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-1. Understanding the meaning(use) of programming languages
- helps understanding the meaning(use) of natural langauges
-
- 1. Richard Montague. 1970. Universal Grammar. _Theoria_ 34:375--98.
- "There is in my opinion no important theoretical difference
- between natural languages and the artificial languages of
- logicians; indeed, I consider it possible to comprehend the
- syntax and semantics of both kinds of languages within a
- single natural and mathematically precise theory."
-
- 2. Similarities:
-
- Function/argument structure:
- f(x)
- kill(it)
- pronominal binding:
- x := x + 1
- John is his own worst enemy
- Quantification:
- foreach x in [1..10] print x
- Print every number from 1 to 10
-
- 3. Possible differences:
-
- Parentheses:
- 3 * (4 + 7)
- ?It was four plus seven that John computed 3 multiplied by
- (compare: John computed 3 multiplied by four plus seven)
- Ambiguity:
- 3 * 4 + 7
- Time flies like and arrow, fruit flies like a banana.
- Vagueness:
- 3 * 4
- A cloud near the mountain
- Unbounded numbers of distinct pronouns:
- f(x1) + f(x2) + f(x3) + ...
- He saw her put it in ...
- [In ASL, dividing up the signing space...]
-
-
-2. Standard methods in linguistics are limited.
-
- 1. First-order predicate calculus
-
- Invented for reasoning about mathematics (Frege's quantification)
-
- Alethic, order insensitive: phi & psi == psi & phi
- But: John left and Mary left too /= Mary left too and John left
-
- 2. Simply-typed lambda calculus
-
- Can't express the Y combinator
-
-
-3. Meaning is computation.
-
- 1. Semantics is programming
-
- 2. Good programming is good semantics
-
- 1. Example
-
- 1. Programming technique
-
- Exceptions
- throw (raise)
- catch (handle)
-
- 2. Application to linguistics
- presupposition
- expressives
-
- Develop application:
- fn application
- divide by zero
- test and repair
- raise and handle
-
- fn application
- presupposition failure
- build into meaning of innocent predicates?
- expressives
- throw
- handle
- resume computation
-