Chapter 14a - McGraw Hill Higher Education
... In pure lambda calculus, expressions like (( x . x2)5) = 52 are uninterpreted. In a functional language, (( x . x2)5) is interpreted normally (25). ...
... In pure lambda calculus, expressions like (( x . x2)5) = 52 are uninterpreted. In a functional language, (( x . x2)5) is interpreted normally (25). ...
The Lambda Calculus: a minimal ML?
... Let’s review the history of Church’s lambda calculus briefly.3 Its ideas first came from logicians who wanted to study functions more carefully. For example, Frege (1893) noticed that it suffices to consider functions of single arguments. Take for example the addition function that takes A and B and r ...
... Let’s review the history of Church’s lambda calculus briefly.3 Its ideas first came from logicians who wanted to study functions more carefully. For example, Frege (1893) noticed that it suffices to consider functions of single arguments. Take for example the addition function that takes A and B and r ...
pl10ch15 - ODU Computer Science
... – An ML function that takes more than one parameter can be defined in curried form by leaving out the commas in the parameters fun add a b = a + b; A function with one parameter, a. Returns a function that takes b as a parameter. Call: add 3 5; Copyright © 2012 Addison-Wesley. All rights reserved. ...
... – An ML function that takes more than one parameter can be defined in curried form by leaving out the commas in the parameters fun add a b = a + b; A function with one parameter, a. Returns a function that takes b as a parameter. Call: add 3 5; Copyright © 2012 Addison-Wesley. All rights reserved. ...
Chapter 11 slides
... well-defined, so applicative order can be used • A non-strict language does not require all arguments to be well-defined; it requires normal-order evaluation ...
... well-defined, so applicative order can be used • A non-strict language does not require all arguments to be well-defined; it requires normal-order evaluation ...
LN10
... Function type 18.1 The function type a->b (“Haskell is strongly typed” – PDG’s notes, p.7) Objects of type a->b are constructed by lambda abstraction \x->e and used in function application f e’. Lambda abstraction: if e has type b and x is a variable of type a then \x->e has type a->b Function appl ...
... Function type 18.1 The function type a->b (“Haskell is strongly typed” – PDG’s notes, p.7) Objects of type a->b are constructed by lambda abstraction \x->e and used in function application f e’. Lambda abstraction: if e has type b and x is a variable of type a then \x->e has type a->b Function appl ...
Chapter 15 Functional Programming
... Free variables are like globals and bound variables are like locals. Free variables can be defined as: ...
... Free variables are like globals and bound variables are like locals. Free variables can be defined as: ...
Defining Functions
... z x:xs patterns must be parenthesised, because application has priority over (:). For example, the following definition gives an error: head x:_ = x ...
... z x:xs patterns must be parenthesised, because application has priority over (:). For example, the following definition gives an error: head x:_ = x ...
Ch1516rev
... A static-scoped functional language with syntax that is closer to Pascal than to LISP Uses type declarations, but also does type inferencing to determine the types of undeclared variables (will see in Chapter 5) It is strongly typed (whereas Scheme is essentially typeless) and has no type coer ...
... A static-scoped functional language with syntax that is closer to Pascal than to LISP Uses type declarations, but also does type inferencing to determine the types of undeclared variables (will see in Chapter 5) It is strongly typed (whereas Scheme is essentially typeless) and has no type coer ...
Chapter 1
... A static-scoped functional language with syntax that is closer to Pascal than to LISP Uses type declarations, but also does type inferencing to determine the types of undeclared variables (will see in Chapter 5) It is strongly typed (whereas Scheme is essentially typeless) and has no type coer ...
... A static-scoped functional language with syntax that is closer to Pascal than to LISP Uses type declarations, but also does type inferencing to determine the types of undeclared variables (will see in Chapter 5) It is strongly typed (whereas Scheme is essentially typeless) and has no type coer ...
19. Introduction to evaluation order
... or not the two expressions are considered as being equal. As noticed in Section 4.5 there are a number of different interpretations of equality around in Scheme, as well as in other programming languages. As we observe in the items below, we can use even the weakest form of equality, namely structur ...
... or not the two expressions are considered as being equal. As noticed in Section 4.5 there are a number of different interpretations of equality around in Scheme, as well as in other programming languages. As we observe in the items below, we can use even the weakest form of equality, namely structur ...
slides 4-up
... however: we cannot check equality of functions (otherwise Haskell would be able to solve the Collatz conjecture) ...
... however: we cannot check equality of functions (otherwise Haskell would be able to solve the Collatz conjecture) ...
Lambda Calculus
... Another form of abbreviations introduced by Church are schematic de nitions [Chu41]. Schematic de nitions de ne the form of expressions and allows a more readable form. As in the case of the nominal de nition the schema is on the left side of the arrow and the schematic de nition is on the right han ...
... Another form of abbreviations introduced by Church are schematic de nitions [Chu41]. Schematic de nitions de ne the form of expressions and allows a more readable form. As in the case of the nominal de nition the schema is on the left side of the arrow and the schematic de nition is on the right han ...
Lisp - University of Connecticut
... x is called a bound variable • Lambda expressions can be applied to parameters e.g., ((LAMBDA (x) (* x x)) 7) • LAMBDA expressions can have any number of parameters (LAMBDA (a b x) (+ (* a x x) (* b x))) Copyright © 2015 Pearson. All rights reserved. ...
... x is called a bound variable • Lambda expressions can be applied to parameters e.g., ((LAMBDA (x) (* x x)) 7) • LAMBDA expressions can have any number of parameters (LAMBDA (a b x) (+ (* a x x) (* b x))) Copyright © 2015 Pearson. All rights reserved. ...
A Tutorial Introduction to the Lambda Calculus
... We can now define the predecessor function combining some of the functions introduced above. When looking for the predecessor of n, the general strategy will be to create a pair (n, n − 1) and then pick the second element of the pair as the result. A pair (a, b) can be represented in λ-calculus usin ...
... We can now define the predecessor function combining some of the functions introduced above. When looking for the predecessor of n, the general strategy will be to create a pair (n, n − 1) and then pick the second element of the pair as the result. A pair (a, b) can be represented in λ-calculus usin ...
7. Introduction to the Lambda Calculus
... “If an expression can be evaluated at all, it can be evaluated by consistently using normal-order evaluation. If an expression can be evaluated in several different orders (mixing normal-order and applicative order reduction), then all of these evaluation orders yield the same result.” ...
... “If an expression can be evaluated at all, it can be evaluated by consistently using normal-order evaluation. If an expression can be evaluated in several different orders (mixing normal-order and applicative order reduction), then all of these evaluation orders yield the same result.” ...
Lambda Calculus
... “If an expression can be evaluated at all, it can be evaluated by consistently using normal-order evaluation. If an expression can be evaluated in several different orders (mixing normal-order and applicative order reduction), then all of these evaluation orders yield the same result.” ...
... “If an expression can be evaluated at all, it can be evaluated by consistently using normal-order evaluation. If an expression can be evaluated in several different orders (mixing normal-order and applicative order reduction), then all of these evaluation orders yield the same result.” ...
Document
... another set, called the range set - A lambda expression specifies the parameter(s) and the mapping of a function in the following form (x) x * x * x for the function cube (x) = x * x * x ...
... another set, called the range set - A lambda expression specifies the parameter(s) and the mapping of a function in the following form (x) x * x * x for the function cube (x) = x * x * x ...
Functional Programming: Scheme
... • Scheme functions are first-class objects: – functions can be created dynamically, stored in data structures, returned as results of expressions or other functions. • functions are defined as lists ⇒ can be treated as data. Lecture 11 ...
... • Scheme functions are first-class objects: – functions can be created dynamically, stored in data structures, returned as results of expressions or other functions. • functions are defined as lists ⇒ can be treated as data. Lecture 11 ...
Slides - Chapter 10
... • Logic programming is tied to the notion of constructive proofs, but at a more abstract level: – the logic programmer writes a set of axioms that allow the computer to discover a constructive proof for each particular set of inputs Copyright © 2005 Elsevier ...
... • Logic programming is tied to the notion of constructive proofs, but at a more abstract level: – the logic programmer writes a set of axioms that allow the computer to discover a constructive proof for each particular set of inputs Copyright © 2005 Elsevier ...
Introduction to Racket
... quote quotes its argument without evaluating it. (quote (map + 0 "cool")) is simply a list of four elements. (quote map) creates a symbol 'map that has nothing to do with the identifier map (except the name). One can directly write ' instead of quote. quote has no effect on literals (numbers, string ...
... quote quotes its argument without evaluating it. (quote (map + 0 "cool")) is simply a list of four elements. (quote map) creates a symbol 'map that has nothing to do with the identifier map (except the name). One can directly write ' instead of quote. quote has no effect on literals (numbers, string ...
15. Functional Programming Languages.
... another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form l(x) x * x * x for the function cube (x) = x * x * x Copyright © 1998 by Addison Wesley Longman, Inc. ...
... another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form l(x) x * x * x for the function cube (x) = x * x * x Copyright © 1998 by Addison Wesley Longman, Inc. ...
Chapter 14 Functional Programming Languages
... another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form λ(x) x * x * x for the function cube (x) = x * x * x Copyright © 1998 by Addison Wesley Longman, Inc. ...
... another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form λ(x) x * x * x for the function cube (x) = x * x * x Copyright © 1998 by Addison Wesley Longman, Inc. ...
slides
... concern and source of complexity for imperative programming - In an FPL, variables are not necessary, as is the case in mathematics - In an FPL, the evaluation of a function always produces the same result given the same parameters - This is called referential transparency ...
... concern and source of complexity for imperative programming - In an FPL, variables are not necessary, as is the case in mathematics - In an FPL, the evaluation of a function always produces the same result given the same parameters - This is called referential transparency ...
arguments (an upper and lower bound (integers) and a function
... Calculate the integrals of f(x)= sin(x) from 0 to pi, Calculate the integrals of f(x)= sin(x)* sin(x) from 0 to pi. (Note you may have to Google to find out how sin and pi work in Python. ) ...
... Calculate the integrals of f(x)= sin(x) from 0 to pi, Calculate the integrals of f(x)= sin(x)* sin(x) from 0 to pi. (Note you may have to Google to find out how sin and pi work in Python. ) ...