Compiling Functional Programming Languages (FPLs) λ
... Amazingly, Y can be defined as a lambda abstraction, i.e., WITHOUT RECURSION. It’s called the fixpoint combinator: ...
... Amazingly, Y can be defined as a lambda abstraction, i.e., WITHOUT RECURSION. It’s called the fixpoint combinator: ...
Chapter 2 - Lambda Calculus - Rensselaer Polytechnic Institute
... f(x) = x2 , g(x) = x+1 f g is the composition of f and g: f g (x) = f(g(x)) f g (x) = f(g(x)) = f(x+1) = (x+1)2 = x2 + 2x + 1 g f (x) = g(f(x)) = g(x2) = x2 + 1 Function composition is therefore not commutative. Function composition can be regarded as a (higher-order) function with the followi ...
... f(x) = x2 , g(x) = x+1 f g is the composition of f and g: f g (x) = f(g(x)) f g (x) = f(g(x)) = f(x+1) = (x+1)2 = x2 + 2x + 1 g f (x) = g(f(x)) = g(x2) = x2 + 1 Function composition is therefore not commutative. Function composition can be regarded as a (higher-order) function with the followi ...
C311 First Class Objects
... Expressible as an anonymous literal value Storable in variables Storable in data structures Having an intrinsic identity (independent of any given name) Comparable for equality with other entities Passable as a parameter to a function Returnable as the result of a function call Constructable at runt ...
... Expressible as an anonymous literal value Storable in variables Storable in data structures Having an intrinsic identity (independent of any given name) Comparable for equality with other entities Passable as a parameter to a function Returnable as the result of a function call Constructable at runt ...
Functional Programming
... performed by a left-to-right reduction sequence. If the expression is reducible, the reduction sequence will terminate. If the expression is irreducible the reduction will not terminate and also, any other reduction sequence will not terminate as well. The left-to-right reduction corresponds to the ...
... performed by a left-to-right reduction sequence. If the expression is reducible, the reduction sequence will terminate. If the expression is irreducible the reduction will not terminate and also, any other reduction sequence will not terminate as well. The left-to-right reduction corresponds to the ...
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 ...
Lambda calculus
... be reduced. However, N and P are assumed to be in normal form, so they don’t allow for any further reductions. The only possible interpretation is that N = P = Q. ...
... be reduced. However, N and P are assumed to be in normal form, so they don’t allow for any further reductions. The only possible interpretation is that N = P = Q. ...
Document
... a) when Y is the abstraction λx.W then [M/x]Y => λx.W b) when Y is the abstraction λy.W and there are no free occurrences of x in W then [M/x]Y is λy.W c) when Y is the abstraction λy.W and there are no free occurrence of y in M then [M/x]Y is λy.[M/x]W d) when Y is the abstraction λy.W and there is ...
... a) when Y is the abstraction λx.W then [M/x]Y => λx.W b) when Y is the abstraction λy.W and there are no free occurrences of x in W then [M/x]Y is λy.W c) when Y is the abstraction λy.W and there are no free occurrence of y in M then [M/x]Y is λy.[M/x]W d) when Y is the abstraction λy.W and there is ...
Lecture 15: The Lambda Calculus
... integer (α → bool) “abc” → False identity (α → α) 456 → 456 identity (α → α) “fred” → “fred” ...
... integer (α → bool) “abc” → False identity (α → α) 456 → 456 identity (α → α) “fred” → “fred” ...
Functional Programming
... • Currying: transform a function with multiple arguments into a chain of single-argument functions. • Partial function application: apply only a subset of the arguments of a curried function (from left to right) to yield another function taking the remaining arguments. • Reduction order: eager (redu ...
... • Currying: transform a function with multiple arguments into a chain of single-argument functions. • Partial function application: apply only a subset of the arguments of a curried function (from left to right) to yield another function taking the remaining arguments. • Reduction order: eager (redu ...
Lambda Calculus and Lisp
... lambda, period, parentheses and numbers. • M -> x | (M M) | x.M • If F and A are both expressions then so is (F A) and indicates the application of the function F with A as its parameter. • If F is a expression then so is x.F This is a function definition and is also called an ABSTRACTION beca ...
... lambda, period, parentheses and numbers. • M -> x | (M M) | x.M • If F and A are both expressions then so is (F A) and indicates the application of the function F with A as its parameter. • If F is a expression then so is x.F This is a function definition and is also called an ABSTRACTION beca ...
LambdaCalculus
... 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
... alpha-renaming, beta reduction, eta conversion, applicative and normal evaluation orders, ChurchRosser theorem, combinators, booleans ...
... alpha-renaming, beta reduction, eta conversion, applicative and normal evaluation orders, ChurchRosser theorem, combinators, booleans ...
Notes
... no computation remaining. Note that no closure is created, and that no computation is performed in body e. • Variable x does not evaluate to anything and immediately results in an error. For this to happen, x must have been free in the expression that is being evaluated. Since it was free, there is ...
... no computation remaining. Note that no closure is created, and that no computation is performed in body e. • Variable x does not evaluate to anything and immediately results in an error. For this to happen, x must have been free in the expression that is being evaluated. Since it was free, there is ...
The λ – Calculus
... So Square( x) x x the corresponding lambda expression would be ( x x x) • An instance of a lambda expression to a particular value ‘a’ takes the form: (( x x x) a) a a a 2 • So, for example: (( x x x)3) 3 3 9 ...
... So Square( x) x x the corresponding lambda expression would be ( x x x) • An instance of a lambda expression to a particular value ‘a’ takes the form: (( x x x) a) a a a 2 • So, for example: (( x x x)3) 3 3 9 ...