Minimalist Machine Derivations

Minimalist Machine Derivations

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Examples:

Relative clause examples from Keenan 1987 (Fong & Ginsburg, ms.) collapse

Example	Instruction stream (clickable)	Notes
(32a) the boy who told the story	[story, the, tell, 'v*', [boy, who_rel], 'Tpast', c_rel, the]	A subject relative clause. Subject who boy attracted to edge of C_rel, i.e. C with an uRel. DP who boy is marked with an iRel feature, originating on who. Note, who_rel is defective, i.e. it doesn't value uD feature on boy. Instead, boy raises from edge of C and its uD feature is checked by the.
(32b) the letter which Dick wrote yesterday	[letter, which_rel, write, 'v*', [dick, d], 'Tpast', [yesterday, d], c_rel, the]	An object relative clause. Assume, substantially following (Haumann, 2007) and (Larson, 1985), that yesterday is a TP-level bare NP adverb. As an adjunct, yesterday is pair merged at TP. Defective which_rel is attracted by c_rel; the entire DP which letter raising to the edge of C, see notes for (32a) above. Finally, letter within the DP raises and its uD feature is valued by the.
(32c) the man who Ann gave the present to the man to who Ann gave the present (pied-piping)	[man, who_rel, to, [present, the], give, 'v*', [ann, d], 'Tpast', c_rel, the]	Relativization of the indirect object of a double object verb. Two analyses, also produces pied-piped variant. C_rel attracts who man, headed by who_rel, to its edge. Defective who, can't value uD on man. man raises. uD on man valued by c-commanding the.
(32d) the box which Pat brought the apples in the box in which Pat brought the apples (pied-piping)	[box, which_rel, in, [apples, the], bring, 'v*', [pat, d], 'Tpast', c_rel, the]	Assume bring...in involves a dyadic preposition in. C_rel attracts which box, headed by which_rel, to its edge. Defective which, can't value uD on box. box raises. uD on box valued by c-commanding the.
(32e) the dog which was taught by John	[dog, which_rel, teach, [[john, d], by], prt, 'v~', 'Tpast', c_rel, the]	Relativization of passivized object. The agentive by-phrase is pair-merged to teach (not PRT or v~ due to merge over move preference). C_rel attracts which dog, headed by which_rel, to its edge. Defective which, can't value uD on dog. dog raises. uD on box valued by c-commanding the.
(33a) the boy who Mike writes better than cf. *the boy than who Mike writes better	[boy, who_rel, than, better, write, 'v_unerg', [mike, d], 'T', c_rel, the]	Relativization of the object of a comparative. Assume than is a preposition, not a C - as needed in the case of Comparative Deletion (not implemented here: e.g. as in Mike writes better than I do/write. The pied-piped counterpart (see cf.) is blocked by a spellout rule (after the parse has been completed). C_rel attracts who boy, headed by who_rel, to its edge. Defective who, can't value uD on boy. boy raises. uD on boy valued by c-commanding the.
(33b) the girl whose friends bought the cake	[cake, the, buy, 'v*', [friends,'\'s',[girl, who_rel]],'Tpast',c_rel,the]	Relativization of a genitive from a subject. Assume the entire possessive 's DP [_'s [_who who_rel girl][_'s 's friends]] raises to edge of C_rel. Defective who_rel cannot value uD on girl. This permits girl to raise out and its uD feature is valued by the. Finally assume spellout rule: who + 's -> whose.
(33b') the girl who friends of bought the cake cf. *the girl of who friends bought the cake	[cake, the, buy, 'v*', [girl, who_rel, of, friends, d], 'Tpast', c_rel, the]	Relativization of a genitive from a subject. Assume DP [_d d [_friends friends [_of of [_who who_rel girl]]]], cf. possessive DP analysis above. C_rel attracts who girl, headed by who_rel, to its edge. Defective who, can't value uD on girl. This permits girl to raise. uD on girl is valued by c-commanding the. The pied-piped counterpart is blocked by a spellout rule that asserts there is no spellout for who_rel.
(33c) the man whose house Patrick bought the man whose house that Patrick bought (T-to-C variant)	[house,'\'s',[man,who_rel],buy,'v*',[patrick,d],'Tpast',c_rel,the]	Relativization of a genitive from the object. Assume possessive 's DP [_'s [_who who_rel man] [_'s 's house]] raises to edge of C_rel. who_rel cannot value uD on man. This permits man to raise out and its uD feature is valued by the. Finally assume spellout rule: who + 's -> whose.
(33c') the man who Patrick bought the house of cf. *the man of who Patrick bought the house	[man, who_rel, of, house, the, buy, 'v*', [patrick, d], 'Tpast', c_rel, the]	Relativization of a genitive from the object. Assume DP [_the the [_house house [_of of [_who who man]]]], cf. possessive DP analysis above in (33c). C_rel attracts who man, headed by who_rel, to its edge. Defective who, can't value uD on man. This permits man to raise. uD on man is valued by c-commanding the. The pied-piped counterpart (see cf.) is blocked by a spellout rule (after the parse has been completed). See also (33b').
(33d) the boy whose brother was taught by Sandra	[brother, '\'s', [boy, who_rel], teach, [[sandra, d], by], prt, 'v~', 'Tpast', c_rel, the]	Relativization of a genitive from the passivized object. Assume possessive DP [_'s [_who who_rel boy][_'s 's brother]] raises to edge of C_rel. who_rel cannot value uD on boy. This permits boy to raise out and its uD feature is valued by the. Finally assume spellout rule: who + 's -> whose.

Machine Parameters: expand

Animation:
(33c) the man whose house Patrick bought
the man whose house that Patrick bought (T-to-C variant)

Derivation:
(33c) the man whose house Patrick bought
the man whose house that Patrick bought (T-to-C variant)

Stream:	[[house!D],['s!case!N],[[man!D],[who_rel!case!N]],[buy],[v*!phi],[[patrick!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	[]

Step 1.

Head of stream [house!D] is the initial SO

Stream:	[['s!case!N],[[man!D],[who_rel!case!N]],[buy],[v*!phi],[[patrick!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	[house!D]

Step 2.

Merge ['s!case!N] and [house!D]

Label from ['s!case!N] (syntactic head with an unvalued uF)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [house!D]

['s!case!N] values D on [house!D]

[house] values N on ['s!case!N]

Stream:	[[[man!D],[who_rel!case!N]],[buy],[v*!phi],[[patrick!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	['s!case['s][house]]

Step 3.

Begin substream

Stream:	[[man!D],[who_rel!case!N]]
Stack (⥥):
SO:	[]

Step 4.

Head of stream [man!D] is the initial SO

Stream:	[[who_rel!case!N]]
Stack (⥥):
SO:	[man!D]

Step 5.

Merge [who_rel!case!N] and [man!D]

Label from [who_rel!case!N] (syntactic head with an unvalued uF)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [man!D]

[man!D] values N on [who_rel!case!N]

Push [man!D] (unvalued uF) onto stack

Stream:	[]
Stack (⥥):	[man!D]
SO:	[who_rel!case[who_rel][man!D]]

End substream, SO [who_rel!case[who_rel][man!D]] re-inserted into main stream

Substream stack [[man!D]] saved for possible stack merge

Step 6.

Stream:	[[who_rel!case[who_rel][man!D]],[buy],[v*!phi],[[patrick!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	['s!case['s][house]]

Step 7.

Theta-mark [who_rel!case[who_rel][man!D]]

['s!case['s][house]] values gen case on [who_rel!case[who_rel][man!D]]

Merge ['s!case['s][house]] and [who_rel[who_rel][man!D]]

Label from ['s!case['s][house]] (edge feature)

Saved substream stack [[man!D]] merged with stack

Stream:	[[buy],[v*!phi],[[patrick!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[man!D]
SO:	['s!case[who_rel[who_rel][man!D]]['s['s][house]]]

Step 8.

Local Extent boundary at ['s!case[who_rel[who_rel..][man..]]['s['s..][house..]]]

Stack element [man!D] with unvalued uF found

New boundary (b) marker stacked

Restack [man!D] onto stack

Stream:	[[buy],[v*!phi],[[patrick!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[man!D] b
SO:	['s!case[who_rel[who_rel][man!D]]['s['s][house]]]

Step 9.

Merge [buy] and ['s!case[who_rel[who_rel..][man..]]['s['s..][house..]]]

Label from [buy] (syntactic head merging with a non-head)

Theta-mark ['s!case[who_rel[who_rel..][man..]]['s['s..][house..]]]

Push ['s!case[who_rel[who_rel..][man..]]['s['s..][house..]]] (unvalued uF) onto stack

Stream:	[[v*!phi],[[patrick!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	['s!case[who_rel[who_rel][man!D]]['s['s][house]]] [man!D] b
SO:	[buy[buy]['s!case[who_rel[who_rel][man!D]]['s['s][house]]]]

Step 10.

Merge [v*!phi] and [buy[buy]['s!case[who_rel..]['s..]]]

Label from [v*!phi] (syntactic head merging with a non-head)

['s!case[who_rel[who_rel..][man..]]['s['s..][house..]]] values uPhi on [v*!phi]

[v*] values acc case on ['s!case[who_rel[who_rel..][man..]]['s['s..][house..]]]

Stream:	[[[patrick!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	['s[who_rel[who_rel][man!D]]['s['s][house]]] [man!D] b
SO:	[v[v][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]

Step 11.

Begin substream

Stream:	[[patrick!D],[d!case!N]]
Stack (⥥):
SO:	[]

Step 12.

Head of stream [patrick!D] is the initial SO

Stream:	[[d!case!N]]
Stack (⥥):
SO:	[patrick!D]

Step 13.

Merge [d!case!N] and [patrick!D]

Label from [d!case!N] (syntactic head with an unvalued uF)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [patrick!D]

[d!case!N] values D on [patrick!D]

[patrick] values N on [d!case!N]

Stream:	[]
Stack (⥥):
SO:	[d!case[d][patrick]]

End substream, SO [d!case[d][patrick]] re-inserted into main stream

Step 14.

Stream:	[[d!case[d][patrick]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	['s[who_rel[who_rel][man!D]]['s['s][house]]] [man!D] b
SO:	[v[v][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]

Step 15.

Merge [v*[v*][buy[buy..]['s..]]] and [d!case[d][patrick]]

Label from [v*[v*][buy[buy..]['s..]]] (edge feature)

Theta-mark [d!case[d][patrick]]

Push [d!case[d][patrick]] (unvalued uF) onto stack

Stream:	[[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d!case[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] [man!D] b
SO:	[v[d!case[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]

Step 16.

Merge [Tpast!phi] and [v*[d!case[d..][patrick..]][v*[v*..][buy..]]]

Label from [Tpast!phi] (syntactic head merging with a non-head)

[d!case[d][patrick]] values uPhi on [Tpast!phi]

[Tpast] values nom case on [d!case[d][patrick]]

Stream:	[[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] [man!D] b
SO:	[Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]]

Step 17.

Internal merge selected

Merge [Tpast[Tpast][v*[d..][v*..]]] and [d[d][patrick]]

Label from [Tpast[Tpast][v*[d..][v*..]]] (edge feature)

Stream:	[[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] [man!D] b
SO:	[Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]]]

Step 18.

Merge [c_rel!rel!T!phi] and [Tpast[d[d..][patrick..]][Tpast[Tpast..][v*..]]]

Label from [c_rel!rel!T!phi] (syntactic head merging with a non-head)

Relativized TOS search for iF(rel) skipping [d[d][patrick]]

['s[who_rel[who_rel..][man..]]['s['s..][house..]]] values rel on [c_rel!rel!T!phi]

[d[d][patrick]] values T on [c_rel!T!phi]

['s[who_rel[who_rel..][man..]]['s['s..][house..]]] values phi on [c_rel!phi] (economy)

[c_rel] values obq case on ['s[who_rel[who_rel..][man..]]['s['s..][house..]]]

Internal merge selected

Merge [c_rel[c_rel][Tpast[d..][Tpast..]]] and [d[d][patrick]]

Label from [c_rel[c_rel][Tpast[d..][Tpast..]]] (edge feature)

Merge [c_rel[d[d..][patrick..]][c_rel[c_rel..][Tpast..]]] and ['s[who_rel[who_rel..][man..]]['s['s..][house..]]]

Label from [c_rel[d[d..][patrick..]][c_rel[c_rel..][Tpast..]]] (edge feature)

Stream:	[[the!case!N]]
Stack (⥥):	[d[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] [man!D] b
SO:	[c_rel['s[who_rel[who_rel][man!D]]['s['s][house]]][c_rel[d[d][patrick]][c_rel[c_rel][Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]]]]]]

Step 19.

Local Extent boundary at [c_rel['s[who_rel..]['s..]][c_rel[d..][c_rel..]]]

Stack element [man!D] with unvalued uF found

New boundary (b) marker stacked

Restack [man!D] onto stack

Stream:	[[the!case!N]]
Stack (⥥):	[man!D] b [d[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] b
SO:	[c_rel['s[who_rel[who_rel][man!D]]['s['s][house]]][c_rel[d[d][patrick]][c_rel[c_rel][Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]]]]]]

Step 20.

Merge [man!D] and [c_rel['s[who_rel..]['s..]][c_rel[d..][c_rel..]]]

Label from [man!D] (syntactic head merging with a non-head)

Stream:	[[the!case!N]]
Stack (⥥):	[man!D] b [d[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] b
SO:	[man!D[man!D][c_rel['s[who_rel[who_rel][man!D]]['s['s][house]]][c_rel[d[d][patrick]][c_rel[c_rel][Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]]]]]]]

Step 21.

Merge [the!case!N] and [man!D[man!D][c_rel['s..][c_rel..]]]

Label from [the!case!N] (syntactic head merging with a non-head)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [man!D[man!D][c_rel['s..][c_rel..]]]

[the!case!N] values D on [man!D[man!D][c_rel['s..][c_rel..]]]

[man[man][c_rel['s..][c_rel..]]] values N on [the!case!N]

Stream:	[]
Stack (⥥):	[man] b [d[d][patrick]] ['s[who_rel[who_rel][man]]['s['s][house]]] b
SO:	[the!case[the][man[man][c_rel['s[who_rel[who_rel][man]]['s['s][house]]][c_rel[d[d][patrick]][c_rel[c_rel][Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man]]['s['s][house]]]]]]]]]]]]]

Parse:

Spell-out:

the man whose house Patrick -ed(sg) buy (after morpheme realization)

the man whose house Patrick buy -ed(sg) (after affix-hop)

the man whose house Patrick buy -ed(sg) (after morpheme realization, stage 2)

the man whose house Patrick bought

Backtrack

Stream:	[[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] [man!D] b
SO:	[Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]]]

re-doing step 18

Step 22.

[c_rel!T!phi] attracts [Tpast[d[d..][patrick..]][Tpast[Tpast..][v*..]]]

['s[who_rel[who_rel..][man..]]['s['s..][house..]]] values phi on [c_rel!phi] (economy)

[c_rel] values obq case on ['s[who_rel[who_rel..][man..]]['s['s..][house..]]]

Internal merge selected

Merge [c_rel[c_rel][Tpast[d..][Tpast..]]] and [Tpast]

Label from [c_rel[c_rel][Tpast[d..][Tpast..]]] (edge feature)

Merge [c_rel[Tpast][c_rel[c_rel..][Tpast..]]] and ['s[who_rel[who_rel..][man..]]['s['s..][house..]]]

Label from [c_rel[Tpast][c_rel[c_rel..][Tpast..]]] (edge feature)

Stream:	[[the!case!N]]
Stack (⥥):	[d[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] [man!D] b
SO:	[c_rel['s[who_rel[who_rel][man!D]]['s['s][house]]][c_rel[Tpast][c_rel[c_rel][Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]]]]]]

Step 23.

Local Extent boundary at [c_rel['s[who_rel..]['s..]][c_rel[Tpast..][c_rel..]]]

Stack element [man!D] with unvalued uF found

New boundary (b) marker stacked

Restack [man!D] onto stack

Stream:	[[the!case!N]]
Stack (⥥):	[man!D] b [d[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] b
SO:	[c_rel['s[who_rel[who_rel][man!D]]['s['s][house]]][c_rel[Tpast][c_rel[c_rel][Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]]]]]]

Step 24.

Merge [man!D] and [c_rel['s[who_rel..]['s..]][c_rel[Tpast..][c_rel..]]]

Label from [man!D] (syntactic head merging with a non-head)

Stream:	[[the!case!N]]
Stack (⥥):	[man!D] b [d[d][patrick]] ['s[who_rel[who_rel][man!D]]['s['s][house]]] b
SO:	[man!D[man!D][c_rel['s[who_rel[who_rel][man!D]]['s['s][house]]][c_rel[Tpast][c_rel[c_rel][Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man!D]]['s['s][house]]]]]]]]]]]]

Step 25.

Merge [the!case!N] and [man!D[man!D][c_rel['s..][c_rel..]]]

Label from [the!case!N] (syntactic head merging with a non-head)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [man!D[man!D][c_rel['s..][c_rel..]]]

[the!case!N] values D on [man!D[man!D][c_rel['s..][c_rel..]]]

[man[man][c_rel['s..][c_rel..]]] values N on [the!case!N]

Stream:	[]
Stack (⥥):	[man] b [d[d][patrick]] ['s[who_rel[who_rel][man]]['s['s][house]]] b
SO:	[the!case[the][man[man][c_rel['s[who_rel[who_rel][man]]['s['s][house]]][c_rel[Tpast][c_rel[c_rel][Tpast[d[d][patrick]][Tpast[Tpast][v[d[d][patrick]][v[v*][buy[buy]['s[who_rel[who_rel][man]]['s['s][house]]]]]]]]]]]]]

Parse:

Spell-out:

the man whose house that Patrick -ed(sg) buy (after morpheme realization)

the man whose house that Patrick buy -ed(sg) (after affix-hop)

the man whose house that Patrick buy -ed(sg) (after morpheme realization, stage 2)

the man whose house that Patrick bought

2 derivations found.

Computational Cost:

Merge: 18, Agree: 21, Unify: 0, Push: 3, Boundaries: 3, Inject: 3

Non-TOS access: 1, Pop: 0, Depth cost: 46

Step:	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
Stack depth:	0	0	0	0	0	1	0	1	2	3	3	0	0	0	3	4	4	4	4	5	5	5	4	5	5	5