Rule ordering

Conditional
Ordering

Suppose that the only things x can be many things, and in most cases we do nothing, bu with lists, we do something special.

Here is a bad program that deals with this situation:

if isinstance(x,str) or\
   isinstance(x,dict) or\
   isinstance(x,float) or\
   isinstance(x,int) or \
   isinstance(x,tuple):
    y = None
elif isinstance(x,list):
    y = x[0]

Long, hard-to-read, and prone to bugs. I forgot the type "long" (Python's long integer type) so this will erroneously do:

y=x[0]

for long integers, raising an exception and terminating execution.

A better program:

if isinstance(x,list):
    y = x[0]
else:
    y = None

The else clause here is called an elsewhere condition.

In general programs are most elegant if they treat the most general case further down the list of cases:

if isinstance(x,float):
   y=x/5.0
elif isinstance
else:
  y = x/5

The second clause actually covers two cases, "int" (integer) and "long"(long integer).

An if-then-else clause works because

Nasal
assimilation

Consider the English prefix in/im as in:

impossible
impracible
immersible
inevitable
indelible
incredible
incessant

Generalization? Does an elsewhere condition help?

Along the same lines, and resembling the "kamman" poroblem, here is a simple example with fake data.

kan	kan	"do"
kan+tat	kantat	"doable"
kan+sen	kansen	"undo"
kan+gus	kangus	"do again"
kan+pat	kampat [!]	"do repeatedly"

We call "kan" the stem and "tat/sen/gus/pat" suffixes.

Notice that in one case the "stem" changes shape.

This is called "nasal assimilation", nasal because it is happening with a nasal sound ("m", "n" and "ng") in English). Assimilation because the nasal is "assimilating" to the following sound. Assimilating means "becoming more alike like". An "m" is more like a "p" than an "n" because "m" and "p" have the same place of articulation (labial=lips).

A simple description of what is going on:

"kan" is pronounced "kan" everywhere except in front of "p"

But it turns out in our fictional language there are many stems that show this change. They end in "n" most places, but they end in "m" before suffixes that start with "p".

A slightly more sophisticated description. We will say "kan" ends not with "n" but with "N", a new sound.

The pronunciation of "N" is determine by rule.

"N" is pronounced "m" in front of p and "n" everywhere else.

We will write this as two rules in special notation.

(a) N --> m \ ___p
(b) N --> n

Rule (a) means N turns into ("is realized as") "m" in the context immediately preceding "p". The "____" stands for where the "N" goes, immediately before the "p". Note the (b) rule has no defining context, just like an "else" clause in a program. It means N turns into "n" everywhere (else).

So this rule means the same as the following programming language statement:

if N immediately precedes p:
   N --> m
else:
   N --> n

Note that in our notation, the ORDER is significant. If the rules were written in the reverse order, it would mean something else:

(a) N --> n 
(b) N --> m \ ___p

means "N" becomes "n" everywhere. So rule (b) now no longer has any effect

Rule
Ordering
Feeding

Consider the following rules:

(1)    Vowel Raising
       e --> i \ ___C_0 i

(2)    Palatalization
       t --> c \ ___i

Rule 1 (Vowel Raising) states that e becomes (is rewritten as) i in the environment:
1. Right context (Rule 1) Ci(0 or more consonants followed by "i")
2. Right context (Rule 2): i (the vowel "i")
A sample derivation of forms to which these rules apply:
```
    UR:    temi
    (1)    timi
    (2)    cimi     [intermediate level]
    SR:    cimi
```
Not only are these rules sequential, they are ordered, such that rule 1 must apply before rule 2. Rule 1 has a feeding relationship to rule 2; that is, rule 1 increases the number of forms that can undergo rule 2 by creating more instances of i.
Consider what would happen if they were applied in the reverse order. Given the input form temi:
1. Rule 2 does not apply....
2. ```
 temi -> *time 
```
  (Rule 1)

English
Flap
Rule

Let's look at the words writer and rider in Canadian English.

Examples:

write + er = writer

"dx" here stands for a FLAP, a quick flap of the tongue against the alveolar ridge. This is a voiceless sound.

ride + er = rider

The difference between the two words is in the vowel:

There are two things going on. First a process called flapping:

Flap Rule: t,d - > dx \ V _ V This turns t and d into flaps between vowels If the flap rule is correct, this means that in general there should be no contrast between t and d between vowels in Canadian English. They all get turned into flaps. This seems to be correct, even for most varieties of American English.

Next: There is a general process of vowel raising before voiceless consonants in Canadian English:

Raising Rule: ai => ^i / _ [-vcd] Examples:

knife	n ^i f	knives	n ai v z
house	h ^w s	houses	h aw z ix z

The crucial thing for present purposes: On one very simple account, flapping and vowel raising need to be ordered. Vowel raising needs to happen BEFORE flapping. When vowel raising applies rider still has a voiced sound in it and the vowel does not raise. Afterward, flapping takes away the voicing, but it's too late for raising to occur.

Notice if the rules apply freely or if they apply in the opposite order this rather simple account goes away. This is one of the most famous, if not the most famous, arguments for rule ordering.

Allomorphy

Latin Verbs

	praise	love	advise	see
2sg	laudas	amas	mones	vides
3sg	laudat	amat	monet	videt
1pl	laudamus	amamamus	monemus	videmus
2pl	laudatis	amatis	monetis	videtis
3pl	laudant	amant	monent	vident
imp	lauda	ama	mone	vide

But uh oh. Now look at the 1st sg forms....

What allomorphy/morpheme-changing rules make this data look nice....?

1sg	laudo	amo	moneo	video

Dutch T-deletion

3rd person singular present tense verb form: t

Suffix changes shape....

Dutch
Vowel
Shortening

Stem changes shape....

Dutch Consonant
Doubling

bel + en = bellen

Allophony

English
Flap
Rule

t - > D \ V _ V

Examples:

write + er = writer

Looks like allomorphy again, but it isn't.

Implementing rule ordering

Scanning Direction	One scanning strategy: Scan right to left looking for rule environments. At each segment, try to apply all the rules IN ORDER. Another: scan left to right.
Abstract example	a - > b \ ab __ ba Apply to: abababababa Three outcomes: abbbabbbaba: LEFT-TO-RIGHT scanning. Apply first to leftmost eligible position; each successive app applies to the output of the previous and further right in the string. ababbbabbba: RIGHT-TO-LEFT scanning. Apply first to rightmost eligible position; each successive app applies to the output of the previous and further left in the string. abbbbbbbbba: Identify all possible rule applications in the ORIGINAL string and carry out simultaneously. Bad news: Phonologists have advocated all 3 strategies. Soln: Each rule marked for its application strategy.
Scanning Direction Example II	Example: Invent a rule that uses right contexts created by another rule: c - > e ___ c Our palatalization rule creates c's. c t i Target RC -- > (Palatalization Rule) c c i -- > (C Deletion Rule) c i Notice that if the rules applied left to right C-deletion couldnt apply.
Turkish Vowel Harmony	Plural: lAr; sometimes realized as "lar", sometimes as "ler" depending on PREceding vowel. Possessive: Im:; sometimes realized as "am", sometimes as "im" depending on PREceding vowel. Only left-to-right works: adress + lAr + Im = adreslerim apartman + lAR + IM = apartmanlarim adres + Im + A = adresime