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Inductively Defined Data Concrete and Abstract syntax

Inductively Defined Data Concrete and Abstract syntax. Karl Lieberherr. Don’t believe the words. Concrete syntax may be more abstract than abstract syntax!!!. Both Abstract and Concrete. Exp ::= Identifier var-exp (id) ::= “(lambda” “(“Identifier”)” Exp”)” lambda-exp (id body)

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Inductively Defined Data Concrete and Abstract syntax

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  1. Inductively Defined DataConcrete and Abstract syntax Karl Lieberherr CSG 111

  2. Don’t believe the words • Concrete syntax may be more abstract than abstract syntax!!! CSG 111

  3. Both Abstract and Concrete Exp ::= Identifier var-exp (id) ::=“(lambda” “(“Identifier”)” Exp”)” lambda-exp (id body) ::= “(“ Exp “(“ Exp “)” “)” app-exp (rator rand) page 49 of EOPL 2: (replace Exp by Expression, capitalize instead of angle) CSG 111

  4. Exp ::= Id var-exp (id) ::=“(lambda” “(“ Id ”)” Exp ”)” lambda-exp (id body) ::= “(“ Exp “(“ Exp “)” “)” app-exp (rator rand) (define-datatype Exp Exp? (var-exp (id Id?)) (lambda-exp (id Id?) (body Exp?)) (app-exp (rator Exp?) (rand Exp?))) Both Abstract and Concrete page 49 of EOPL 2: (Exp by Expression, Id by Identifier, capitalize instead of angle) CSG 111

  5. Exp ::= Id var-exp (id) ::=“(lambda” “(“ Id ”)” Exp ”)” lambda-exp (id body) ::= “(“ Exp “(“ Exp “)” “)” app-exp (rator rand) (define-datatype Exp Exp? (var-exp (id symbol?)) (lambda-exp (id symbol?) (body Exp?)) (app-exp (rator Exp?) (rand Exp?))) Represent Id as symbol page 49 of EOPL 2: (Exp by Expression, Id by Identifier, capitalize instead of angle) CSG 111

  6. cases (define occurs-free? (lambda (var exp) (cases Exp e (var-exp (id) (eqv? id var)) (lambda-exp (id body) and (not (eqv? id var)) (occurs-free? var body))) (app-exp (rator rand) (or … )))))) CSG 111

  7. Exercises for define-datatype • Arithmetic expressions ( * (+ 3 5) 7) • two arguments only • include evaluator • Nested containers CSG 111

  8. Exp ::= Id var-exp (id) ::=“(lambda” “(“ Id ”)” Exp ”)” lambda-exp (id body) ::= “(“ Exp “(“ Exp “)” “)” app-exp (rator rand) (define-datatype Exp Exp? (var-exp (id symbol?)) (lambda-exp (id symbol?) (body Exp?)) (app-exp (rator Exp?) (rand Exp?))) Variants are also data types Better way: Exp : VarExp | LambdaExp | AppExp. VarExp = Id. LambdaExp = “(lambda” “(“ <id> Id <body> Exp “)”. AppExp = “(“ <rator> Exp <rand> Exp “)”. Test = <first> LambdaExp <second> AppExp. Each non-terminal defines a data type. CSG 111

  9. Concern analysis (define (check ac) (local (;; Container -> Number ;; the weight of a container ;; effect: the number of capacity violations in a container (define (weight-container ac) (local ([define witems (weight-loi (Container-contents ac))]) (when (> witems (Container-capacity ac)) (set! violations (+ 1 violations))) witems)) ;; (Listof Item) -> Number ;; the weight of a list of items (define (weight-loi l) (foldr + 0 (map weight-item l))) ;; Item -> Number ;; the weight of an item (define (weight-item l) (cond [(Simple? l) (Simple-weight l)] [(Container? l) (weight-container l)])) (define violations 0)) ;; the number of violations detected (weight-container ac) violations)) Concerns: traversal summing weights summing violations CSG 111

  10. Concrete syntax more Abstract than Abstract Syntax: example Exp ::= Identifier var-exp (id) ::=“(lambda” “(“Identifier”)” List(Exp)”)” lambda-exp (id body) ::= “(“ Exp “(“ List(Exp) “)” “)” app-exp (rator rand) page 49 of EOPL 2: (replace Exp by Expression, capitalize instead of angle) CSG 111

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