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:
(2) The violin is easy to play the sonata on

Derivation:
(2) The violin is easy to play the sonata on

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

Step 1.

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

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

Step 2.

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

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

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

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

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

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

Doubling Constitutent (DC) merge

Step 3.

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

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][violin]]

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

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

Step 4.

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

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

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

[on] values obq case on [pro!case[pro][the!case[the..][violin..]]]

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

Step 5.

Begin substream

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

Step 6.

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

Stream:	[[the!case!N]]
Stack (⥥):
SO:	[sonata!D]

Step 7.

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

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

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

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

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

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

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

Step 8.

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

Step 9.

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

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

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

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

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

Step 10.

Merge [play] and [on[the!case[the..][sonata..]][on[on..][pro..]]]

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

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

Step 11.

Merge [v*!phi] and [play[play][on[the..][on..]]]

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

[the!case[the][sonata]] values uPhi on [v*!phi]

[v*] values acc case on [the!case[the][sonata]]

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

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 (⥥):	[the[the][sonata]] inactive([the!case[the][violin]])
SO:	[v[v][play[play][on[the[the][sonata]][on[on][pro[pro][the!case[the][violin]]]]]]]

Step 16.

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

Label from [v*[v*][play[play..][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]] [the[the][sonata]] inactive([the!case[the][violin]])
SO:	[v[d0!case[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the!case[the][violin]]]]]]]]

Step 17.

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

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]] [the[the][sonata]] inactive([the!case[the][violin]])
SO:	[Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the!case[the][violin]]]]]]]]]

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]] [the[the][sonata]] inactive([the!case[the][violin]])
SO:	[Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the!case[the][violin]]]]]]]]]]

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]] [the[the][sonata]] inactive([the!case[the][violin]])
SO:	[c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the!case[the][violin]]]]]]]]]]]

Step 20.

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

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

New boundary (b) marker stacked

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

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

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][violin]] b [d0[d0][PRO]] [the[the][sonata]]
SO:	[easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the!case[the][violin]]]]]]]]]]]]

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][violin]] b [d0[d0][PRO]] [the[the][sonata]]
SO:	[v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the!case[the][violin]]]]]]]]]]]]]

Step 23.

Internal merge selected

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

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][violin]] b [d0[d0][PRO]] [the[the][sonata]]
SO:	[v_be[the!case[the][violin]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the[the][violin]]]]]]]]]]]]]]

Step 24.

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

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

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

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

Stream:	[[c]]
Stack (⥥):	[the[the][violin]] b [d0[d0][PRO]] [the[the][sonata]]
SO:	[T[T][v_be[the[the][violin]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the[the][violin]]]]]]]]]]]]]]]

Step 25.

Internal merge selected

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

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

Stream:	[[c]]
Stack (⥥):	[the[the][violin]] b [d0[d0][PRO]] [the[the][sonata]]
SO:	[T[the[the][violin]][T[T][v_be[the[the][violin]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the[the][violin]]]]]]]]]]]]]]]]

Step 26.

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

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

Stream:	[]
Stack (⥥):	[the[the][violin]] b [d0[d0][PRO]] [the[the][sonata]]
SO:	[c[c][T[the[the][violin]][T[T][v_be[the[the][violin]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the[the][violin]]]]]]]]]]]]]]]]]

Step 27.

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

New boundary (b) marker stacked

Stream:	[]
Stack (⥥):	b [the[the][violin]] b [d0[d0][PRO]] [the[the][sonata]]
SO:	[c[c][T[the[the][violin]][T[T][v_be[the[the][violin]][v_be[v_be][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on[the[the][sonata]][on[on][pro[pro][the[the][violin]]]]]]]]]]]]]]]]]

Parse:

Spell-out:

the violin -s be easy to play the sonata on (after morpheme realization)

the violin be -s easy to play the sonata on (after affix-hop)

the violin be -s easy to play the sonata on (after morpheme realization, stage 2)

the violin is easy to play the sonata on

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	1	1	0	0	0	1	2	2	2	0	0	0	2	3	3	3	3	4	4	4	4	4	4	4	5