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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

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

  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)

  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)

  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)

  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 … ))))))

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

  8. Exercise: Test data type • Contains in first a Lambda expression lambda-exp and in second an Application app-exp. • Would like something like: (define-struct Test ( first ;; type lambda-exp second ;; type app-exp ) but with the dynamic checking benefit of define-datatype.

  9. 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?))) Better Way: variants are first class 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.

  10. 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

  11. 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)

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