7V      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~None,023459:;DIQRT2A wrapper to tag vectors with a type level length.O(1)& Yield the length of the vector as an .O(1)% Yield the length of the vector as a .O(1) Indexing using an Int.O(1) Safe indexing using a .O(1)/ Indexing using an Int without bounds checking.O(1)/ Yield the first element of a non-empty vector.O(1). Yield the last element of a non-empty vector.O(1)0 Indexing in a monad. See the documentation for + for an explanation of why this is useful. O(1)" Safe indexing in a monad using a . See the documentation for * for an explanation of why this is useful. O(1)K Indexing using an Int without bounds checking. See the documentation for * for an explanation of why this is useful. O(1)V Yield the first element of a non-empty vector in a monad. See the documentation for * for an explanation of why this is useful. O(1)U Yield the last element of a non-empty vector in a monad. See the documentation for * for an explanation of why this is useful. O(1)R Yield a slice of the vector without copying it with an inferred length argument.O(1)R Yield a slice of the vector without copying it with an explicit length argument.O(1)G Yield all but the last element of a non-empty vector without copying.O(1)H Yield all but the first element of a non-empty vector without copying.O(1) Yield the first n elements. The resultant vector always contains this many elements. The length of the resultant vector is inferred from the type.O(1) Yield the first n elements. The resultant vector always contains this many elements. The length of the resultant vector is given explicitly as a  argument.O(1) Yield all but the the first n elements. The given vector must contain at least this many elements The length of the resultant vector is inferred from the type.O(1) Yield all but the the first n elements. The given vector must contain at least this many elements The length of the resultant vector is givel explicitly as a  argument.O(1) Yield the first n elements paired with the remainder without copying. The lengths of the resultant vector are inferred from the type.O(1) Yield the first n elements paired with the remainder without copying. The length of the first resultant vector is passed explicitly as a  argument.O(1) Empty vector.O(1)! Vector with exactly one element.O(n)g Construct a vector with the same element in each position where the length is inferred from the type.O(n)f Construct a vector with the same element in each position where the length is given explicitly as a  argument.O(n){ construct a vector of the given length by applying the function to each index where the length is inferred from the type.O(n)z construct a vector of the given length by applying the function to each index where the length is given explicitly as a  argument.O(n)j Apply function n times to value. Zeroth element is original value. The length is inferred from the type.O(n)i Apply function n times to value. Zeroth element is original value. The length is given explicitly as a  argument.O(n) Execute the monadic action n0 times and store the results in a vector where n is inferred from the type. O(n) Execute the monadic action n0 times and store the results in a vector where n is given explicitly as a  argument.!O(n) Construct a vector of length nQ by applying the monadic action to each index where n is inferred from the type."O(n) Construct a vector of length nP by applying the monadic action to each index where n is given explicitly as a  argument.#O(n)! Construct a vector with exactly nT elements by repeatedly applying the generator function to the a seed. The length, n, is inferred from the type.$O(n)! Construct a vector with exactly nT elements by repeatedly applying the generator function to the a seed. The length, n, is given explicitly as a  argument.%O(n) Yield a vector of length n containing the values x, x+1 etc. The length, n, is inferred from the type.&O(n) Yield a vector of length n containing the values x, x+1 etc. The length, n, is given explicitly as a  argument.'O(n): Yield a vector of the given length containing the values x, x+y, x+y+y etc. The length, n, is inferred from the type.(O(n): Yield a vector of the given length containing the values x, x+y, x+y+y etc. The length, n, is given explicitly as a  argument.)O(n) Prepend an element.*O(n) Append an element.+O(m+n) Concatenate two vectors.,O(n)Y Yield the argument but force it not to retain any extra memory, possibly by copying it.@This is especially useful when dealing with slices. For example: force (slice 0 2 <huge vector>)Here, the slice retains a reference to the huge vector. Forcing it creates a copy of just the elements that belong to the slice and allows the huge vector to be garbage collected.-O(m+n) For each pair (i,a)8 from the list, replace the vector element at position i by a. ,<5,9,2,7> // [(2,1),(0,3),(2,8)] = <3,9,8,7>.O(m+n) For each pair (i,a)O from the vector of index/value pairs, replace the vector element at position i by a. 0update <5,9,2,7> <(2,1),(0,3),(2,8)> = <3,9,8,7>/O(m+n) For each index i4 from the index vector and the corresponding value aO from the value vector, replace the element of the initial vector at position i by a. .update_ <5,9,2,7> <2,0,2> <1,3,8> = <3,9,8,7>)This function is useful for instances of & that cannot store pairs. Otherwise, . is probably more convenient. update_ xs is ys = . xs (P is ys) 0 Same as (-) but without bounds checking.1Same as . but without bounds checking.2Same as / but without bounds checking.3O(m+n) For each pair (i,b), from the list, replace the vector element a at position i by f a b. ?accum (+) <5,9,2> [(2,4),(1,6),(0,3),(1,7)] = <5+3, 9+6+7, 2+4>4O(m+n) For each pair (i,b)7 from the vector of pairs, replace the vector element a at position i by f a b. Daccumulate (+) <5,9,2> <(2,4),(1,6),(0,3),(1,7)> = <5+3, 9+6+7, 2+4>5O(m+n) For each index i4 from the index vector and the corresponding value bT from the the value vector, replace the element of the initial vector at position i by f a b. ?accumulate_ (+) <5,9,2> <2,1,0,1> <4,6,3,7> = <5+3, 9+6+7, 2+4>)This function is useful for instances of & that cannot store pairs. Otherwise, 4 is probably more convenient: accumulate_ f as is bs = 4 f as (P is bs) 6Same as 3 but without bounds checking.7Same as 4 but without bounds checking.8Same as 5 but without bounds checking.9O(n) Reverse a vector:O(n)5 Yield the vector obtained by replacing each element i of the index vector by xs!i. This is equivalent to = (xs!) is# but is often much more efficient. 3backpermute <a,b,c,d> <0,3,2,3,1,0> = <a,d,c,d,b,a>;Same as : but without bounds checking.<O(n)- Pair each element in a vector with its index=O(n) Map a function over a vector>O(n)< Apply a function to every element of a vector and its index?O(n*m)} Map a function over a vector and concatenate the results. The function is required to always return the same length vector.@O(n)V Apply the monadic action to all elements of the vector, yielding a vector of resultsAO(n)c Apply the monadic action to every element of a vector and its index, yielding a vector of resultsBO(n)M Apply the monadic action to all elements of a vector and ignore the resultsCO(n)[ Apply the monadic action to every element of a vector and its index, ignoring the resultsDO(n)e Apply the monadic action to all elements of the vector, yielding a vector of results. Equvalent to flip @.EO(n)] Apply the monadic action to all elements of a vector and ignore the results. Equivalent to flip B.FO(n)< Zip two vectors of the same length with the given function.G*Zip three vectors with the given function.KO(n)\ Zip two vectors of the same length with a function that also takes the elements' indices).PO(n)# Zip two vectors of the same lengthUO(n)^ Zip the two vectors of the same length with the monadic action and yield a vector of resultsVO(n)k Zip the two vectors with a monadic action that also takes the element index and yield a vector of resultsWO(n)C Zip the two vectors with the monadic action and ignore the resultsXO(n)d Zip the two vectors with a monadic action that also takes the element index and ignore the resultsY O(min(m,n)) Unzip a vector of pairs.^O(n)( Check if the vector contains an element_O(n)= Check if the vector does not contain an element (inverse of ^)`O(n) Yield - the first element matching the predicate or  if no such element exists.aO(n) Yield ; the index of the first element matching the predicate or  if no such element exists.bO(n) Yield ; the index of the first occurence of the given element or O if the vector does not contain the element. This is a specialised version of a.cO(n) Left folddO(n) Left fold on non-empty vectorseO(n)" Left fold with strict accumulatorfO(n)7 Left fold on non-empty vectors with strict accumulatorgO(n) Right foldhO(n) Right fold on non-empty vectorsiO(n)% Right fold with a strict accumulatorjO(n)8 Right fold on non-empty vectors with strict accumulatorkO(n); Left fold (function applied to each element and its index)lO(n)T Left fold with strict accumulator (function applied to each element and its index)mO(n)< Right fold (function applied to each element and its index)nO(n)U Right fold with strict accumulator (function applied to each element and its index)oO(n)- Check if all elements satisfy the predicate.pO(n). Check if any element satisfies the predicate.qO(n) Check if all elements are rO(n) Check if any element is sO(n) Compute the sum of the elementstO(n)$ Compute the produce of the elementsuO(n)3 Yield the maximum element of the non-empty vector.vO(n)_ Yield the maximum element of the non-empty vector according to the given comparison function.wO(n)3 Yield the minimum element of the non-empty vector.xO(n)_ Yield the minimum element of the non-empty vector according to the given comparison function.yO(n)@ Yield the index of the maximum element of the non-empty vector.zO(n)l Yield the index of the maximum element of the non-empty vector according to the given comparison function.{O(n)@ Yield the index of the minimum element of the non-empty vector.|O(n)l Yield the index of the minimum element of the non-empty vector according to the given comparison function.}O(n) Monadic fold~O(n)< Monadic fold (action applied to each element and its index)O(n)$ Monadic fold over non-empty vectorsO(n)% Monadic fold with strict accumulatorO(n)U Monadic fold with strict accumulator (action applied to each element and its index)O(n)< Monadic fold over non-empty vectors with strict accumulatorO(n)& Monadic fold that discards the resultO(n)V Monadic fold that discards the result (action applied to each element and its index)O(n)= Monadic fold over non-empty vectors that discards the resultO(n)> Monadic fold with strict accumulator that discards the resultO(n)n Monadic fold with strict accumulator that discards the result (action applied to each element and its index)O(n)T Monad fold over non-empty vectors with strict accumulator that discards the result,Evaluate each action and collect the results,Evaluate each action and discard the resultsO(n) Prescan prescanl f z =  .  f z  Example: $prescanl (+) 0 <1,2,3,4> = <0,1,3,6>O(n) Prescan with strict accumulatorO(n) ScanO(n) Scan with strict accumulatorO(n) Haskell-style scanO(n)+ Haskell-style scan with strict accumulatorO(n) Scan over a non-empty vectorO(n)7 Scan over a non-empty vector with a strict accumulatorO(n) Right-to-left prescanO(n). Right-to-left prescan with strict accumulatorO(n) Right-to-left scanO(n)+ Right-to-left scan with strict accumulatorO(n)! Right-to-left Haskell-style scanO(n)9 Right-to-left Haskell-style scan with strict accumulatorO(n)+ Right-to-left scan over a non-empty vectorO(n)F Right-to-left scan over a non-empty vector with a strict accumulatorO(n) Convert a vector to a listO(n) Convert a list to a vectorO(n) Convert the first n_ elements of a list to a vector. The length of the resultant vector is inferred from the type.O(n) Convert the first n^ elements of a list to a vector. The length of the resultant vector is given explicitly as a  argument.O(n) Convert different vector types Convert a  into a 7 if it has the correct size, otherwise return Nothing.Apply a function on unsized vectors to a sized vector. The function must preserve the size of the vector, this is not checked.The E instance for sized vectors does not have the same behaviour as the 0 instance for the unsized vectors found in the vectors package. Its mempty is a vector of mempty s and its mappend is zipWith mappend.The E instance for sized vectors does not have the same behaviour as the 0 instance for the unsized vectors found in the vectorsC package. The instance defined here has the same behaviour as the  instance.AAny sized vector containing storable elements is itself storable. starting indexstarting indexlength !"#$%&'()*+,-initial vector (of length m)%list of index/value pairs (of length n).initial vector (of length m)'vector of index/value pairs (of length n)/initial vector (of length m)index vector (of length n)value vector (of length n)0initial vector (of length m)%list of index/value pairs (of length n)1initial vector (of length m)'vector of index/value pairs (of length n)2initial vector (of length m)index vector (of length n)value vector (of length n)3accumulating function finitial vector (of length m)%list of index/value pairs (of length n)4accumulating function finitial vector (of length m)'vector of index/value pairs (of length n)5accumulating function finitial vector (of length m)index vector (of length n)value vector (of length n)6accumulating function finitial vector (of length m)%list of index/value pairs (of length n)7accumulating function finitial vector (of length m)'vector of index/value pairs (of length n)8accumulating function finitial vector (of length m)index vector (of length n)value vector (of length n)9:xs value vectoris index vector (of length n);xs value vectoris index vector (of length n)<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~^4_4None ,9:;DIQRT specialized to use  O(1)& Yield the length of the vector as an .O(1)% Yield the length of the vector as a .O(1) Indexing using an Int.O(1) Safe indexing using a .O(1)/ Indexing using an Int without bounds checking.O(1)/ Yield the first element of a non-empty vector.O(1). Yield the last element of a non-empty vector.O(1)0 Indexing in a monad. See the documentation for  + for an explanation of why this is useful.O(1)" Safe indexing in a monad using a . See the documentation for  * for an explanation of why this is useful.O(1)K Indexing using an Int without bounds checking. See the documentation for  * for an explanation of why this is useful.O(1)V Yield the first element of a non-empty vector in a monad. See the documentation for  * for an explanation of why this is useful.O(1)U Yield the last element of a non-empty vector in a monad. See the documentation for  * for an explanation of why this is useful.O(1)R Yield a slice of the vector without copying it with an inferred length argument.O(1)R Yield a slice of the vector without copying it with an explicit length argument.O(1)G Yield all but the last element of a non-empty vector without copying.O(1)H Yield all but the first element of a non-empty vector without copying.O(1) Yield the first n elements. The resultant vector always contains this many elements. The length of the resultant vector is inferred from the type.O(1) Yield the first n elements. The resultant vector always contains this many elements. The length of the resultant vector is given explicitly as a  argument.O(1) Yield all but the the first n elements. The given vector must contain at least this many elements The length of the resultant vector is inferred from the type.O(1) Yield all but the the first n elements. The given vector must contain at least this many elements The length of the resultant vector is givel explicitly as a  argument.O(1) Yield the first n elements paired with the remainder without copying. The lengths of the resultant vector are inferred from the type.O(1) Yield the first n elements paired with the remainder without copying. The length of the first resultant vector is passed explicitly as a  argument.O(1) Empty vector.O(1)! Vector with exactly one element.O(n)g Construct a vector with the same element in each position where the length is inferred from the type.O(n)f Construct a vector with the same element in each position where the length is given explicitly as a  argument.O(n){ construct a vector of the given length by applying the function to each index where the length is inferred from the type.O(n)z construct a vector of the given length by applying the function to each index where the length is given explicitly as a  argument.O(n)j Apply function n times to value. Zeroth element is original value. The length is inferred from the type.O(n)i Apply function n times to value. Zeroth element is original value. The length is given explicitly as a  argument.O(n) Execute the monadic action n0 times and store the results in a vector where n is inferred from the type.O(n) Execute the monadic action n0 times and store the results in a vector where n is given explicitly as a  argument.O(n) Construct a vector of length nQ by applying the monadic action to each index where n is inferred from the type.O(n) Construct a vector of length nP by applying the monadic action to each index where n is given explicitly as a  argument.O(n)! Construct a vector with exactly nT elements by repeatedly applying the generator function to the a seed. The length, n, is inferred from the type.O(n)! Construct a vector with exactly nT elements by repeatedly applying the generator function to the a seed. The length, n, is given explicitly as a  argument.O(n) Yield a vector of length n containing the values x, x+1 etc. The length, n, is inferred from the type.O(n) Yield a vector of length n containing the values x, x+1 etc. The length, n, is given explicitly as a  argument.O(n): Yield a vector of the given length containing the values x, x+y, x+y+y etc. The length, n, is inferred from the type.O(n): Yield a vector of the given length containing the values x, x+y, x+y+y etc. The length, n, is given explicitly as a  argument.O(n) Prepend an element.O(n) Append an element.O(m+n) Concatenate two vectors.O(n)Y Yield the argument but force it not to retain any extra memory, possibly by copying it.@This is especially useful when dealing with slices. For example: force (slice 0 2 <huge vector>)Here, the slice retains a reference to the huge vector. Forcing it creates a copy of just the elements that belong to the slice and allows the huge vector to be garbage collected.O(m+n) For each pair (i,a)8 from the list, replace the vector element at position i by a. ,<5,9,2,7> // [(2,1),(0,3),(2,8)] = <3,9,8,7>O(m+n) For each pair (i,a)O from the vector of index/value pairs, replace the vector element at position i by a. 0update <5,9,2,7> <(2,1),(0,3),(2,8)> = <3,9,8,7>O(m+n) For each index i4 from the index vector and the corresponding value aO from the value vector, replace the element of the initial vector at position i by a. .update_ <5,9,2,7> <2,0,2> <1,3,8> = <3,9,8,7>)This function is useful for instances of & that cannot store pairs. Otherwise,  is probably more convenient. update_ xs is ys =  xs ( is ys)  Same as () but without bounds checking.Same as  but without bounds checking.Same as  but without bounds checking.O(m+n) For each pair (i,b), from the list, replace the vector element a at position i by f a b. ?accum (+) <5,9,2> [(2,4),(1,6),(0,3),(1,7)] = <5+3, 9+6+7, 2+4>O(m+n) For each pair (i,b)7 from the vector of pairs, replace the vector element a at position i by f a b. Daccumulate (+) <5,9,2> <(2,4),(1,6),(0,3),(1,7)> = <5+3, 9+6+7, 2+4>O(m+n) For each index i4 from the index vector and the corresponding value bT from the the value vector, replace the element of the initial vector at position i by f a b. ?accumulate_ (+) <5,9,2> <2,1,0,1> <4,6,3,7> = <5+3, 9+6+7, 2+4>)This function is useful for instances of & that cannot store pairs. Otherwise,  is probably more convenient: accumulate_ f as is bs =  f as ( is bs) Same as  but without bounds checking.Same as  but without bounds checking.Same as  but without bounds checking.O(n) Reverse a vectorO(n)5 Yield the vector obtained by replacing each element i of the index vector by xs!i. This is equivalent to  (xs!) is# but is often much more efficient. 3backpermute <a,b,c,d> <0,3,2,3,1,0> = <a,d,c,d,b,a>Same as  but without bounds checking.O(n)- Pair each element in a vector with its indexO(n) Map a function over a vectorO(n)< Apply a function to every element of a vector and its indexO(n*m)} Map a function over a vector and concatenate the results. The function is required to always return the same length vector.O(n)V Apply the monadic action to all elements of the vector, yielding a vector of resultsO(n)c Apply the monadic action to every element of a vector and its index, yielding a vector of resultsO(n)M Apply the monadic action to all elements of a vector and ignore the resultsO(n)[ Apply the monadic action to every element of a vector and its index, ignoring the resultsO(n)e Apply the monadic action to all elements of the vector, yielding a vector of results. Equvalent to flip .O(n)] Apply the monadic action to all elements of a vector and ignore the results. Equivalent to flip .O(n)< Zip two vectors of the same length with the given function.*Zip three vectors with the given function.O(n)\ Zip two vectors of the same length with a function that also takes the elements' indices).O(n)# Zip two vectors of the same lengthO(n)^ Zip the two vectors of the same length with the monadic action and yield a vector of resultsO(n)k Zip the two vectors with a monadic action that also takes the element index and yield a vector of resultsO(n)C Zip the two vectors with the monadic action and ignore the resultsO(n)d Zip the two vectors with a monadic action that also takes the element index and ignore the results  O(min(m,n)) Unzip a vector of pairs.O(n)( Check if the vector contains an elementO(n)= Check if the vector does not contain an element (inverse of )O(n) Yield - the first element matching the predicate or  if no such element exists.O(n) Yield ; the index of the first element matching the predicate or  if no such element exists.O(n) Yield ; the index of the first occurence of the given element or O if the vector does not contain the element. This is a specialised version of .O(n) Left foldO(n) Left fold on non-empty vectorsO(n)" Left fold with strict accumulatorO(n)7 Left fold on non-empty vectors with strict accumulatorO(n) Right foldO(n) Right fold on non-empty vectorsO(n)% Right fold with a strict accumulatorO(n)8 Right fold on non-empty vectors with strict accumulatorO(n); Left fold (function applied to each element and its index)O(n)T Left fold with strict accumulator (function applied to each element and its index)O(n)< Right fold (function applied to each element and its index)O(n)U Right fold with strict accumulator (function applied to each element and its index)O(n)- Check if all elements satisfy the predicate. O(n). Check if any element satisfies the predicate.!O(n) Check if all elements are "O(n) Check if any element is #O(n) Compute the sum of the elements$O(n)$ Compute the produce of the elements%O(n)3 Yield the maximum element of the non-empty vector.&O(n)_ Yield the maximum element of the non-empty vector according to the given comparison function.'O(n)3 Yield the minimum element of the non-empty vector.(O(n)_ Yield the minimum element of the non-empty vector according to the given comparison function.)O(n)@ Yield the index of the maximum element of the non-empty vector.*O(n)l Yield the index of the maximum element of the non-empty vector according to the given comparison function.+O(n)@ Yield the index of the minimum element of the non-empty vector.,O(n)l Yield the index of the minimum element of the non-empty vector according to the given comparison function.-O(n) Monadic fold.O(n)< Monadic fold (action applied to each element and its index)/O(n)$ Monadic fold over non-empty vectors0O(n)% Monadic fold with strict accumulator1O(n)U Monadic fold with strict accumulator (action applied to each element and its index)2O(n)< Monadic fold over non-empty vectors with strict accumulator3O(n)& Monadic fold that discards the result4O(n)V Monadic fold that discards the result (action applied to each element and its index)5O(n)= Monadic fold over non-empty vectors that discards the result6O(n)> Monadic fold with strict accumulator that discards the result7O(n)n Monadic fold with strict accumulator that discards the result (action applied to each element and its index)8O(n)T Monad fold over non-empty vectors with strict accumulator that discards the result9,Evaluate each action and collect the results:,Evaluate each action and discard the results;O(n) Prescan prescanl f z =  . ? f z  Example: $prescanl (+) 0 <1,2,3,4> = <0,1,3,6><O(n) Prescan with strict accumulator=O(n) Scan>O(n) Scan with strict accumulator?O(n) Haskell-style scan@O(n)+ Haskell-style scan with strict accumulatorAO(n) Scan over a non-empty vectorBO(n)7 Scan over a non-empty vector with a strict accumulatorCO(n) Right-to-left prescanDO(n). Right-to-left prescan with strict accumulatorEO(n) Right-to-left scanFO(n)+ Right-to-left scan with strict accumulatorGO(n)! Right-to-left Haskell-style scanHO(n)9 Right-to-left Haskell-style scan with strict accumulatorIO(n)+ Right-to-left scan over a non-empty vectorJO(n)F Right-to-left scan over a non-empty vector with a strict accumulatorKO(n) Convert a vector to a listLO(n) Convert a list to a vectorMO(n) Convert the first n_ elements of a list to a vector. The length of the resultant vector is inferred from the type.NO(n) Convert the first n^ elements of a list to a vector. The length of the resultant vector is given explicitly as a  argument.O Convert a  into a 7 if it has the correct size, otherwise return Nothing.QApply a function on unsized vectors to a sized vector. The function must preserve the size of the vector, this is not checked.starting indexstarting indexlengthinitial vector (of length m)%list of index/value pairs (of length n)initial vector (of length m)'vector of index/value pairs (of length n)initial vector (of length m)index vector (of length n)value vector (of length n)initial vector (of length m)%list of index/value pairs (of length n)initial vector (of length m)'vector of index/value pairs (of length n)initial vector (of length m)index vector (of length n)value vector (of length n)accumulating function finitial vector (of length m)%list of index/value pairs (of length n)accumulating function finitial vector (of length m)'vector of index/value pairs (of length n)accumulating function finitial vector (of length m)index vector (of length n)value vector (of length n)accumulating function finitial vector (of length m)%list of index/value pairs (of length n)accumulating function finitial vector (of length m)'vector of index/value pairs (of length n)accumulating function finitial vector (of length m)index vector (of length n)value vector (of length n)xs value vectoris index vector (of length n)xs value vectoris index vector (of length n)      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQ      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQ      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQ      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQ44None ,9:;DIQRTR specialized to use  SO(1)& Yield the length of the vector as an .TO(1)% Yield the length of the vector as a .UO(1) Indexing using an Int.VO(1) Safe indexing using a .WO(1)/ Indexing using an Int without bounds checking.XO(1)/ Yield the first element of a non-empty vector.YO(1). Yield the last element of a non-empty vector.ZO(1)0 Indexing in a monad. See the documentation for  + for an explanation of why this is useful.[O(1)" Safe indexing in a monad using a . See the documentation for  * for an explanation of why this is useful.\O(1)K Indexing using an Int without bounds checking. See the documentation for  * for an explanation of why this is useful.]O(1)V Yield the first element of a non-empty vector in a monad. See the documentation for  * for an explanation of why this is useful.^O(1)U Yield the last element of a non-empty vector in a monad. See the documentation for  * for an explanation of why this is useful._O(1)R Yield a slice of the vector without copying it with an inferred length argument.`O(1)R Yield a slice of the vector without copying it with an explicit length argument.aO(1)G Yield all but the last element of a non-empty vector without copying.bO(1)H Yield all but the first element of a non-empty vector without copying.cO(1) Yield the first n elements. The resultant vector always contains this many elements. The length of the resultant vector is inferred from the type.dO(1) Yield the first n elements. The resultant vector always contains this many elements. The length of the resultant vector is given explicitly as a  argument.eO(1) Yield all but the the first n elements. The given vector must contain at least this many elements The length of the resultant vector is inferred from the type.fO(1) Yield all but the the first n elements. The given vector must contain at least this many elements The length of the resultant vector is givel explicitly as a  argument.gO(1) Yield the first n elements paired with the remainder without copying. The lengths of the resultant vector are inferred from the type.hO(1) Yield the first n elements paired with the remainder without copying. The length of the first resultant vector is passed explicitly as a  argument.iO(1) Empty vector.jO(1)! Vector with exactly one element.kO(n)g Construct a vector with the same element in each position where the length is inferred from the type.lO(n)f Construct a vector with the same element in each position where the length is given explicitly as a  argument.mO(n){ construct a vector of the given length by applying the function to each index where the length is inferred from the type.nO(n)z construct a vector of the given length by applying the function to each index where the length is given explicitly as a  argument.oO(n)j Apply function n times to value. Zeroth element is original value. The length is inferred from the type.pO(n)i Apply function n times to value. Zeroth element is original value. The length is given explicitly as a  argument.qO(n) Execute the monadic action n0 times and store the results in a vector where n is inferred from the type.rO(n) Execute the monadic action n0 times and store the results in a vector where n is given explicitly as a  argument.sO(n) Construct a vector of length nQ by applying the monadic action to each index where n is inferred from the type.tO(n) Construct a vector of length nP by applying the monadic action to each index where n is given explicitly as a  argument.uO(n)! Construct a vector with exactly nT elements by repeatedly applying the generator function to the a seed. The length, n, is inferred from the type.vO(n)! Construct a vector with exactly nT elements by repeatedly applying the generator function to the a seed. The length, n, is given explicitly as a  argument.wO(n) Yield a vector of length n containing the values x, x+1 etc. The length, n, is inferred from the type.xO(n) Yield a vector of length n containing the values x, x+1 etc. The length, n, is given explicitly as a  argument.yO(n): Yield a vector of the given length containing the values x, x+y, x+y+y etc. The length, n, is inferred from the type.zO(n): Yield a vector of the given length containing the values x, x+y, x+y+y etc. The length, n, is given explicitly as a  argument.{O(n) Prepend an element.|O(n) Append an element.}O(m+n) Concatenate two vectors.~O(n)Y Yield the argument but force it not to retain any extra memory, possibly by copying it.@This is especially useful when dealing with slices. For example: force (slice 0 2 <huge vector>)Here, the slice retains a reference to the huge vector. Forcing it creates a copy of just the elements that belong to the slice and allows the huge vector to be garbage collected.O(m+n) For each pair (i,a)8 from the list, replace the vector element at position i by a. ,<5,9,2,7> // [(2,1),(0,3),(2,8)] = <3,9,8,7>O(m+n) For each pair (i,a)O from the vector of index/value pairs, replace the vector element at position i by a. 0update <5,9,2,7> <(2,1),(0,3),(2,8)> = <3,9,8,7>O(m+n) For each index i4 from the index vector and the corresponding value aO from the value vector, replace the element of the initial vector at position i by a. .update_ <5,9,2,7> <2,0,2> <1,3,8> = <3,9,8,7>)This function is useful for instances of R& that cannot store pairs. Otherwise,  is probably more convenient. update_ xs is ys =  xs ( is ys)  Same as () but without bounds checking.Same as  but without bounds checking.Same as  but without bounds checking.O(m+n) For each pair (i,b), from the list, replace the vector element a at position i by f a b. ?accum (+) <5,9,2> [(2,4),(1,6),(0,3),(1,7)] = <5+3, 9+6+7, 2+4>O(m+n) For each pair (i,b)7 from the vector of pairs, replace the vector element a at position i by f a b. Daccumulate (+) <5,9,2> <(2,4),(1,6),(0,3),(1,7)> = <5+3, 9+6+7, 2+4>O(m+n) For each index i4 from the index vector and the corresponding value bT from the the value vector, replace the element of the initial vector at position i by f a b. ?accumulate_ (+) <5,9,2> <2,1,0,1> <4,6,3,7> = <5+3, 9+6+7, 2+4>)This function is useful for instances of R& that cannot store pairs. Otherwise,  is probably more convenient: accumulate_ f as is bs =  f as ( is bs) Same as  but without bounds checking.Same as  but without bounds checking.Same as  but without bounds checking.O(n) Reverse a vectorO(n)5 Yield the vector obtained by replacing each element i of the index vector by xs!i. This is equivalent to  (xs!) is# but is often much more efficient. 3backpermute <a,b,c,d> <0,3,2,3,1,0> = <a,d,c,d,b,a>Same as  but without bounds checking.O(n)- Pair each element in a vector with its indexO(n) Map a function over a vectorO(n)< Apply a function to every element of a vector and its indexO(n*m)} Map a function over a vector and concatenate the results. The function is required to always return the same length vector.O(n)V Apply the monadic action to all elements of the vector, yielding a vector of resultsO(n)c Apply the monadic action to every element of a vector and its index, yielding a vector of resultsO(n)M Apply the monadic action to all elements of a vector and ignore the resultsO(n)[ Apply the monadic action to every element of a vector and its index, ignoring the resultsO(n)e Apply the monadic action to all elements of the vector, yielding a vector of results. Equvalent to flip .O(n)] Apply the monadic action to all elements of a vector and ignore the results. Equivalent to flip .O(n)< Zip two vectors of the same length with the given function.*Zip three vectors with the given function.O(n)\ Zip two vectors of the same length with a function that also takes the elements' indices).O(n)# Zip two vectors of the same lengthO(n)^ Zip the two vectors of the same length with the monadic action and yield a vector of resultsO(n)k Zip the two vectors with a monadic action that also takes the element index and yield a vector of resultsO(n)C Zip the two vectors with the monadic action and ignore the resultsO(n)d Zip the two vectors with a monadic action that also takes the element index and ignore the results O(min(m,n)) Unzip a vector of pairs.O(n)( Check if the vector contains an elementO(n)= Check if the vector does not contain an element (inverse of )O(n) Yield - the first element matching the predicate or  if no such element exists.O(n) Yield ; the index of the first element matching the predicate or  if no such element exists.O(n) Yield ; the index of the first occurence of the given element or O if the vector does not contain the element. This is a specialised version of .O(n) Left foldO(n) Left fold on non-empty vectorsO(n)" Left fold with strict accumulatorO(n)7 Left fold on non-empty vectors with strict accumulatorO(n) Right foldO(n) Right fold on non-empty vectorsO(n)% Right fold with a strict accumulatorO(n)8 Right fold on non-empty vectors with strict accumulatorO(n); Left fold (function applied to each element and its index)O(n)T Left fold with strict accumulator (function applied to each element and its index)O(n)< Right fold (function applied to each element and its index)O(n)U Right fold with strict accumulator (function applied to each element and its index)O(n)- Check if all elements satisfy the predicate.O(n). Check if any element satisfies the predicate.O(n) Check if all elements are O(n) Check if any element is O(n) Compute the sum of the elementsO(n)$ Compute the produce of the elementsO(n)3 Yield the maximum element of the non-empty vector.O(n)_ Yield the maximum element of the non-empty vector according to the given comparison function.O(n)3 Yield the minimum element of the non-empty vector.O(n)_ Yield the minimum element of the non-empty vector according to the given comparison function.O(n)@ Yield the index of the maximum element of the non-empty vector.O(n)l Yield the index of the maximum element of the non-empty vector according to the given comparison function.O(n)@ Yield the index of the minimum element of the non-empty vector.O(n)l Yield the index of the minimum element of the non-empty vector according to the given comparison function.O(n) Monadic foldO(n)< Monadic fold (action applied to each element and its index)O(n)$ Monadic fold over non-empty vectorsO(n)% Monadic fold with strict accumulatorO(n)U Monadic fold with strict accumulator (action applied to each element and its index)O(n)< Monadic fold over non-empty vectors with strict accumulatorO(n)& Monadic fold that discards the resultO(n)V Monadic fold that discards the result (action applied to each element and its index)O(n)= Monadic fold over non-empty vectors that discards the resultO(n)> Monadic fold with strict accumulator that discards the resultO(n)n Monadic fold with strict accumulator that discards the result (action applied to each element and its index)O(n)T Monad fold over non-empty vectors with strict accumulator that discards the result,Evaluate each action and collect the results,Evaluate each action and discard the resultsO(n) Prescan prescanl f z = a .  f z  Example: $prescanl (+) 0 <1,2,3,4> = <0,1,3,6>O(n) Prescan with strict accumulatorO(n) ScanO(n) Scan with strict accumulatorO(n) Haskell-style scanO(n)+ Haskell-style scan with strict accumulatorO(n) Scan over a non-empty vectorO(n)7 Scan over a non-empty vector with a strict accumulatorO(n) Right-to-left prescanO(n). Right-to-left prescan with strict accumulatorO(n) Right-to-left scanO(n)+ Right-to-left scan with strict accumulatorO(n)! Right-to-left Haskell-style scanO(n)9 Right-to-left Haskell-style scan with strict accumulatorO(n)+ Right-to-left scan over a non-empty vectorO(n)F Right-to-left scan over a non-empty vector with a strict accumulatorO(n) Convert a vector to a listO(n) Convert a list to a vectorO(n) Convert the first n_ elements of a list to a vector. The length of the resultant vector is inferred from the type.O(n) Convert the first n^ elements of a list to a vector. The length of the resultant vector is given explicitly as a  argument. Convert a  into a 7 if it has the correct size, otherwise return Nothing.Apply a function on unsized vectors to a sized vector. 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