Breck, Hartline
... We have developed a number of tools for describing programming languages, but so far we have only applied the toolbox to IMP. IMP has no functions, (procedures, routines, methods). It has no way to write a functional abstraction. This makes it pretty uninteresting as a programming language. So we wi ...
... We have developed a number of tools for describing programming languages, but so far we have only applied the toolbox to IMP. IMP has no functions, (procedures, routines, methods). It has no way to write a functional abstraction. This makes it pretty uninteresting as a programming language. So we wi ...
Handout 10 from Models of Computation
... Example: We rename (λx.y x x) to (λz.y z z). We say that two λ-terms are α-equivalent if one can be gained from the other by α renaming. For pure λ-terms α-equivalence can be very easily seen by comparing their abstract syntax trees. Example: Obviously (λx.y x x) and (λz.y z z) are α-equivalent. How ...
... Example: We rename (λx.y x x) to (λz.y z z). We say that two λ-terms are α-equivalent if one can be gained from the other by α renaming. For pure λ-terms α-equivalence can be very easily seen by comparing their abstract syntax trees. Example: Obviously (λx.y x x) and (λz.y z z) are α-equivalent. How ...
arguments (an upper and lower bound (integers) and a function
... Calculate the integrals of f(x)= sin(x) from 0 to pi, Calculate the integrals of f(x)= sin(x)* sin(x) from 0 to pi. (Note you may have to Google to find out how sin and pi work in Python. ) ...
... Calculate the integrals of f(x)= sin(x) from 0 to pi, Calculate the integrals of f(x)= sin(x)* sin(x) from 0 to pi. (Note you may have to Google to find out how sin and pi work in Python. ) ...
Haskell: Lambda Expressions
... Finally, λ-calculus allows one to clearly designate in every expression the variables that can be instantiated, by using a λ operator (which gave the calculus its name, in the first place). For example, if we want to express that in f x, the x is a parameter that can be instantiated, we write λx.f x ...
... Finally, λ-calculus allows one to clearly designate in every expression the variables that can be instantiated, by using a λ operator (which gave the calculus its name, in the first place). For example, if we want to express that in f x, the x is a parameter that can be instantiated, we write λx.f x ...
PowerPoint - School of Computing Science
... Do we have a Better Functional Language? We have functions, e.g. x.x+2 is a function, but can we really do functional programming? It’s essential to be able to define recursive functions, but our language has no direct support for recursive definitions. We have no way of associating a name with a ...
... Do we have a Better Functional Language? We have functions, e.g. x.x+2 is a function, but can we really do functional programming? It’s essential to be able to define recursive functions, but our language has no direct support for recursive definitions. We have no way of associating a name with a ...
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 ...
Functional Programming Languages
... These symbols are not variables – they are like the names bound by Java’s final declarations ...
... These symbols are not variables – they are like the names bound by Java’s final declarations ...
CS 170 * Intro to Programming for Scientists and Engineers
... is like EQ?, except that it works for both symbolic and numeric atoms; it is a value comparison, not a pointer ...
... is like EQ?, except that it works for both symbolic and numeric atoms; it is a value comparison, not a pointer ...
Introduction to Lambda Calculus - CSE IITK
... [source: http://www.cs.nott.ac.uk/~gmh/chapter1.ppt] ...
... [source: http://www.cs.nott.ac.uk/~gmh/chapter1.ppt] ...
pptx
... • Skipping parsing by writing language B programs directly in terms of language A constructors • An interpreter written in A recursively evaluates What we know about macros: • Extend the syntax of a language • Use of a macro expands into language syntax before the program is run, i.e., before callin ...
... • Skipping parsing by writing language B programs directly in terms of language A constructors • An interpreter written in A recursively evaluates What we know about macros: • Extend the syntax of a language • Use of a macro expands into language syntax before the program is run, i.e., before callin ...
15. Functional Programming
... A mathematical function is a mapping of members of one set, called the domain set, to another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form ...
... A mathematical function is a mapping of members of one set, called the domain set, to another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form ...
The λ – Calculus
... said to be bound in the sub-expression M 2. A bound variable is one whose name is the same as the parameter. Otherwise the variable is said to be free 3. Any variable not bound in M is said to be free Note: bound variables are placeholders just like function parameters in the imperative and OOP para ...
... said to be bound in the sub-expression M 2. A bound variable is one whose name is the same as the parameter. Otherwise the variable is said to be free 3. Any variable not bound in M is said to be free Note: bound variables are placeholders just like function parameters in the imperative and OOP para ...
First-Class Functions What is functional programming? First
... Our examples of first-class functions so far all: – Take one function as an argument to another function – Process a number or a list But first-class functions are useful anywhere for any kind of data ...
... Our examples of first-class functions so far all: – Take one function as an argument to another function – Process a number or a list But first-class functions are useful anywhere for any kind of data ...
15. Functional Programming
... In an FPL, variables are not necessary, as is the case in mathematics ...
... In an FPL, variables are not necessary, as is the case in mathematics ...
Advanced Formal Methods
... Intended as foundation for mathematics Discovered to be inconsistent, so interest faded (see later) Foundational importance in programming languages Lisp, McCarthy 1959 Programming languages and denotational semantics • Landin, Scott, Strachey 60’s and 70’s ...
... Intended as foundation for mathematics Discovered to be inconsistent, so interest faded (see later) Foundational importance in programming languages Lisp, McCarthy 1959 Programming languages and denotational semantics • Landin, Scott, Strachey 60’s and 70’s ...