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... There are 3 rules called conversion rules:α : if there are no free occurrences of y in Z then λx.Z cnvα λy.[y/x]Z β : (λx.M) N cnvβ [N/x] M η: if there are no free occurrences of x in M then (λx.M x) cnvη M β and η usually simplify (reduce the complexity of) expressions and are therefore called redu ...
... There are 3 rules called conversion rules:α : if there are no free occurrences of y in Z then λx.Z cnvα λy.[y/x]Z β : (λx.M) N cnvβ [N/x] M η: if there are no free occurrences of x in M then (λx.M x) cnvη M β and η usually simplify (reduce the complexity of) expressions and are therefore called redu ...
Here
... handling. This minimizes confusion about their purpose. In particular, I never use a built-in type, such as int, as an exception.” -- The C++ Programming Language, 3rd ed. ...
... handling. This minimizes confusion about their purpose. In particular, I never use a built-in type, such as int, as an exception.” -- The C++ Programming Language, 3rd ed. ...
ML Basics
... Higher-Order Functions • A function that takes a function as argument and/or returns a function as result is called a higher-order function or a functional. • ML/Scheme treat functions as first-class (primitive) values. – Can be supplied as input to functions. » Not allowed in Ada. ...
... Higher-Order Functions • A function that takes a function as argument and/or returns a function as result is called a higher-order function or a functional. • ML/Scheme treat functions as first-class (primitive) values. – Can be supplied as input to functions. » Not allowed in Ada. ...
Proglan Midterms Set X 1st Term AY201516 Ronald L. Ramos
... reusable because it also used functions and pre defined functions you can use over and over. It is also readable since it uses basic words for their syntax. It may look different but it still uses understandable language. For example their print is printf() but you are sure that this function prints ...
... reusable because it also used functions and pre defined functions you can use over and over. It is also readable since it uses basic words for their syntax. It may look different but it still uses understandable language. For example their print is printf() but you are sure that this function prints ...
Lambda Calculus
... the right hand side. The schemantic de nition is written in square brackets [] to be able to dier between a schematic de nition and a nominal de nition. An example of this is [M × N ] → (λa(M (N a))). M and N can be replaced by any variable or abbreviation and thus will also be replaced on the righ ...
... the right hand side. The schemantic de nition is written in square brackets [] to be able to dier between a schematic de nition and a nominal de nition. An example of this is [M × N ] → (λa(M (N a))). M and N can be replaced by any variable or abbreviation and thus will also be replaced on the righ ...
Chapter 7: Functional Programming Languages
... γ ` f ⇓ (λx → e){δ} δ, x := a{γ} ` e ⇓ v γ ` (f a) ⇓ v Notice that γ is the proper way to close the expression a, because it is the environment in which a would be evaluated if we were performing call by value. ...
... γ ` f ⇓ (λx → e){δ} δ, x := a{γ} ` e ⇓ v γ ` (f a) ⇓ v Notice that γ is the proper way to close the expression a, because it is the environment in which a would be evaluated if we were performing call by value. ...
slides 4-up
... (λhx, y i. x) h3, 5i → x[x, y := 3, 5] = 3 length of a non-empty list: (λ(h : t). 1 + (length t)) (1 : nil) → (1 + (length t))[t := nil] = 1 + length nil ...
... (λhx, y i. x) h3, 5i → x[x, y := 3, 5] = 3 length of a non-empty list: (λ(h : t). 1 + (length t)) (1 : nil) → (1 + (length t))[t := nil] = 1 + length nil ...
02/06
... Efficiency is the primary concern, rather than the suitability of the language for software development ...
... Efficiency is the primary concern, rather than the suitability of the language for software development ...
Functional Pearls - Probabilistic Functional Programming in Haskell
... any simulation without altering the code which defines it. In the following we will present the definitions of most functions, but also leave out some details for the sake of brevity. These details should be obvious enough to be filled in easily by the reader. In any case, all function definitions c ...
... any simulation without altering the code which defines it. In the following we will present the definitions of most functions, but also leave out some details for the sake of brevity. These details should be obvious enough to be filled in easily by the reader. In any case, all function definitions c ...
LISP
... In imperative programming an expression is evaluated and the result is stored in memory location which is represented as a variable in the program. A purely functional programming language does not use variables and assignment statements. Without variables iterative constructs are not possible. Repe ...
... In imperative programming an expression is evaluated and the result is stored in memory location which is represented as a variable in the program. A purely functional programming language does not use variables and assignment statements. Without variables iterative constructs are not possible. Repe ...
Lambda Calculus
... 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 following type: • : (Z → Z) x ...
... 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 following type: • : (Z → Z) x ...
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: ...