Defining Functions
... using the a symbol, as in x a x + x. z In Haskell, the use of the l symbol for nameless functions comes from the lambda calculus, the theory of functions on which Haskell is based. ...
... using the a symbol, as in x a x + x. z In Haskell, the use of the l symbol for nameless functions comes from the lambda calculus, the theory of functions on which Haskell is based. ...
CS3234 Logic and Formal Systems
... Answer 14: The first sequent is not valid. One counter-example is a model M whose universe has two elements, say a and b, such that P M = {(a, a), (b, b)}. Clearly ∀x∃ P (x, y) holds in this model, but ∃y∀x P (x, y) does not hold. The second sequent ∃y ∀x P (x, y) ` ∀x∃y P (x, y) is valid, and here ...
... Answer 14: The first sequent is not valid. One counter-example is a model M whose universe has two elements, say a and b, such that P M = {(a, a), (b, b)}. Clearly ∀x∃ P (x, y) holds in this model, but ∃y∀x P (x, y) does not hold. The second sequent ∃y ∀x P (x, y) ` ∀x∃y P (x, y) is valid, and here ...
(formal) logic? - Departamento de Informática
... Much of standard mathematics can be done within the framework of intuitionistic logic, but the task is very difficult, so mathematicians use methods of classical logic (as proofs by contradiction). However the philosophy behind intuitionistic logic is appealing for a computer scientist. For an intuiti ...
... Much of standard mathematics can be done within the framework of intuitionistic logic, but the task is very difficult, so mathematicians use methods of classical logic (as proofs by contradiction). However the philosophy behind intuitionistic logic is appealing for a computer scientist. For an intuiti ...
Lambda-calculus. - UT Computer Science
... Lambda Calculus Formal system with three parts • Notation for function expressions • Proof system for equations • Calculation rules called reduction ...
... Lambda Calculus Formal system with three parts • Notation for function expressions • Proof system for equations • Calculation rules called reduction ...
A short article for the Encyclopedia of Artificial Intelligence: Second
... an individual. Similarly, an expression that is of the type o is defined to be a formula. Typed expressions are built by application (if M is of type σ → τ and N is of type σ, then their application (M N ) is of type τ ) and abstraction (if x is a variable of type σ and M is of type τ , then the abs ...
... an individual. Similarly, an expression that is of the type o is defined to be a formula. Typed expressions are built by application (if M is of type σ → τ and N is of type σ, then their application (M N ) is of type τ ) and abstraction (if x is a variable of type σ and M is of type τ , then the abs ...
First-Order Logic - Columbia University
... Sound and complete for first-order definite clauses Datalog is first-order definite clauses and no functions May not terminate in general if is not entailed This is unavoidable: entailment with definite clauses is semi-decidable Forward chaining is widely used in deductive databases ...
... Sound and complete for first-order definite clauses Datalog is first-order definite clauses and no functions May not terminate in general if is not entailed This is unavoidable: entailment with definite clauses is semi-decidable Forward chaining is widely used in deductive databases ...
valid - Informatik Uni Leipzig
... For restricted classes of frames there are more tableau rules. ; For reflexive (T) frames we may extend any branch with wRw. ; For transitive (4) frames we need one additional rule : ◦ If there are wRv and vRu on one branch, we can extend this branch by wRu. ; For serial (D) frames we need the follo ...
... For restricted classes of frames there are more tableau rules. ; For reflexive (T) frames we may extend any branch with wRw. ; For transitive (4) frames we need one additional rule : ◦ If there are wRv and vRu on one branch, we can extend this branch by wRu. ; For serial (D) frames we need the follo ...
Lect 1
... Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no assignment but only a true mathematical equality. ...
... Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no assignment but only a true mathematical equality. ...
Document
... Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no assignment but only a true mathematical equality. ...
... Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no assignment but only a true mathematical equality. ...
ppt
... - Functions as first class objects (can be value of an expression, passed as an argument, put in a data structure) ...
... - Functions as first class objects (can be value of an expression, passed as an argument, put in a data structure) ...
Foundations of Functional Programming
... The idea that λ-abstractions represent functions is formally expressed through conversion rules for manipulating them. There are α-conversions, β-conversions and η-conversions. The α-conversion (λx.M) →α (λy.M[y/x]) renames the abstraction’s bound variable from x to y. It is valid provided y does no ...
... The idea that λ-abstractions represent functions is formally expressed through conversion rules for manipulating them. There are α-conversions, β-conversions and η-conversions. The α-conversion (λx.M) →α (λy.M[y/x]) renames the abstraction’s bound variable from x to y. It is valid provided y does no ...
Lecture Notes
... definition, but generally speaking: Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; ...
... definition, but generally speaking: Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; ...
ppt
... - Functions as first class objects (can be value of an expression, passed as an argument, put in a data structure) ...
... - Functions as first class objects (can be value of an expression, passed as an argument, put in a data structure) ...
Functional Programming in Scheme Functional Programming
... - Functions as first class objects (can be value of an expression, passed as an argument, put in a data structure) ...
... - Functions as first class objects (can be value of an expression, passed as an argument, put in a data structure) ...
Handout 14
... provable is a tautology. Thus, the formal system of propositional logic is not only sound (i.e. generates only valid formulas) but also generates all of them. Theorem 5.2 (completeness of propositional logic). Let T be a set of formulas and A a formula. Then T (A ...
... provable is a tautology. Thus, the formal system of propositional logic is not only sound (i.e. generates only valid formulas) but also generates all of them. Theorem 5.2 (completeness of propositional logic). Let T be a set of formulas and A a formula. Then T (A ...
No Slide Title - Computer Science
... A model of Trans is a pair (X,R) with X a set and R a transitive binary relation on it. ...
... A model of Trans is a pair (X,R) with X a set and R a transitive binary relation on it. ...
Predicate Logic
... appealing because you can derive new knowledge from old mathematical deduction. • In this formalism you can conclude that a new statement is true if by proving that it follows from the statement that are already known. • It provides a way of deducing new statements from old ones. ...
... appealing because you can derive new knowledge from old mathematical deduction. • In this formalism you can conclude that a new statement is true if by proving that it follows from the statement that are already known. • It provides a way of deducing new statements from old ones. ...
pdf
... The beauty of logic they see The logic we teach they will claim Is useful in many domain The students will feel That logic’s for real And helps them develop their brain The students will also acclaim Developing proof’s a neat game It’s opened their eye [to] how math to apply And now they know math’s ...
... The beauty of logic they see The logic we teach they will claim Is useful in many domain The students will feel That logic’s for real And helps them develop their brain The students will also acclaim Developing proof’s a neat game It’s opened their eye [to] how math to apply And now they know math’s ...
Propositional Logic
... as the propositonal satisfiability (PSAT) problem. An exhaustive procedure for solving the PSAT problem is to try systematically all of the ways to assign True and False to the atoms in the formula, checking the assignment to see if all formulas have value True under that assignment. If there are n ...
... as the propositonal satisfiability (PSAT) problem. An exhaustive procedure for solving the PSAT problem is to try systematically all of the ways to assign True and False to the atoms in the formula, checking the assignment to see if all formulas have value True under that assignment. If there are n ...
Natural Deduction Calculus for Quantified Propositional Linear
... While the propositional quantification does not add any expressiveness to the classical logic QPTL is more expressive than PLTL presenting the same potential of expressiveness as linear-time µ-calculus (linear-time propositional temporal fixpoint logic) [Kaivola (1997)], ETL (propositional linear-ti ...
... While the propositional quantification does not add any expressiveness to the classical logic QPTL is more expressive than PLTL presenting the same potential of expressiveness as linear-time µ-calculus (linear-time propositional temporal fixpoint logic) [Kaivola (1997)], ETL (propositional linear-ti ...
Functions, recursion and lists
... (let ((x1 E1) (x2 E2)) E3) ; declare local variables x1 and x2 (let* ((x1 E2) (x2 E2)) E3) ; E2 can use x1 as a local variable cs3723 ...
... (let ((x1 E1) (x2 E2)) E3) ; declare local variables x1 and x2 (let* ((x1 E2) (x2 E2)) E3) ; E2 can use x1 as a local variable cs3723 ...