Learn you a F# and Lambda Calculus to better understand academic computer science papers related to languages, types, and data structures.

1. Tools for Reading
Academic
Computer Science
Papers

2. Reading a paper
Abstract
Introduction
Conclusion
Information
dense words
and symbols
Approach only if
surrounding is interesting
Read it like math, not like a story
Read first

3. 3 Useful Tools*
• F#
• Lambda Calculus
• Programming Theory Notation
* Selection bias for programming language related papers

4. Why F# ?
• Standard ML (SML) – does not have guards
• Caml / Ocaml
• Coq
Many authors will use an ML language in the paper’s body.

5. 2 Ideas from ML Languages
• Lists (singly linked lists)
• Pattern Matching (next page)
::X
Deconstruct:
Construct
:
M A S [
]
TailHead
Cons Empty

6. let rec printLoop printState buffer =
match buffer with
| "("::x::")"::tail when notParen x ->
…
printLoop newState tail
| "("::"("::"("::x::tail when notParen x ->
…
parenOffset = (offset + 1)::(offset + 2)::(offset + 3)::parenOffset
…
printLoop newState tail
| x::")"::")"::")"::tail when notParen x ->
…
parenOffset = parenOffset.Tail.Tail.Tail
…
printLoop newState tail
| [] -> ()

7. Lambda Calculus
Syntax
t ::= terms:
x variable
λx.t abstraction
t t application
v ::= values:
λx.t abstraction value

8. λx. x
Ultra concise function representation
1 input
per λ
Everything after the dot is the
function body, what gets emitted
λx. λy. y x
Multipe inputs
require multiple
λs

9. λx. x
λx. λy. y x
This is the identity function.
It emits whatever the input is
The body of this function applies the term
represented by the value “y” to the term
represented by the value “x”
(λx. λy. y x) x (λx. x) What will this emit?

10. (λx. λy. y x) x (λx. x)
(λy. y x) (λx. x)
(λx. x) x
x
Evaluation

11. Programming Theory Notation
Horizontal line representing IF / THEN rule.
something
something else something
If
Then
Just a rule out of
whole cloth

12. Lambda Calculus Evaluation Rules
t1 t1'
/* E-APP1 */
t1 t2 -> t1' t2
t2 -> t2'
/* E-APP2 */
v1 t2 -> v1 t2'
(λx.t12) v2 -> [x ↦ v2]t12 /* abstraction value */

13. Conclusion
Abstract
Introduction
Conclusion
Information
dense words
and symbols
• Singly linked lists
• Pattern matching
• Lambda Calculus
• Rules
Read first

14. Jeremy Siek
Crash Course on Notation in Programming Language Theory
http://siek.blogspot.com/2012/07/crash-course-on-notation-in-programming.html