[Fix] nvm install: apply --alias, --default and --save after every install

`nvm_install_binary` set the alias from its caller's variables,
so a source install or an `$NVM_INSTALL_THIRD_PARTY_HOOK` install never got it,
and no fresh install wrote `.nvmrc`.
Apply both at the end of `nvm install`, after the install is validated.

`--lts` without a version, or `lts/*`, leaves no provided version,
and `nvm alias` treats an empty target as `nvm unalias`:
`nvm install --lts --default` on an installed version removed the default alias.
In that case point the alias at `lts/<name>`, as the default alias already is.

nvm.sh

@@ -3680,9 +3680,6 @@ nvm_install_binary() {
   fi
 
   if nvm_install_binary_extract "${NVM_OS}" "${PREFIXED_VERSION}" "${VERSION}" "${TARBALL}" "${TMPDIR}"; then
-    if [ -n "${ALIAS-}" ]; then
-      nvm alias "${ALIAS}" "${provided_version}"
-    fi
     return 0
   fi
 
@@ -5340,7 +5337,12 @@ nvm() {
         fi
 
         if [ $EXIT_CODE -eq 0 ] && [ -n "${ALIAS-}" ]; then
-          nvm alias "${ALIAS}" "${provided_version}"
+          # an LTS install may have no provided version, and an empty target would remove the alias
+          if [ -z "${provided_version}" ] && [ -n "${LTS-}" ]; then
+            nvm alias "${ALIAS}" "lts/${LTS}"
+          else
+            nvm alias "${ALIAS}" "${provided_version}"
+          fi
           EXIT_CODE=$?
         fi
 
@@ -5453,6 +5455,20 @@ nvm() {
         fi
       fi
 
+      if [ $EXIT_CODE -eq 0 ] && [ $NVM_WRITE_TO_NVMRC -eq 1 ]; then
+        nvm_write_nvmrc "${VERSION}"
+        EXIT_CODE=$?
+      fi
+
+      if [ $EXIT_CODE -eq 0 ] && [ -n "${ALIAS-}" ]; then
+        if [ -z "${provided_version}" ] && [ -n "${LTS-}" ]; then
+          nvm alias "${ALIAS}" "lts/${LTS}"
+        else
+          nvm alias "${ALIAS}" "${provided_version}"
+        fi
+        EXIT_CODE=$?
+      fi
+
       return $EXIT_CODE
     ;;
     "uninstall")

test/fast/Unit tests/nvm install --alias, --default and --save

@@ -0,0 +1,80 @@
+#!/bin/sh
+
+cleanup() {
+  [ -n "${NVM_DIR}" ] && [ -d "${NVM_DIR}" ] && rm -rf "${NVM_DIR}"
+  rm -f .nvmrc
+  if [ -f .nvmrc.orig ]; then mv .nvmrc.orig .nvmrc; fi
+  unset -f die cleanup reset nvm_remote_version nvm_has_executable nvm_binary_available \
+    nvm_get_make_jobs nvm_install_binary nvm_install_source nvm_install_npm_if_needed \
+    nvm_install_default_packages
+  unset NVM_DIR version OUTPUT
+}
+
+die() { echo "$@" ; cleanup ; exit 1; }
+
+: nvm.sh
+\. ../../../nvm.sh
+
+\. ../../common.sh
+
+unset npm_config_prefix NPM_CONFIG_PREFIX
+
+if [ -f .nvmrc ]; then mv .nvmrc .nvmrc.orig; fi
+
+NVM_DIR="$(mktemp -d)"
+[ -n "${NVM_DIR}" ] || die 'unable to create temp NVM_DIR'
+version='v20.0.0'
+
+# Stay offline: both install methods create a fake node.
+nvm_remote_version() { nvm_echo "${version}"; }
+nvm_has_executable() { return 0; }
+nvm_binary_available() { return 0; }
+nvm_get_make_jobs() { NVM_MAKE_JOBS=1; }
+nvm_install_binary() { make_fake_node "${version}"; }
+nvm_install_source() { make_fake_node "${version}"; }
+nvm_install_npm_if_needed() { return 0; }
+nvm_install_default_packages() { :; }
+
+reset() {
+  rm -rf "${NVM_DIR:?}/versions" "${NVM_DIR}/alias" .nvmrc
+}
+
+reset
+nvm install -s --alias=foo "${version}" > /dev/null 2>&1 || die "\`nvm install -s --alias=foo ${version}\` failed"
+OUTPUT="$(nvm_alias foo)"
+[ "${OUTPUT}" = "${version}" ] || die "expected the foo alias to be ${version} after a source install, got >${OUTPUT}<"
+
+reset
+nvm install --alias=foo "${version}" > /dev/null 2>&1 || die "\`nvm install --alias=foo ${version}\` failed"
+OUTPUT="$(nvm_alias foo)"
+[ "${OUTPUT}" = "${version}" ] || die "expected the foo alias to be ${version} after a binary install, got >${OUTPUT}<"
+
+reset
+nvm alias default v18.0.0 > /dev/null 2>&1
+nvm install -s --default "${version}" > /dev/null 2>&1 || die "\`nvm install -s --default ${version}\` failed"
+OUTPUT="$(nvm_alias default)"
+[ "${OUTPUT}" = "${version}" ] || die "expected the default alias to be ${version} after a source install, got >${OUTPUT}<"
+
+reset
+nvm alias default v18.0.0 > /dev/null 2>&1
+nvm install -s --lts --default > /dev/null 2>&1 || die '`nvm install -s --lts --default` failed'
+OUTPUT="$(nvm_alias default)"
+[ "${OUTPUT}" = 'lts/*' ] || die "expected the default alias to be lts/* after an LTS install, got >${OUTPUT}<"
+
+# again, now that the version is installed
+nvm install -s --lts --default > /dev/null 2>&1 || die '`nvm install -s --lts --default` failed for an installed version'
+OUTPUT="$(nvm_alias default)"
+[ "${OUTPUT}" = 'lts/*' ] || die "expected the default alias to stay lts/* for an installed version, got >${OUTPUT}<"
+
+# with `--lts` and an explicit version, the alias points at that version
+reset
+nvm install -s --lts --default "${version}" > /dev/null 2>&1 || die "\`nvm install -s --lts --default ${version}\` failed"
+OUTPUT="$(nvm_alias default)"
+[ "${OUTPUT}" = "${version}" ] || die "expected the default alias to be ${version} for \`--lts ${version}\`, got >${OUTPUT}<"
+
+reset
+nvm install --save "${version}" > /dev/null 2>&1 || die "\`nvm install --save ${version}\` failed"
+OUTPUT="$(cat .nvmrc 2> /dev/null)"
+[ "${OUTPUT}" = "${version}" ] || die "expected \`nvm install --save ${version}\` to write .nvmrc, got >${OUTPUT}<"
+
+cleanup