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Lect 3.2 Scheme_nt - CPE425/CSC301/SC433 Programming...

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CPE425/CSC301/SC433 Programming Languages Lecture 3.2 Scheme
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Scheme 2 Topics Scheme Basic components Objects Binding forms: lambda, let, define, set! Data structures: lists, vectors Functions: primitive, user-defined Comparison of Scheme and FP Comparison of Functional and Imperative Languages
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Scheme 3 Functions Any function application is written in prefix form: e.g. (+ 10 20) 10+20 (/ (* (+ 10 20) 5) 2) (10+20) * 5 / 2 (function_name arg1 arg2 arg3 …)
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Scheme 4 Objects Scheme (like LISP) is a language for symbolic computation (AI applications) Values are represented by symbolic expressions (or S-expressions ) An expression is either: atoms e.g. a, 1, “hello world” lists e.g. (a b c d), (hello world) Vector e.g. #(a b c d)
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Scheme 5 Binding Forms Syntactic forms used to bind or assign identifiers Lambda Let Definitions Assignments
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Scheme 6 λ - Calculus Developed by Alonzo Church Lambda-calculus is a formal system for functional definition in mathematical theory Anonymous functions A fundamental goal To described what can be computed LISP is based on λ-calculus
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Scheme 7 f(x) = x + 3 (λx . x+3) λ - Function A mathematical function may be expressed in λ-form e.g. The lambda form clearly shows which variables are bound or free e.g. defining form bound variable f(x) = x + 3*a (λx . x+3*a) free variable bound variable
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Scheme 8 Lambda Expression in Scheme Aka lambda expression Analogous to λ -calculus expressions idspec : formal parameter s of procedure The expressions expr1, expr2 , … are evaluated in sequence Creates (returns) an anonymous procedure (lambda (idspec) expr1 expr2 …)
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Scheme 9 Lambda Expression in Scheme (cont’d) Examples (lambda (x) (+ x 3)) λx . x+3 ( ( lambda (x) (+ x 3) ) 7) λx . x+3 : 7 #<procedure> 10 ( ( lambda (f x) (f x x ) ) + 11) 22 ( ( lambda ( ) (+ 3 4) ) ) 7 + 11 11
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Scheme 10 Lambda Expression in Scheme (cont’d) Examples ((lambda (x) ((lambda (y) (- x y)) 15)) 20) λx . (λy . x-y : 15) : 20 The variable x is free in the body of the inner lambda expr, but its binding is found in the local environment for the outer lambda expr Global environment Local environment 1 x Local environment 2 y Result : 5
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Scheme 11 Local Binding using Let Temporary (local) binding of identifiers to values in the body of let Order of evaluation of val_*, expr_* is at discretion of Scheme implementation Any free (i.e. unbound) variable appearing in val1 , val2 , … is looked up in a non-local environment (let ( (id1 val1) (id2 val2) … ) expr1 expr2 … )
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Scheme 12 Local Binding using Let (cont’d) Examples (let ( (a 2) (b 3) ) (+ a b) ) (let ( (sum (+ 2 4)) ) (* sum sum)) ( let ((b 3)) ( let ((b 10) (c b)) c ) ) 5 36 3 Global environment Local environment 1-a a, b Local environment 1-b sum Local environment 1-c b Local environment 2 b, c ( b = 3 (( b = 10) (c = b)) ) (1-a) (1-b) (1-c)
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Scheme 13 Let and Lambda The let construct does not add any new semantic facility to Scheme Every let expression can be rewritten as a lambda expression applied to arguments (let ( (x 3) (y (+ 2 5)) ) (+ x y)) ( ( lambda (x y) (+ x y) ) 3 (+ 2 5)) 2 + 5
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Scheme 14 Using Let* Syntax is similar to let
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