Procedures EOPL3: Section 3.3 PROC and App B: SLLGEN
The PROC language Expression ::= proc (Identifier) Expression AST: proc-exp (var body) Expression ::= (Expression Expression) AST: call-exp (rator rand) PROC includes all of LET language Anonymous procedure One parameter always CS7100(pm) 2
Semantics of Procedures (This slide is for procedures in general.) Procedure Definition Store formal parameters and body Procedure Invocation Evaluate body in an environment that binds formals to actual argument values Interpretation of free-variables: Two methods Use env at proc definition (lexical/static scoping) Use env at proc call (dynamic scoping) CS7100(pm) 3
Scoping and Binding references (f x y) f, x, and y declarations (lambda (x) (+ x 3)) (let ((x (+ y 7))) (+ x 3)) y, and second/right x are refs first/left x is a declaration lexical scoping rules CS7100(pm) 4
Kinds of Scope Static or Lexical scope determined by structure of program Scheme, C++, Java, and many compiled languages Dynamic scope determined by path of execution Lisp dialects, Perl, and many interpreted languages Global Scope File scope Local Scope Block Body of a procedure Body of a loop Scope alters the meaning CS7100(pm) 5
Example-1 of PROC let f = proc (x) --(x,11) in (f (f 77)) Defines an anonymous procedure with one formal parameter named x. Body of the procedure: --(x,11) Binds the name f to this procedure. Invokes f with actual argument 77. Invokes f again with the result of above. (will use two -- just for visibility) CS7100(pm) 6
Example-2 of PROC (proc (f) (f (f 77)) proc (x) --(x,11)) This example is derived from the production Expression ::= (Expression Expression) so is (f (f 77)) so is (f 77) proc (f) (f (f 77)) is the rator. It defines an anonymous procedure with one formal parameter named f. proc (x) --(x,11)) is the rand. It also defines an anonymous procedure with one formal parameter named x. CS7100(pm) 7
Example-3 of PROC let x = 200 in let f = proc (z) --(z, x) in let x = 100 in let g = proc (z) --(z, x) in --((f 1), (g 1)) Illustrates scope issues x and z appear four times each. Lexical scoping In --((f 1), (g 1)), the bodies of f and g must be evaluated in the env they were defined. In f, x is bound to 200 In g, x is bound to 100 CS7100(pm) 8
Example Programs of PROC Example-1 and -2 produce same result, but different mechanisms. Previous two slides gave semantics informally Watch out: a very seductive approach Next few slides: interpreter based CS7100(pm) 9
Example Calc w/ Spec 1 CS7100(pm) 10
Example Calc w/ Spec 2 CS7100(pm) 11
Example Calc w/ Spec 3 CS7100(pm) 12
Example Calc w/ Spec 4 CS7100(pm) 13
Recall value-of value-of is an operator with two operands an AST an environment (value-of ast env) PROC = LET + two more productions Bring in all value-of specs from LET Additions are shown on next few slides CS7100(pm) 14
additional value-of specs (value-of (proc-exp var body) ρ) = (proc-val (procedure var body ρ)) (value-of (call-exp rator rand) ρ) = (let ( (proc (expval->proc (value-of rator ρ))) (arg (value-of rand ρ))) (apply-procedure proc arg)) To be defined: proc-val, apply-procedure CS7100(pm) 15
Spec of apply-procedure (apply-procedure (procedure var body ρ) val) = (value-of body [var=val]ρ ) apply-procedure takes two arguments: an AST of a procedure definition an argument for the parameter of the procedure yields an expressed value CS7100(pm) 16
Impl of apply-procedure (define proc? (lambda (pc) (procedure? pc))) (define procedure (lambda (var body env) (lambda (val) (value-of body (extend-env var val (define apply-procedure (lambda (pc val) (pc val))) env))))) procedure? provided from r5rs Names being bound: proc? procedure apply-procedure env is an environment ASTs: body, pc, val, var Use of procedure? is too liberal. procedure is not self-contained; takes three arguments: param name var body AST environment CS7100(pm) 17
Alternate impl called Closures (define-datatype proc proc? (procedure (var identifier?) (body expression?) (saved-env environment?))) (define apply-procedure (lambda (pc val) (cases proc pc (procedure (var body saved-env) (value-of body (extend-env var val saved-env)))))) Defining a new data type called proc Has only one variant procedure That has three parts var which must be an id body an expression saved-env an environment apply-procedure takes pc and val. cases proc pc pc is expected to be of type proc code for each variant of proc only one variant procedure here CS7100(pm) 18
the data type expval is now (define-datatype expval expval? (num-val (num number?)) (bool-val (bool boolean?)) (proc-val (proc proc?))) CS7100(pm) 19
value-of: two new clauses (proc-exp (var body) (proc-val (procedure var body env))) (call-exp (rator rand) (let ( (proc (expval->proc (value-of rator env))) (arg (value-of rand env))) (apply-procedure proc arg))) CS7100(pm) 20
Curried procedures In PROC, procedures with multiple arguments can be had as in: let f = proc (x) proc (y)... in ((f 3) 4) proc (x) yields a procedure Named after Haskell Brooks Curry (1900 1982), a combinatory logician. CS7100(pm) 21
chapter3/proc-lang/ Two subdirectories chapter3/proc-lang/proc-rep: procedural implementation chapter3/proc-lang/ds-rep: data type based (i.e., closure) Both directories have the following files data-structures.scm drscheme-init.scm environments.scm interp.scm lang.scm tests.scm top.scm CS7100(pm) 22
EOPL3 Appendix B SLLGEN (define scanner-spec-1...) (define grammar-1...) (sllgen:make-define-datatypes scanner-spec-1 grammar-1) (define list-the-datatypes (lambda () (sllgen:list-define-datatypes scanner-spec-1 grammar-1))) (define just-scan (sllgen:make-string-scanner scannerspec-1 grammar-1)) (define scan&parse (sllgen:make-string-parser scannerspec-1 grammar-1)) (define read-eval-print (sllgen:make-rep-loop "--> " valueof--program (sllgen:make-stream-parser scannerspec-1 grammar-1))) sllgen:make-definedatatypes: generates a define-datatype for each production of the grammar, for use by cases. sllgen:make-string-scanner takes a scanner spec and a grammar and generates a scanning procedure read-eval-print loop CS7100(pm) 23
Lexical Analysis (define the-lexical-spec '((whitespace (whitespace) skip) (comment ("%" (arbno (not #\newline))) skip) (identifier (letter (arbno (or letter digit "_" "-" "?"))) symbol) (number (digit (arbno digit)) number) (number ("-" digit (arbno digit)) number) )) the-lexical-spec from chapter3/ proc-lang/*/lang.scm scanners are specified by reg exp next slide All our languages use this lexical analysis. CS7100(pm) 24
SLLGEN Scanner Spec Scanner-spec ::= ({Regexp-and-action} ) Regexp-and-action ::= (Name ({Regexp} ) Action) Name ::= Symbol Regexp ::= String letter digit whitespace any ::= (not Character) (or {Regexp} ) ::= (arbno Regexp) (concat {Regexp} ) Action ::= skip symbol number string A scanner specification in SLLGEN is a list that satisfies the grammar at left CS7100(pm) 25
The SLLGEN Parsing System (define the-grammar '((program (expression) a-program) (expression (number) const-exp) (expression ("-" "(" expression "," expression ")") diff-exp) (expression ("zero?" "(" expression ")") zero?-exp) (expression ("if" expression "then" expression "else" expression) if-exp) (expression (identifier) var-exp) (expression ("let" identifier "=" expression "in" expression) let-exp) the-grammar of PROC from chapter3/ proc-lang/*/lang.scm Double-quoted items are terminals/tokens. (expression ("proc" "(" identifier ")" expression) proc-exp) (expression ("(" expression expression ")") call-exp) )) CS7100(pm) 26
Specifying Grammars Grammar ::= ({Production} ) Production ::= (Lhs ({Ritem} ) Prodname) Lhs ::= Symbol Ritem ::= Symbol String ::= (arbno {Ritem} ) ::= (separated-list {Ritem} String) Prod-name ::= Symbol A grammar in SLLGEN is a list described by the grammar at left CS7100(pm) 27
HW2 Problem (define closure (lambda (ids body env) (let ((freevars (set-diff (free-vars body) ids))) (let ((saved-env (extend-env freevars (map (lambda (v) freevars) (empty-env)))) (lambda (args) (eval-expression body (extend-env ids args saved-env))))))) (apply-env env v)) http://www.cs.wright.edu/~pmateti/cour ses/7100/top/7100-hw2.html In our data-structure representation of procedures, we have kept the entire environment in the closure. But of course all we need are the bindings for the free variables. Modify the representation of procedures to retain only the free variables. flat closure rep shown left consists of exactly one rib of free variables and their values. free-vars: ykwim ;-) set-diff: difference of two sets map provided from r5rs CS7100(pm) 28