Lambda expressions in Toaq

Dec 22nd, 2019
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  1. @Toaq.#general @2019-08-17
  4. [Ntsékees]
  5. "kảqgāı jí súq" is a clause, it has a verb and might contain one or more noun, and it can be a standalone sentence.
  6. Sentences can contain a single clause, or several clauses linked with conjunctions like "and" in English, and clauses can contain other clauses embedded in them, as in "I know that [you know that [I know]]"
  7. and "the man [which knows the woman [which knows……]]"
  9. [Christmas Bird!]
  10. Yea
  12. [Ntsékees]
  13. "I know that [you know that [I know]]" has nested noun clauses, that is, clauses that assume the role of nouns: "I know it" → "I know [that you know]".
  14. In Toaq, **lû** and the ^-tone play the role of making noun clauses
  15. a normal noun clause expresses a full proposition, which has a truth value, like "I am sleeping", "I see you", "I am a green cat"…
  16. those can be true or false
  18. [Christmas Bird!]
  19. Yea that makes sense
  21. [Ntsékees]
  22. One can also arguably say that propositions are the same thing as nullary predicates, i.e. predicates with no "open slot" (marked with ▯ in the dictionary)
  23. in English, "it is raining" is a nullary predicate
  24. at least it's rare to use "raining" with another subject that that dummy "it"
  25. properties and relations (predicates with more than one "open slot") are like clauses from which you'd have erased at least one part, to use it as a template in which you could latter plug anything you want
  26. for example, if I have the clause "I know it", you could erase the "it" and make it a fillable blank: ``I know ___``
  27. it becomes a template
  28. it's no longer a proposition, it has no truth value, it cannot be true or false, because it's incomplete as of now
  29. it would be able to be true or false only when completed by filling it with something
  30. ``I know ___`` is a *property*, or a unary predicate
  31. they can be useful when passed to *higher order predicates*, that is, predicates which take other predicates as arguments: it's as if they'd take incomplete templates of clauses as described above, and then the job of filling the blanks would be assumed by them instead of being your job
  32. for example,
  33. % tulī
  35. [nuogai BOT]
  36. 1–2/2 — tulī ± — common to, kampu / everything has property ▯ (among ▯)
  37.  — tulī ± — everything has the property ▯ (among the things that have the property ▯).
  39. [Ntsékees]
  40. tulī = the property ▯ is universal
  41. ``tủlī nûo ja ráı`` = ``the property [___ sleeps] is universal, everything has it``
  42. the predicate **tulī** assumes the role of filling the blank in ``___ sleeps`` with everything in the universe
  43. which would be a very tedious task if you had to do it by yourself
  44. "John sleeps, the cat sleeps, the house sleeps, the sky sleeps……"
  45. So you pass an unfinished clause to **tulī**, and it assumes the role of filling in the unfinished parts (the "open slots")
  47. [Christmas Bird!]
  48. Oh okay
  49. I think I get it?
  51. [Ntsékees]
  52. A better example of the utility of higher-order predicates (predicates taking other predicates (i.e. templates) as arguments) is **cheo**
  53. % cheo
  55. [nuogai BOT]
  56. 1–3/85 — cheo ± — tu dó lủ mẻa hóa dóshī ceı tu lú mẻa hóa dóshī na ru hẻo hóa dó pa, gủjēo dógū da
  57.  — cheo ± — = [XX2] Tu shí tảmēa dỏshī tu bú hỏı shǐ tảmēa dỏshī pa sa dỏgū.
  58.  — ❦ cheo ± — predicate: ‘reciprocally’; ▯ are in reciprocal relationship ▯ with each other.
  60. [Ntsékees]
  61. which you are already acquitained with
  62. chẻo hó râqdēoq ja ráı ja ráı kátō = ``they are in the reciprocal relation [___ talks to ___ about the cat]``
  63. if hó refers to me, you and Hỏemāı, then you could say instead "I talk to you about the cat, you talk to me about the cat, I talk to Hỏemāı about the cat, Hỏemāı talks to me about the cat, you talk to Hỏemāı about the cat, Hỏemāı talks to you about the cat"
  64. but it's all long and tedious
  65. the common part in all those repetitive sentences is the template ``___ talks to ___ about the cat``
  66. so it's way easier to just take this template, a list of people (here **hó**) and appoint our faithful **cheo** to do the dirty work of filling in the template with all those people in our stead
  67. I hope this demonstrates why higher-order predicates are useful :)
  69. [Christmas Bird!]
  70. Yea, it does, thanks!
  72. [Hoemāı]
  73. Another way to think of properties (lambda stuff) is to think of them as infinitives
  74. "to talk" is abstract and doesn't have anything in the first place of "talk", it's the verb itself, without any subject or object supplied
  75. lî fả ja rảı = to go ("the property [___ goes]")
  76. where ``ja`` marks the place that is "removed" or "open"
  77. Imagine, for example, ``lî fả súq ja rảı``
  78. Here, the second place is "removed" or "open", so the infinitive means "to be gone to by you"
  79. or, "the property [you go to ___]"
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