Lecture 5 Lazy Scheme Thunking about Thunks CS655 Programming Languages University of Virginia David Evans Computer Science http www cs virginia edu evans Menu Finish Mini Scheme Interpreter Changing Language Semantics 1 Feb 2001 CS 655 Lecture 5 2 Last Time Mini Scheme define apply proc operand env bind variable car car cdr proc operand extend environment env define eval expr env if number expr expr if symbol expr lookup variable value expr env if and list expr eq car expr lambda list procedure car cdr expr car cdr cdr expr apply eval car expr env eval car cdr expr env env 1 Feb 2001 CS 655 Lecture 5 3 Handling Primitives represented by primitive func define apply proc operand env if eq car proc primitive car cdr proc operand same as before 1 Feb 2001 CS 655 Lecture 5 4 Handling Primitives Eval define eval expr env if or number expr and list expr eq car expr primitive expr rest is same 1 Feb 2001 CS 655 Lecture 5 5 Primitives Environment define global env bind variable minus list primitive bind variable inc list primitive lambda x x 1 1 Feb 2001 CS 655 Lecture 5 6 Mini Scheme Examples eval minus 3 global env 3 eval lambda x inc x 3 global env 4 1 Feb 2001 CS 655 Lecture 5 7 An Entire Mini Scheme Interpreter define apply proc operand env if eq car proc primitive car cdr proc operand eval car cdr cdr proc bind variable car car cdr proc operand extend environment env define eval expr env if or number expr and list expr eq car expr primitive expr if symbol expr lookup variable value expr env if and list expr eq car expr lambda list procedure car cdr expr car cdr cdr expr apply eval car expr env eval car cdr expr env env 1 Feb 2001 CS 655 Lecture 5 8 All Programs are Really Language Implementations Recall our definition of a language Lecture 1 A description of pairs S M where S stands for sound or any kind of surface forms and M stands for meaning A theory of language must specify the properties of S and M and how they are related 1 Feb 2001 CS 655 Lecture 5 9 What is a Language Implementation A description of pairs S M where S stands for sound or any kind of surface forms and M stands for meaning A theory of language must specify the properties of S and M and how they are related An implementation of a language is a function from S to M 1 Feb 2001 CS 655 Lecture 5 10 Examples of Language Implementations Our Mini Scheme Interpreter eval S expression environment M value number procedure eval S M 1 Feb 2001 CS 655 Lecture 5 11 Language Implementations Mystery Language Implementation S HTML x user input M pixels on screen x user input HTTP Web Browser S M Mystery Language Implementation S user input x network input M pixels on screen x network output Doom S M 1 Feb 2001 CS 655 Lecture 5 12 Language Implementations My Gyromouse S physical gestures in space x mouse clicks M Windows events Gyromouse and software S M 1 Feb 2001 CS 655 Lecture 5 13 Changing Languages Change S Allow new surface forms new surface forms map to the old surface forms and then to the old meanings Gyromouse without its software is just a new surface form for the regular mouse Change M Change the meaning of surface forms Gyromouse recognizes special gestures and assigns them meanings not available using regular mouse 1 Feb 2001 CS 655 Lecture 5 14 Scheme Evaluation 1 To evaluate a compound expression evaluate the subexpressions then apply the value of the first subexpression to the values of the other subexpressions 2 To apply a procedure to a list of arguments evaluate the procedure in a new environment that binds the formal parameters of the procedure to the arguments it is applied to 1 Feb 2001 CS 655 Lecture 5 15 Evaluation Order Applicative Order Eager Evaluation Procedure operands are evaluated when the procedure is applied To evaluate a compound expression evaluate the subexpressions Normal Order Lazy Evaluation Evaluate and expression only when you really need its value 1 Feb 2001 CS 655 Lecture 5 16 Laziness can save work Eager Evaluation Applicative Read all assignments as soon as they are assigned Lazy Evaluation Normal Read something only when you absolutely need it to do the problem set Lazy Evaluation requires less total work since some reading assignments may not be necessary to do problem set but is not recommended for students in this class 1 Feb 2001 CS 655 Lecture 5 17 Laziness Can Be Useful define p x p x define f x 3 f p 6 Eager no value does infinite work Lazy 3 never needs to evaluate p 6 1 Feb 2001 CS 655 Lecture 5 18 Lazy Scheme Evaluation 1 To evaluate a compound expression evaluate the first subexpression then apply the value of the first subexpression to the other subexpressions 2 To apply a procedure to a list of arguments evaluate the procedure in a new environment that binds the formal parameters of the procedure to the arguments it is applied to Evaluate an argument when its value is really needed 1 Feb 2001 CS 655 Lecture 5 19 Really Needed The value of an expression is really needed when It is passed to a primitive procedure Primitive procedures are strict It needs to be printed for human Until then we just need something called a thunk we can evaluate when necessary to produce the value we would have gotten if we evaluated it at first application 1 Feb 2001 CS 655 Lecture 5 20 Lazy Eval define eval expr env if or number expr define make thunk exp env list thunk exp env and list expr eq car expr primitive expr if symbol expr lookup variable value expr env if and list expr eq car expr lambda list procedure car cdr expr car cdr cdr expr apply eval car expr env make thunk car cdr expr env env was eval before 1 Feb 2001 CS 655 Lecture 5 21 Unthunking define apply proc operand env if eq car proc primitive force eval operand env car cdr proc operand eval car cdr cdr proc bind variable car car cdr proc operand extend environment env 1 Feb 2001 CS 655 Lecture 5 22 Unthunking define force eval expr env if or number expr has tag expr primitive expr if has tag expr thunk force eval cadr expr caddr expr if symbol expr force eval lookup variable value expr env env if has tag expr lambda list procedure car cdr expr car cdr cdr expr force eval apply force eval car expr env make thunk car cdr expr env env 1 Feb 2001 CS 655 Lecture 5 23 Some Handy Definitions The world s most commonly written function define nt x nt x nt the non terminating function Global environment define global env bind variable minus list primitive bind variable nt list primitive nt 1 Feb 2001 CS …