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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___The_sp__Macaulay2_splanguage.html" title="">The Macaulay2 language</a> > <a href="_mapping_spover_sphash_sptables.html" title="apply a function to each element of a hash table">mapping over hash tables</a></div>
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<div><h1>mapping over hash tables -- apply a function to each element of a hash table</h1>
<div>Each entry in a hash table consists of a key and a value. We provide three ways to map functions over a hash table, depending on whether the function is to receive a value and return a new value, to receive a key and return a new key, or to receive a key-value pair and return a new key-value pair. The corresponding functions, <a href="_apply__Values.html" title="apply a function to each value">applyValues</a>, <a href="_apply__Keys.html" title="apply a function to each key in a hash table">applyKeys</a>, and <a href="_apply__Pairs.html" title="apply a function to each pair in a hash table">applyPairs</a> are illustrated in the next example.<table class="examples"><tr><td><pre>i1 : x = new HashTable from {a=>1, b=>2}
o1 = HashTable{a => 1}
b => 2
o1 : HashTable</pre>
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<tr><td><pre>i2 : applyValues(x, value -> 1000*value)
o2 = HashTable{a => 1000}
b => 2000
o2 : HashTable</pre>
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<tr><td><pre>i3 : applyKeys(x, key -> {key})
o3 = HashTable{{a} => 1}
{b} => 2
o3 : HashTable</pre>
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<tr><td><pre>i4 : applyPairs(x, (key,value) -> (value,key))
o4 = HashTable{1 => a}
2 => b
o4 : HashTable</pre>
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The functions, <a href="_scan__Values.html" title="apply a function to each value in a hash table">scanValues</a>, <a href="_scan__Keys.html" title="apply a function to each key in a hash table or database">scanKeys</a>, and <a href="_scan__Pairs.html" title="apply a function to pairs in a hash table">scanPairs</a> are similar, but the values returned are discarded instead of being assembled into a new hash table.<table class="examples"><tr><td><pre>i5 : x = new HashTable from {a=>1, b=>2}
o5 = HashTable{a => 1}
b => 2
o5 : HashTable</pre>
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<tr><td><pre>i6 : scanValues(x, print)
1
2</pre>
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<tr><td><pre>i7 : scanKeys(x, print)
a
b</pre>
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<tr><td><pre>i8 : scanPairs(x, print)
(a, 1)
(b, 2)</pre>
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The function <a href="_merge_lp__Hash__Table_cm__Hash__Table_cm__Function_rp.html" title="merge hash tables">merge</a> can be used to merge two hash tables. The result is a hash table whose keys are those occurring in one of the two incoming hash tables. We must provide a function of two arguments that is used to combine the values when a key occurs in both hash tables.<table class="examples"><tr><td><pre>i9 : y = new HashTable from {b=>200, c=>300}
o9 = HashTable{b => 200}
c => 300
o9 : HashTable</pre>
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<tr><td><pre>i10 : merge(x, y, plus)
o10 = HashTable{a => 1 }
b => 202
c => 300
o10 : HashTable</pre>
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The function <a href="_combine.html" title="combine hash tables">combine</a> can be used to combine two hash tables <tt>x</tt> and <tt>y</tt> into a new hash table. Three functions must be provided. The first one produces new keys from a key of <tt>x</tt> and a key of <tt>y</tt>. The second one produces a new values from a value of <tt>x</tt> and a value of <tt>y</tt>. The third one is used to combine values when two new keys turn out to be the same.<table class="examples"><tr><td><pre>i11 : combine(x,y,identity,times,plus)
o11 = HashTable{(a, b) => 200}
(a, c) => 300
(b, b) => 400
(b, c) => 600
o11 : HashTable</pre>
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