More Monoids and Folds

Announcement #

• TL1 doc
• Disk issues, update page soon
• Session from last time on web page
• Issues with accounts
• git branch clean-start main
• new-homework and the plan

Plan #

Here we will work through the beginning of HW1 and use it as a platform for the ideas and also tooling/practices such as:

git

creating and using a repository

package

basic practice

command line driver

creating a stub that satisfies the requirements

structuring data and behavior

classes/methods or similar

types

basic type thinking

Primary focus is on digging in to the ideas to get you started in a good direction.

Review Results of Puzzle 2 and Puzzle 3 #

• Check-in any changes

  def puzzle2_3(predicate, transform, foldable):
      accumulator = []
      for item in foldable:
          if predicate(item):
              accumulator.append(transform(item))
          else:
              accumulator.append(item)
      return accumulator
  
  # wrapping function: identity
  # initial accumulator: []
  # step function
  
  def make_step(predicate, transform_true, transform_false=identity):
      def step(acc, item):
          if predicate(item):
              acc.append(transform_true(item))
          else:
              acc.append(transform_false(item))
          return acc
      return step
  
  make_step(lambda x: x % 2 == 0, lambda x: x + 1)
  
  # finalizer: identity
  

Sub-task #1: Defining Folds #

1. A data structure to store the Fold’s data

2. A method to construct a fold given that data

3. A (generic) function fold: Fold v w r -> Foldable v -> r

4. Unpacking the type

5. A simple view

6. What might this look like in R/Python

7. What does fold do? (cf. Puzzle 2) Look at the pattern

Defining Monoids #

• Strategy: Carrier with no data, used to interpret the data.

• The essence: generic operations and dispatch

  Discuss dispatch, message passing, objects very briefly

• Implementation (refer to the supplied files)

Monoidal Folds #

• What needs to be specified here
• Late binding of the Fold value. Explain and motivate.
• Transformation
• foldTree puzzle (if time allows)

Folds and Type Specifications #

Try Puzzle 2 #

Try Puzzle 3 #

Discuss main type specification #

Do Puzzle 4 with partner #

Define fold structure #