SML

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SML
0, 1, 2, ..., , -, ...
true, false, if e then e else e
fun f x e
variables
exceptions
e1 e2
patterns
functors
fn x gt e
structures
datatypes
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What lies in the core of SML?
0, 1, 2, ..., , -, ...
true, false, if e then e else e
fun f x e
variables
exceptions
e1 e2
patterns
functors
fn x gt e
structures
datatypes
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Candidates?

• booleans and if/then/else
• integers
• lists
• variables
• functions and function applications
• datatypes
• patterns
• structures
• functors
• ...

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Core of SML
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?-calculus is Turing-complete
?-calculus
Turing machine

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CSE-321 Programming Languages?-Calculus
???

• POSTECH
• March 21, 2007

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Outline

• Abstract syntax of the ?-calculus
• Operational semantics of the l-calculus
• Substitutions
• Programming in the ?-calculus

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Syntax for a Programming Language

• Concrete syntax
• program string of characters
• specifies rules for parsing.
• operator precedence
• associativity
• keywords, ...
• 1 2 3
• 1 (2 3)
• 1 (2 (3))

• Abstract syntax
• abstracts away from details of parsing.
• focuses on the high-level structure of programs.
• suitable for studying the semantics

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Abstract Syntax of the ?-Calculus

• x
• variable
• z, s, t, f, arg, accum, ...
• ?x. e
• ?-abstraction
• x formal argument, e body
• ¼ fn x gt e
• e1 e2
• application
• left-associative (as in SML)
• e1 e2 e3 (e1 e2 ) e3
• e1 e2 e3 ? e1 (e2 e3 )

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Examples
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Outline

• Abstract syntax of the ?-calculus V
• Operational semantics of the l-calculus
• Substitutions
• Programming in the ?-calculus

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Semantics of Languages

• Answers "what is the meaning of a given program?"
• SML has a formal semantics.
• What about C?
• Three styles
• denotational semantics
• axiomatic semantics
• operational semantics
• The 1990s saw the renaissance of operational
  semantics.

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Operational Semantics

• Specifies how to transform a program into a value
  via a sequence of operations

Program
let fun fac 1 1 fac n n fac (n -
1) in fac 4 end
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Operational Semantics of ?-Calculus

• Specifies how to transform an expression into a
  value via a sequence of reductions

Expr
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Values and Reductions
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Reductions
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_____ Redex
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_____ Redex
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?-Reduction Not Unique
So we need a reduction strategy.
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?-Reduction Not Unique
So we need a reduction strategy.
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Call-by-name Call-by-value

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Call-by-name Call-by-value
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Call-by-name Call-by-value

• Used in Haskell
• Lazy or non-strict functional languages
• The implementation uses call-by-need.
• Superb!

• Used in SML
• Eager or strict functional languages
• Superb!

(fn x gt 0) ltsome horrible computationgt
(fn x gt 0) ltnon-terminating computationgt
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Assignments

• Assignment 2
• average 86.68
• Be sure to take a look at the sample solution.
• Assignment 3
• to be out by midnight tonight.
• ???
• due on April 2
• Start early! (? Start coding early!)

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Quiz 1

• Next Monday
• Read Chapter 2 of Course Notes.
• 'fill in the blank' problems (i.e., easy)
• 15 minutes
• Please show up on time.Otherwise you might miss
  the quiz!

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Anonymous Feedback

• To be set up sometime today (hopefully)
• http//pl.postech.ac.kr/gla/feedback/
• I will appreciate your feedback on this course.
• lectures
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