1 / 11

Formalization of Oscilloscope

Formalization of Oscilloscope. On Formalism. High-level (implementation-independent) specification Recall: Larch – An Algebraic Formal Spec. Lang. Why formal? Precise, consistent, and complete Formal semantics: Formal = grammar, e.g., syllogism All persons die. Adam is a person

nadine
Télécharger la présentation

Formalization of Oscilloscope

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Formalization of Oscilloscope

  2. On Formalism • High-level (implementation-independent) specification • Recall: Larch – An Algebraic Formal Spec. Lang. • Why formal? Precise, consistent, and complete • Formal semantics: Formal = grammar, e.g., syllogism All persons die. Adam is a person ------------------------ Adam dies. Semantics?

  3. Introduction to Z • Based on typed set theory and first order logic • Sets: • oneTwoThree == {1, 2, 3} • Person == {Adam, Eve} S: P X == 2 X--- S is a set of X’s powerset, i.e., the set of all subsets of X • oneTwoThreeSet == P oneTwoThree == P {1, 2, 3} == ? • personSet == P person == P {Adam, Eve} == ? • |P X| == ?

  4. Introduction to Z • Sets (cont’d) • x memberOf S ? 1 memberOf {1, 2, 3} ? 1 memberof P {1, 2, 3} ? {1} memberof P {1, 2, 3} ? Adam memberOf P Person ? Adam memberOf Person ? {Adam, Eve} memberOf P Person

  5. Introduction to Z • Sets (cont’d) • S subsetOf S’ ? 1 subsetOf {1, 2, 3} ? {1, 2} subsetOf P {1, 2, 3} ? {{1, 2}} subsetOf P {1, 2, 3} ? Adam subsetOf P Person ? Adam subsetOf Person ? Person subsetOf Person ? {Person} subsetOf P Person

  6. Introduction to Z • Sets (cont’d) • S X S’ (cross/cartesian product) oneTwoThree X person == {1, 2, 3} X {Adam, Eve} == {{1, Adam}, {1, Eve}, {2, Adam}, {2, Eve}, {3, Adam}, {3, Eve}} ? {1, 2} subsetOf {1, 2} X {1, 2} • S U S’, S intersect S’, S\S’, etc. (skip)

  7. Introduction to Z • Functions • dom f --- The set of values x for which f(x) is defined f(x) = x 2 , dom f = {n memberOf N| 1 <= n <= 5} • ran f --- The set of values taken by f(x), where x memberOf dom f ran f = ? • f: X -> Y --- f is a total function from X to Y i.e., f is defined for all x memberOf dom(f), i.e., dom(f) = X • f: X -|-> Y --- f is a partial function from X to Y i.e., f is defined for some values in X if f(x) = 1/x, ? dom(f) = Z ? spouse: Person -> Person

  8. Introduction to Z • Functions (cont’d) • (lambda x: T . t) returns the value of the term t (lambda x: N . X 2 ) 5 == 25 (lambda x: N . (X 2 , 1/x) == ? (lambda x, y: N . (X 2 + y, y -1/x) 5 1 == ?

  9. Introduction to Z • First Order Logic • Logical connectives: AND, OR, NOT, =>, <=> • Quantifiers ? Exists n: N . n = n 2 ? Exists p: Person . P == father (Adam) ? Forall i: N . I 2 >= I ? Forall I, j: N . I > j => I 2 > j 2 ? Forall x, y: Person, x == spouse(y) <=> y == spouse(x)

  10. Introduction to Z • Schemas A schema consists of a set of declarations olf variables and a predicate constraining these variables (i.e., state space and operations) ----- BirthdayBook ---------------------------------------- | known: P Person | birthday: Person -|-> Date ----------------------------------------------------------------- | known = dom birthday ----------------------------------------------------------------- One possible state: known = {Adam, Eve} birthday = {Adam |-> Apr/01, Eve |-> Apr/01}

  11. A Simple Oscilloscope • Overview

More Related