Minimalist Machine Derivations

Minimalist Machine Derivations

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

Examples:

Examples from A New Approach to Tough-Constructions (Fong & Ginsburg, 2014).
Doubling Constituent (DC) approach. collapse

Example	Instruction stream (clickable)	Notes
(1) John is easy to please	[john, d, pro, please, 'v*', ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c]	Doubling Constituent (DC) pro-John. At the Local Extent (LE) boundary, the embedded CP, John (with unvalued uCase) is re-stacked. T picks up TOS John.
(2) The violin is easy to play the sonata on	[violin, the, pro, on, [sonata, the], play, 'v*', ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c]	DC pro-the-violin. At the LE boundary, the embedded CP, the violin (with unvalued uCase) is re-stacked. Matrix T picks up TOS the violin.
(3) *What sonata is the violin easy to play on?	[violin, the, pro, on, [sonata, what:d], play, 'v*', ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c_Q]	Does not converge. DC pro-the-violin. what sonata is stacked (uScope). At the LE boundary, the embedded CP, what sonata (unvalued uScope) and the violin (unvalued uCase) are re-stacked. Matrix T fails to agree with TOS what sonata: nom Case clashes with acc Case assigned by embedded v*.
(4) The sonata is easy to play on this violin	[violin, this, on, [sonata, the, pro], play, 'v*', ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c]	DC pro-the-sonata. At the LE boundary, the embedded CP, the sonata (unvalued uCase) is restacked. Matrix T picks up TOS the sonata.
(5) What violin is the sonata easy to play on?	[violin, what:d, on, [sonata, the, pro], play, 'v*', ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c_Q]	DC pro-the-sonata. what violin is stacked (uScope). At the LE boundary, the embedded CP, the sonata (unvalued uCase) and what violin (unvalued uScope) are restacked. Matrix T picks up TOS the sonata. c_Q finds iWh what violin.
(6) Linguists are tough to please	[linguists, d, pro, please, 'v*', ['PRO', d0], 'Tinf', c, tough, v_be, 'T', c]	(Same as (1).) DC pro-linguists. At the LE boundary, the embedded CP, linguists (with unvalued uCase) is re-stacked. T picks up TOS linguists.
(7) It is tough to please linguists	[linguists, d, please,'v*', ['PRO', d0], 'Tinf', c, tough, v_be, it, 'T', c]	v* assigns Case to linguists. (No restacking is done at the LE boundary, the embedded CP.) Expletive it merge to the edge of v_be. Agree(matrix T,it) obtains.
(8) The book is easy to put on the table	[table, the, on, [book, the, pro], put, 'v*', ['PRO', d0], 'Tinf', c, easy, 'v_be', 'T', c]	(Same as (4).) DC pro-the-book. At the LE boundary, the embedded CP, the book (unvalued uCase) is restacked. Matrix T picks up TOS the book.
(9) What table is the book easy to put on?	[table, what:d, on, [book, the, pro], put, 'v*', ['PRO', d0], 'Tinf', c, easy, 'v_be', 'T', c_Q]	(Same as (5).) what table is stacked (uScope). DC pro-the-book. At the LE boundary, the embedded CP, the book (unvalued uCase) and what table (unvalued uScope) are restacked. Matrix T picks up TOS the book. c_Q finds iWh what table.

Machine Parameters: expand

Animation:
(8) The book is easy to put on the table

Derivation:
(8) The book is easy to put on the table

Stream:	[[table!D],[the!case!N],[on],[[book!D],[the!case!N],[pro!case]],[put],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):
SO:	[]

Step 1.

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

Stream:	[[the!case!N],[on],[[book!D],[the!case!N],[pro!case]],[put],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):
SO:	[table!D]

Step 2.

Merge [the!case!N] and [table!D]

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

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

[the!case!N] values D on [table!D]

[table] values N on [the!case!N]

Stream:	[[on],[[book!D],[the!case!N],[pro!case]],[put],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):
SO:	[the!case[the][table]]

Step 3.

Merge [on] and [the!case[the][table]]

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

Theta-mark [the!case[the][table]]

[on] values obq case on [the!case[the][table]]

Stream:	[[[book!D],[the!case!N],[pro!case]],[put],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):
SO:	[on[on][the[the][table]]]

Step 4.

Begin substream

Stream:	[[book!D],[the!case!N],[pro!case]]
Stack (⥥):
SO:	[]

Step 5.

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

Stream:	[[the!case!N],[pro!case]]
Stack (⥥):
SO:	[book!D]

Step 6.

Merge [the!case!N] and [book!D]

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

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

[the!case!N] values D on [book!D]

[book] values N on [the!case!N]

Stream:	[[pro!case]]
Stack (⥥):
SO:	[the!case[the][book]]

Doubling Constitutent (DC) merge

Step 7.

Merge [pro!case] and [the!case[the][book]]

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

Inherit interpretable feature(s) [f(theta),f(phi,[3,sg,n])] from [the!case[the][book]]

Push [the!case[the][book]] (unvalued uF) onto stack

Stream:	[]
Stack (⥥):	inactive([the!case[the][book]])
SO:	[pro!case[pro][the!case[the][book]]]

End substream, SO [pro!case[pro][the!case[the][book]]] re-inserted into main stream

Substream stack [inactive([the!case[the][book]])] merged with main stack

Step 8.

Stream:	[[pro!case[pro][the!case[the][book]]],[put],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):	inactive([the!case[the][book]])
SO:	[on[on][the[the][table]]]

Step 9.

Merge [on[on][the[the..][table..]]] and [pro!case[pro][the!case[the..][book..]]]

Label from [on[on][the[the..][table..]]] (edge feature)

Theta-mark [pro!case[pro][the!case[the..][book..]]]

Push [pro!case[pro][the!case[the..][book..]]] (unvalued uF) onto stack

Stream:	[[put],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):	[pro!case[pro][the!case[the][book]]] inactive([the!case[the][book]])
SO:	[on[pro!case[pro][the!case[the][book]]][on[on][the[the][table]]]]

Step 10.

Merge [put] and [on[pro!case[pro..][the..]][on[on..][the..]]]

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

Stream:	[[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):	[pro!case[pro][the!case[the][book]]] inactive([the!case[the][book]])
SO:	[put[put][on[pro!case[pro][the!case[the][book]]][on[on][the[the][table]]]]]

Step 11.

Merge [v*!phi] and [put[put][on[pro..][on..]]]

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

[pro!case[pro][the!case[the..][book..]]] values uPhi on [v*!phi]

[v*] values acc case on [pro!case[pro][the!case[the..][book..]]]

Stream:	[[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):	[pro[pro][the!case[the][book]]] inactive([the!case[the][book]])
SO:	[v[v][put[put][on[pro[pro][the!case[the][book]]][on[on][the[the][table]]]]]]

Step 12.

Begin substream

Stream:	[[PRO!D],[d0!case!N]]
Stack (⥥):
SO:	[]

Step 13.

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

Stream:	[[d0!case!N]]
Stack (⥥):
SO:	[PRO!D]

Step 14.

Merge [d0!case!N] and [PRO!D]

Label from [d0!case!N] (head with an unvalued uF)

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

[d0!case!N] values D on [PRO!D]

[PRO] values N on [d0!case!N]

Stream:	[]
Stack (⥥):
SO:	[d0!case[d0][PRO]]

End substream, SO [d0!case[d0][PRO]] re-inserted into main stream

Step 15.

Stream:	[[d0!case[d0][PRO]],[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):	[pro[pro][the!case[the][book]]] inactive([the!case[the][book]])
SO:	[v[v][put[put][on[pro[pro][the!case[the][book]]][on[on][the[the][table]]]]]]

Step 16.

Merge [v*[v*][put[put..][on..]]] and [d0!case[d0][PRO]]

Label from [v*[v*][put[put..][on..]]] (edge feature)

Theta-mark [d0!case[d0][PRO]]

Push [d0!case[d0][PRO]] (unvalued uF) onto stack

Stream:	[[Tinf!phi],[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):	[d0!case[d0][PRO]] [pro[pro][the!case[the][book]]] inactive([the!case[the][book]])
SO:	[v[d0!case[d0][PRO]][v[v*][put[put][on[pro[pro][the!case[the][book]]][on[on][the[the][table]]]]]]]

Step 17.

Merge [Tinf!phi] and [v*[d0!case[d0..][PRO..]][v*[v*..][put..]]]

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

[d0!case[d0][PRO]] values uPhi on [Tinf!phi]

[Tinf] values nullCase case on [d0[d0][PRO]]

Stream:	[[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):	[d0[d0][PRO]] [pro[pro][the!case[the][book]]] inactive([the!case[the][book]])
SO:	[Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the!case[the][book]]][on[on][the[the][table]]]]]]]]

Step 18.

Internal merge selected

Merge [Tinf[Tinf][v*[d0..][v*..]]] and [d0[d0][PRO]]

Label from [Tinf[Tinf][v*[d0..][v*..]]] (edge feature)

Stream:	[[c],[easy],[v_be],[T!phi],[c]]
Stack (⥥):	[d0[d0][PRO]] [pro[pro][the!case[the][book]]] inactive([the!case[the][book]])
SO:	[Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the!case[the][book]]][on[on][the[the][table]]]]]]]]]

Step 19.

Merge [c] and [Tinf[d0[d0..][PRO..]][Tinf[Tinf..][v*..]]]

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

Stream:	[[easy],[v_be],[T!phi],[c]]
Stack (⥥):	[d0[d0][PRO]] [pro[pro][the!case[the][book]]] inactive([the!case[the][book]])
SO:	[c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the!case[the][book]]][on[on][the[the][table]]]]]]]]]]

Step 20.

Local Extent boundary at [c[c][Tinf[d0..][Tinf..]]]

Inactive stack element inactive([the!case[the][book]]) found

New boundary (b) marker stacked

Restack [the!case[the][book]] onto stack

Stream:	[[easy],[v_be],[T!phi],[c]]
Stack (⥥):	[the!case[the][book]] b [d0[d0][PRO]] [pro[pro][the!case[the][book]]]
SO:	[c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the!case[the][book]]][on[on][the[the][table]]]]]]]]]]

Step 21.

Merge [easy] and [c[c][Tinf[d0..][Tinf..]]]

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

Stream:	[[v_be],[T!phi],[c]]
Stack (⥥):	[the!case[the][book]] b [d0[d0][PRO]] [pro[pro][the!case[the][book]]]
SO:	[easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the!case[the][book]]][on[on][the[the][table]]]]]]]]]]]

Step 22.

Merge [v_be] and [easy[easy][c[c..][Tinf..]]]

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

Stream:	[[T!phi],[c]]
Stack (⥥):	[the!case[the][book]] b [d0[d0][PRO]] [pro[pro][the!case[the][book]]]
SO:	[v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the!case[the][book]]][on[on][the[the][table]]]]]]]]]]]]

Step 23.

Internal merge selected

Merge [v_be[v_be][easy[easy..][c..]]] and [the!case[the][book]]

Label from [v_be[v_be][easy[easy..][c..]]] (edge feature)

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

Stream:	[[T!phi],[c]]
Stack (⥥):	[the!case[the][book]] b [d0[d0][PRO]] [pro[pro][the!case[the][book]]]
SO:	[v_be[the!case[the][book]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the[the][book]]][on[on][the[the][table]]]]]]]]]]]]]

Step 24.

Merge [T!phi] and [v_be[the!case[the..][book..]][v_be[v_be..][easy..]]]

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

[the!case[the][book]] values uPhi on [T!phi]

[T] values nom case on [the!case[the][book]]

Stream:	[[c]]
Stack (⥥):	[the[the][book]] b [d0[d0][PRO]] [pro[pro][the[the][book]]]
SO:	[T[T][v_be[the[the][book]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the[the][book]]][on[on][the[the][table]]]]]]]]]]]]]]

Step 25.

Internal merge selected

Merge [T[T][v_be[the..][v_be..]]] and [the[the][book]]

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

Stream:	[[c]]
Stack (⥥):	[the[the][book]] b [d0[d0][PRO]] [pro[pro][the[the][book]]]
SO:	[T[the[the][book]][T[T][v_be[the[the][book]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the[the][book]]][on[on][the[the][table]]]]]]]]]]]]]]]

Step 26.

Merge [c] and [T[the[the..][book..]][T[T..][v_be..]]]

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

Stream:	[]
Stack (⥥):	[the[the][book]] b [d0[d0][PRO]] [pro[pro][the[the][book]]]
SO:	[c[c][T[the[the][book]][T[T][v_be[the[the][book]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the[the][book]]][on[on][the[the][table]]]]]]]]]]]]]]]]

Step 27.

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

New boundary (b) marker stacked

Stream:	[]
Stack (⥥):	b [the[the][book]] b [d0[d0][PRO]] [pro[pro][the[the][book]]]
SO:	[c[c][T[the[the][book]][T[T][v_be[the[the][book]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][put[put][on[pro[pro][the[the][book]]][on[on][the[the][table]]]]]]]]]]]]]]]]

Parse:

Spell-out:

the book -s be easy to put on the table (after morpheme realization)

the book be -s easy to put on the table (after affix-hop)

the book be -s easy to put on the table (after morpheme realization, stage 2)

the book is easy to put on the table

One derivation found.

Computational Cost:

Merge: 18, Agree: 13, Unify: 0, Push: 3, Boundaries: 2, Inject: 1

Non-TOS access: 0, Pop: 0, Depth cost: 37

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	26	27
Stack depth:	0	0	0	0	0	0	0	1	1	2	2	2	0	0	0	2	3	3	3	3	4	4	4	4	4	4	4	5