, f : SI -> SI) : LSI ==
        [f(el) for el in l]

    -- helper for list_inc
    inc_SI(el : SI) : SI == el + 1

    list_inc(l : LSI) : LSI ==
        list_map1(l, inc_SI)

    arr_inc(pa : PSI) : PSI ==
        [pa(i) + 1 for i in 0..(#pa - 1)]

    list_fill(l : LSI, x : SI) : LSI ==
        list_map1(l, (y : SI) : SI +-> x)

    list_map2(l1 : LSI, l2 : LSI, f : (SI, SI) -> SI) : LSI ==
        [f(el1, el2) for el1 in l1 for el2 in l2]

    -- helper for list_add1
    add_SI(x1 : SI, x2 : SI) : SI == x1 + x2

    list_add1(l1 : LSI, l2 : LSI) : LSI ==
       list_map2(l1, l2, add_SI)

    list_add2(l1 : LSI, l2 : LSI) : LSI ==
        [el1 + el2 for el1 in l1 for el2 in l2]

    list_add3(l1 : LSI, l2 : LSI) : LSI ==
        list_map2(l1, l2, (x1 : SI, x2 : SI) : SI +-> x1 + x2)

    list_filter(l : LSI, f : SI -> Boolean) : LSI ==
        [el for el in l | f(el)]

    filter_pos1(l : LSI) : LSI ==
        [el for el in l | 0 < el]

    pos_SI(x : SI) : Boolean == 0 < x

    filter_pos2(l : LSI) : LSI ==
        list_filter(l, pos_SI)

    filter_pos3(pa : PSI) : PSI ==
        [pa(i) for i in 0..(#pa - 1) | 0 < pa(i)]

    setelt3(pa : PSI, l : LSI) : Void ==
        for i in 0..(#pa - 1) by 3 for el in l repeat
            pa(i) := el

spad

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8626208773152027304-25px001.spad
      using old system compiler.
   TTT abbreviates package TTT 
------------------------------------------------------------------------
   initializing NRLIB TTT for TTT 
   compiling into NRLIB TTT 
   compiling exported list_map1 : (List SingleInteger,SingleInteger -> SingleInteger) -> List SingleInteger
Time: 0 SEC.

   compiling local inc_SI : SingleInteger -> SingleInteger
      TTT;inc_SI is replaced by add_SIel1 
Time: 0 SEC.

   compiling exported list_inc : List SingleInteger -> List SingleInteger
Time: 0 SEC.

   compiling exported arr_inc : PrimitiveArray SingleInteger -> PrimitiveArray SingleInteger
Time: 0 SEC.

   compiling exported list_fill : (List SingleInteger,SingleInteger) -> List SingleInteger
Time: 0.01 SEC.

   compiling exported list_map2 : (List SingleInteger,List SingleInteger,(SingleInteger,SingleInteger) -> SingleInteger) -> List SingleInteger
Time: 0 SEC.

   compiling local add_SI : (SingleInteger,SingleInteger) -> SingleInteger
      TTT;add_SI is replaced by add_SI 
Time: 0 SEC.

   compiling exported list_add1 : (List SingleInteger,List SingleInteger) -> List SingleInteger
Time: 0 SEC.

   compiling exported list_add2 : (List SingleInteger,List SingleInteger) -> List SingleInteger
Time: 0 SEC.

   compiling exported list_add3 : (List SingleInteger,List SingleInteger) -> List SingleInteger
Time: 0 SEC.

   compiling exported list_filter : (List SingleInteger,SingleInteger -> Boolean) -> List SingleInteger
Time: 0 SEC.

   compiling exported filter_pos1 : List SingleInteger -> List SingleInteger
Time: 0 SEC.

   compiling local pos_SI : SingleInteger -> Boolean
      TTT;pos_SI is replaced by less_SI0x 
Time: 0 SEC.

   compiling exported filter_pos2 : List SingleInteger -> List SingleInteger
Time: 0 SEC.

   compiling exported filter_pos3 : PrimitiveArray SingleInteger -> PrimitiveArray SingleInteger
Time: 0 SEC.

   compiling exported setelt3 : (PrimitiveArray SingleInteger,List SingleInteger) -> Void
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       TTT REDEFINED

;;;     ***       TTT REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor TTT
      Time: 0.01 seconds

   finalizing NRLIB TTT 
   Processing TTT for Browser database:
--->-->TTT(constructor): Not documented!!!!
--->-->TTT((list_map1 ((List (SingleInteger)) (List (SingleInteger)) (Mapping (SingleInteger) (SingleInteger))))): Not documented!!!!
--->-->TTT((list_inc ((List (SingleInteger)) (List (SingleInteger))))): Not documented!!!!
--->-->TTT((arr_inc ((PrimitiveArray (SingleInteger)) (PrimitiveArray (SingleInteger))))): Not documented!!!!
--->-->TTT((list_fill ((List (SingleInteger)) (List (SingleInteger)) (SingleInteger)))): Not documented!!!!
--->-->TTT((list_map2 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger)) (Mapping (SingleInteger) (SingleInteger) (SingleInteger))))): Not documented!!!!
--->-->TTT((list_add1 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger))))): Not documented!!!!
--->-->TTT((list_add2 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger))))): Not documented!!!!
--->-->TTT((list_add3 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger))))): Not documented!!!!
--->-->TTT((list_filter ((List (SingleInteger)) (List (SingleInteger)) (Mapping (Boolean) (SingleInteger))))): Not documented!!!!
--->-->TTT((filter_pos1 ((List (SingleInteger)) (List (SingleInteger))))): Not documented!!!!
--->-->TTT((filter_pos2 ((List (SingleInteger)) (List (SingleInteger))))): Not documented!!!!
--->-->TTT((filter_pos3 ((PrimitiveArray (SingleInteger)) (PrimitiveArray (SingleInteger))))): Not documented!!!!
--->-->TTT((setelt3 ((Void) (PrimitiveArray (SingleInteger)) (List (SingleInteger))))): Not documented!!!!
--->-->TTT(): Missing Description
; compiling file "/var/aw/var/LatexWiki/TTT.NRLIB/TTT.lsp" (written 19 FEB 2014 08:14:37 PM):

; /var/aw/var/LatexWiki/TTT.NRLIB/TTT.fasl written
; compilation finished in 0:00:00.066
------------------------------------------------------------------------
   TTT is now explicitly exposed in frame initial 
   TTT will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/TTT.NRLIB/TTT

Try it out:

fricas

list_map1([-1, 2, 0], x +-> x*2)

$\label{eq1}\left[ - 2, \: 4, \: 0 \right]$

(1)

Type: List(SingleInteger?)

fricas

list_inc([-1, 2, 0])

$\label{eq2}\left[ 0, \: 3, \: 1 \right]$

(2)

Type: List(SingleInteger?)

fricas

a := construct([-1, 2, 0])$PrimitiveArray(SingleInteger)

$\label{eq3}\left[ - 1, \: 2, \: 0 \right]$

(3)

Type: PrimitiveArray?(SingleInteger?)

fricas

arr_inc(a)

$\label{eq4}\left[ 0, \: 3, \: 1 \right]$

(4)

Type: PrimitiveArray?(SingleInteger?)

fricas

list_fill([-1, 2, 0], 42)

$\label{eq5}\left[{42}, \:{42}, \:{42}\right]$

(5)

Type: List(SingleInteger?)

fricas

list_map2([-1, 2, 0], [17, 1, 3], (x, y) +-> 42)

$\label{eq6}\left[{42}, \:{42}, \:{42}\right]$

(6)

Type: List(SingleInteger?)

fricas

list_add1([-1, 2, 0], [17, 1, 3])

$\label{eq7}\left[{16}, \: 3, \: 3 \right]$

(7)

Type: List(SingleInteger?)

fricas

list_add2([-1, 2, 0], [17, 1, 3])

$\label{eq8}\left[{16}, \: 3, \: 3 \right]$

(8)

Type: List(SingleInteger?)

fricas

list_add3([-1, 2, 0], [17, 1, 3])

$\label{eq9}\left[{16}, \: 3, \: 3 \right]$

(9)

Type: List(SingleInteger?)

fricas

list_filter([17, 1, 3], x +-> x = 1)

$\label{eq10}\left[ 1 \right]$

(10)

Type: List(SingleInteger?)

fricas

filter_pos1([-1, 2, 0])

$\label{eq11}\left[ 2 \right]$

(11)

Type: List(SingleInteger?)

fricas

filter_pos2([-1, 2, 0])

$\label{eq12}\left[ 2 \right]$

(12)

Type: List(SingleInteger?)

fricas

filter_pos3(a)

$\label{eq13}\left[ 2 \right]$

(13)

Type: PrimitiveArray?(SingleInteger?)

fricas

b := construct([-1, 2, 0, 4])$PrimitiveArray(SingleInteger)

$\label{eq14}\left[ - 1, \: 2, \: 0, \: 4 \right]$

(14)

Type: PrimitiveArray?(SingleInteger?)

fricas

setelt3(b, [1, 2])

Type: Void

fricas

$\label{eq15}\left[ 1, \: 2, \: 0, \: 2 \right]$

(15)

Type: PrimitiveArray?(SingleInteger?)