Environments Announcements Environments for Higher-Order Functions - - PowerPoint PPT Presentation

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Environments Announcements Environments for Higher-Order Functions - - PowerPoint PPT Presentation

Jan 31, 2024 12 likes •963 views

Environments Announcements Environments for Higher-Order Functions Environments Enable Higher-Order Functions 4 Environments Enable Higher-Order Functions Functions are first-class: Functions are values in our programming language 4

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SLIDE 1

Environments

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SLIDE 2

Announcements

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SLIDE 3

Environments for Higher-Order Functions

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SLIDE 4

Environments Enable Higher-Order Functions

4

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SLIDE 5

Environments Enable Higher-Order Functions

4

Functions are first-class: Functions are values in our programming language

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SLIDE 6

Environments Enable Higher-Order Functions

4

Functions are first-class: Functions are values in our programming language Higher-order function: A function that takes a function as an argument value or A function that returns a function as a return value

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SLIDE 7

Environments Enable Higher-Order Functions

4

Environment diagrams describe how higher-order functions work! Functions are first-class: Functions are values in our programming language Higher-order function: A function that takes a function as an argument value or A function that returns a function as a return value

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SLIDE 8

Environments Enable Higher-Order Functions

(Demo)

4

Environment diagrams describe how higher-order functions work! Functions are first-class: Functions are values in our programming language Higher-order function: A function that takes a function as an argument value or A function that returns a function as a return value

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SLIDE 9

Names can be Bound to Functional Arguments

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pythontutor.com/composingprograms.html#code=def%20apply_twice%28f,%20x%29%3A%0A%20%20%20%20return%20f%28f%28x%29%29%0A%20%20%20%20%0Adef%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%20%20%20%20%0Aresult%20%3D%20apply_twice%28square,%202%29&mode=display&origin=composingprograms.js&cumulative=true&py=3&rawInputLstJSON=[]&curInstr=0

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SLIDE 10

Names can be Bound to Functional Arguments

5

pythontutor.com/composingprograms.html#code=def%20apply_twice%28f,%20x%29%3A%0A%20%20%20%20return%20f%28f%28x%29%29%0A%20%20%20%20%0Adef%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%20%20%20%20%0Aresult%20%3D%20apply_twice%28square,%202%29&mode=display&origin=composingprograms.js&cumulative=true&py=3&rawInputLstJSON=[]&curInstr=0

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SLIDE 11

Names can be Bound to Functional Arguments

5

Applying a user-defined function:

  • Create a new frame
  • Bind formal parameters

(f & x) to arguments

  • Execute the body:

return f(f(x))

pythontutor.com/composingprograms.html#code=def%20apply_twice%28f,%20x%29%3A%0A%20%20%20%20return%20f%28f%28x%29%29%0A%20%20%20%20%0Adef%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%20%20%20%20%0Aresult%20%3D%20apply_twice%28square,%202%29&mode=display&origin=composingprograms.js&cumulative=true&py=3&rawInputLstJSON=[]&curInstr=0

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SLIDE 12

Names can be Bound to Functional Arguments

5

Applying a user-defined function:

  • Create a new frame
  • Bind formal parameters

(f & x) to arguments

  • Execute the body:

return f(f(x))

pythontutor.com/composingprograms.html#code=def%20apply_twice%28f,%20x%29%3A%0A%20%20%20%20return%20f%28f%28x%29%29%0A%20%20%20%20%0Adef%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%20%20%20%20%0Aresult%20%3D%20apply_twice%28square,%202%29&mode=display&origin=composingprograms.js&cumulative=true&py=3&rawInputLstJSON=[]&curInstr=0

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SLIDE 13

Names can be Bound to Functional Arguments

5

Applying a user-defined function:

  • Create a new frame
  • Bind formal parameters

(f & x) to arguments

  • Execute the body:

return f(f(x))

pythontutor.com/composingprograms.html#code=def%20apply_twice%28f,%20x%29%3A%0A%20%20%20%20return%20f%28f%28x%29%29%0A%20%20%20%20%0Adef%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%20%20%20%20%0Aresult%20%3D%20apply_twice%28square,%202%29&mode=display&origin=composingprograms.js&cumulative=true&py=3&rawInputLstJSON=[]&curInstr=0

2 1

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SLIDE 14

Names can be Bound to Functional Arguments

5

Applying a user-defined function:

  • Create a new frame
  • Bind formal parameters

(f & x) to arguments

  • Execute the body:

return f(f(x))

pythontutor.com/composingprograms.html#code=def%20apply_twice%28f,%20x%29%3A%0A%20%20%20%20return%20f%28f%28x%29%29%0A%20%20%20%20%0Adef%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%20%20%20%20%0Aresult%20%3D%20apply_twice%28square,%202%29&mode=display&origin=composingprograms.js&cumulative=true&py=3&rawInputLstJSON=[]&curInstr=0

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SLIDE 15

Environments for Nested Definitions

(Demo)

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SLIDE 16

Environment Diagrams for Nested Def Statements

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 17

Environment Diagrams for Nested Def Statements

Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 18

Environment Diagrams for Nested Def Statements

Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 19

Environment Diagrams for Nested Def Statements

Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 20

Environment Diagrams for Nested Def Statements

Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 21

Environment Diagrams for Nested Def Statements

Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 22

Environment Diagrams for Nested Def Statements

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Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 23

Environment Diagrams for Nested Def Statements

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Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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Environment Diagrams for Nested Def Statements

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  • Every user-defined function has

a parent frame (often global) Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 25

Environment Diagrams for Nested Def Statements

2 1 3

  • Every user-defined function has

a parent frame (often global)

  • The parent of a function is the

frame in which it was defined Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 26

Environment Diagrams for Nested Def Statements

2 1 3

  • Every user-defined function has

a parent frame (often global)

  • The parent of a function is the

frame in which it was defined

  • Every local frame has a parent

frame (often global) Nested def

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http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 27

Environment Diagrams for Nested Def Statements

2 1 3

  • Every user-defined function has

a parent frame (often global)

  • The parent of a function is the

frame in which it was defined

  • Every local frame has a parent

frame (often global)

  • The parent of a frame is the

parent of the function called Nested def

7

http://pythontutor.com/composingprograms.html#code=def%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Athree_more_than%20%3D%20make_adder%283%29%0Aresult%20%3D%20three_more_than%284%29&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 28

How to Draw an Environment Diagram

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SLIDE 29

How to Draw an Environment Diagram

When a function is defined:

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SLIDE 30

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>]

8

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SLIDE 31

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>] Its parent is the current frame.

8

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SLIDE 32

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>] Its parent is the current frame.

8

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SLIDE 33

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>] Its parent is the current frame. Bind <name> to the function value in the current frame

8

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SLIDE 34

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>] Its parent is the current frame. Bind <name> to the function value in the current frame When a function is called:

8

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SLIDE 35

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>] Its parent is the current frame. Bind <name> to the function value in the current frame When a function is called:

  • 1. Add a local frame, titled with the <name> of the function being called.

8

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SLIDE 36

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>] Its parent is the current frame. Bind <name> to the function value in the current frame When a function is called:

  • 1. Add a local frame, titled with the <name> of the function being called.
  • 2. Copy the parent of the function to the local frame: [parent=<label>]

8

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SLIDE 37

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>] Its parent is the current frame. Bind <name> to the function value in the current frame When a function is called:

  • 1. Add a local frame, titled with the <name> of the function being called.
  • 2. Copy the parent of the function to the local frame: [parent=<label>]
  • 3. Bind the <formal parameters> to the arguments in the local frame.

8

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SLIDE 38

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>] Its parent is the current frame. Bind <name> to the function value in the current frame When a function is called:

  • 1. Add a local frame, titled with the <name> of the function being called.
  • 2. Copy the parent of the function to the local frame: [parent=<label>]
  • 3. Bind the <formal parameters> to the arguments in the local frame.
  • 4. Execute the body of the function in the environment that starts with the local frame.

8

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SLIDE 39

Local Names

(Demo)

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SLIDE 40

Local Names are not Visible to Other (Non-Nested) Functions

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http://pythontutor.com/composingprograms.html#code=def%20f%28x, %20y%29%3A%0A%20%20%20%20return%20g%28x%29%0A%0Adef%20g%28a%29%3A%0A%20%20%20%20return%20a%20%2B%20y%0A%20%20%20%20%0Aresult%20%3D%20f%281,%202%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 41

Local Names are not Visible to Other (Non-Nested) Functions

2 1

10

http://pythontutor.com/composingprograms.html#code=def%20f%28x, %20y%29%3A%0A%20%20%20%20return%20g%28x%29%0A%0Adef%20g%28a%29%3A%0A%20%20%20%20return%20a%20%2B%20y%0A%20%20%20%20%0Aresult%20%3D%20f%281,%202%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 42

Local Names are not Visible to Other (Non-Nested) Functions

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10

http://pythontutor.com/composingprograms.html#code=def%20f%28x, %20y%29%3A%0A%20%20%20%20return%20g%28x%29%0A%0Adef%20g%28a%29%3A%0A%20%20%20%20return%20a%20%2B%20y%0A%20%20%20%20%0Aresult%20%3D%20f%281,%202%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 43

Local Names are not Visible to Other (Non-Nested) Functions

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“y” is not found

10

http://pythontutor.com/composingprograms.html#code=def%20f%28x, %20y%29%3A%0A%20%20%20%20return%20g%28x%29%0A%0Adef%20g%28a%29%3A%0A%20%20%20%20return%20a%20%2B%20y%0A%20%20%20%20%0Aresult%20%3D%20f%281,%202%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 44

Local Names are not Visible to Other (Non-Nested) Functions

2 1

“y” is not found “y” is not found, again

10

http://pythontutor.com/composingprograms.html#code=def%20f%28x, %20y%29%3A%0A%20%20%20%20return%20g%28x%29%0A%0Adef%20g%28a%29%3A%0A%20%20%20%20return%20a%20%2B%20y%0A%20%20%20%20%0Aresult%20%3D%20f%281,%202%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 45

Local Names are not Visible to Other (Non-Nested) Functions

2 1

“y” is not found “y” is not found, again Error

10

http://pythontutor.com/composingprograms.html#code=def%20f%28x, %20y%29%3A%0A%20%20%20%20return%20g%28x%29%0A%0Adef%20g%28a%29%3A%0A%20%20%20%20return%20a%20%2B%20y%0A%20%20%20%20%0Aresult%20%3D%20f%281,%202%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 46

Local Names are not Visible to Other (Non-Nested) Functions

2 1

“y” is not found “y” is not found, again Error

  • An environment is a sequence of frames.

10

http://pythontutor.com/composingprograms.html#code=def%20f%28x, %20y%29%3A%0A%20%20%20%20return%20g%28x%29%0A%0Adef%20g%28a%29%3A%0A%20%20%20%20return%20a%20%2B%20y%0A%20%20%20%20%0Aresult%20%3D%20f%281,%202%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 47

Local Names are not Visible to Other (Non-Nested) Functions

2 1

“y” is not found “y” is not found, again Error

  • An environment is a sequence of frames.
  • The environment created by calling a top-level function (no def within def)

consists of one local frame, followed by the global frame.

10

http://pythontutor.com/composingprograms.html#code=def%20f%28x, %20y%29%3A%0A%20%20%20%20return%20g%28x%29%0A%0Adef%20g%28a%29%3A%0A%20%20%20%20return%20a%20%2B%20y%0A%20%20%20%20%0Aresult%20%3D%20f%281,%202%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 48

Lambda Expressions

(Demo)

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SLIDE 49

Lambda Expressions

12

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SLIDE 50

Lambda Expressions

>>> x = 10

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SLIDE 51

Lambda Expressions

>>> x = 10 >>> square = x * x

12

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SLIDE 52

Lambda Expressions

>>> x = 10 >>> square = x * x An expression: this one evaluates to a number

12

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SLIDE 53

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x An expression: this one evaluates to a number

12

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SLIDE 54

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x An expression: this one evaluates to a number Also an expression: evaluates to a function

12

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SLIDE 55

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x An expression: this one evaluates to a number Also an expression: evaluates to a function A function

12

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SLIDE 56

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x An expression: this one evaluates to a number Also an expression: evaluates to a function with formal parameter x A function

12

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SLIDE 57

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x An expression: this one evaluates to a number Also an expression: evaluates to a function that returns the value of "x * x" with formal parameter x A function

12

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SLIDE 58

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x An expression: this one evaluates to a number Also an expression: evaluates to a function that returns the value of "x * x" with formal parameter x A function Important: No "return" keyword!

12

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SLIDE 59

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x An expression: this one evaluates to a number Also an expression: evaluates to a function that returns the value of "x * x" with formal parameter x A function Important: No "return" keyword! Must be a single expression

12

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SLIDE 60

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x >>> square(4) 16 An expression: this one evaluates to a number Also an expression: evaluates to a function that returns the value of "x * x" with formal parameter x A function Important: No "return" keyword! Must be a single expression

12

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SLIDE 61

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x >>> square(4) 16 An expression: this one evaluates to a number Also an expression: evaluates to a function that returns the value of "x * x" with formal parameter x A function Lambda expressions are not common in Python, but important in general Important: No "return" keyword! Must be a single expression

12

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SLIDE 62

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x >>> square(4) 16 An expression: this one evaluates to a number Also an expression: evaluates to a function that returns the value of "x * x" with formal parameter x A function Lambda expressions are not common in Python, but important in general Important: No "return" keyword! Must be a single expression

12

Lambda expressions in Python cannot contain statements at all!

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SLIDE 63

Lambda Expressions Versus Def Statements

13

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SLIDE 64

Lambda Expressions Versus Def Statements

VS

13

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SLIDE 65

Lambda Expressions Versus Def Statements

square = lambda x: x * x

VS

13

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SLIDE 66

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

13

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SLIDE 67

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

  • Both create a function with the same domain, range, and behavior.

13

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SLIDE 68

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

  • Both create a function with the same domain, range, and behavior.
  • Both bind that function to the name square.

13

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SLIDE 69

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

  • Both create a function with the same domain, range, and behavior.
  • Both bind that function to the name square.
  • Only the def statement gives the function an intrinsic name, which shows up in

environment diagrams but doesn't affect execution (unless the function is printed).

13

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SLIDE 70

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

  • Both create a function with the same domain, range, and behavior.
  • Both bind that function to the name square.
  • Only the def statement gives the function an intrinsic name, which shows up in

environment diagrams but doesn't affect execution (unless the function is printed).

13

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SLIDE 71

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

  • Both create a function with the same domain, range, and behavior.
  • Both bind that function to the name square.
  • Only the def statement gives the function an intrinsic name, which shows up in

environment diagrams but doesn't affect execution (unless the function is printed).

13

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SLIDE 72

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

  • Both create a function with the same domain, range, and behavior.
  • Both bind that function to the name square.
  • Only the def statement gives the function an intrinsic name, which shows up in

environment diagrams but doesn't affect execution (unless the function is printed). The Greek letter lambda

13

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SLIDE 73

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

  • Both create a function with the same domain, range, and behavior.
  • Both bind that function to the name square.
  • Only the def statement gives the function an intrinsic name, which shows up in

environment diagrams but doesn't affect execution (unless the function is printed). The Greek letter lambda

13

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SLIDE 74

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

  • Both create a function with the same domain, range, and behavior.
  • Both bind that function to the name square.
  • Only the def statement gives the function an intrinsic name, which shows up in

environment diagrams but doesn't affect execution (unless the function is printed). The Greek letter lambda

13

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SLIDE 75

Function Composition

(Demo)

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SLIDE 76

The Environment Diagram for Function Composition

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 77

The Environment Diagram for Function Composition

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 78

The Environment Diagram for Function Composition

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 79

The Environment Diagram for Function Composition

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 80

The Environment Diagram for Function Composition

Return value of make_adder is an argument to compose1

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 81

The Environment Diagram for Function Composition

Return value of make_adder is an argument to compose1

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 82

The Environment Diagram for Function Composition

Return value of make_adder is an argument to compose1

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 83

The Environment Diagram for Function Composition

Return value of make_adder is an argument to compose1

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 84

The Environment Diagram for Function Composition

2 1 3

Return value of make_adder is an argument to compose1

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 85

The Environment Diagram for Function Composition

2 1 3

Return value of make_adder is an argument to compose1

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 86

The Environment Diagram for Function Composition

2 1 3 1 2 3

Return value of make_adder is an argument to compose1

15

http://pythontutor.com/composingprograms.html#code=def%20square%28x%29%3A%0A%20%20%20%20return%20x%20*%20x%0A%0Adef%20make_adder%28n%29%3A%0A%20%20%20%20def%20adder%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20k%20%2B%20n%0A%20%20%20%20return%20adder%0A%20%20%20%20%0Adef%20compose1%28f, %20g%29%3A%0A%20%20%20%20def%20h%28x%29%3A%0A%20%20%20%20%20%20%20%20return%20f%28g%28x%29%29%0A%20%20%20%20return%20h%0A%20%20%20%20%0Acompose1%28square,%20make_adder%282%29%29%283%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 87

Self-Reference

(Demo)

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SLIDE 88

Returning a Function Using Its Own Name

17

http://pythontutor.com/composingprograms.html#code=def%20print_all%28k%29%3A%0A%20%20%20%20print%28k%29%0A%20%20%20%20return%20print_all%0A%20%20%20%20%0Aprint_all%281%29%283%29%285%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D http://pythontutor.com/composingprograms.html#code=def%20print_sums%28n%29%3A%0A%20%20%20%20print%28n%29%0A%20%20%20%20def%20next_sum%28k%29%3A%0A%20%20%20%20%20%20%20%20return%20print_sums%28n%2Bk%29%0A%20%20%20%20return%20next_sum%0A%0Aprint_sums%281%29%283%29%285%29&cumulative=true&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D

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SLIDE 89

Currying

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SLIDE 90

Function Currying

19

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SLIDE 91

Function Currying

def make_adder(n): return lambda k: n + k

19

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SLIDE 92

Function Currying

def make_adder(n): return lambda k: n + k >>> make_adder(2)(3) 5 >>> add(2, 3) 5

19

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SLIDE 93

Function Currying

def make_adder(n): return lambda k: n + k >>> make_adder(2)(3) 5 >>> add(2, 3) 5 There's a general relationship between these functions

19

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SLIDE 94

Function Currying

def make_adder(n): return lambda k: n + k >>> make_adder(2)(3) 5 >>> add(2, 3) 5 There's a general relationship between these functions

19

(Demo)

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SLIDE 95

Function Currying

def make_adder(n): return lambda k: n + k >>> make_adder(2)(3) 5 >>> add(2, 3) 5 There's a general relationship between these functions Curry: Transform a multi-argument function into a single-argument, higher-order function

19

(Demo)