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          • A Tiny Warning Sign
          • About the Prompt
          • ACL2 Symbols
          • Common Lisp
          • About Types
          • The Event Summary
          • An Example of ACL2 in Use
          • The Tours
          • Corroborating Models
          • The Proof of the Associativity of App
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          • About the Admission of Recursive Definitions
          • Free Variables in Top-Level Input
          • Common Lisp as a Modeling Language
          • ACL2 as an Interactive Theorem Prover (cont)
          • A Flying Tour of ACL2
          • Analyzing Common Lisp Models
          • A Walking Tour of ACL2
          • The Theorem that App is Associative
          • The End of the Walking Tour
          • Proving Theorems about Models
          • Functions for Manipulating these Objects
          • About the ACL2 Home Page
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          • The Associativity of App
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          • A Sketch of How the Rewriter Works
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          • The Admission of App
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          • The WARNING about the Trivial Consequence
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          • Revisiting the Admission of App
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          • Hey Wait! Is ACL2 Typed or Untyped(Q)
          • The Falling Body Model
          • Rewrite Rules are Generated from DEFTHM Events
          • A Typical State
          • The Time Taken to do the Associativity of App Proof
          • The Simplification of the Induction Conclusion (Step 1)
          • The Rules used in the Associativity of App Proof
          • Subsumption of Induction Candidates in App Example
          • Other Requirements
          • Models in Engineering
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          • Suggested Inductions in the Associativity of App Example
          • Overview of the Proof of a Trivial Consequence
          • Evaluating App on Sample Input
          • The Induction Step in the App Example
          • Modeling in ACL2
          • The Simplification of the Induction Conclusion (Step 9)
          • The Induction Scheme Selected for the App Example
          • The First Application of the Associativity Rule
          • Overview of the Expansion of ENDP in the Induction Step
          • Flawed Induction Candidates in App Example
          • ACL2 as an Interactive Theorem Prover
          • Using the Associativity of App to Prove a Trivial Consequence
          • The Simplification of the Induction Conclusion (Step 8)
          • The Instantiation of the Induction Scheme
          • The Final Simplification in the Base Case (Step 0)
          • Overview of the Simplification of the Induction Step to T
          • Overview of the Simplification of the Induction Conclusion
          • On the Naming of Subgoals
          • Nontautological Subgoals
          • What is a Mechanical Theorem Prover(Q) (cont)
          • The Simplification of the Induction Conclusion (Step 12)
          • The Simplification of the Induction Conclusion (Step 10)
          • The End of the Flying Tour
          • The Base Case in the App Example
          • The Simplification of the Induction Conclusion (Step 11)
          • The Final Simplification in the Base Case (Step 3)
          • The Expansion of ENDP in the Induction Step (Step 1)
          • The Expansion of ENDP in the Induction Step (Step 0)
          • The End of the Proof of the Associativity of App
          • Overview of the Simplification of the Base Case to T
          • The Summary of the Proof of the Trivial Consequence
          • The Simplification of the Induction Conclusion (Step 7)
          • The Simplification of the Induction Conclusion (Step 6)
          • The Simplification of the Induction Conclusion (Step 5)
          • The Simplification of the Induction Conclusion (Step 4)
          • The Simplification of the Induction Conclusion (Step 2)
          • The Simplification of the Induction Conclusion (Step 0)
          • The Justification of the Induction Scheme
          • The Final Simplification in the Base Case (Step 1)
          • The Expansion of ENDP in the Induction Step (Step 2)
          • Popping out of an Inductive Proof
          • Overview of the Expansion of ENDP in the Base Case
          • The Simplification of the Induction Conclusion (Step 3)
          • The Q.E.D. Message
          • Overview of the Final Simplification in the Base Case
          • The Final Simplification in the Base Case (Step 2)
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          • Name the Formula Above
          • Undocumented Topic
          • A Trivial Proof
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• Pages Written Especially for the Tours

A Walking Tour of ACL2

A Walking Tour of ACL2

On this tour you will learn a little more about the ACL2 logic, the theorem prover, and the user interface.

This time we will stick with really simple things, such as the associativity of list concatenation.

We assume you have taken the Flying Tour but that you did not necessarily follow all the ``off-tour'' links because we encouraged you not to. With the Walking Tour we encourage you to visit off-tour links — provided they are not marked with the tiny warning sign (). But they are ``branches'' in the tour that lead to ``dead ends.'' When you reach a dead end, remember to use your browser's Back Button to return to the Walking Tour to continue.

When you get to the end of the tour we'll give you a chance to repeat quickly both the Flying and the Walking Tours to visit any off-tour links still of interest.