Functional Programming, an introduction
... the two parameters that f is "waiting" for. • A nice way to think of this is that all functions are really just a function of zero or a single parameter. • The function f a b c is the function that takes one parameter, a, and returns a function that takes the remaining two parameters, b and c. • Thi ...
... the two parameters that f is "waiting" for. • A nice way to think of this is that all functions are really just a function of zero or a single parameter. • The function f a b c is the function that takes one parameter, a, and returns a function that takes the remaining two parameters, b and c. • Thi ...
Functional Programming Paradigm Learning Outcomes:
... • The objective of the design of a FPL is to mimic mathematical functions to the greatest extent possible • The basic process of computation is fundamentally different in a FPL than in an imperative language – In an imperative language, operations are done and the results are stored in variables for ...
... • The objective of the design of a FPL is to mimic mathematical functions to the greatest extent possible • The basic process of computation is fundamentally different in a FPL than in an imperative language – In an imperative language, operations are done and the results are stored in variables for ...
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 ...
Relevant deduction
... every more comprehensive observational report which entails D and is consistent with T confirms T, too. All this seems to be fine. But look what happens. Some easy steps of propositional logic show that (3) together with (4) imply the following ...
... every more comprehensive observational report which entails D and is consistent with T confirms T, too. All this seems to be fine. But look what happens. Some easy steps of propositional logic show that (3) together with (4) imply the following ...
pdf
... he also allows for different subjective domains at each world. He goes further by using what is called neighborhood semantics, also called Montague-Scott structures (Fagin et al., 1995). As is well known, neighborhood semantics provide a more general approach for modeling knowledge than the standar ...
... he also allows for different subjective domains at each world. He goes further by using what is called neighborhood semantics, also called Montague-Scott structures (Fagin et al., 1995). As is well known, neighborhood semantics provide a more general approach for modeling knowledge than the standar ...
scheme1
... objects, minimal use of side-effects • Uniform Representation of Data and Code – (A B C D) can be interpreted as data (i.e., a list of four elements) or code (calling function ‘A’ to the three parameters B, C, and D) • Reliance on Recursion – iteration is provided too, but recursion is much more nat ...
... objects, minimal use of side-effects • Uniform Representation of Data and Code – (A B C D) can be interpreted as data (i.e., a list of four elements) or code (calling function ‘A’ to the three parameters B, C, and D) • Reliance on Recursion – iteration is provided too, but recursion is much more nat ...
On the Notion of Coherence in Fuzzy Answer Set Semantics
... negation in the context of residuated logic programming is provided in terms of the notion of coherence as a generalization in the fuzzy framework of the concept of consistence. Then, fuzzy answer sets for general residuated logic programs are defined as a suitable generalization of the Gelfond-Lifs ...
... negation in the context of residuated logic programming is provided in terms of the notion of coherence as a generalization in the fuzzy framework of the concept of consistence. Then, fuzzy answer sets for general residuated logic programs are defined as a suitable generalization of the Gelfond-Lifs ...
A general introduction to Functional Programming using Haskell
... A lambda expression is used to define an anonymous function It is made of: – a pattern for each argument of the function – a body, which defines how the result is computed from the values of the arguments – Examples: \x > x+x \(x,y) > x+y \(x:xs) > x^2 • then, if we evaluate the expression (\(x:x ...
... A lambda expression is used to define an anonymous function It is made of: – a pattern for each argument of the function – a body, which defines how the result is computed from the values of the arguments – Examples: \x > x+x \(x,y) > x+y \(x:xs) > x^2 • then, if we evaluate the expression (\(x:x ...
The Foundations
... is true ? => The proposition: “It_is_raining” is true if the meaning (or fact) that the proposition is intended to represent occurs (happens, exists) in the situation which the proposition is intended to describe. =>Example: Since it is not raining now (the current situation), the statement “It_is_r ...
... is true ? => The proposition: “It_is_raining” is true if the meaning (or fact) that the proposition is intended to represent occurs (happens, exists) in the situation which the proposition is intended to describe. =>Example: Since it is not raining now (the current situation), the statement “It_is_r ...
Completeness in modal logic - Lund University Publications
... become largely “l’art pour l’art”, as the authors express it, and semantics often seem to be viewed by logicians as mere “collectors of completeness results” rather than tools for actually interpreting modal logics. To illustrate this point, they constructed a semantics that makes every classical mo ...
... become largely “l’art pour l’art”, as the authors express it, and semantics often seem to be viewed by logicians as mere “collectors of completeness results” rather than tools for actually interpreting modal logics. To illustrate this point, they constructed a semantics that makes every classical mo ...
A sequent calculus demonstration of Herbrand`s Theorem
... We assume a particular form of variable use for sequent proofs in GS. Variables should be used strictly: each universal rule binds a unique eigenvariable, and that eigenvariable occurs only in the subproof above the rule which binds it. Further, we enforce a Barendregt-style convention on the use of ...
... We assume a particular form of variable use for sequent proofs in GS. Variables should be used strictly: each universal rule binds a unique eigenvariable, and that eigenvariable occurs only in the subproof above the rule which binds it. Further, we enforce a Barendregt-style convention on the use of ...
Week 1
... Features of functional languages • usually strongly typed (modern languages) • algebraic type definitions – mathematical based notation – no (implicit) pointers • higher-order functions – can accept functions as parameters – can return functions as results • recursion as a basic principle • applicat ...
... Features of functional languages • usually strongly typed (modern languages) • algebraic type definitions – mathematical based notation – no (implicit) pointers • higher-order functions – can accept functions as parameters – can return functions as results • recursion as a basic principle • applicat ...
Functional programming languages - Part I - Gallium
... In what environment should the body of the function f evaluate when we compute the value of f 0 ? Dynamic scoping: in the environment current at the time we evaluate f 0. In this environment, x is bound to "foo". This is inconsistent with the λ-calculus model and is generally considered as a bad ide ...
... In what environment should the body of the function f evaluate when we compute the value of f 0 ? Dynamic scoping: in the environment current at the time we evaluate f 0. In this environment, x is bound to "foo". This is inconsistent with the λ-calculus model and is generally considered as a bad ide ...
Proofs in Propositional Logic
... We will now add to Minimal Propositional Logic introduction and elimination rules and tactics for the constants True and False, and the connectives and (/\), or (\/), iff (↔) and not (∼). ...
... We will now add to Minimal Propositional Logic introduction and elimination rules and tactics for the constants True and False, and the connectives and (/\), or (\/), iff (↔) and not (∼). ...
Proofs in Propositional Logic
... We will now add to Minimal Propositional Logic introduction and elimination rules and tactics for the constants True and False, and the connectives and (/\), or (\/), iff (↔) and not (∼). ...
... We will now add to Minimal Propositional Logic introduction and elimination rules and tactics for the constants True and False, and the connectives and (/\), or (\/), iff (↔) and not (∼). ...
Intuitionistic Type Theory - The collected works of Per Martin-Löf
... Mathematical logic and the relation between logic and mathematics have been interpreted in at least three different ways: (1) mathematical logic as symbolic logic, or logic using mathematical symbolism; (2) mathematical logic as foundations (or philosophy) of mathematics; (3) mathematical logic as l ...
... Mathematical logic and the relation between logic and mathematics have been interpreted in at least three different ways: (1) mathematical logic as symbolic logic, or logic using mathematical symbolism; (2) mathematical logic as foundations (or philosophy) of mathematics; (3) mathematical logic as l ...
CATEGORICAL MODELS OF FIRST
... It seems intuitive that under this interpretation classes of logically equivalent propositions are no longer identified: a proof of ψ ∧ ψ is not a proof of ψ. What is not immediately obvious is how we might formalize this notion; in order to do so, we must first know when two proofs are identical. T ...
... It seems intuitive that under this interpretation classes of logically equivalent propositions are no longer identified: a proof of ψ ∧ ψ is not a proof of ψ. What is not immediately obvious is how we might formalize this notion; in order to do so, we must first know when two proofs are identical. T ...
Deep Sequent Systems for Modal Logic
... Labelled systems are formulated in a hybrid language which not only contains modalities but also variables and an accessibility relation. There are some concerns about incorporating the semantics into the syntax of a proof system in this way. Avron discusses them in [1], for example. However, even w ...
... Labelled systems are formulated in a hybrid language which not only contains modalities but also variables and an accessibility relation. There are some concerns about incorporating the semantics into the syntax of a proof system in this way. Avron discusses them in [1], for example. However, even w ...
Intuitionistic Type Theory
... Mathematical logic and the relation between logic and mathematics have been interpreted in at least three different ways: (1) mathematical logic as symbolic logic, or logic using mathematical symbolism; (2) mathematical logic as foundations (or philosophy) of mathematics; (3) mathematical logic as l ...
... Mathematical logic and the relation between logic and mathematics have been interpreted in at least three different ways: (1) mathematical logic as symbolic logic, or logic using mathematical symbolism; (2) mathematical logic as foundations (or philosophy) of mathematics; (3) mathematical logic as l ...
