• Top
    • Documentation
    • Books
    • Recursion-and-induction
    • Boolean-reasoning
    • Projects
    • Debugging
    • Std
    • Proof-automation
    • Macro-libraries
    • ACL2
      • Theories
      • Rule-classes
      • Proof-builder
      • Hons-and-memoization
      • Events
      • History
      • Parallelism
      • Programming
      • Start-here
        • Gentle-introduction-to-ACL2-programming
        • ACL2-tutorial
          • Introduction-to-the-theorem-prover
          • Pages Written Especially for the Tours
            • 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
            • Guards in ACL2
            • Numbers in ACL2
            • 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
            • ACL2 Conses or Ordered Pairs
            • The Associativity of App
            • Models of Computer Hardware and Software
            • How To Find Out about ACL2 Functions (cont)
            • A Sketch of How the Rewriter Works
            • ACL2 System Architecture
            • Running Models
            • ACL2 is an Untyped Language
            • How To Find Out about ACL2 Functions
            • How Long Does It Take to Become an Effective User(Q)
            • The Admission of App
            • Guiding the ACL2 Theorem Prover
            • What Is ACL2(Q)
            • Conversion
            • An Example Common Lisp Function Definition
            • ACL2 Characters
            • You Must Think about the Use of a Formula as a Rule
            • The WARNING about the Trivial Consequence
            • Guessing the Type of a Newly Admitted Function
            • ACL2 Strings
            • What is a Mathematical Logic(Q)
            • Revisiting the Admission of App
            • What is a Mechanical Theorem Prover(Q)
            • About Models
            • What is Required of the User(Q)
            • 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
              • Symbolic Execution of Models
              • 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)
              • Perhaps
              • Name the Formula Above
              • Undocumented Topic
              • A Trivial Proof
            • The-method
            • Advanced-features
            • Interesting-applications
            • Tips
            • Alternative-introduction
            • Tidbits
            • Annotated-ACL2-scripts
            • Startup
            • ACL2-as-standalone-program
            • ACL2-sedan
            • Talks
            • Nqthm-to-ACL2
            • Emacs
          • About-ACL2
        • Real
        • Debugging
        • Miscellaneous
        • Output-controls
        • Macros
        • Interfacing-tools
      • Interfacing-tools
      • Hardware-verification
      • Software-verification
      • Testing-utilities
      • Math
    • Pages Written Especially for the Tours

    Hey Wait! Is ACL2 Typed or Untyped(Q)

    Hey Wait! Is ACL2 Typed or Untyped?

    The example

    ACL2 !>(app 7 27) 
     
    ACL2 Error in TOP-LEVEL:  The guard for the function symbol ENDP, which 
    is (OR (CONSP X) (EQUAL X NIL)), is violated by the arguments in the 
    call (ENDP 7). 
    

    illustrates the fact that while ACL2 is an untyped language the ACL2 evaluator can be configured so as to check ``types'' at runtime. We should not say ``types'' here but ``guards.'' See Guards in ACL2 for a discussion of guards.

    The guard on endp requires its argument to be a true list. Since 7 is not a true list, and since ACL2 is checking guards in this example, an error is signaled by ACL2. How do you know ACL2 is checking guards? Because the prompt tells us (click here) with its ``!''.