Minimalist Machine Derivations

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Examples:

  • T-to-C Movement: Causes and Consequences. Pesetsky & Torrego (2001). collapse
    Example Instruction stream (clickable) Notes
    (5a) What did Mary buy?
    (5b) *What Mary bought?    		 [what:n, q, buy, 'v*', [mary, d], 'Tpast', c_Q] (5a) T to matrix C => do-support.
    (5b) Mary to edge C blocked (FI: exclamatory).
    (5c) *Who did buy the book?
    (5d) Who bought the book?    		 [book, the, buy, 'v*', [who, q], 'Tpast', c_Q] No do-support triggered.
    (5c) ruled out by economy.
    (23) What will Mary buy? [what:n, q, buy, 'v*', [mary, d], will, 'T', c_Q] Auxilary will raises to edge of C.
    (24) What did John say that Mary will buy? [what:n, q, buy, 'v*', [mary, d], will, 'T', c_eQ, say, v_unerg, [john, d], 'Tpast', c_Q] Two derivations: (24) T to C realized as that.
    Or that can be omitted. c_eQ hosts wh-movement only.
    (28a) Who did John say will buy the book?
    (28b) *Who did John say that will buy the book?    		 [book, the, buy, 'v*', [who, q], will, 'T', c_eQ, say, v_unerg, [john, d], 'Tpast', c_Q] That-trace effect.
    (28b) ruled out by economy.
    (31) Mary thinks that Sue will buy the book
    (33) Mary thinks Sue will buy the book    		 [book, the, buy, 'v*', [sue, d], will, 'T', c_e, think, v_unerg, [mary, d], 'T', c] Two derivations: (31) T to embedded C (c_e) realized as that. (33) c_e attracts subject Sue
    (43a) *What a silly book did Mary buy!
    (43b) What a silly book Mary bought!    		 [book, silly, a, what:d, q, buy, 'v*', [mary, d], 'Tpast', c_Q] (43a) T to C blocked by CI: exclamative.
    (43b) Mary in edge of C.
    (47a) Bill asked what Mary bought
    (47b) *Bill asked what did Mary buy
    (47c) *Bill asked what that Mary bought    		 [what:n, q, buy, 'v*', [mary, d], 'Tpast', c_Qe, ask, v_unerg, [bill, d], 'Tpast', c] Interrogative embedded C does not support T displacement.
    Note: same parse derived twice.
    Extra test cases
    Who was John meeting? [who, q, meet, 'v*', [john, d], prog, 'v~', 'Tpast', c_Q] Object wh-movement. Auxiliary be pied-piping.
    Who was meeting John? [john, d, meet, 'v*', [who, q], prog, 'v~', 'Tpast', c_Q] Subject wh-movement. Auxiliary be pied-piping.
    *Who do you think that saw John?
    Who do you think saw John?    		 [john, d, see, 'v*', [who, q], 'Tpast', c_eQ, think, 'v_unerg', [you, d], 'T', c_Q] That-trace effect.
    Economy: no T to C.
    Who do you think that John saw?
    Who do you think John saw?    		 [who, q, see, 'v*', [john, d], 'Tpast', c_eQ, think, 'v_unerg', [you, d], 'T', c_Q] Two derivations.
    No that-trace effect with object.
    • Machine Parameters: expand

    Animation:
    (31) Mary thinks that Sue will buy the book
    (33) Mary thinks Sue will buy the book

    Derivation:
    (31) Mary thinks that Sue will buy the book
    (33) Mary thinks Sue will buy the book

    Stream:[[book!D],[the!case!N],[buy],[v*!phi],[[sue!D],[d!case!N]],[will],[T!phi],[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):
    SO:[]

    Step 1.

    Head of stream [book!D] is the initial SO
    Stream:[[the!case!N],[buy],[v*!phi],[[sue!D],[d!case!N]],[will],[T!phi],[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):
    SO:[book!D]

    Step 2.

    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:[[buy],[v*!phi],[[sue!D],[d!case!N]],[will],[T!phi],[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):
    SO:[the!case[the][book]]

    Step 3.

    Merge [buy] and [the!case[the][book]]
    Label from [buy] (head merging with a non-head)
    Theta-mark [the!case[the][book]]
    Push [the!case[the][book]] (unvalued uF) onto stack
    Stream:[[v*!phi],[[sue!D],[d!case!N]],[will],[T!phi],[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[the!case[the][book]]
    SO:[buy[buy][the!case[the][book]]]

    Step 4.

    Merge [v*!phi] and [buy[buy][the!case[the..][book..]]]
    Label from [v*!phi] (head merging with a non-head)
    [the!case[the][book]] values uPhi on [v*!phi]
    [v*] values acc case on [the!case[the][book]]
    Stream:[[[sue!D],[d!case!N]],[will],[T!phi],[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[the[the][book]]
    SO:[v*[v*][buy[buy][the[the][book]]]]

    Step 5.

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

    Step 6.

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

    Step 7.

    Merge [d!case!N] and [sue!D]
    Label from [d!case!N] (head with an unvalued uF)
    Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [sue!D]
    [d!case!N] values D on [sue!D]
    [sue] values N on [d!case!N]
    Stream:[]
    Stack (⥥):
    SO:[d!case[d][sue]]
    End substream, SO [d!case[d][sue]] re-inserted into main stream

    Step 8.

    Stream:[[d!case[d][sue]],[will],[T!phi],[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[the[the][book]]
    SO:[v*[v*][buy[buy][the[the][book]]]]

    Step 9.

    Merge [v*[v*][buy[buy..][the..]]] and [d!case[d][sue]]
    Label from [v*[v*][buy[buy..][the..]]] (edge feature)
    Theta-mark [d!case[d][sue]]
    Push [d!case[d][sue]] (unvalued uF) onto stack
    Stream:[[will],[T!phi],[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[d!case[d][sue]]
    [the[the][book]]
    SO:[v*[d!case[d][sue]][v*[v*][buy[buy][the[the][book]]]]]

    Step 10.

    Merge [will] and [v*[d!case[d..][sue..]][v*[v*..][buy..]]]
    Label from [will] (head merging with a non-head)
    Stream:[[T!phi],[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[d!case[d][sue]]
    [the[the][book]]
    SO:[will[will][v*[d!case[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]

    Step 11.

    Merge [T!phi] and [will[will][v*[d..][v*..]]]
    Label from [T!phi] (head merging with a non-head)
    [d!case[d][sue]] values uPhi on [T!phi]
    [T] values nom case on [d!case[d][sue]]
    Stream:[[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[d[d][sue]]
    [the[the][book]]
    SO:[T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]

    Step 12.

    Internal merge selected
    Merge [T[T][will[will..][v*..]]] and [d[d][sue]]
    Label from [T[T][will[will..][v*..]]] (edge feature)
    Stream:[[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[d[d][sue]]
    [the[the][book]]
    SO:[T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]

    Step 13.

    Merge [ce!T] and [T[d[d..][sue..]][T[T..][will..]]]
    Label from [ce!T] (head merging with a non-head)
    [d[d][sue]] values T on [ce!T]
    Internal merge selected
    Merge [ce[ce][T[d..][T..]]] and [d[d][sue]]
    Label from [ce[ce][T[d..][T..]]] (edge feature)
    Stream:[[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[d[d][sue]]
    [the[the][book]]
    SO:[ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]

    Step 14.

    Local Extent boundary at [ce[d[d..][sue..]][ce[ce..][T..]]]
    New boundary (b) marker stacked
    Stream:[[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):b
    [d[d][sue]]
    [the[the][book]]
    SO:[ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]

    Step 15.

    Merge [think] and [ce[d[d..][sue..]][ce[ce..][T..]]]
    Label from [think] (head merging with a non-head)
    Theta-mark [ce[d[d..][sue..]][ce[ce..][T..]]]
    Stream:[[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):b
    [d[d][sue]]
    [the[the][book]]
    SO:[think[think][ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]

    Step 16.

    Merge [vunerg] and [think[think][ce[d..][ce..]]]
    Label from [vunerg] (head merging with a non-head)
    Stream:[[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):b
    [d[d][sue]]
    [the[the][book]]
    SO:[vunerg[vunerg][think[think][ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]

    Step 17.

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

    Step 18.

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

    Step 19.

    Merge [d!case!N] and [mary!D]
    Label from [d!case!N] (head with an unvalued uF)
    Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [mary!D]
    [d!case!N] values D on [mary!D]
    [mary] values N on [d!case!N]
    Stream:[]
    Stack (⥥):
    SO:[d!case[d][mary]]
    End substream, SO [d!case[d][mary]] re-inserted into main stream

    Step 20.

    Stream:[[d!case[d][mary]],[T!phi],[c]]
    Stack (⥥):b
    [d[d][sue]]
    [the[the][book]]
    SO:[vunerg[vunerg][think[think][ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]

    Step 21.

    Merge [vunerg[vunerg][think[think..][ce..]]] and [d!case[d][mary]]
    Label from [vunerg[vunerg][think[think..][ce..]]] (edge feature)
    Theta-mark [d!case[d][mary]]
    Push [d!case[d][mary]] (unvalued uF) onto stack
    Stream:[[T!phi],[c]]
    Stack (⥥):[d!case[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[vunerg[d!case[d][mary]][vunerg[vunerg][think[think][ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]

    Step 22.

    Merge [T!phi] and [vunerg[d!case[d..][mary..]][vunerg[vunerg..][think..]]]
    Label from [T!phi] (head merging with a non-head)
    [d!case[d][mary]] values uPhi on [T!phi]
    [T] values nom case on [d!case[d][mary]]
    Stream:[[c]]
    Stack (⥥):[d[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[T[T][vunerg[d[d][mary]][vunerg[vunerg][think[think][ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]]

    Step 23.

    Internal merge selected
    Merge [T[T][vunerg[d..][vunerg..]]] and [d[d][mary]]
    Label from [T[T][vunerg[d..][vunerg..]]] (edge feature)
    Stream:[[c]]
    Stack (⥥):[d[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[T[d[d][mary]][T[T][vunerg[d[d][mary]][vunerg[vunerg][think[think][ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]

    Step 24.

    Merge [c] and [T[d[d..][mary..]][T[T..][vunerg..]]]
    Label from [c] (head merging with a non-head)
    Stream:[]
    Stack (⥥):[d[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[c[c][T[d[d][mary]][T[T][vunerg[d[d][mary]][vunerg[vunerg][think[think][ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]

    Step 25.

    Local Extent boundary at [c[c][T[d..][T..]]]
    New boundary (b) marker stacked
    Stream:[]
    Stack (⥥):b
    [d[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[c[c][T[d[d][mary]][T[T][vunerg[d[d][mary]][vunerg[vunerg][think[think][ce[d[d][sue]][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]

    Parse:
    Spell-out:
    mary -s think sue -s will buy the book (after morpheme realization)
    mary think -s sue will -s buy the book (after affix-hop)
    mary think -s sue will -s buy the book (after morpheme realization, stage 2)
    mary thinks sue will buy the book  

    Backtrack

    Stream:[[ce!T],[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[d[d][sue]]
    [the[the][book]]
    SO:[T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]
    re-doing step 13

    Step 26.

    [ce!T] attracts [T[d[d..][sue..]][T[T..][will..]]]
    Internal merge selected
    Merge [ce[ce][T[d..][T..]]] and [T]
    Label from [ce[ce][T[d..][T..]]] (edge feature)
    Stream:[[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):[d[d][sue]]
    [the[the][book]]
    SO:[ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]

    Step 27.

    Local Extent boundary at [ce[T][ce[ce..][T..]]]
    New boundary (b) marker stacked
    Stream:[[think],[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):b
    [d[d][sue]]
    [the[the][book]]
    SO:[ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]

    Step 28.

    Merge [think] and [ce[T][ce[ce..][T..]]]
    Label from [think] (head merging with a non-head)
    Theta-mark [ce[T][ce[ce..][T..]]]
    Stream:[[vunerg],[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):b
    [d[d][sue]]
    [the[the][book]]
    SO:[think[think][ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]

    Step 29.

    Merge [vunerg] and [think[think][ce[T..][ce..]]]
    Label from [vunerg] (head merging with a non-head)
    Stream:[[[mary!D],[d!case!N]],[T!phi],[c]]
    Stack (⥥):b
    [d[d][sue]]
    [the[the][book]]
    SO:[vunerg[vunerg][think[think][ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]

    Step 30.

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

    Step 31.

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

    Step 32.

    Merge [d!case!N] and [mary!D]
    Label from [d!case!N] (head with an unvalued uF)
    Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [mary!D]
    [d!case!N] values D on [mary!D]
    [mary] values N on [d!case!N]
    Stream:[]
    Stack (⥥):
    SO:[d!case[d][mary]]
    End substream, SO [d!case[d][mary]] re-inserted into main stream

    Step 33.

    Stream:[[d!case[d][mary]],[T!phi],[c]]
    Stack (⥥):b
    [d[d][sue]]
    [the[the][book]]
    SO:[vunerg[vunerg][think[think][ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]

    Step 34.

    Merge [vunerg[vunerg][think[think..][ce..]]] and [d!case[d][mary]]
    Label from [vunerg[vunerg][think[think..][ce..]]] (edge feature)
    Theta-mark [d!case[d][mary]]
    Push [d!case[d][mary]] (unvalued uF) onto stack
    Stream:[[T!phi],[c]]
    Stack (⥥):[d!case[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[vunerg[d!case[d][mary]][vunerg[vunerg][think[think][ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]

    Step 35.

    Merge [T!phi] and [vunerg[d!case[d..][mary..]][vunerg[vunerg..][think..]]]
    Label from [T!phi] (head merging with a non-head)
    [d!case[d][mary]] values uPhi on [T!phi]
    [T] values nom case on [d!case[d][mary]]
    Stream:[[c]]
    Stack (⥥):[d[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[T[T][vunerg[d[d][mary]][vunerg[vunerg][think[think][ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]]

    Step 36.

    Internal merge selected
    Merge [T[T][vunerg[d..][vunerg..]]] and [d[d][mary]]
    Label from [T[T][vunerg[d..][vunerg..]]] (edge feature)
    Stream:[[c]]
    Stack (⥥):[d[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[T[d[d][mary]][T[T][vunerg[d[d][mary]][vunerg[vunerg][think[think][ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]

    Step 37.

    Merge [c] and [T[d[d..][mary..]][T[T..][vunerg..]]]
    Label from [c] (head merging with a non-head)
    Stream:[]
    Stack (⥥):[d[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[c[c][T[d[d][mary]][T[T][vunerg[d[d][mary]][vunerg[vunerg][think[think][ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]

    Step 38.

    Local Extent boundary at [c[c][T[d..][T..]]]
    New boundary (b) marker stacked
    Stream:[]
    Stack (⥥):b
    [d[d][mary]]
    b
    [d[d][sue]]
    [the[the][book]]
    SO:[c[c][T[d[d][mary]][T[T][vunerg[d[d][mary]][vunerg[vunerg][think[think][ce[T][ce[ce][T[d[d][sue]][T[T][will[will][v*[d[d][sue]][v*[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]

    Parse:
    Spell-out:
    mary -s think that sue -s will buy the book (after morpheme realization)
    mary think -s that sue will -s buy the book (after affix-hop)
    mary think -s that sue will -s buy the book (after morpheme realization, stage 2)
    mary thinks that sue will buy the book  

    2 derivations found.
    Computational Cost:
    Merge: 25, Agree: 18, Unify: 0, Push: 4, Boundaries: 4, Inject: 0
    Non-TOS access: 0, Pop: 0, Depth cost: 54
    Step:01234567891011121314151617181920212223242526272829303132333435363738
    Stack depth:000110001222223330003444452333000344445

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