Table of Contents
CSE583: Programming Languages
Functional programming: two weeks
Flash!
Shift: From Scheme to theory
Functions and their combination
The lambda calculus
Function definition
Function application
That it!
Currying
Beta reduction rule
Representation
(Non-negative) integers
Defining addition
Reduction
Representing booleans
Defining cond
Normal form
Reduction order
Example
High-level view
A different high-level view
An aside: call by name
Call by name
Jensen’s device
Comparing reduction orders
Strict functions
More strictness
Fixed-points (or fixpoints)
Example
The good news
But its complicated
In theory, there is no difference between theory and practice
But…
Example
What do to?
Theory
ML
What’s different from Scheme?
Basic datatypes
Lists
List examples
Tuples
Records
Bindings
Local variables for expressions
Named function definitions
Anonymous functions
Function types
Using tuples
Minor notes
Another function type example
Pattern matching: on tuples
Another couple of examples
Pattern matching with functions
Another example
And here is such an example
Polymorphic functions
Polymorphic types
On invocation
Examples
Currying
Exploiting juxtaposition
A pattern-based curried map
Clean syntactic sugar for currying
Reminder: currying is
Polymorphism vs. overloading
How does ML handle overloading?
Equality types
Examples
Type inference: infer types of expressions automatically
Type inference: partial refinement
Properties of ML’s type system
Examples
Next time
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