1 Subt. model interpreter: Introduction Abstract Syntax Parser Abstract Syntax Parser Derived Expressions Core Test Data Structures Utils (a racket lib) Global Env. Evaluator values Substitution Op. semantics Special forms ADT per expression An abstraction barrier, used by all evaluators Components of the interpreter:

2 Subt. model interpreter: Tests Tests package: Should be run with every modification! The procedure test: Receives a single expression, e, and an expected value, v. Returns #t if and only if e evaluates to v. The procedure run-tests: Runs multiple number test expressions (test (derive-eval ‘(* 3 4)) => ‘(value 12)) (run-tests (test (derive-eval ‘(+ 3 4)) => ‘(value 7)) (test (derive-eval ‘(- 3 4)) => ‘(value -1)) (test (derive-eval ‘(/ 4 2)) => ‘(value 2))) (run-tests (test (derive-eval ‘(+ 3 4)) => ‘(value 7)) (test (derive-eval ‘(- 3 4)) => ‘(value -1)) (test (derive-eval ‘(/ 4 2)) => ‘(value 2)))

3 applicative -eval apply- procedure (define applicative-eval (lambda (exp) (cond ((atomic? exp) (eval-atomic exp)) ((special-form? exp) (eval-special-form exp)) ((evaluator-value? exp) exp) ((application? exp) (let ((renamed-exp (rename exp))) (apply-procedure (applicative-eval (operator renamed-exp)) (list-of-values (operands renamed-exp))))) (else (error 'eval "unknown expression type: ~s" exp))))) (define applicative-eval (lambda (exp) (cond ((atomic? exp) (eval-atomic exp)) ((special-form? exp) (eval-special-form exp)) ((evaluator-value? exp) exp) ((application? exp) (let ((renamed-exp (rename exp))) (apply-procedure (applicative-eval (operator renamed-exp)) (list-of-values (operands renamed-exp))))) (else (error 'eval "unknown expression type: ~s" exp))))) (define apply-procedure (lambda (procedure arguments) (cond ((primitive-procedure? procedure) (apply-primitive-procedure procedure arguments)) ((compound-procedure? procedure) (let ((parameters (procedure-parameters procedure)) (body (rename (procedure-body procedure)))) (eval-sequence (substitute body parameters arguments)))) (else (error 'apply "Unknown procedure type: ~s" procedure))))) (define apply-procedure (lambda (procedure arguments) (cond ((primitive-procedure? procedure) (apply-primitive-procedure procedure arguments)) ((compound-procedure? procedure) (let ((parameters (procedure-parameters procedure)) (body (rename (procedure-body procedure)))) (eval-sequence (substitute body parameters arguments)))) (else (error 'apply "Unknown procedure type: ~s" procedure))))) Subt. model interpreter: Core Core main-loop:

4 1.( (lambda(x) 2. (lambda(y) (y x))) 3. (lambda(x) (+ x y)) ) 1.( (lambda(x) 2. (lambda(y) (y x))) 3. (lambda(x) (+ x y)) ) Subt. model interpreter: Core The problem: (lambda(y) (y (lambda(x) (+ x y)))) (lambda(y) (y (lambda(x) (+ x y)))) y in line 2 is bound. y in line 3 is free. The free occurrence of y is now bound by the formal parameter. 1.( (lambda(x) 2. (lambda(y1) (y1 x))) 3. (lambda(x) (+ x y)) ) 1.( (lambda(x) 2. (lambda(y1) (y1 x))) 3. (lambda(x) (+ x y)) ) (lambda(y1) (y1 (lambda(x) (+ x y)))) (lambda(y1) (y1 (lambda(x) (+ x y)))) The solution: consistently rename bound occurrences and their binding instances: A reminder: Why do we need renaming?

5 Subt. model interpreter: Supporting case expressions 5 (define fib (lambda (n) (case n (0 0) (1 1) (else (+ (fib (- n 1)) (fib (- n 2))))))) (define fib (lambda (n) (case n (0 0) (1 1) (else (+ (fib (- n 1)) (fib (- n 2))))))) Example of using a case expression: control clauses last clause What are the components of a case expressions? What are the components of a case-clause? ASP Derived expressions Core Data structures compared actions

(define eval-special-form (lambda (exp) (cond ((quoted? exp) (make-value exp)) ((lambda? exp) (eval-lambda exp)) ((definition? exp) (eval-definition exp)) ((if? exp) (eval-if exp)) ((begin? exp) (eval-begin exp)) ((case? exp) (eval-case exp))))) (define eval-special-form (lambda (exp) (cond ((quoted? exp) (make-value exp)) ((lambda? exp) (eval-lambda exp)) ((definition? exp) (eval-definition exp)) ((if? exp) (eval-if exp)) ((begin? exp) (eval-begin exp)) ((case? exp) (eval-case exp))))) 6 Subt. model interpreter: Core - Special Forms Supporting case as a special form Step 1: call the appropriate special evaluation procedure (define special-form? (lambda (exp) (or (quoted? exp) (lambda? exp) (definition? exp) (if? exp) (begin? exp) (case? exp)))) (define special-form? (lambda (exp) (or (quoted? exp) (lambda? exp) (definition? exp) (if? exp) (begin? exp) (case? exp)))) Step 2: Identify the expression as a special form ASP Derived expressions Core Data structures

Determining the evaluation rule for a case expression: 1.Evaluate the control. 2.Compare its value to each of the compared components by order (assume numerical values). 3.Evaluate the actions of the first clause in which the compared value equals the control value. 4.If no such clause exists, evaluate the actions of the else-clause by order. 7 Subt. model interpreter: Core - Special Forms Supporting case as a special form (define fib (lambda (n) (case n (0 0) (1 1) (else (+ (fib (- n 1)) (fib (- n 2)…) (define fib (lambda (n) (case n (0 0) (1 1) (else (+ (fib (- n 1)) (fib (- n 2)…) Step 3: Write the relevant special evaluation procedure

8 Subt. model interpreter: Core - Special Forms Supporting case as a special form (define fib (lambda (n) (case n (0 0) (1 1) (else (+ (fib (- n 1)) (fib (- n 2)…) (define fib (lambda (n) (case n (0 0) (1 1) (else (+ (fib (- n 1)) (fib (- n 2)…) Step 3: Write the relevant special evaluation procedure (define (eval-case exp) (letrec ((eval-clauses (lambda (control clauses) (cond ((null? clauses) 'unspecified) ((or (case-last-clause? clauses) (= (applicative-eval (case-compared (case-first-clause clauses))) control)) (eval-sequence (case-actions (case-first-clause clauses)))) (else (eval-clauses control (case-rest-clauses clauses))))))) (eval-clauses (applicative-eval (case-control exp)) (case-clauses exp)))) (define (eval-case exp) (letrec ((eval-clauses (lambda (control clauses) (cond ((null? clauses) 'unspecified) ((or (case-last-clause? clauses) (= (applicative-eval (case-compared (case-first-clause clauses))) control)) (eval-sequence (case-actions (case-first-clause clauses)))) (else (eval-clauses control (case-rest-clauses clauses))))))) (eval-clauses (applicative-eval (case-control exp)) (case-clauses exp))))

9 Subt. model interpreter: ASP - Handling lambda expressions 9 ; Signature: make-lambda(parameters, body) ; Type: [LIST(Symbol)*LIST -> LIST] ; Signature: make-lambda(parameters, body) ; Type: [LIST(Symbol)*LIST -> LIST] ; Signature: lambda-parameters(exp) ; Type: [LIST -> LIST(Symbol)] ; Signature: lambda-parameters(exp) ; Type: [LIST -> LIST(Symbol)] ; Signature: lambda-body(exp) ; Type: [LIST -> LIST] ; Signature: lambda-body(exp) ; Type: [LIST -> LIST] ; Signature: lambda?(exp) ; Type: [T -> Boolean] ; Signature: lambda?(exp) ; Type: [T -> Boolean] ADT and implementation : ; Signature: make-lambda(parameters, body) ; Type: [LIST(Symbol)*LIST -> LIST] (define make-lambda (lambda (parameters body) (attach-tag (cons parameters body) 'lambda))) ; Signature: make-lambda(parameters, body) ; Type: [LIST(Symbol)*LIST -> LIST] (define make-lambda (lambda (parameters body) (attach-tag (cons parameters body) 'lambda))) ; Signature: lambda-parameters(exp) ; Type: [LIST -> LIST(Symbol)] (define lambda-parameters (lambda (exp) (car (get-content exp)))) ; Signature: lambda-parameters(exp) ; Type: [LIST -> LIST(Symbol)] (define lambda-parameters (lambda (exp) (car (get-content exp)))) ; Signature: lambda-body(exp) ; Type: [LIST -> LIST] (define lambda-body (lambda (exp) (cdr (get-content exp)))) ; Signature: lambda-body(exp) ; Type: [LIST -> LIST] (define lambda-body (lambda (exp) (cdr (get-content exp)))) ; Signature: lambda?(exp) ; Type: [T -> Boolean] (define lambda? (lambda (exp) (tagged-by? exp 'lambda))) ; Signature: lambda?(exp) ; Type: [T -> Boolean] (define lambda? (lambda (exp) (tagged-by? exp 'lambda))) ASP Derived expressions Core Data structures

10 Subt. model interpreter: Supporting case expressions 10 ADT for case expressions (including ADT for case-clause): make-case(control case-clauses) Type: [Symbol*LIST->Case-expression] make-case(control case-clauses) Type: [Symbol*LIST->Case-expression] Constructor for case case?(exp) Type: [T -> Boolean] case?(exp) Type: [T -> Boolean] Predicate case-clauses(case-exp) Type: [LIST -> LIST] case-clauses(case-exp) Type: [LIST -> LIST] case-control(case-exp) Type: [LIST -> Symbol] case-control(case-exp) Type: [LIST -> Symbol] Selectors make-case-clause(compared actions) Type: [T*LIST -> LIST] make-case-clause(compared actions) Type: [T*LIST -> LIST] Constructor for case-clause case-last-clause? Predicate case-actions case-compared Selectors case-first-clause case-rest-clauses Example of use (client side): (make-case 'n (list (make-case-clause '0 '(0)) (make-case-clause '1 '(1)) (make-case-clause 'else '(+ (fib (- n 1)) (fib (– n 2)))))) (make-case 'n (list (make-case-clause '0 '(0)) (make-case-clause '1 '(1)) (make-case-clause 'else '(+ (fib (- n 1)) (fib (– n 2))))))

(define case? (lambda (exp) (tagged-by? exp 'case))) (define case? (lambda (exp) (tagged-by? exp 'case))) (define make-case-clause (lambda (compared actions) (cons compared actions))) (define make-case-clause (lambda (compared actions) (cons compared actions))) (define make-case (lambda (control case-clauses) (attach-tag (cons control case-clauses) 'case))) (define make-case (lambda (control case-clauses) (attach-tag (cons control case-clauses) 'case))) (define case-control (lambda (case-exp) (car (get-content case-exp)))) (define case-control (lambda (case-exp) (car (get-content case-exp)))) (define case-clauses (lambda (case-exp) (cdr (get-content case-exp)))) (define case-clauses (lambda (case-exp) (cdr (get-content case-exp)))) (define case-compared car) (define case-actions cdr) (define case-first-clause (lambda (clauses) (car clauses))) (define case-first-clause (lambda (clauses) (car clauses))) (define case-rest-clauses (lambda (clauses) (cdr clauses))) (define case-rest-clauses (lambda (clauses) (cdr clauses))) (define case-last-clause? (lambda (clauses) (and (null? (cdr clauses)) (eq? (case-compared (case-first-clause clauses)) 'else)))) (define case-last-clause? (lambda (clauses) (and (null? (cdr clauses)) (eq? (case-compared (case-first-clause clauses)) 'else)))) 11 Adding the implementation in the ASP: Subt. model interpreter: Supporting case expressions Constructor Selectors Predicate

12 Subt. model interpreter: Derived expressions ASP Derived expressions Core Data structures shallow- derive derive Recursively applies shallow-derive derived? How? 1.Edit derive? to consider the new exp as derived. 2.Edit shallow-derive to call the relevant translation procedure. 3.Add a shallow translation procedure. Identifies the derived expression, calls the appropriate shallow translation procedure: ((cond? exp) (cond->if exp)) ⁞ ((let? exp) (let->combination exp)) Why? Smaller, simpler core! (let ((x 1)) x)  ((lambda(x) x) 1)

13 (define derive (lambda (exp) (if (atomic? exp) exp (let ((derived-exp (let ((mapped-derive-exp (map derive exp))) (if (not (derived? exp)) mapped-derive-exp (shallow-derive mapped-derive-exp))))) (if (equal? exp derived-exp) exp (derive derived-exp)))))) (define derive (lambda (exp) (if (atomic? exp) exp (let ((derived-exp (let ((mapped-derive-exp (map derive exp))) (if (not (derived? exp)) mapped-derive-exp (shallow-derive mapped-derive-exp))))) (if (equal? exp derived-exp) exp (derive derived-exp)))))) Subt. model interpreter: Derived expressions (define derived? (lambda (exp) (or (cond? exp) (function-definition? exp) (let? exp) (letrec? exp)))) (define derived? (lambda (exp) (or (cond? exp) (function-definition? exp) (let? exp) (letrec? exp)))) (define shallow-derive (lambda (exp) (cond ((cond? exp) (cond->if exp)) ((function-definition? exp) (function-define->define exp)) ((let? exp) (let->combination exp)) ((letrec? exp) (letrec->let exp)) (else "Unhandled derivision" exp)))) (define shallow-derive (lambda (exp) (cond ((cond? exp) (cond->if exp)) ((function-definition? exp) (function-define->define exp)) ((let? exp) (let->combination exp)) ((letrec? exp) (letrec->let exp)) (else "Unhandled derivision" exp)))) ASP Derived expressions Core Data structures

14 Subt. model interpreter: Derived expressions ASP Derived expressions Core Data structures 1.Edit derive? to consider the new exp as derived. 2.Edit shallow-derive to call the relevant translation procedure. 3.Add a shallow translation procedure.

15 Subt. model interpreter: Data Structures ASP Derived expressions Core Data structures The Global Environment: (define make-the-global-environment (lambda () (let* ((primitive-procedures (list (list 'car car) (list 'cdr cdr) (list 'cons cons) (list 'null? null?) (list '+ +) (list '* *) (list '/ /) (list '> >) (list '< <) (list '- -) (list '= =) (list 'list list) (list 'append append) )) (prim-variables (map car primitive-procedures)) (prim-values (map (lambda (x) (make-primitive-procedure (cadr x))) primitive-procedures)) ) (make-sub prim-variables prim-values)))) (define make-the-global-environment (lambda () (let* ((primitive-procedures (list (list 'car car) (list 'cdr cdr) (list 'cons cons) (list 'null? null?) (list '+ +) (list '* *) (list '/ /) (list '> >) (list '< <) (list '- -) (list '= =) (list 'list list) (list 'append append) )) (prim-variables (map car primitive-procedures)) (prim-values (map (lambda (x) (make-primitive-procedure (cadr x))) primitive-procedures)) ) (make-sub prim-variables prim-values))))