MathAction SequenceIteration

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Sequence Iteration

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.

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(1) -> <spad>
SI ==> SingleInteger
LSI ==> List SI
PSI ==> PrimitiveArray SI

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)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>

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Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8834476310057333648-25px001.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: 0.01 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: 0.05 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: 0.01 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: 0.01 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: 0.01 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: 0.10 seconds

   finalizing NRLIB TTT 
   Processing TTT for Browser database:
--->-->TTT(constructor): Not documented!!!!
--------(list_map1 ((List (SingleInteger)) (List (SingleInteger)) (Mapping (SingleInteger) (SingleInteger))))---------
--------(list_inc ((List (SingleInteger)) (List (SingleInteger))))---------
--------(arr_inc ((PrimitiveArray (SingleInteger)) (PrimitiveArray (SingleInteger))))---------
--------(list_fill ((List (SingleInteger)) (List (SingleInteger)) (SingleInteger)))---------
--------(list_map2 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger)) (Mapping (SingleInteger) (SingleInteger) (SingleInteger))))---------
--->-->TTT((list_map2 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger)) (Mapping (SingleInteger) (SingleInteger) (SingleInteger))))): Improper first word in comments: list_map1
"\\spad{list_map1}(\\spad{l1},{} \\spad{l2},{} \\spad{f}) creates list from values obtained by applying \\spad{f} to corresponding elements of \\spad{l1} and \\spad{l2} Note: we truncate result to length of shorter list,{} excess elements of \\spad{l1} or \\spad{l2} are ignored."
--------(list_add1 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger))))---------
--------(list_add2 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger))))---------
--->-->TTT((list_add2 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger))))): Improper initial operator in comments: is
"\\spad{list_add2} is the same as \\spad{list_add1} but using simple iteration"
--------(list_add3 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger))))---------
--->-->TTT((list_add3 ((List (SingleInteger)) (List (SingleInteger)) (List (SingleInteger))))): Improper initial operator in comments: is
"\\spad{list_add2} is the same as \\spad{list_add1} but uses anonymous function"
--------(list_filter ((List (SingleInteger)) (List (SingleInteger)) (Mapping (Boolean) (SingleInteger))))---------
--------(filter_pos1 ((List (SingleInteger)) (List (SingleInteger))))---------
--------(filter_pos2 ((List (SingleInteger)) (List (SingleInteger))))---------
--------(filter_pos3 ((PrimitiveArray (SingleInteger)) (PrimitiveArray (SingleInteger))))---------
--------(setelt3 ((Void) (PrimitiveArray (SingleInteger)) (List (SingleInteger))))---------
--->-->TTT(): Missing Description
; compiling file "/var/aw/var/LatexWiki/TTT.NRLIB/TTT.lsp" (written 21 FEB 2023 12:46:26 PM):

; /var/aw/var/LatexWiki/TTT.NRLIB/TTT.fasl written
; compilation finished in 0:00:00.087
------------------------------------------------------------------------
   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:

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

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

(1)

Type: List(SingleInteger?)

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list_inc([-1, 2, 0])

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

(2)

Type: List(SingleInteger?)

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

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

(3)

Type: PrimitiveArray?(SingleInteger?)

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arr_inc(a)

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

(4)

Type: PrimitiveArray?(SingleInteger?)

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

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

(5)

Type: List(SingleInteger?)

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

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

(6)

Type: List(SingleInteger?)

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

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

(7)

Type: List(SingleInteger?)

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

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

(8)

Type: List(SingleInteger?)

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

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

(9)

Type: List(SingleInteger?)

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

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

(10)

Type: List(SingleInteger?)

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filter_pos1([-1, 2, 0])

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

(11)

Type: List(SingleInteger?)

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filter_pos2([-1, 2, 0])

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

(12)

Type: List(SingleInteger?)

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filter_pos3(a)

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

(13)

Type: PrimitiveArray?(SingleInteger?)

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

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

(14)

Type: PrimitiveArray?(SingleInteger?)

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setelt3(b, [1, 2])

Type: Void

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

(15)

Type: PrimitiveArray?(SingleInteger?)

Subject: Be Bold !!

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