Minimalist Machine Derivations

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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.
    cQ 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 vbe.
    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.
    cQ finds iWh what table.
  • Machine Parameters: expand

    Animation:
    (1) John is easy to please

    Derivation:
    (1) John is easy to please

    Stream:[[john!D],[d!case!N],[pro!case],[please],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[vbe],[T!phi],[c]]
    Stack (⥥):
    SO:[]

    Step 1.

    Head of stream [john!D] is the initial SO
    Stream:[[d!case!N],[pro!case],[please],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[vbe],[T!phi],[c]]
    Stack (⥥):
    SO:[john!D]

    Step 2.

    Merge [d!case!N] and [john!D]
    Label from [d!case!N] (head with an unvalued uF)
    Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [john!D]
    [d!case!N] values D on [john!D]
    [john] values N on [d!case!N]
    Stream:[[pro!case],[please],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[vbe],[T!phi],[c]]
    Stack (⥥):
    SO:[d!case[d][john]]
    Doubling Constitutent (DC) merge

    Step 3.

    Merge [pro!case] and [d!case[d][john]]
    Label from [pro!case] (head merging with a non-head)
    Inherit interpretable feature(s) [f(theta),f(phi,[3,sg,n])] from [d!case[d][john]]
    Push [d!case[d][john]] (unvalued uF) onto stack
    Stream:[[please],[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[vbe],[T!phi],[c]]
    Stack (⥥):inactive([d!case[d][john]])
    SO:[pro!case[pro][d!case[d][john]]]

    Step 4.

    Merge [please] and [pro!case[pro][d!case[d..][john..]]]
    Label from [please] (head merging with a non-head)
    Theta-mark [pro!case[pro][d!case[d..][john..]]]
    Push [pro!case[pro][d!case[d..][john..]]] (unvalued uF) onto stack
    Stream:[[v*!phi],[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[vbe],[T!phi],[c]]
    Stack (⥥):[pro!case[pro][d!case[d][john]]]
    inactive([d!case[d][john]])
    SO:[please[please][pro!case[pro][d!case[d][john]]]]

    Step 5.

    Merge [v*!phi] and [please[please][pro!case[pro..][d..]]]
    Label from [v*!phi] (head merging with a non-head)
    [pro!case[pro][d!case[d..][john..]]] values uPhi on [v*!phi]
    [v*] values acc case on [pro!case[pro][d!case[d..][john..]]]
    Stream:[[[PRO!D],[d0!case!N]],[Tinf!phi],[c],[easy],[vbe],[T!phi],[c]]
    Stack (⥥):[pro[pro][d!case[d][john]]]
    inactive([d!case[d][john]])
    SO:[v*[v*][please[please][pro[pro][d!case[d][john]]]]]

    Step 6.

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

    Step 7.

    Head of stream [PRO!D] is the initial SO
    Stream:[[d0!case!N]]
    Stack (⥥):
    SO:[PRO!D]

    Step 8.

    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 9.

    Stream:[[d0!case[d0][PRO]],[Tinf!phi],[c],[easy],[vbe],[T!phi],[c]]
    Stack (⥥):[pro[pro][d!case[d][john]]]
    inactive([d!case[d][john]])
    SO:[v*[v*][please[please][pro[pro][d!case[d][john]]]]]

    Step 10.

    Merge [v*[v*][please[please..][pro..]]] and [d0!case[d0][PRO]]
    Label from [v*[v*][please[please..][pro..]]] (edge feature)
    Theta-mark [d0!case[d0][PRO]]
    Push [d0!case[d0][PRO]] (unvalued uF) onto stack
    Stream:[[Tinf!phi],[c],[easy],[vbe],[T!phi],[c]]
    Stack (⥥):[d0!case[d0][PRO]]
    [pro[pro][d!case[d][john]]]
    inactive([d!case[d][john]])
    SO:[v*[d0!case[d0][PRO]][v*[v*][please[please][pro[pro][d!case[d][john]]]]]]

    Step 11.

    Merge [Tinf!phi] and [v*[d0!case[d0..][PRO..]][v*[v*..][please..]]]
    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],[vbe],[T!phi],[c]]
    Stack (⥥):[d0[d0][PRO]]
    [pro[pro][d!case[d][john]]]
    inactive([d!case[d][john]])
    SO:[Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d!case[d][john]]]]]]]

    Step 12.

    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],[vbe],[T!phi],[c]]
    Stack (⥥):[d0[d0][PRO]]
    [pro[pro][d!case[d][john]]]
    inactive([d!case[d][john]])
    SO:[Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d!case[d][john]]]]]]]]

    Step 13.

    Merge [c] and [Tinf[d0[d0..][PRO..]][Tinf[Tinf..][v*..]]]
    Label from [c] (head merging with a non-head)
    Stream:[[easy],[vbe],[T!phi],[c]]
    Stack (⥥):[d0[d0][PRO]]
    [pro[pro][d!case[d][john]]]
    inactive([d!case[d][john]])
    SO:[c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d!case[d][john]]]]]]]]]

    Step 14.

    Local Extent boundary at [c[c][Tinf[d0..][Tinf..]]]
    Inactive stack element inactive([d!case[d][john]]) found
    New boundary (b) marker stacked
    Restack [d!case[d][john]] onto stack
    Stream:[[easy],[vbe],[T!phi],[c]]
    Stack (⥥):[d!case[d][john]]
    b
    [d0[d0][PRO]]
    [pro[pro][d!case[d][john]]]
    SO:[c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d!case[d][john]]]]]]]]]

    Step 15.

    Merge [easy] and [c[c][Tinf[d0..][Tinf..]]]
    Label from [easy] (head merging with a non-head)
    Stream:[[vbe],[T!phi],[c]]
    Stack (⥥):[d!case[d][john]]
    b
    [d0[d0][PRO]]
    [pro[pro][d!case[d][john]]]
    SO:[easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d!case[d][john]]]]]]]]]]

    Step 16.

    Merge [vbe] and [easy[easy][c[c..][Tinf..]]]
    Label from [vbe] (head merging with a non-head)
    Stream:[[T!phi],[c]]
    Stack (⥥):[d!case[d][john]]
    b
    [d0[d0][PRO]]
    [pro[pro][d!case[d][john]]]
    SO:[vbe[vbe][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d!case[d][john]]]]]]]]]]]

    Step 17.

    Internal merge selected
    Merge [vbe[vbe][easy[easy..][c..]]] and [d!case[d][john]]
    Label from [vbe[vbe][easy[easy..][c..]]] (edge feature)
    Preference: [vbe] edge merge from the stack (not stream)
    Stream:[[T!phi],[c]]
    Stack (⥥):[d!case[d][john]]
    b
    [d0[d0][PRO]]
    [pro[pro][d!case[d][john]]]
    SO:[vbe[d!case[d][john]][vbe[vbe][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d[d][john]]]]]]]]]]]]

    Step 18.

    Merge [T!phi] and [vbe[d!case[d..][john..]][vbe[vbe..][easy..]]]
    Label from [T!phi] (head merging with a non-head)
    [d!case[d][john]] values uPhi on [T!phi]
    [T] values nom case on [d!case[d][john]]
    Stream:[[c]]
    Stack (⥥):[d[d][john]]
    b
    [d0[d0][PRO]]
    [pro[pro][d[d][john]]]
    SO:[T[T][vbe[d[d][john]][vbe[vbe][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d[d][john]]]]]]]]]]]]]

    Step 19.

    Internal merge selected
    Merge [T[T][vbe[d..][vbe..]]] and [d[d][john]]
    Label from [T[T][vbe[d..][vbe..]]] (edge feature)
    Stream:[[c]]
    Stack (⥥):[d[d][john]]
    b
    [d0[d0][PRO]]
    [pro[pro][d[d][john]]]
    SO:[T[d[d][john]][T[T][vbe[d[d][john]][vbe[vbe][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d[d][john]]]]]]]]]]]]]]

    Step 20.

    Merge [c] and [T[d[d..][john..]][T[T..][vbe..]]]
    Label from [c] (head merging with a non-head)
    Stream:[]
    Stack (⥥):[d[d][john]]
    b
    [d0[d0][PRO]]
    [pro[pro][d[d][john]]]
    SO:[c[c][T[d[d][john]][T[T][vbe[d[d][john]][vbe[vbe][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d[d][john]]]]]]]]]]]]]]]

    Step 21.

    Local Extent boundary at [c[c][T[d..][T..]]]
    New boundary (b) marker stacked
    Stream:[]
    Stack (⥥):b
    [d[d][john]]
    b
    [d0[d0][PRO]]
    [pro[pro][d[d][john]]]
    SO:[c[c][T[d[d][john]][T[T][vbe[d[d][john]][vbe[vbe][easy[easy][c[c][Tinf[d0[d0][PRO]][Tinf[Tinf][v*[d0[d0][PRO]][v*[v*][please[please][pro[pro][d[d][john]]]]]]]]]]]]]]]

    Parse:
    Spell-out:
    john -s be easy to please (after morpheme realization)
    john be -s easy to please (after affix-hop)
    john be -s easy to please (after morpheme realization, stage 2)
    john is easy to please  

    One derivation found.
    Computational Cost:
    Merge: 15, Agree: 10, Unify: 0, Push: 3, Boundaries: 2, Inject: 1
    Non-TOS access: 0, Pop: 0, Depth cost: 36
    Step:0123456789101112131415161718192021
    Stack depth:0001220002333344444445

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