1. Semantics of PLs via Interpreters: Getting Started
CS7100: Programming Languages
Prabhaker Mateti 1

2. Study … EOPL3 Chapter 3: 3.1, 3.2 source code: chapter3/let-lang/*
1722 data-structures.scm
4415 drscheme-init.scm
1450 environments.scm
2057 interp.scm
1501 lang.scm
1857 tests.scm
2007 top.scm
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3. EOPL3 Source Code All the code in the book, as a zip archive (211 Kb).
tested under PLT Scheme versions 372 and 4.2.
It should run unchanged in Racket
at the top of the file instead.
(NOT #lang racket -- the syntax for require/provide is slightly different).
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4. Interpreter vs Compiler
Input: Abstract Syntax of a program (AST)
Output:“Meaning” of the program
An interpreter carries out the meaning of a program.
A compiler transforms a program in one language into a program in a lower-level language preserving the meaning.
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5. Fig 3.2 The LET language Concrete/Abstract Syntax
Comments on the syntax
Six kinds of expressions.
Assume Scheme syntax for id and number.
Minus is used as a function name.
Uses std math notation for apply.
then-body and else-body are single expressions.
exp1 is the first expression and body is the second expression.
Beware: minus is used as a function name, and uses std math notation for apply.
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6. Examples in the LET language
let x = 5 in -(x,3)
in -(z, -(x,y)) % here x = 4
in -(-(x,8), y)
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7. scan&parse (scan&parse "-(55, -(x,11))") #(struct:a-program
#(struct:diff-exp
#(struct:const-exp 55)
#(struct:var-exp x)
#(struct:const-exp 11))))
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8. Values Of The Language Expressed values are the values of exp.
Denoted values are bound to variables.
Not always the same, in general.
In LET, they are the same:
ExpVal = Int + Bool
DenVal = Int + Bool
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9. Functions in our LET-Interpreter
constructors
const-exp : Int →Exp
zero?-exp : Exp → Exp
if-exp : Exp × Exp × Exp → Exp
diff-exp : Exp × Exp → Exp
var-exp : Var → Exp
let-exp : Var × Exp × Exp → Exp
observer
value-of : Exp × Env → ExpVal
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10. Spec of value-of (value-of (const-exp n) ρ) = (num-val n)
= (apply-env ρ var)
(expval->num (value-of exp2 ρ))))
Three more remaining.
Note the Scheme minus.
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11. Notation Notation Denotes  env [] Empty env [ var = val ] 
(extend-env var val )
«exp»
AST for expression exp
n
(num-val n),
val
(expval->num val).
Note: [[n]] =n
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12. Figure 3.3 An example calculation
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13. Specifying Programs initial environment [i=1, v=5, x=10]
= (value-of exp [i=[1],v=[5], x= [10]])
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14. Spec of value-of (value-of exp3 ρ)) [var = (value-of exp1 ρ)] ρ)
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15. Fig 3.4 A conditional expression
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16. Eval of an example let
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17. Eval of an example let (contd)
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18. Fig 3.6 LET lang AST def (exp1 expression?)))
(define-datatype expression expression?
(const-exp
(num number?))
(diff-exp
(exp1 expression?)
(exp2 expression?))
(zero?-exp
(exp1 expression?))
(if-exp
(exp1 expression?)
(exp2 expression?)
(exp3 expression?))
(var-exp
(var identifier?))
(let-exp
(var identifier?)
(body expression?)))
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19. (init-env) = [i= 1,v= 5,x=10] (define init-env (lambda () (extend-env
'i (num-val 1)
'v (num-val 5)
'x (num-val 10)
(empty-env))))))
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20. Fig 3.7a Expressed values
(bool boolean?)))
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21. Fig 3.7b Expressed values
’num val)))))
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22. Fig 3.7c Expressed values
(else (report-expval-extractor-error `bool val)))))
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23. value-of: Exp × Env → ExpVal
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24. run, value-of-program
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25. (value-of (zero?-exp exp1) env)
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26. (value-of (if-exp e1 e2 e3) env)
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27. (value-of (let-exp …) env)
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