Foundations of Programming Languages Seyed H. Roosta
... – It is purely functional. Thus we can think exclusively in terms of the substitution model. ...
... – It is purely functional. Thus we can think exclusively in terms of the substitution model. ...
slides 4-up
... a list is obtained by repeatedly forming a pair for example: [1, 2, 3] is (1, (2, (3, nil))) ...
... a list is obtained by repeatedly forming a pair for example: [1, 2, 3] is (1, (2, (3, nil))) ...
Lambda Calculus and Functional Programming
... A sequence of abstractions are contracted: λ x λ y λ z. N is abbreviated as λ x y z. N C. Free and bound variables The abstraction operator, λ, is said to bind its variable wherever it occurs in the body of the abstraction. Variables that fall within the scope of a lambda are said to be bound. All o ...
... A sequence of abstractions are contracted: λ x λ y λ z. N is abbreviated as λ x y z. N C. Free and bound variables The abstraction operator, λ, is said to bind its variable wherever it occurs in the body of the abstraction. Variables that fall within the scope of a lambda are said to be bound. All o ...
Lambda Calculus
... As the names of variables are arbitrary there must be a way to determine functions that only dier in the name of their bound variables. For example λx.x is equivalent to λy.y , because the result will be the same if both functions are applied to the same operand. It is important to check whether tw ...
... As the names of variables are arbitrary there must be a way to determine functions that only dier in the name of their bound variables. For example λx.x is equivalent to λy.y , because the result will be the same if both functions are applied to the same operand. It is important to check whether tw ...
Functional Programming
... In informal mathematics, when talking about a function, one normally gives it a name, e.g., “define f(x) = E[x] … then … f …” Similarly, most programming languages will only let you define functions if you are prepared to give them a name. This approach is rather inconsistent, as we are not treating ...
... In informal mathematics, when talking about a function, one normally gives it a name, e.g., “define f(x) = E[x] … then … f …” Similarly, most programming languages will only let you define functions if you are prepared to give them a name. This approach is rather inconsistent, as we are not treating ...
ppt
... Only bound variables can be renamed. No free variables can be captured (become bound) in the process. For example, we cannot alpha-rename x to y. ...
... Only bound variables can be renamed. No free variables can be captured (become bound) in the process. For example, we cannot alpha-rename x to y. ...
Fundamentals
... Functional programming: Example 1 Devise a representation for stacks and implementations for functions push (elt, stk) returns stack with elt on top of stk ...
... Functional programming: Example 1 Devise a representation for stacks and implementations for functions push (elt, stk) returns stack with elt on top of stk ...
notes
... The λ-calculus (λ = “lambda”, the Greek letter l)1 was introduced by Alonzo Church (1903–1995) and Stephen Cole Kleene (1909–1994) in the 1930s to study the interaction of functional abstraction and functional application. The λ-calculus provides a succinct and unambiguous notation for the intension ...
... The λ-calculus (λ = “lambda”, the Greek letter l)1 was introduced by Alonzo Church (1903–1995) and Stephen Cole Kleene (1909–1994) in the 1930s to study the interaction of functional abstraction and functional application. The λ-calculus provides a succinct and unambiguous notation for the intension ...
fund
... 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 ...
ppt
... Only bound variables can be renamed. No free variables can be captured (become bound) in the process. For example, we cannot alpha-rename x to y. ...
... Only bound variables can be renamed. No free variables can be captured (become bound) in the process. For example, we cannot alpha-rename x to y. ...
Lecture10
... • Can I pass a function as an argument to another function • YES! • The first time you see this, it looks crazy • Just start thinking of a function as a machine that turns ...
... • Can I pass a function as an argument to another function • YES! • The first time you see this, it looks crazy • Just start thinking of a function as a machine that turns ...
Functional Programming Languages
... 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 A is applied to the two parameters, B and C • The first LI ...
... 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 A is applied to the two parameters, B and C • The first LI ...
Functional Programming COMP2003
... 1. When the function definition is specific to a particular situation, and so can be defined and used in just one place. Usually the motive for forming the computation into a function is that it is being passed in as argument to some other functions which will use that computation in various ways, p ...
... 1. When the function definition is specific to a particular situation, and so can be defined and used in just one place. Usually the motive for forming the computation into a function is that it is being passed in as argument to some other functions which will use that computation in various ways, p ...
Lecture 10
... Map, filter and reduce Python provides this as • Map – transform everything in the iterable • Filter – filter those that return the value true • Reduce – a two argument function ls1 = map(lambda x: x +2, a) ls2 = filter(lambda x: x%2 == 0, a) ls3 = reduce(lambda x, y : x+y, a ) ...
... Map, filter and reduce Python provides this as • Map – transform everything in the iterable • Filter – filter those that return the value true • Reduce – a two argument function ls1 = map(lambda x: x +2, a) ls2 = filter(lambda x: x%2 == 0, a) ls3 = reduce(lambda x, y : x+y, a ) ...
Advanced Formal Methods
... Exercise 4: Define ”Church lists”. A list [x,y,z] can be thought of as a function taking two arguments c (for cons) and n (for nil), and returns c x (c y (c z n)), similar to the Church numerals. Write a function nil representing the empty list, and a function cons that takes arguments h and (a func ...
... Exercise 4: Define ”Church lists”. A list [x,y,z] can be thought of as a function taking two arguments c (for cons) and n (for nil), and returns c x (c y (c z n)), similar to the Church numerals. Write a function nil representing the empty list, and a function cons that takes arguments h and (a func ...
Functional Programming
... want to pass it only once (defun consval (x) (cons val x)) An obvious solution is just to pass the function’s body (mapcar ‘(cons val x) L) It is ambiguous : we do not know which names are parameters and which ones are global “lambda expressions” come in hand (mapcar ‘(lambda (x) (cons val x)) ...
... want to pass it only once (defun consval (x) (cons val x)) An obvious solution is just to pass the function’s body (mapcar ‘(cons val x) L) It is ambiguous : we do not know which names are parameters and which ones are global “lambda expressions” come in hand (mapcar ‘(lambda (x) (cons val x)) ...
PowerPoint - School of Computing Science
... Different reduction strategies are based on where in a term it is possible to apply beta reduction. We will concentrate on call by value reduction, which means adding the following rules: e e' e1 e'1 ve ve' e1e2 e'1 e2 Values v are -abstractions, and any other values which we might incorpor ...
... Different reduction strategies are based on where in a term it is possible to apply beta reduction. We will concentrate on call by value reduction, which means adding the following rules: e e' e1 e'1 ve ve' e1e2 e'1 e2 Values v are -abstractions, and any other values which we might incorpor ...
Handout 10 from Models of Computation
... It may be that a λ-term offers many opportunities for reduction at the same time. In order for the whole calculus to make sense, it is necessary that the result of a computation is independent from the order of reduction. We would like to express this property for all terms, not just for those which ...
... It may be that a λ-term offers many opportunities for reduction at the same time. In order for the whole calculus to make sense, it is necessary that the result of a computation is independent from the order of reduction. We would like to express this property for all terms, not just for those which ...
Breck, Hartline
... evaluate the function. As an aside, this class is quite a bit about how to get from an intensional representation, an algorithm, to the extension, meaning, or effect of a function. Real programming languages such as Lisp, Scheme, Haskell and ML are very much based on lambda calculus, although there a ...
... evaluate the function. As an aside, this class is quite a bit about how to get from an intensional representation, an algorithm, to the extension, meaning, or effect of a function. Real programming languages such as Lisp, Scheme, Haskell and ML are very much based on lambda calculus, although there a ...
List
... – The list is the fundamental data structure – Developed by John McCarthy in the 60’s • Used for symbolic data processing • Example apps: symbolic calculations in integral and differential calculus, circuit design, logic, game playing, AI • As we will see the syntax for the language is extremely sim ...
... – The list is the fundamental data structure – Developed by John McCarthy in the 60’s • Used for symbolic data processing • Example apps: symbolic calculations in integral and differential calculus, circuit design, logic, game playing, AI • As we will see the syntax for the language is extremely sim ...