02157 Functional Programming - A brief introduction to Lambda

... Free and bound variables A occurrence of a variable x is bound in t, if it occurs within the scope of an abstraction λx.M in t; otherwise it is free. If x has at least one free occurrence in t, then it is called a free variable of t. ...

... Free and bound variables A occurrence of a variable x is bound in t, if it occurs within the scope of an abstraction λx.M in t; otherwise it is free. If x has at least one free occurrence in t, then it is called a free variable of t. ...

User`s Functions in Standard Prolog

... unifying substitution be θ. Next, (if conditionθ is successful with the substitution ϕ), the current subexpression is replaced by expressionθϕ. The pln clauses are tried sequentially, and choice points are generated, if there are more candidates. If no pln clause can perform the actual step of evalu ...

... unifying substitution be θ. Next, (if conditionθ is successful with the substitution ϕ), the current subexpression is replaced by expressionθϕ. The pln clauses are tried sequentially, and choice points are generated, if there are more candidates. If no pln clause can perform the actual step of evalu ...

Functional Programming in Haskell

... Haskell allows multiple definitions of the same function. All must have the same type. It uses the first one that matches the actual parameters. The formal parameters are patterns that need to be matched by the actual parameters. ...

... Haskell allows multiple definitions of the same function. All must have the same type. It uses the first one that matches the actual parameters. The formal parameters are patterns that need to be matched by the actual parameters. ...

Functional Programming

... effective computation. Lambda calculus works with anonymous unary functions and the core action is the function application. In particular, function application is performed by a purely substitutive process: the (free) occurrences , within the function body, of the formal parameter of the function a ...

... effective computation. Lambda calculus works with anonymous unary functions and the core action is the function application. In particular, function application is performed by a purely substitutive process: the (free) occurrences , within the function body, of the formal parameter of the function a ...

Types and Programming Languages

... x : U x: U x : U x : U T App x : U xx : T We can see that U must be of the form U T but this is not possible (unless we have recursive types, which are coming later). ...

... x : U x: U x : U x : U T App x : U xx : T We can see that U must be of the form U T but this is not possible (unless we have recursive types, which are coming later). ...

Lazy evaluation - Computer Science and Engineering

... returns values as and when required. • For example, in tree equality, if first value of both the trees in preorder sequence are equal then second element of first tree is computed followed by second element of second tree and so on otherwise false is returned. ...

... returns values as and when required. • For example, in tree equality, if first value of both the trees in preorder sequence are equal then second element of first tree is computed followed by second element of second tree and so on otherwise false is returned. ...

Semantics Directed Program Execution Monitoring

... As discussed in Section 1, we require that the standard semantics be given in a continuationpassing style (often written “CPS”). At ﬁrst this may seem odd for a purely functional language, but in fact for a non-strict language it is quite useful, since it allows us to explicate the manipulation of t ...

... As discussed in Section 1, we require that the standard semantics be given in a continuationpassing style (often written “CPS”). At ﬁrst this may seem odd for a purely functional language, but in fact for a non-strict language it is quite useful, since it allows us to explicate the manipulation of t ...

funprog

... To evaluate (E1 E2 ... En), recursively evaluate E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various spec ...

... To evaluate (E1 E2 ... En), recursively evaluate E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various spec ...

Expressing C++ Template Metaprograms as Lambda expressions

... Abstract: Template metaprogramming is an emerging new direction of generative programming: with clever definitions of templates we can enforce the C++ compiler to execute algorithms at compilation time. Although the relationship between template metaprograms and functional programming is well-known, ...

... Abstract: Template metaprogramming is an emerging new direction of generative programming: with clever definitions of templates we can enforce the C++ compiler to execute algorithms at compilation time. Although the relationship between template metaprograms and functional programming is well-known, ...

Programming Language Theory and its Implementation

... that computer science students are taught at Cambridge University. There is growing evidence that (i) programmers can solve problems more quickly if they use a functional language, and (ii) the resulting solutions are more likely to be correct. Because of (ii), and the relative ease of verifying the ...

... that computer science students are taught at Cambridge University. There is growing evidence that (i) programmers can solve problems more quickly if they use a functional language, and (ii) the resulting solutions are more likely to be correct. Because of (ii), and the relative ease of verifying the ...

Computational lambda calculus: A combination of functional and

... Functional programming languages, cf Lisp, have their roots in the lambda calculus and are widely known for their expressive power and simple semantics. Because of their mathematical simplicity are considered to be a great tool for formal analysis and program verification. Functional programs do not ...

... Functional programming languages, cf Lisp, have their roots in the lambda calculus and are widely known for their expressive power and simple semantics. Because of their mathematical simplicity are considered to be a great tool for formal analysis and program verification. Functional programs do not ...

A Representation Theorem for Second-Order Functionals

... on morphisms given by R (f ) (a, g) = (a, f ◦ g). Hence, we can instantiate a polymorphic function h : T to the functor R and obtain hR : (A → R B) → R C, which amounts to the type hR : (A → (A × (B → B))) → A × (B → C). ϕ : (∀F : Functor. (A → F B) → F C) → A × (B → C) ϕ h = hR (λ a. (a, idB )) The ...

... on morphisms given by R (f ) (a, g) = (a, f ◦ g). Hence, we can instantiate a polymorphic function h : T to the functor R and obtain hR : (A → R B) → R C, which amounts to the type hR : (A → (A × (B → B))) → A × (B → C). ϕ : (∀F : Functor. (A → F B) → F C) → A × (B → C) ϕ h = hR (λ a. (a, idB )) The ...

Introduction Into Functional Programming

... 2.2 If the searched word is “less” then the shown ones, then 2.2.1 continue search within the left half of the book; otherwise 2.2.2 continue search within with the right half of the book. ...

... 2.2 If the searched word is “less” then the shown ones, then 2.2.1 continue search within the left half of the book; otherwise 2.2.2 continue search within with the right half of the book. ...

Functional Programming in CLEAN

... The first programming language based on the notion of functions was LISP, developed in the early 60s by John McCarthy. The name is an abbreviation of `list processor', which reflects the fact that functions can operate on lists (sequences) of values. An important feature of the language was that fun ...

... The first programming language based on the notion of functions was LISP, developed in the early 60s by John McCarthy. The name is an abbreviation of `list processor', which reflects the fact that functions can operate on lists (sequences) of values. An important feature of the language was that fun ...

X - Rensselaer Polytechnic Institute: Computer Science

... – Delayed evaluation (also called explicit lazy evaluation): build just a small part of a data structure, with functions at the extremities that can be called to build more. The consumer can control explicitly how much of the data structure is built. C. Varela; Adapted w/permission from S. Haridi an ...

... – Delayed evaluation (also called explicit lazy evaluation): build just a small part of a data structure, with functions at the extremities that can be called to build more. The consumer can control explicitly how much of the data structure is built. C. Varela; Adapted w/permission from S. Haridi an ...

Q-Midi - Q - Equational Programming Language

... operators are left-associative, except the exponentiation/index operators which are rightassociative, and the relational operators which are non-associative. Function application takes precedence over all these operators. Default precedences can be overridden by grouping expressions with parentheses ...

... operators are left-associative, except the exponentiation/index operators which are rightassociative, and the relational operators which are non-associative. Function application takes precedence over all these operators. Default precedences can be overridden by grouping expressions with parentheses ...

Chapter 5 THE LAMBDA CALCULUS

... In the spirit of software engineering, we allow identifiers of more than one letter to stand as variables and constants. The pure lambda calculus has no predefined constants, but it still allows the definition of all of the common constants and functions of arithmetic and list manipulation. We will ...

... In the spirit of software engineering, we allow identifiers of more than one letter to stand as variables and constants. The pure lambda calculus has no predefined constants, but it still allows the definition of all of the common constants and functions of arithmetic and list manipulation. We will ...

Tools for Refactoring Functional Programs

... Why refactor Haskell? The only design artefact is (in) the code. Semantics of functional languages support largescale transformations (?) Building real tools to support functional programming … heavy lifting. Platform for research and experimentation. ...

... Why refactor Haskell? The only design artefact is (in) the code. Semantics of functional languages support largescale transformations (?) Building real tools to support functional programming … heavy lifting. Platform for research and experimentation. ...

Lambda the Ultimate - Rice University Campus Wiki

... that the rule uses safe substitution, where safe substitution renames local variables in the code body that is being modified by the substitution to avoid capturing free variables in the argument expression that is being ...

... that the rule uses safe substitution, where safe substitution renames local variables in the code body that is being modified by the substitution to avoid capturing free variables in the argument expression that is being ...

A fully abstract semantics for a higher

... In Section 3 we present a λ-calculus with an explicit type constructor, and show (assuming the programs satisfy certain equivalences) that its models are precisely given by categorical structures: Programming construct Categorical equivalent Algebraic datatypes Categories with finite products Let-ex ...

... In Section 3 we present a λ-calculus with an explicit type constructor, and show (assuming the programs satisfy certain equivalences) that its models are precisely given by categorical structures: Programming construct Categorical equivalent Algebraic datatypes Categories with finite products Let-ex ...

7. Introduction to the Lambda Calculus

... Most modern functional languages, on the other hand, use lazy evaluation, that is, expressions are only evaluated when they are needed. Consider: ...

... Most modern functional languages, on the other hand, use lazy evaluation, that is, expressions are only evaluated when they are needed. Consider: ...

Computer Science 203 Programming Languages Bindings

... • There are many parameter-passing modes, such as: – By value: the formal is bound to a variable with an unused location, set to the actual’s value. – By name (in the ALGOL sense): the actual is not evaluated until the point of use. – By reference: the formal is bound to the variable designated ...

... • There are many parameter-passing modes, such as: – By value: the formal is bound to a variable with an unused location, set to the actual’s value. – By name (in the ALGOL sense): the actual is not evaluated until the point of use. – By reference: the formal is bound to the variable designated ...

popl13

... • Operations on values of basic types are defined in each type – (ex.) Operations on values of int type: 2+3, 5*6, 2=2, 2≠2, etc. ...

... • Operations on values of basic types are defined in each type – (ex.) Operations on values of int type: 2+3, 5*6, 2=2, 2≠2, etc. ...

Programming with Miranda

... Benefits of the functional programming style Functional languages are an example of the declarative style of programming, whereby a program gives a description (or “declaration”) of a problem to be solved together with various relationships that hold for it. It is the responsibility of the language ...

... Benefits of the functional programming style Functional languages are an example of the declarative style of programming, whereby a program gives a description (or “declaration”) of a problem to be solved together with various relationships that hold for it. It is the responsibility of the language ...