Inductively Defined Data Concrete and Abstract syntax

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Inductively Defined DataConcrete and Abstract
syntax

• Karl Lieberherr

2
Dont 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)
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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)
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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)
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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 ))))))

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Exercises for define-datatype

• Arithmetic expressions ( ( 3 5) 7)
• two arguments only
• include evaluator
• Nested containers

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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
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 (
ltidgt Id ltbodygt Exp ). AppExp ( ltratorgt Exp
ltrandgt Exp ). Test ltfirstgt LambdaExp ltsecondgt
AppExp. Each non-terminal defines a data type.
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Concern analysis

• (define (check ac)
• (local ( Container -gt 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 (gt witems (Container-capacity
  ac))
• (set! violations ( 1
  violations)))
• witems))
• (Listof Item) -gt Number
• the weight of a list of items
• (define (weight-loi l)
• (foldr 0 (map weight-item l)))
• Item -gt Number
• the weight of an item
• (define (weight-item l)
• (cond
• (Simple? l) (Simple-weight l)
• (Container? l) (weight-container
  l)))

Concerns traversal summing weights summing
violations
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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)