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:
(19b) Pictures of John₁ are hard for him₁ to like

Derivation:
(19b) Pictures of John₁ are hard for him₁ to like

Stream:	[[he!D],[d!case!N],[john!D],[d!case!N],[of],[pictures!D],[d!case!N],[pro!case],[like],[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):
SO:	[]

Step 1.

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

Stream:	[[d!case!N],[john!D],[d!case!N],[of],[pictures!D],[d!case!N],[pro!case],[like],[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):
SO:	[he!D]

Step 2.

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

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

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

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

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

Stream:	[[john!D],[d!case!N],[of],[pictures!D],[d!case!N],[pro!case],[like],[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):
SO:	[d!case[d][he]]

Step 3.

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

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

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

Stream:	[[d!case!N],[of],[pictures!D],[d!case!N],[pro!case],[like],[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][he]]
SO:	[john!D[john!D][d!case[d][he]]]

Step 4.

Merge [d!case!N] and [john!D[john!D][d!case[d..][he..]]]

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

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

[d!case!N] values D on [john!D[john!D][d!case[d..][he..]]]

[john[john][d!case[d..][he..]]] values N on [d!case!N]

Stream:	[[of],[pictures!D],[d!case!N],[pro!case],[like],[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][he]]
SO:	[d!case[d][john[john][d!case[d][he]]]]

Step 5.

Merge [of] and [d!case[d][john[john..][d..]]]

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

Theta-mark [d!case[d][john[john..][d..]]]

[of] values obq case on [d!case[d][john[john..][d..]]]

Stream:	[[pictures!D],[d!case!N],[pro!case],[like],[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][he]]
SO:	[of[of][d[d][john[john][d!case[d][he]]]]]

Step 6.

Merge [pictures!D] and [of[of][d[d..][john..]]]

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

Stream:	[[d!case!N],[pro!case],[like],[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][he]]
SO:	[pictures!D[pictures!D][of[of][d[d][john[john][d!case[d][he]]]]]]

Step 7.

Merge [d!case!N] and [pictures!D[pictures!D][of[of..][d..]]]

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

Inherit interpretable feature(s) [f(phi,[3,pl,n])] from [pictures!D[pictures!D][of[of..][d..]]]

[d!case!N] values D on [pictures!D[pictures!D][of[of..][d..]]]

[pictures[pictures][of[of..][d..]]] values N on [d!case!N]

Stream:	[[pro!case],[like],[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][he]]
SO:	[d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]

Doubling Constitutent (DC) merge

Step 8.

Merge [pro!case] and [d!case[d][pictures[pictures..][of..]]]

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

Inherit interpretable feature(s) [f(theta),f(phi,[3,pl,n])] from [d!case[d][pictures[pictures..][of..]]]

Push [d!case[d][pictures[pictures..][of..]]] (unvalued uF) onto stack

Stream:	[[like],[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	inactive([d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]) [d!case[d][he]]
SO:	[pro!case[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]]

Step 9.

Merge [like] and [pro!case[pro][d!case[d..][pictures..]]]

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

Theta-mark [pro!case[pro][d!case[d..][pictures..]]]

Push [pro!case[pro][d!case[d..][pictures..]]] (unvalued uF) onto stack

Stream:	[[v*!phi],[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[pro!case[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]] inactive([d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]) [d!case[d][he]]
SO:	[like[like][pro!case[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]]]

Step 10.

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

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

[pro!case[pro][d!case[d..][pictures..]]] values uPhi on [v*!phi]

[v*] values acc case on [pro!case[pro][d!case[d..][pictures..]]]

Stream:	[[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]] inactive([d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]) [d!case[d][he]]
SO:	[v[v][like[like][pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]]]]

Step 11.

Relativized TOS search for unvalued_iF(theta) skipping [pro[pro][d!case[d..][pictures..]]]

Internal merge selected

Merge [v*[v*][like[like..][pro..]]] and [d!case[d][he]]

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

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

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

Stream:	[[Tinf!phi],[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][he]] [pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]] inactive([d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]])
SO:	[v[d!case[d][he]][v[v*][like[like][pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]

Step 12.

Merge [Tinf!phi] and [v*[d!case[d..][he..]][v*[v*..][like..]]]

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

[d!case[d][he]] values uPhi on [Tinf!phi]

Stream:	[[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][he]] [pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]] inactive([d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]])
SO:	[Tinf[Tinf][v[d!case[d][he]][v[v*][like[like][pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]

Step 13.

Internal merge selected

Merge [Tinf[Tinf][v*[d..][v*..]]] and [d!case[d][he]]

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

Stream:	[[for!phi],[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][he]] [pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]]] inactive([d!case[d][pictures[pictures][of[of][d[d][john[john][d!case[d][he]]]]]]])
SO:	[Tinf[d!case[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]

Step 14.

Merge [for!phi] and [Tinf[d!case[d..][he..]][Tinf[Tinf..][v*..]]]

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

[d!case[d][he]] values uPhi on [for!phi]

[for] values obq case on [d!case[d][he]]

Stream:	[[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d[d][he]] [pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]] inactive([d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]])
SO:	[for[for][Tinf[d[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]]

Step 15.

Local Extent boundary at [for[for][Tinf[d..][Tinf..]]]

Inactive stack element inactive([d!case[d][pictures[pictures..][of..]]]) found

New boundary (b) marker stacked

Restack [d!case[d][pictures[pictures..][of..]]] onto stack

Stream:	[[hard],[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]] b [d[d][he]] [pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]
SO:	[for[for][Tinf[d[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]]

Step 16.

Merge [hard] and [for[for][Tinf[d..][Tinf..]]]

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

Stream:	[[v_be],[T!phi],[c]]
Stack (⥥):	[d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]] b [d[d][he]] [pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]
SO:	[hard[hard][for[for][Tinf[d[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]]]

Step 17.

Merge [v_be] and [hard[hard][for[for..][Tinf..]]]

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

Stream:	[[T!phi],[c]]
Stack (⥥):	[d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]] b [d[d][he]] [pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]
SO:	[v_be[v_be][hard[hard][for[for][Tinf[d[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]]]]

Step 18.

Internal merge selected

Merge [v_be[v_be][hard[hard..][for..]]] and [d!case[d][pictures[pictures..][of..]]]

Label from [v_be[v_be][hard[hard..][for..]]] (edge feature)

Preference: [v_be] edge merge from the stack (not stream)

Stream:	[[T!phi],[c]]
Stack (⥥):	[d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]] b [d[d][he]] [pro[pro][d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]
SO:	[v_be[d!case[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]][v_be[v_be][hard[hard][for[for][Tinf[d[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]]]]]

Step 19.

Merge [T!phi] and [v_be[d!case[d..][pictures..]][v_be[v_be..][hard..]]]

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

[d!case[d][pictures[pictures..][of..]]] values uPhi on [T!phi]

[T] values nom case on [d!case[d][pictures[pictures..][of..]]]

Stream:	[[c]]
Stack (⥥):	[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]] b [d[d][he]] [pro[pro][d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]
SO:	[T[T][v_be[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]][v_be[v_be][hard[hard][for[for][Tinf[d[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]]]]]]

Step 20.

Internal merge selected

Merge [T[T][v_be[d..][v_be..]]] and [d[d][pictures[pictures..][of..]]]

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

Stream:	[[c]]
Stack (⥥):	[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]] b [d[d][he]] [pro[pro][d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]
SO:	[T[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]][T[T][v_be[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]][v_be[v_be][hard[hard][for[for][Tinf[d[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]]]]]]]

Step 21.

Merge [c] and [T[d[d..][pictures..]][T[T..][v_be..]]]

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

Stream:	[]
Stack (⥥):	[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]] b [d[d][he]] [pro[pro][d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]
SO:	[c[c][T[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]][T[T][v_be[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]][v_be[v_be][hard[hard][for[for][Tinf[d[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]]]]]]]]

Step 22.

Local Extent boundary at [c[c][T[d..][T..]]]

New boundary (b) marker stacked

Stream:	[]
Stack (⥥):	b [d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]] b [d[d][he]] [pro[pro][d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]
SO:	[c[c][T[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]][T[T][v_be[d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]][v_be[v_be][hard[hard][for[for][Tinf[d[d][he]][Tinf[Tinf][v[d[d][he]][v[v*][like[like][pro[pro][d[d][pictures[pictures][of[of][d[d][john[john][d[d][he]]]]]]]]]]]]]]]]]]]]

Parse:

Spell-out:

pictures of -obq john -re be hard for -obq he to like (after morpheme realization)

pictures of john -obq be -re hard for he -obq to like (after affix-hop)

pictures of john -obq be -re hard for he -obq to like (after morpheme realization, stage 2)

pictures of john are hard for him to like

One derivation found.

Computational Cost:

Merge: 19, Agree: 14, Unify: 0, Push: 4, Boundaries: 2, Inject: 1

Non-TOS access: 2, Pop: 0, Depth cost: 38

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