Minimalist Machine Derivations

Minimalist Machine Derivations

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Examples:

A Minimalist account of reconstruction asymmetries (Munn, 1994). collapse

Example	Instruction stream (clickable)	Notes
(15a) The picture of himself₁ that Bill₁ likes The picture of himself₁ Bill₁ likes	[bill, d, he, self, of, picture, d_rel, like, 'v*', 'T', c_rel, the]	Two derivations. Doubling Constituent (DC) self-he-Bill object of preposition of. Object of likes is d_rel-picture-of-DC. d_rel has iRel but cannot check picture's uD feature. Bill restacked at Local Extent (LE) boundary headed by self. v* merges TOS Bill to its edge. c_rel has uT and uRel, and heads a LE. Two ways to satisfy c_rel using Pesetsky and Torrego (2001): (1) T to edge of c_rel => that (2) Nom Case-marked Bill to edge of c_rel => empty At the LE boundary, picture of self-he-Bill (uD) is restacked. Head picture of the TOS picture of self-he-Bill merges with c_relP. picture labels (head merging with non-head). Stream the merges with SO headed by picture. [Spellout Note: Bill has been separately moved to the subject of the embedded clause. Thus although d_rel pictures of self-he-~~Bill~~ is raised higher (to the edge of c_rel), Bill is pronounced in the lower position, not at the edge of the clause.]
(15b) The picture of Bill₁ that he₁ likes The picture of Bill₁ he₁ likes	[he, d, bill, d, of, picture, d_rel, like, 'v*', 'T', c_rel, the]	Bill-he is not a regular DC (cf. he-Bill). [Note: in a regular DC, e.g. he-John, the pronominal he triggers DC merge in which John will be stacked but not made visible to stack operations such as probe-goal and internal merge until a LE boundary is encountered later on in the derivation.] he (uCase) is (visibly) stacked when merged with Bill. d_rel has iRel but cannot check picture's uD feature. v* merges he to its edge. c_rel has uT and uRel, and heads a LE. c_rel satisfied by either T or he (locally nom Case-marked) to C. At the LE boundary, picture of Bill-he (uD) is restacked. Extract head picture (uD) and merge with c_relP. picture labels (head merging with non-head). Stream the merges with SO headed by picture.
(19a) Pictures of himself₁ are hard for John₁ to like	[john, d, he, self, of, pictures, d, pro, like, 'v*', 'Tinf', for, hard, 'v_be', 'T', c]	Doubling Constituent (DC) pro-pictures of self-he-John with another DC self-he-John embedded inside. Determiner self heads a Local Extent (LE) phrase. Doubling constituent (DC) self-he-John triggers stacking of John. Embedded v* merges TOS John to its edge. T_inf does not value case for John. Assume for is a complementizer that probes and values Case. Then John's uCase feature is valued. Assume for heads a LE phase. Then at the LE boundary, pictures of self-he-John (with unvalued uCase) is re-stacked. Matrix v_be merges TOS pictures of self-he-John to its edge. [Spellout Note: John has been separately moved to the subject of the embedded clause. Thus although pictures of self-he-~~John~~ is raised higher (to the matrix subject), John is pronounced in the lower clause, not the matrix clause.]
(19b) Pictures of John₁ are hard for him₁ to like	[he, d, john, d, of, pictures, d, pro, like, 'v*', 'Tinf', for, hard, 'v_be', 'T', c]	DC pro-pictures of John-he with a (pseudo) DC John-he embedded inside. John-he is not a regular DC (cf. he-John). In particular, he (with unvalued uCase) is stacked when merged with John. [Note: in a regular DC, e.g. he-John, the pronominal he triggers DC merge in which John will be stacked but not made visible to stack operations such as probe-goal and internal merge until a LE boundary is encountered later on in the derivation.] Regular DC head pro merges with pictures of John-he. pictures of John-he is stacked but will not be available until the boundary of a LE has been built. Embedded v* merges non-TOS he to its edge. [Note: TOS pictures of John-he is not selected because it already has a theta-role assigned. Edge of v* is a theta-position.] Assume for is a complementizer that probes and values Case. Then he's uCase feature is valued. Assume for heads a LE phase. Then at the LE boundary, pictures of he-John (with unvalued uCase) is re-stacked. Matrix v_be merges TOS pictures of he-John to its edge.
Extra test cases
(x1) *The picture of him₁ that Bill₁ likes	[bill, d, he, d, of, picture, d_rel, like, 'v*', 'T', c_rel, the]	Doubling Constituent (DC) he-Bill. Bill is not restacked in time for merge to the edge of v* (no LE boundary).
(x2) *Pictures of him₁ are hard for John₁ to like	[john, d, he, d, of, pictures, d, pro, like, 'v*', 'Tinf', for, hard, 'v_be', 'T', c]	DC he-John and DC pro-pictures of he-John. John is not restacked in time for merge to the edge of v* (no LE boundary).

Machine Parameters: expand

Animation:
(15a) The picture of himself₁ that Bill₁ likes
The picture of himself₁ Bill₁ likes

Derivation:
(15a) The picture of himself₁ that Bill₁ likes
The picture of himself₁ Bill₁ likes

Stream:	[[bill!D],[d!case!N],[he!D],[self!case!N],[of],[picture!D],[d_rel!case!N],[like],[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):
SO:	[]

Step 1.

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

Stream:	[[d!case!N],[he!D],[self!case!N],[of],[picture!D],[d_rel!case!N],[like],[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):
SO:	[bill!D]

Step 2.

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

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

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

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

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

Stream:	[[he!D],[self!case!N],[of],[picture!D],[d_rel!case!N],[like],[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):
SO:	[d!case[d][bill]]

Doubling Constitutent (DC) merge

Step 3.

Merge [he!D] and [d!case[d][bill]]

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

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

Stream:	[[self!case!N],[of],[picture!D],[d_rel!case!N],[like],[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):	inactive([d!case[d][bill]])
SO:	[he!D[he!D][d!case[d][bill]]]

Step 4.

Merge [self!case!N] and [he!D[he!D][d!case[d..][bill..]]]

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

Inherit interpretable feature(s) [f(phi,[3,sg,m])] from [he!D[he!D][d!case[d..][bill..]]]

[self!case!N] values D on [he!D[he!D][d!case[d..][bill..]]]

[he[he][d!case[d..][bill..]]] values N on [self!case!N]

Stream:	[[of],[picture!D],[d_rel!case!N],[like],[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):	inactive([d!case[d][bill]])
SO:	[self!case[self][he[he][d!case[d][bill]]]]

Step 5.

Local Extent boundary at [self!case[self][he[he..][d..]]]

Inactive stack element inactive([d!case[d][bill]]) found

New boundary (b) marker stacked

Restack [d!case[d][bill]] onto stack

Stream:	[[of],[picture!D],[d_rel!case!N],[like],[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):	once([d!case[d][bill]]) b
SO:	[self!case[self][he[he][d!case[d][bill]]]]

Step 6.

Merge [of] and [self!case[self][he[he..][d..]]]

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

Theta-mark [self!case[self][he[he..][d..]]]

[of] values obq case on [self!case[self][he[he..][d..]]]

Stream:	[[picture!D],[d_rel!case!N],[like],[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):	once([d!case[d][bill]]) b
SO:	[of[of][self[self][he[he][d!case[d][bill]]]]]

Step 7.

Merge [picture!D] and [of[of][self[self..][he..]]]

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

Stream:	[[d_rel!case!N],[like],[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):	once([d!case[d][bill]]) b
SO:	[picture!D[picture!D][of[of][self[self][he[he][d!case[d][bill]]]]]]

Step 8.

Merge [d_rel!case!N] and [picture!D[picture!D][of[of..][self..]]]

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

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [picture!D[picture!D][of[of..][self..]]]

[picture!D[picture!D][of[of..][self..]]] values N on [d_rel!case!N]

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

Stream:	[[like],[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):	[picture!D] once([d!case[d][bill]]) b
SO:	[d_rel!case[d_rel][picture!D[picture!D][of[of][self[self][he[he][d!case[d][bill]]]]]]]

Step 9.

Merge [like] and [d_rel!case[d_rel][picture!D[picture..][of..]]]

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

Theta-mark [d_rel!case[d_rel][picture!D[picture..][of..]]]

Push [d_rel!case[d_rel][picture!D[picture..][of..]]] (unvalued uF) onto stack

Stream:	[[v*!phi],[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):	[d_rel!case[d_rel][picture!D[picture!D][of[of][self[self][he[he][d!case[d][bill]]]]]]] [picture!D] once([d!case[d][bill]]) b
SO:	[like[like][d_rel!case[d_rel][picture!D[picture!D][of[of][self[self][he[he][d!case[d][bill]]]]]]]]

Step 10.

Merge [v*!phi] and [like[like][d_rel!case[d_rel..][picture..]]]

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

[d_rel!case[d_rel][picture!D[picture..][of..]]] values uPhi on [v*!phi]

[v*] values acc case on [d_rel!case[d_rel][picture!D[picture..][of..]]]

Stream:	[[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):	[d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d!case[d][bill]]]]]]] [picture!D] once([d!case[d][bill]]) b
SO:	[v[v][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d!case[d][bill]]]]]]]]]

Step 11.

Relativized TOS search for unvalued_iF(theta) skipping [d_rel[d_rel][picture!D[picture..][of..]]]

Relativized TOS search for unvalued_iF(theta) skipping [picture!D]

Internal merge selected

Merge [v*[v*][like[like..][d_rel..]]] and [d!case[d][bill]]

Label from [v*[v*][like[like..][d_rel..]]] (edge feature)

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

Move [d!case[d][bill]] (unvalued uF) to the front of the stack

Stream:	[[T!phi],[c_rel!rel!T],[the!case!N]]
Stack (⥥):	[d!case[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d!case[d][bill]]]]]]] [picture!D] b
SO:	[v[d!case[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]

Step 12.

Merge [T!phi] and [v*[d!case[d..][bill..]][v*[v*..][like..]]]

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

[d!case[d][bill]] values uPhi on [T!phi]

[T] values nom case on [d!case[d][bill]]

Stream:	[[c_rel!rel!T],[the!case!N]]
Stack (⥥):	[d[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]] [picture!D] b
SO:	[T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]

Step 13.

Internal merge selected

Merge [T[T][v*[d..][v*..]]] and [d[d][bill]]

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

Stream:	[[c_rel!rel!T],[the!case!N]]
Stack (⥥):	[d[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]] [picture!D] b
SO:	[T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]

Step 14.

Merge [c_rel!rel!T] and [T[d[d..][bill..]][T[T..][v*..]]]

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

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

[d_rel[d_rel][picture!D[picture..][of..]]] values rel on [c_rel!rel!T]

[d[d][bill]] values T on [c_rel!T]

Internal merge selected

Merge [c_rel[c_rel][T[d..][T..]]] and [d[d][bill]]

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

Merge [c_rel[d[d..][bill..]][c_rel[c_rel..][T..]]] and [d_rel[d_rel][picture!D[picture..][of..]]]

Label from [c_rel[d[d..][bill..]][c_rel[c_rel..][T..]]] (edge feature)

Stream:	[[the!case!N]]
Stack (⥥):	[d[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]] [picture!D] b
SO:	[c_rel[d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]][c_rel[d[d][bill]][c_rel[c_rel][T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]]]]

Step 15.

Local Extent boundary at [c_rel[d_rel[d_rel..][picture..]][c_rel[d..][c_rel..]]]

Stack element [picture!D] with unvalued uF found

New boundary (b) marker stacked

Restack [picture!D] onto stack

Stream:	[[the!case!N]]
Stack (⥥):	[picture!D] b [d[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]] b
SO:	[c_rel[d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]][c_rel[d[d][bill]][c_rel[c_rel][T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]]]]

Step 16.

Merge [picture!D] and [c_rel[d_rel[d_rel..][picture..]][c_rel[d..][c_rel..]]]

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

Stream:	[[the!case!N]]
Stack (⥥):	[picture!D] b [d[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]] b
SO:	[picture!D[picture!D][c_rel[d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]][c_rel[d[d][bill]][c_rel[c_rel][T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]]]]]

Step 17.

Merge [the!case!N] and [picture!D[picture!D][c_rel[d_rel..][c_rel..]]]

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

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

[the!case!N] values D on [picture!D[picture!D][c_rel[d_rel..][c_rel..]]]

[picture[picture][c_rel[d_rel..][c_rel..]]] values N on [the!case!N]

Stream:	[]
Stack (⥥):	[picture] b [d[d][bill]] [d_rel[d_rel][picture[picture][of[of][self[self][he[he][d[d][bill]]]]]]] b
SO:	[the!case[the][picture[picture][c_rel[d_rel[d_rel][picture[picture][of[of][self[self][he[he][d[d][bill]]]]]]][c_rel[d[d][bill]][c_rel[c_rel][T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture[picture][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]]]]]]

Parse:

Spell-out:

the picture of -self -obq he bill -s like (after morpheme realization)

the picture of he -obq -self bill like -s (after affix-hop)

the picture of he -obq -self bill like -s (after morpheme realization, stage 2)

the picture of himself bill likes

Backtrack

Stream:	[[c_rel!rel!T],[the!case!N]]
Stack (⥥):	[d[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]] [picture!D] b
SO:	[T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]

re-doing step 14

Step 18.

[c_rel!T] attracts [T[d[d..][bill..]][T[T..][v*..]]]

Internal merge selected

Merge [c_rel[c_rel][T[d..][T..]]] and [T]

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

Merge [c_rel[T][c_rel[c_rel..][T..]]] and [d_rel[d_rel][picture!D[picture..][of..]]]

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

Stream:	[[the!case!N]]
Stack (⥥):	[d[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]] [picture!D] b
SO:	[c_rel[d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]][c_rel[T][c_rel[c_rel][T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]]]]

Step 19.

Local Extent boundary at [c_rel[d_rel[d_rel..][picture..]][c_rel[T..][c_rel..]]]

Stack element [picture!D] with unvalued uF found

New boundary (b) marker stacked

Restack [picture!D] onto stack

Stream:	[[the!case!N]]
Stack (⥥):	[picture!D] b [d[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]] b
SO:	[c_rel[d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]][c_rel[T][c_rel[c_rel][T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]]]]

Step 20.

Merge [picture!D] and [c_rel[d_rel[d_rel..][picture..]][c_rel[T..][c_rel..]]]

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

Stream:	[[the!case!N]]
Stack (⥥):	[picture!D] b [d[d][bill]] [d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]] b
SO:	[picture!D[picture!D][c_rel[d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]][c_rel[T][c_rel[c_rel][T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture!D[picture!D][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]]]]]

Step 21.

Merge [the!case!N] and [picture!D[picture!D][c_rel[d_rel..][c_rel..]]]

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

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

[the!case!N] values D on [picture!D[picture!D][c_rel[d_rel..][c_rel..]]]

[picture[picture][c_rel[d_rel..][c_rel..]]] values N on [the!case!N]

Stream:	[]
Stack (⥥):	[picture] b [d[d][bill]] [d_rel[d_rel][picture[picture][of[of][self[self][he[he][d[d][bill]]]]]]] b
SO:	[the!case[the][picture[picture][c_rel[d_rel[d_rel][picture[picture][of[of][self[self][he[he][d[d][bill]]]]]]][c_rel[T][c_rel[c_rel][T[d[d][bill]][T[T][v[d[d][bill]][v[v*][like[like][d_rel[d_rel][picture[picture][of[of][self[self][he[he][d[d][bill]]]]]]]]]]]]]]]]]

Parse:

Spell-out:

the picture of -self -obq he that bill -s like (after morpheme realization)

the picture of he -obq -self that bill like -s (after affix-hop)

the picture of he -obq -self that bill like -s (after morpheme realization, stage 2)

the picture of himself that bill likes

2 derivations found.

Computational Cost:

Merge: 20, Agree: 17, Unify: 0, Push: 4, Boundaries: 3, Inject: 3

Non-TOS access: 4, Pop: 0, Depth cost: 50

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