what is the equivalent xml file for layout xml in magento 2

Question

How to write the corresponding layout xml file in Magento 2?

<?xml version="1.0"?>
<layout version="0.1.0">
 <catalogsearch_result_index>        
    <reference name="catalogsearch.leftnav">
        <action method="setTemplate">
            <setTemplate>tagalys_search/filter.phtml</setTemplate>
        </action>
    </reference>
      <reference name="content">
        <reference type="catalogsearch/result" name="search.result">
            <reference name="search_result_list">
                <reference name="product_list_toolbar">
                    <action method="setTemplate">
                        <template>tagalys_toolbar/toolbar.phtml</template>
                    </action>
                 </reference>
            </reference>
        </reference>
    </reference>
</catalogsearch_result_index>

Answer 1

In Magento 2 every layout handle is its own file.
So you don't have one big file for a module, you have many smaller files.

In you case the file should be [Namespace]/[Module]/view/frontend/layout/catalogsearch_result_index.xml with the content:

<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" layout="1column" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
    <referenceBlock name="catalogsearch.leftnav">
        <action method="setTemplate">
            <setTemplate>tagalys_search/filter.phtml</setTemplate>
        </action>
    </referenceBlock>
      <referenceContainer name="content">
        <!-- Not sure of the rest of the code because it's looks strange. Too many references -->
    </referenceContainer>
</page>

Basically reference becomes referenceBLock or referenceContainer depending on what you are referencing.
Containers in M2 are core/text_list blocks in M1 (content, left, right,...)