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) ::= “(“ Exp “(“ Exp “)” “)” app-exp (rator rand) page 49 of EOPL 2: (replace Exp by Expression, capitalize instead of angle)

Both Abstract and Concrete 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?))) page 49 of EOPL 2: (Exp by Expression, Id by Identifier, capitalize instead of angle)

Represent Id as symbol 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?))) page 49 of EOPL 2: (Exp by Expression, Id by Identifier, capitalize instead of angle)

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 … ))))))

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

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.

Better Way: variants are first class 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: Exp : VarExp | LambdaExp | AppExp. VarExp = Id. LambdaExp = “(lambda” “(“ Id Exp “)”. AppExp = “(“ Exp Exp “)”. Test = LambdaExp AppExp. Each non-terminal defines a data type.

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

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)