Chapter 1 - KSU Web Home
... Lambda notation is used to specify functions and function definitions. Function applications and data have the same form. e.g., If the list (A B C) is interpreted as data it is a simple list of three atoms, A, B, and C If it is interpreted as a function application, it means that the function named ...
... Lambda notation is used to specify functions and function definitions. Function applications and data have the same form. e.g., If the list (A B C) is interpreted as data it is a simple list of three atoms, A, B, and C If it is interpreted as a function application, it means that the function named ...
scheme1 - Department of Computer Science and Electrical
... How Programming Language Fanboys See Each Others’ Languages ...
... How Programming Language Fanboys See Each Others’ Languages ...
x + 1 - Postech
... Variables are NOT variable. • The contents of a variable never change. • Surprise? – That’s because you are thinking about variables in imperative programming. variables in SML ...
... Variables are NOT variable. • The contents of a variable never change. • Surprise? – That’s because you are thinking about variables in imperative programming. variables in SML ...
Theorems for free! - Computing Science
... extent by Sheeran [She89]. So there is reason to believe that further research will further extend the applicability of this method. Many functional languages, including Standard ML [Mil84, Mil87], Miranda1 [Tur85], and Haskell [HW88], are based on the Hindley/Milner type system [Hin69, Mil78, DM82] ...
... extent by Sheeran [She89]. So there is reason to believe that further research will further extend the applicability of this method. Many functional languages, including Standard ML [Mil84, Mil87], Miranda1 [Tur85], and Haskell [HW88], are based on the Hindley/Milner type system [Hin69, Mil78, DM82] ...
CA320 - Computability & Complexity
... | bmi <= normal = "Supposedly normal!" | bmi <= comfortable = "How about a walk?" | otherwise = "Skip that snack" where bmi = weight / height ^ 2 (skinny, normal, comfortable) ...
... | bmi <= normal = "Supposedly normal!" | bmi <= comfortable = "How about a walk?" | otherwise = "Skip that snack" where bmi = weight / height ^ 2 (skinny, normal, comfortable) ...
1 Salient Features of Functional Programming
... • Functional program code has no assignment statements. 1. When a variable x is created, it is given an initial value v 2. which is never modified later. • In a piece of functional code, we can be certain that each occurrence of x denotes the same value v. – In the code, x is a variable in the mathe ...
... • Functional program code has no assignment statements. 1. When a variable x is created, it is given an initial value v 2. which is never modified later. • In a piece of functional code, we can be certain that each occurrence of x denotes the same value v. – In the code, x is a variable in the mathe ...
pl11ch15
... • Includes exception handling and a module facility for implementing abstract data types • Includes lists and list operations Copyright © 2015 Pearson. All rights reserved. ...
... • Includes exception handling and a module facility for implementing abstract data types • Includes lists and list operations Copyright © 2015 Pearson. All rights reserved. ...
Principles of Programming Languages - 815338A
... • Includes exception handling and a module facility for implementing abstract data types • Includes lists and list operations ...
... • Includes exception handling and a module facility for implementing abstract data types • Includes lists and list operations ...
Lambda-Lifting in Quadratic Time
... floating is thus straightforward: the program is merely traversed, all local functions are collected and all blocks are replaced by their bodies. The collected function definitions are then appended to the program as global mutually recursive functions, making all functions globally visible. Lambda- ...
... floating is thus straightforward: the program is merely traversed, all local functions are collected and all blocks are replaced by their bodies. The collected function definitions are then appended to the program as global mutually recursive functions, making all functions globally visible. Lambda- ...
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 ...
Appendix B
... scoping: the calling chain is following until the variable is found local to a function. Scheme and Common Lisp use static scoping ...
... scoping: the calling chain is following until the variable is found local to a function. Scheme and Common Lisp use static scoping ...
Chapter 3
... • Free variable: a variable referenced within a function that is not also a formal parameter to that function and is not bound within a nested function • Bound variable: a variable within a function that is also a formal parameter to that function • Lexical scoping fixes the meaning of free variable ...
... • Free variable: a variable referenced within a function that is not also a formal parameter to that function and is not bound within a nested function • Bound variable: a variable within a function that is also a formal parameter to that function • Lexical scoping fixes the meaning of free variable ...
Chapter 3
... • Free variable: a variable referenced within a function that is not also a formal parameter to that function and is not bound within a nested function • Bound variable: a variable within a function that is also a formal parameter to that function • Lexical scoping fixes the meaning of free variable ...
... • Free variable: a variable referenced within a function that is not also a formal parameter to that function and is not bound within a nested function • Bound variable: a variable within a function that is also a formal parameter to that function • Lexical scoping fixes the meaning of free variable ...
The current topic: Scheme Announcements Review: car, cdr, and
... • The functions number?, symbol?, and list? check the type of the given argument and return boolean values (#t or #f). ...
... • The functions number?, symbol?, and list? check the type of the given argument and return boolean values (#t or #f). ...
Functionalprogramming
... Scheme is a small but well-designed subset/dialect of Lisp. • Lexical scope rule. • Correct treatment of functional arguments (thanks to lexical scoping): functions are first-class objects, that is, they can be created, assigned to variables, passed as arguments, returned as values. ...
... Scheme is a small but well-designed subset/dialect of Lisp. • Lexical scope rule. • Correct treatment of functional arguments (thanks to lexical scoping): functions are first-class objects, that is, they can be created, assigned to variables, passed as arguments, returned as values. ...
PPT
... – Skip discussion of ML assignment There are some slides that we may skip today. This outline is to help you remember what we did not skip. If we need some time in next lecture, we will do that. ...
... – Skip discussion of ML assignment There are some slides that we may skip today. This outline is to help you remember what we did not skip. If we need some time in next lecture, we will do that. ...
PROGRAMMING LANGUAGES 6.5 Higher Order Functions A
... Mathematically, a function is a single-valued mapping: it associates every element in one set (the domain) with (at most) one element in another set (the range). In conventional notation, we indicate the domain and range of, say, the square root function by writing ...
... Mathematically, a function is a single-valued mapping: it associates every element in one set (the domain) with (at most) one element in another set (the range). In conventional notation, we indicate the domain and range of, say, the square root function by writing ...
Joy: Forth`s Functional Cousin
... where "Lx" is sometimes written "\x" or "lambda x" of "fn x". The expression on the right side of the definition then is to be read as "the function of one argument x which yields the value x * x". An expression like that is known as a lambda abstraction. Almost all programming languages use such a ...
... where "Lx" is sometimes written "\x" or "lambda x" of "fn x". The expression on the right side of the definition then is to be read as "the function of one argument x which yields the value x * x". An expression like that is known as a lambda abstraction. Almost all programming languages use such a ...
Lisp vs Scheme
... • In CL, functions and values have different namespaces. In a form, • car position corresponds to function space • cdr positions correspond to value space • So you can say (flet ((fun (x) (1+ x))) (let ((fun 42)) (fun fun))) ...
... • In CL, functions and values have different namespaces. In a form, • car position corresponds to function space • cdr positions correspond to value space • So you can say (flet ((fun (x) (1+ x))) (let ((fun 42)) (fun fun))) ...
19th Century Logic and 21st Century Computing
... that from assumptions A and B one can deduce A ∧ B. But it does so in a roundabout way: it first demonstrates that from no assumptions one can deduce (B∧A) → (A∧B), and that from the assumptions A and B one can deduce B ∧ A, and then applies modus ponens. One might reasonably expect that such a proo ...
... that from assumptions A and B one can deduce A ∧ B. But it does so in a roundabout way: it first demonstrates that from no assumptions one can deduce (B∧A) → (A∧B), and that from the assumptions A and B one can deduce B ∧ A, and then applies modus ponens. One might reasonably expect that such a proo ...
ppt - Rensselaer Polytechnic Institute: Computer Science
... represents the same f function, except it is anonymous. To represent the function evaluation f(2) = 4, we use the following -calculus syntax: ...
... represents the same f function, except it is anonymous. To represent the function evaluation f(2) = 4, we use the following -calculus syntax: ...
ppt
... variables when beta-reducing a lambda calculus expression. In the following, we rename x to z, (or any other fresh variable): (x.(y x) x) ...
... variables when beta-reducing a lambda calculus expression. In the following, we rename x to z, (or any other fresh variable): (x.(y x) x) ...
Elements of Functional Programming
... first of the arguments to the original function, and returns a new function which takes the remainder of the arguments and returns the result, is called currying. The technique is named after logician Haskell Curry, though it was invented by other scientists before. Thanks to currying, multiple-argum ...
... first of the arguments to the original function, and returns a new function which takes the remainder of the arguments and returns the result, is called currying. The technique is named after logician Haskell Curry, though it was invented by other scientists before. Thanks to currying, multiple-argum ...