Szemerényi's law (or Szemerényi's lengthening) is both a sound change and a synchronic phonological rule that operated during an early stage of the Proto-Indo-European language (PIE). Though its effects are evident in many reconstructed as well as attested forms, it did not operate in late PIE, having become morphologized (with exceptions reconstructible via the comparative method). It is named for Hungarian-British linguist Oswald Szemerényi.
The rule deleted coda fricatives *s or laryngeals *h₁, *h₂ or *h₃ (cover symbol *H), with compensatory lengthening occurring in a word-final position after resonants. In other words:
*/-VRs/, */-VRH/ > *-VːR
*/-VRH-/ > *-VR- (no examples of s-deletion can be reconstructed for PIE)
The law affected the nominative singular forms of the many masculine and feminine nouns whose stem ended in a resonant:
The rule also affected the nominative-accusative forms of neuter plural/collective nouns, which ended in :
Also in the third-person plural perfect ending:
Compare:
According to another synchronic PIE phonological rule, word-final *n was deleted after *ō, usually by the operation of Szemerényi's law:
The PIE reconstruction for "heart" is the single instance where *d is deleted after *r, with compensatory lengthening of the preceding vowel. It is not clear whether that is an isolated example or a part of a broader process.
Some cases were apparently not affected by Szemerényi's law:
In PIE, the resulting long vowels had already begun to spread analogically to other nominative singular forms that were not phonologically justified by the law (PIE 'foot'). The word-final sonorants other than *-n were sometimes dropped as well, which demonstrates that this law was already morphologized in the period of "PIE proper", and the long vowel produced was no longer synchronically viewed as the outcome of a process of fricative deletion. Exceptions to Szemerényi's law are found in word-final:
as well as medial positions:
The forms without a laryngeal are considered to be more archaic and were likely to have been lexicalized at a later stage of PIE.