Inductively Defined Data Concrete and Abstract syntax Karl
Inductively Defined Data Concrete and Abstract syntax Karl Lieberherr CSG 111 1
Don’t believe the words • Concrete syntax may be more abstract than abstract syntax!!! CSG 111 2
Both Abstract and Concrete Exp : : = Identifier var-exp (id) : : = “(lambda” “(“Identifier”)” Exp”)” lambda-exp (id body) : : = “(“ Exp “)” app-exp (rator rand) page 49 of EOPL 2: (replace Exp by Expression, capitalize instead of angle) CSG 111 3
Both Abstract and Concrete Exp : : = Id var-exp (id) : : = “(lambda” “(“ Id ”)” Exp ”)” lambda-exp (id body) : : = “(“ Exp “)” app-exp (rator rand) (define-datatype Exp? (var-exp (id Id? )) (lambda-exp (id Id? ) (body Exp? )) (app-exp (rator Exp? ) (rand Exp? ))) page 49 of EOPL 2: (Exp by Expression, Id by Identifier, capitalize instead of angle) CSG 111 4
Represent Id as symbol Exp : : = Id var-exp (id) : : = “(lambda” “(“ Id ”)” Exp ”)” lambda-exp (id body) : : = “(“ Exp “)” app-exp (rator rand) (define-datatype Exp? (var-exp (id symbol? )) (lambda-exp (id symbol? ) (body Exp? )) (app-exp (rator Exp? ) (rand Exp? ))) page 49 of EOPL 2: (Exp by Expression, Id by Identifier, capitalize instead of angle) CSG 111 5
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 6
Exercises for define-datatype • Arithmetic expressions ( * (+ 3 5) 7) – two arguments only – include evaluator • Nested containers CSG 111 7
Variants are also data types Exp : : = Id var-exp (id) : : = “(lambda” “(“ Id ”)” Exp ”)” lambda-exp (id body) : : = “(“ Exp “)” app-exp (rator rand) (define-datatype Exp? (var-exp (id symbol? )) (lambda-exp (id symbol? ) (body Exp? )) (app-exp (rator Exp? ) (rand Exp? ))) Better way: Exp : Var. Exp | Lambda. Exp | App. Exp. Var. Exp = Id. Lambda. Exp = “(lambda” “(“ <id> Id <body> Exp “)”. App. Exp = “(“ <rator> Exp <rand> Exp “)”. Test = <first> Lambda. Exp <second> App. Exp. Each non-terminal defines a data type. CSG 111 8
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)) CSG 111 Concerns: traversal summing weights summing violations 9
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 10
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