CPS 343/543 Lecture notes: Recursion

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Adding recursion to our language and interpreter

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• new production rule and constructor on p. 93
• sample programs on p. 93
• we will evaluate the body of a recursive procedure in a recursively-extended environment (see Fig. 3.8 on p. 94)
• behavior of recursively-extended environment on p. 93
• we use Scheme's letrec itself to recursively extend a procedurally-represented environment
  • involves packaging up an instance of the closure data type
  • see Fig. 3.9 on p. 95
• we can represent a recursively-extended environment using abstract syntax as well
  • involves adding a new variant to the environment data type,
  • adding a extend-env-recursively procedure, and
  • adding a new case to apply-env which packages up an instance of the closure data type
  • see Fig. 3.10 on p. 96
• notice that in each of the above recursively-extended environment representations, `we build a new closure each time a procedure is retrieved from the environment' [EOPL2] p. 95
• `this is unnecessary since the environment for the closure is always the same' [EOPL2] p. 95
• `if we use a ribcage representation of the environment, we can build the closures only once, by building an environment with a circular structure' [EOPL2] p. 95
  • return to the original environment representation (that without the recursively-extended-env-record variant)
    
  
  
  (regenerated from [EOPL2] Fig. 3.11 on p. 97)
  
  
  • see code for extend-env-recursively in Fig. 3.12 on p. 97
    • use of vector-set! (function built into Scheme)
    • use of for-each (function built into Scheme)
    • use of iota (function not built into Scheme)

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References

[EOPL2]

D.P. Friedman, M. Wand, and C.T. Haynes. Essentials of Programming Languages. MIT Press, Cambridge, MA, Second edition, 2001.