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Procedures and Processes: The Substitution Model, Recursion & Iteration
A foundational exploration of procedures, processes, and the substitution model, integral to understanding computation as taught in MIT's 6.001 'Structure and Interpretation of Computer Programs'.
Lecture guide · Written by AI from the lecture. For the lecture’s own words, open the Transcript tab.
Hal Abelson and Gerald Jay Sussman introduce the substitution model to explain how procedures evolve computational processes. They contrast iterative processes (which execute in constant space) with recursive ones (which require deferred operations), analyzing their time and space complexity through examples including addition, Fibonacci numbers, and the Towers of Hanoi.
This lecture assumes
Key Takeaways
- The substitution model is a formal engineering model for understanding how expressions evaluate and how procedures yield processes.
- Linear iteration has space complexity because its state is entirely captured in explicit variables.
- Linear recursion consumes space due to deferred operations stored under the hood by the computer.
- Tree recursion, such as a naive Fibonacci implementation, grows exponentially in time because it recomputes identical subtrees.
Concepts Explained13
Substitution Model—The simplest model we have for understanding how procedures and processes work by evaluating operators and operands and substituting arguments for formal parameters in procedure bodies.
Substitution Rule—A method of evaluating an application by evaluating the operator and operands, applying the procedure to the arguments, copying the body with substituted arguments, and evaluating the new body.
Normal Order of Evaluation—An alternate evaluation rule where substitution of expressions for formal parameters is done inside the body first.
Conditional Expressions—An expression evaluated by checking a predicate, and depending on whether it is true or false, evaluating either the consequent or the alternative expression.
Examples, Proofs & Derivations
Part of course·Lecture 2 of 10
6.001: Structure and Interpretation of Computer Programs (SICP)
Lecturers
2Professor of Electrical Engineering and Computer Science at MIT
MIT Professor of Electrical Engineering and Computer Science and co-author of Structure and Interpretation of Computer Programs (SICP).
3 courses · 36 lectures in archiveView profile
Professor of Electrical Engineering and Computer Science
MIT Professor and co-author of SICP and Structure and Interpretation of Classical Mechanics, co-inventor of the Scheme programming language.
3 courses · 36 lectures in archiveView profile
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