Szemerényi's law

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.

Overview
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)

Morphological effects
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:
 * PIE "father" >  (Ancient Greek patḗr, Sanskrit pitā́)
 * PIE "parent" >  (Ancient Greek genétōr, Latin genitor)
 * PIE "earth" >  (Ancient Greek khthṓn, Sanskrit kṣa, Hittite te-e-kán)
 * PIE "seeds" >  >  (on n-deletion see below)
 * PIE */-ers/ (the third-person plural perfect ending) > *-ēr (Latin ēr-e, Hittite -er, -ir)

Compare:
 * PIE "word" >  (Latin verbum)

Further effects
According to another synchronic PIE phonological rule, word-final *n was deleted after *ō, usually by the operation of Szemerényi's law:
 * PIE "dog" >  >  (Sanskrit ś(u)vā́, Old Irish cú)

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.
 * PIE "heart" >  (Ancient Greek kêr, Hittite ker)

Exceptions
Some cases were apparently not affected by Szemerényi's law:
 * The accusative plural *-ons of thematic nominals.
 * The genitive singular of stems ending in sonorants, such as *déms "of the house" (fossilised in the phrase *dems potis "master of the house").
 * Secondary 2nd person singular verb ending *-s with verbs ending in sonorants, such as *gʷéms (from the root *gʷem- "to step, to come").

Morphologization
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:
 * PIE "woman" >  (Old Irish bé) but also *gʷénh₂ (Sanskrit jáni)
 * PIE *gen- > Sanskrit janman, PIE *genh₁- > Sanskrit jánitrī

The forms without a laryngeal are considered to be more archaic and were likely to have been lexicalized at a later stage of PIE.