Minimalist Machine Derivations

Minimalist Machine Derivations

Files: grammar.pl / m12.pl / Back to homepage

Examples:

Relative clause constructions: inspired by (Gallego, 2010) and (Chen, (p.c.)). collapse

Example	Instruction stream (clickable)	Notes
(14a) the book that I read (14c) the book I read	[book, d_rel, read, 'v*', [i, d], 'Tpast', c_rel, the]	Two derivations. d_rel has iRel but cannot check book's uD feature. c_rel has uT and uRel, and heads a Local Extent (LE). Two ways to satisfy c_rel using Pesetsky and Torrego (2001): (1) T to edge of c_rel => that (2) Nom Case-marked I to edge of c_rel => empty At the LE boundary, book (uD) is restacked. TOS book merges with c_relP. book labels (head merging with non-head). Stream the merges with SO headed by book.
(14b) the book which I read *the book which that I read	[book, which_rel, read, 'v*', [i, d], 'Tpast', c_rel, the]	Single derivation. which_rel has iRel. which_rel can check uT but not uD feature. c_rel heads a LE, and has uT and uRel. Internal merge of which_rel book will satisfy both uT and uRel on c_rel. (By economy, T to C is not available.) At the LE boundary, book (uD) is restacked. book merges with c_relP, then with the.
(16a) the man to whom I talked the man whom I talked to *the man whom that I talked to	[man, who_rel, to, talk, 'v*', [i, d], 'Tpast', c_rel, the]	Two derivations. who_rel has iRel. who_rel can check uT but not uD feature. c_rel heads a LE, and has uT and uRel. Internal merge of who_rel man will satisfy both uT and uRel on c_rel. (By economy, T to C is not available.) At the LE boundary, man (uD) is restacked. man merges with c_relP, then with the. Optional pied-piping of verb particle to.
(16b) The man to that I talked (16c) The man to I talked The man I talked to The man that I talked to	[man, d_rel, to, talk, 'v*', [i, d], 'Tpast', c_rel, the]	Two derivations. d_rel has iRel but cannot check man's uD feature. 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 I to edge of c_rel => empty At the LE boundary, man (uD) is restacked. TOS man merges with c_relP. man labels (head merging with non-head). Stream the merges with SO headed by man. [Note: no pied-piping of verb particle to with d_rel-man. [An] EC [Empty Category] disallows pied-piping (Chomsky, 2001:28)]
(22) The man who John saw *The man who that John saw	[man, who_rel, see, 'v*', [john, d], 'Tpast', c_rel, the]	One derivation. who_rel has iRel. who_rel can check uT but not uD feature. c_rel heads a LE, and has uT and uRel. Internal merge of who_rel man will satisfy both uT and uRel on c_rel. (By economy, T to C is not available.) At the LE boundary, man (uD) is restacked. man merges with c_relP, then with the.
(29) The man who loves Mary *The man who that loves Mary	[mary, d, love, 'v*', [man, who_rel], 'T', c_rel, the]	One derivation. who_rel has iRel. who_rel can check uT but not uD feature. The subject who_rel-man is formed in a substream. man (uD) will be initially stacked in the substream and transferred back to the main stream. c_rel heads a LE, and has uT and uRel. Internal merge of who_rel man will satisfy both uT and uRel on c_rel. (By economy, T to C is not available.) At the LE boundary, man (uD) is restacked. man merges with c_relP, then with the. [Note: under machine parameter setting substream(subsume_ss), main stream subject who-man (uCase) will subsume man (uD) from a substream on the stack. To prevent this, tentatively we implement the policy of letting heads through.]
(35) The boy *(that) called Mary	[mary, d, call, 'v*', [boy, d_rel], 'Tpast', c_rel, the]	d_rel has iRel but cannot check man's uD feature. c_rel has uT and uRel, and heads a LE. Assume d_rel cannot check uT, i.e. d_rel-boy, despite getting nom Case, fails to satisfy uT on c_rel. Then c_rel's uT can only be satisfied by moving T to the edge of c_rel => that.
Extra test cases
(x1) What I read *What that I read	[pro_n, what_rel, read, 'v*', [i, d], 'Tpast', c_rel, d]	Headless relative. One derivation. Assume what is what_rel + pro_n (empty pronominal). what_rel has iRel. what_rel can check uT but not uD feature. c_rel heads a LE, and has uT and uRel. Internal merge of what_rel pro_n will satisfy both uT and uRel on c_rel. (By economy, T to C is not available.) At the LE boundary, pro_n (uD) is restacked. pro_n merges with c_relP, then with d.
(x2) What annoys John *What that annoys John	[john, d, annoy, 'v*', [pro_n, what_rel], 'T', c_rel, d]	Headless relative. One derivation. Assume what is what_rel + pro_n (empty pronominal). what_rel has iRel. what_rel can check uT but not uD feature. c_rel heads a LE, and has uT and uRel. Internal merge of what_rel pro_n will satisfy both uT and uRel on c_rel. (By economy, T to C is not available.) At the LE boundary, pro_n (uD) is restacked. pro_n merges with c_relP, then with d.

Machine Parameters: expand

Animation:
(16b) The man to that I talked
(16c) The man to I talked
The man I talked to
The man that I talked to

Derivation:
(16b) The man to that I talked
(16c) The man to I talked
The man I talked to
The man that I talked to

Stream:	[[man!D],[d_rel!case!N],[to],[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	[]

Step 1.

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

Stream:	[[d_rel!case!N],[to],[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	[man!D]

Step 2.

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

Label from [d_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 [d_rel!case!N]

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

Stream:	[[to],[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[man!D]
SO:	[d_rel!case[d_rel][man!D]]

Step 3.

Merge [to] and [d_rel!case[d_rel][man!D]]

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

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

[to] values obq case on [d_rel!case[d_rel][man!D]]

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

Stream:	[[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel[d_rel][man!D]] [man!D]
SO:	[to[to][d_rel[d_rel][man!D]]]

Step 4.

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

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

Internal merge to edge of [to[to][d_rel[d_rel][man!D]]] failed

No possible action for stream [[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]] and [to[to][d_rel[d_rel..][man..]]]

Stream:	[[man!D],[d_rel!case!N],[to],[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	[]

Step 5.

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

Stream:	[[d_rel!case!N],[to],[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):
SO:	[man!D]

Step 6.

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

Label from [d_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 [d_rel!case!N]

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

Stream:	[[to],[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[man!D]
SO:	[d_rel!case[d_rel][man!D]]

Step 7.

Merge [to] and [d_rel!case[d_rel][man!D]]

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

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

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

Stream:	[[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel!case[d_rel][man!D]] [man!D]
SO:	[to[to][d_rel!case[d_rel][man!D]]]

Step 8.

Merge [talk] and [to[to][d_rel!case[d_rel..][man..]]]

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

Stream:	[[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel!case[d_rel][man!D]] [man!D]
SO:	[talk[talk][to[to][d_rel!case[d_rel][man!D]]]]

Step 9.

Merge [v*!phi] and [talk[talk][to[to..][d_rel..]]]

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

[d_rel!case[d_rel][man!D]] values uPhi on [v*!phi]

[v*] values acc case on [d_rel!case[d_rel][man!D]]

Stream:	[[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel[d_rel][man!D]] [man!D]
SO:	[v[v][talk[talk][to[to][d_rel[d_rel][man!D]]]]]

Step 10.

Begin substream

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

Step 11.

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

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

Step 12.

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

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

Inherit interpretable feature(s) [f(phi,[1,sg,mf])] from [i!D]

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

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

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

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

Step 13.

Stream:	[[d!case[d][i]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel[d_rel][man!D]] [man!D]
SO:	[v[v][talk[talk][to[to][d_rel[d_rel][man!D]]]]]

Step 14.

Merge [v*[v*][talk[talk..][to..]]] and [d!case[d][i]]

Label from [v*[v*][talk[talk..][to..]]] (edge feature)

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

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

Stream:	[[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d!case[d][i]] [d_rel[d_rel][man!D]] [man!D]
SO:	[v[d!case[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]

Step 15.

Merge [Tpast!phi] and [v*[d!case[d..][i..]][v*[v*..][talk..]]]

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

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

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

Stream:	[[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d[d][i]] [d_rel[d_rel][man!D]] [man!D]
SO:	[Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]]

Step 16.

Internal merge selected

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

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

Stream:	[[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d[d][i]] [d_rel[d_rel][man!D]] [man!D]
SO:	[Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]]]

Step 17.

Merge [c_rel!rel!T!phi] and [Tpast[d[d..][i..]][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][i]]

[d_rel[d_rel][man!D]] values rel on [c_rel!rel!T!phi]

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

[d_rel[d_rel][man!D]] values phi on [c_rel!phi] (economy)

[c_rel] values obq case on [d_rel[d_rel][man!D]]

Internal merge selected

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

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

Merge [c_rel[d[d..][i..]][c_rel[c_rel..][Tpast..]]] and [d_rel[d_rel][man!D]]

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

Stream:	[[the!case!N]]
Stack (⥥):	[d[d][i]] [d_rel[d_rel][man!D]] [man!D]
SO:	[c_rel[d_rel[d_rel][man!D]][c_rel[d[d][i]][c_rel[c_rel][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]]]]]]

Step 18.

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

Stack element [d_rel[d_rel][man!D]] with unvalued uF found

Stack element [man!D] with unvalued uF found

New boundary (b) marker stacked

Restack [man!D] onto stack

Restack [d_rel[d_rel][man!D]] onto stack

Stream:	[[the!case!N]]
Stack (⥥):	[d_rel[d_rel][man!D]] [man!D] b [d[d][i]]
SO:	[c_rel[d_rel[d_rel][man!D]][c_rel[d[d][i]][c_rel[c_rel][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]]]]]]

Step 19.

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

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

Stream:	[[the!case!N]]
Stack (⥥):	b [d[d][i]]
SO:	[man!D[man!D][c_rel[d_rel[d_rel][man!D]][c_rel[d[d][i]][c_rel[c_rel][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]]]]]]]

Step 20.

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

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

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

Stream:	[]
Stack (⥥):	b [d[d][i]]
SO:	[the!case[the][man[man][c_rel[d_rel[d_rel][man]][c_rel[d[d][i]][c_rel[c_rel][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man]]]]]]]]]]]]]

Parse:

Spell-out:

the man I -ed(sg) talk to (after morpheme realization)

the man I talk -ed(sg) to (after affix-hop)

the man I talk -ed(sg) to (after morpheme realization, stage 2)

the man I talked to

Backtrack

Stream:	[[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d[d][i]] [d_rel[d_rel][man!D]] [man!D]
SO:	[Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]]]

re-doing step 17

Step 21.

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

[d_rel[d_rel][man!D]] values phi on [c_rel!phi] (economy)

[c_rel] values obq case on [d_rel[d_rel][man!D]]

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 [d_rel[d_rel][man!D]]

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

Stream:	[[the!case!N]]
Stack (⥥):	[d[d][i]] [d_rel[d_rel][man!D]] [man!D]
SO:	[c_rel[d_rel[d_rel][man!D]][c_rel[Tpast][c_rel[c_rel][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]]]]]]

Step 22.

Local Extent boundary at [c_rel[d_rel[d_rel..][man..]][c_rel[Tpast..][c_rel..]]]

Stack element [d_rel[d_rel][man!D]] with unvalued uF found

Stack element [man!D] with unvalued uF found

New boundary (b) marker stacked

Restack [man!D] onto stack

Restack [d_rel[d_rel][man!D]] onto stack

Stream:	[[the!case!N]]
Stack (⥥):	[d_rel[d_rel][man!D]] [man!D] b [d[d][i]]
SO:	[c_rel[d_rel[d_rel][man!D]][c_rel[Tpast][c_rel[c_rel][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]]]]]]

Step 23.

Merge [man!D] and [c_rel[d_rel[d_rel..][man..]][c_rel[Tpast..][c_rel..]]]

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

Stream:	[[the!case!N]]
Stack (⥥):	b [d[d][i]]
SO:	[man!D[man!D][c_rel[d_rel[d_rel][man!D]][c_rel[Tpast][c_rel[c_rel][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man!D]]]]]]]]]]]]

Step 24.

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

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

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

Stream:	[]
Stack (⥥):	b [d[d][i]]
SO:	[the!case[the][man[man][c_rel[d_rel[d_rel][man]][c_rel[Tpast][c_rel[c_rel][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][talk[talk][to[to][d_rel[d_rel][man]]]]]]]]]]]]]

Parse:

Spell-out:

the man that I -ed(sg) talk to (after morpheme realization)

the man that I talk -ed(sg) to (after affix-hop)

the man that I talk -ed(sg) to (after morpheme realization, stage 2)

the man that I talked to

2 derivations found.

Backtrack

Stream:	[[talk],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c_rel!rel!T!phi],[the!case!N]]
Stack (⥥):	[d_rel[d_rel][man!D]] [man!D]
SO:	[to[to][d_rel[d_rel][man!D]]]

re-doing step 4

Step 25.

Computational Cost:

Merge: 19, Agree: 20, Unify: 0, Push: 5, Boundaries: 2, Inject: 4

Non-TOS access: 3, Pop: 0, Depth cost: 25

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
Stack depth:	0	0	1	2	0	0	1	2	2	2	0	0	0	2	3	3	3	3	4	2	2	3	4	2	2