Math 409 Examination 2 March 30, 2000 1. Define each of the
... 2. State and prove either the mean value theorem or Taylor’s theorem. 3. (a) State the definition of the derivative f 0 (x) in terms of a limit. (b) Use this definition to derive the product rule: namely, if f and g are differentiable functions, then (f g)0 = f 0 g + g 0 f . n−1 X ...
... 2. State and prove either the mean value theorem or Taylor’s theorem. 3. (a) State the definition of the derivative f 0 (x) in terms of a limit. (b) Use this definition to derive the product rule: namely, if f and g are differentiable functions, then (f g)0 = f 0 g + g 0 f . n−1 X ...
Lambda Calculus and Lisp
... More CAR and CDR The general form is: CxxxR where you can have any number of x's (at least one) and each x is A or D signifying CAR or CDR. The order of the A's and D's indicates the order of CAR's and CDR's in the expression. Thus, (CDAR x) (CDR( CAR x)) (CADDR x) (CAR( CDR( CDR x)) ) What is ...
... More CAR and CDR The general form is: CxxxR where you can have any number of x's (at least one) and each x is A or D signifying CAR or CDR. The order of the A's and D's indicates the order of CAR's and CDR's in the expression. Thus, (CDAR x) (CDR( CAR x)) (CADDR x) (CAR( CDR( CDR x)) ) What is ...
Solution
... NCAAPMT Calculus Challenge Problem #10 SOLUTION For each of the functions below, use the information about the function to determine its equation. ...
... NCAAPMT Calculus Challenge Problem #10 SOLUTION For each of the functions below, use the information about the function to determine its equation. ...
Problem 1 - IDA.LiU.se
... the code should conform to conventions, and the reader should - with some thought - be able to follow the logic of the program. This both in terms of the procedure bodies (within the lambda) and the names themselves. A good rule of thumb in cases like this is to let the name follow the return value, ...
... the code should conform to conventions, and the reader should - with some thought - be able to follow the logic of the program. This both in terms of the procedure bodies (within the lambda) and the names themselves. A good rule of thumb in cases like this is to let the name follow the return value, ...
function
... occurrences in M, then the term M[N/x] is formed by replacing all free occurrences of x in M by N. 2. Otherwise, assume that the variable y is free in N and bound in M. Consistently replace the binding and the corresponding bound occurrences of y in M by a new variable (say u). Repeat renaming bound ...
... occurrences in M, then the term M[N/x] is formed by replacing all free occurrences of x in M by N. 2. Otherwise, assume that the variable y is free in N and bound in M. Consistently replace the binding and the corresponding bound occurrences of y in M by a new variable (say u). Repeat renaming bound ...
PPT
... Formal system with three parts • Notation for function expressions • Proof system for equations • Calculation rules called reduction ...
... Formal system with three parts • Notation for function expressions • Proof system for equations • Calculation rules called reduction ...
Notes
... be many types t for which this holds; the type inferencer we discussed last class will infer the most lenient type for t possible. Likewise, the evaluation rules (using closures) are what you’d expect: • Variable x evaluates to whatever value is bound to x in the current dynamic environment. (Again, ...
... be many types t for which this holds; the type inferencer we discussed last class will infer the most lenient type for t possible. Likewise, the evaluation rules (using closures) are what you’d expect: • Variable x evaluates to whatever value is bound to x in the current dynamic environment. (Again, ...
LambdaCalculus
... 20. Lambda Calculus Handout Exercise 1. 21. Lambda Calculus Handout Exercise 2. 22. Lambda Calculus Handout Exercise 5. 23. Lambda Calculus Handout Exercise 6. ...
... 20. Lambda Calculus Handout Exercise 1. 21. Lambda Calculus Handout Exercise 2. 22. Lambda Calculus Handout Exercise 5. 23. Lambda Calculus Handout Exercise 6. ...
Lambda λ Calculus
... Lambda Calculus Struggles with normal typed functions if a function is type N→N, you can’t determine the lambda-term structure due to passing it only n’s ○ This is referred to as lambda is unable to realize f:N→N However, Lambda Calculus performs well with higher typed functions ● Realizability infe ...
... Lambda Calculus Struggles with normal typed functions if a function is type N→N, you can’t determine the lambda-term structure due to passing it only n’s ○ This is referred to as lambda is unable to realize f:N→N However, Lambda Calculus performs well with higher typed functions ● Realizability infe ...
Functional Programming and the Lambda Calculus
... The leftmost redex is the one whose λ is to the left of all other redexes. You can guess which is the rightmost. The outermost redex is not contained in any other. The innermost redex does not contain any other. For (λx . λy . y) ( (λz . z z) (λz . z z) ), ...
... The leftmost redex is the one whose λ is to the left of all other redexes. You can guess which is the rightmost. The outermost redex is not contained in any other. The innermost redex does not contain any other. For (λx . λy . y) ( (λz . z z) (λz . z z) ), ...