Minimalist Machine Derivations

Minimalist Machine Derivations

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

Examples:

Tough-Constructions. A Case-theoretic approach. collapse

Example	Instruction stream (clickable)	Notes
(1) John is easy to please	[john, d, please, 'v_unerg', ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c]	John (with unvalued uCase) is stacked after merge with please. v_unerg doesn't assign Case to John. Tinf assigns null Case to PRO. 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, on_nc, [sonata, the], play, 'v*', ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c]	on_nc (no case) selects for the violin but does not assign it Case. At the Local Extent (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, on_nc, [sonata, what:d], play, 'v*', ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c_Q]	Does not converge. on_nc (no case) selects for the violin but does not assign it Case. 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], play, 'v_unerg', ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c]	on assigns Case to this violin. v_unerg doesn't assign Case to 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], play, v_unerg, ['PRO', d0], 'Tinf', c, easy, v_be, 'T', c_Q]	on assigns Case to this violin. v_unerg doesn't assign Case to the sonata. 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, please, v_unerg, ['PRO', d0], 'Tinf', c, tough, v_be, 'T', c]	(Same as (1).) Linguists (with unvalued uCase) is stacked after merge with please. v_unerg doesn't assign Case to linguists. Tinf assigns null Case to PRO. 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], put, v_unerg, ['PRO', d0], 'Tinf', c, easy, 'v_be', 'T', c]	(Same as (4).) on assigns Case to the table. v_unerg doesn't assign Case to 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], put, v_unerg, ['PRO', d0], 'Tinf', c, easy, 'v_be', 'T', c_Q]	(Same as (5).) on assigns Case to what table. v_unerg doesn't assign Case to 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],[on_nc],[[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],[on_nc],[[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:	[[on_nc],[[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]]

Step 3.

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

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

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

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

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

Step 4.

Begin substream

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

Step 5.

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

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

Step 6.

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 7.

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

Step 8.

Merge [on_nc[on_nc][the!case[the..][violin..]]] and [the!case[the][sonata]]

Label from [on_nc[on_nc][the!case[the..][violin..]]] (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]] [the!case[the][violin]]
SO:	[on_nc[the!case[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]

Step 9.

Merge [play] and [on_nc[the!case[the..][sonata..]][on_nc[on_nc..][the..]]]

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]] [the!case[the][violin]]
SO:	[play[play][on_nc[the!case[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]]

Step 10.

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

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]] [the!case[the][violin]]
SO:	[v[v][play[play][on_nc[the[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]]]

Step 11.

Begin substream

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

Step 12.

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

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

Step 13.

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 14.

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

Step 15.

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

Label from [v*[v*][play[play..][on_nc..]]] (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]] [the!case[the][violin]]
SO:	[v[d0!case[d0][PRO]][v[v*][play[play][on_nc[the[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]]]]

Step 16.

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]] [the!case[the][violin]]
SO:	[Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on_nc[the[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]]]]]

Step 17.

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]] [the!case[the][violin]]
SO:	[Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on_nc[the[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]]]]]]

Step 18.

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]] [the!case[the][violin]]
SO:	[c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v[d0[d0][PRO]][v[v*][play[play][on_nc[the[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]]]]]]]

Step 19.

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

Stack element [the!case[the][violin]] with unvalued uF 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_nc[the[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]]]]]]]

Step 20.

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_nc[the[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]]]]]]]]

Step 21.

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_nc[the[the][sonata]][on_nc[on_nc][the!case[the][violin]]]]]]]]]]]]

Step 22.

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_nc[the[the][sonata]][on_nc[on_nc][the[the][violin]]]]]]]]]]]]]

Step 23.

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_nc[the[the][sonata]][on_nc[on_nc][the[the][violin]]]]]]]]]]]]]]

Step 24.

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_nc[the[the][sonata]][on_nc[on_nc][the[the][violin]]]]]]]]]]]]]]]

Step 25.

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_nc[the[the][sonata]][on_nc[on_nc][the[the][violin]]]]]]]]]]]]]]]]

Step 26.

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_nc[the[the][sonata]][on_nc[on_nc][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: 17, Agree: 12, 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
Stack depth:	0	0	0	1	0	0	0	1	2	2	2	0	0	0	2	3	3	3	3	4	4	4	4	4	4	4	5