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The U.S. Navy Arleigh Burke-class guided-missile destroyer USS Hopper was named for her, as was the Cray XE6 "Hopper" supercomputer at NERSC. During her lifetime, Hopper was awarded 40 honorary degrees from universities across the world. A college at Yale University was renamed in her honor. In 1991, she received the National Medal of Technology. On November 22, 2016, she was posthumously awarded the Presidential Medal of Freedom by President Barack Obama.

Following her retirement from the Navy, she was hired as a senior consultant to Digital Equipment Corporation (DEC). Hopper was initially offered a position by Rita Yavinsky, but she insisted on going through the typical formal interview process. She then proposed in jest that she would be willing to accept a position which made her available on alternating Thursdays, exhibited at their museum of computing as a pioneer, in exchange for a generous salary and unlimited expense account. Instead, she was hired as a full-time senior consultant. In this position, Hopper represented the company at industry forums, serving on various industry committees, along with other obligations. She retained that position until her death at age 85 in 1992.

On New Year's Day 1992, Hopper died in her sleep of natural causes at her home in Arlington, Virginia; she was 85 years of age. She was interred with full military honors in Arlington National Cemetery.

Following a career that spanned more than 42 years, Admiral Hopper took retirement from the Navy on August 14, 1986. At a celebration held in Boston on the USS Constitution to commemorate her retirement, Hopper was awarded the Defense Distinguished Service Medal, the highest non-combat decoration awarded by the Department of Defense.

After Republican Representative Philip Crane saw her on a March 1983 segment of 60 Minutes, he championed H.J.Res. 341, a joint resolution originating in the House of Representatives, which led to her promotion on 15 December 1983 to commodore by special Presidential appointment by President Ronald Reagan. She remained on active duty for several years beyond mandatory retirement by special approval of Congress. Effective November 8, 1985, the rank of commodore was renamed rear admiral (lower half) and Hopper became one of the Navy's few female admirals.

In the 1970s, Hopper advocated for the Defense Department to replace large, centralized systems with networks of small, distributed computers. Any user on any computer node could access common databases located on the network. She developed the implementation of standards for testing computer systems and components, most significantly for early programming languages such as FORTRAN and COBOL. The Navy tests for conformance to these standards led to significant convergence among the programming language dialects of the major computer vendors. In the 1980s, these tests (and their official administration) were assumed by the National Bureau of Standards (NBS), known today as the National Institute of Standards and Technology (NIST).

From 1967 to 1977, Hopper served as the director of the Navy Programming Languages Group in the Navy's Office of Information Systems Planning and was promoted to the rank of captain in 1973. She developed validation software for COBOL and its compiler as part of a COBOL standardization program for the entire Navy.

In accordance with Navy attrition regulations, Hopper retired from the Naval Reserve with the rank of commander at age 60 at the end of 1966. She was recalled to active duty in August 1967 for a six-month period that turned into an indefinite assignment. She again retired in 1971 but was again asked to return to active duty in 1972. She was promoted to captain in 1973 by Admiral Elmo R. Zumwalt, Jr.

In the spring of 1959, computer experts from industry and government were brought together in a two-day conference known as the Conference on Data Systems Languages (CODASYL). Hopper served as a technical consultant to the committee, and many of her former employees served on the short-term committee that defined the new language COBOL (an acronym for COmmon Business-Oriented Language). The new language extended Hopper's FLOW-MATIC language with some ideas from the IBM equivalent, COMTRAN. Hopper's belief that programs should be written in a language that was close to English (rather than in machine code or in languages close to machine code, such as assembly languages) was captured in the new business language, and COBOL went on to be the most ubiquitous business language to date. Among the members of the committee that worked on COBOL was Mount Holyoke College alumnus Jean E. Sammet.

In 1954, Eckert–Mauchly chose Hopper to lead their department for automatic programming, and she led the release of some of the first compiled languages like FLOW-MATIC. In 1959, she participated in the CODASYL consortium, which consulted Hopper to guide them in creating a machine-independent programming language. This led to the COBOL language, which was inspired by her idea of a language being based on English words. In 1966, she retired from the Naval Reserve, but in 1967 the Navy recalled her to active duty. She retired from the Navy in 1986 and found work as a consultant for the Digital Equipment Corporation, sharing her computing experiences.

In 1954 Hopper was named the company's first director of automatic programming, and her department released some of the first compiler-based programming languages, including MATH-MATIC and FLOW-MATIC.

Her idea was not accepted for 3 years. In the meantime, she published her first paper on the subject, compilers, in 1952. In the early 1950s, the company was taken over by the Remington Rand corporation, and it was while she was working for them that her original compiler work was done. The program was known as the A compiler and its first version was A-0.

In 1952, she had an operational link-loader, which at the time was referred to as a compiler. She later said that "Nobody believed that," and that she "had a running compiler and nobody would touch it. They told me computers could only do arithmetic." She goes on to say that her compiler "translated mathematical notation into machine code. Manipulating symbols was fine for mathematicians but it was no good for data processors who were not symbol manipulators. Very few people are really symbol manipulators. If they are they become professional mathematicians, not data processors. It's much easier for most people to write an English statement than it is to use symbols. So I decided data processors ought to be able to write their programs in English, and the computers would translate them into machine code. That was the beginning of COBOL, a computer language for data processors. I could say 'Subtract income tax from pay' instead of trying to write that in octal code or using all kinds of symbols. COBOL is the major language used today in data processing."

In 1949, Hopper became an employee of the Eckert–Mauchly Computer Corporation as a senior mathematician and joined the team developing the UNIVAC I. Hopper also served as UNIVAC director of Automatic Programming Development for Remington Rand. The UNIVAC was the first known large-scale electronic computer to be on the market in 1950, and was more competitive at processing information than the Mark I.

Prior to joining the Navy, Hopper earned a Ph.D. in mathematics from Yale University and was a professor of mathematics at Vassar College. Hopper attempted to enlist in the Navy during World War II but was rejected because she was 34 years old. She instead joined the Navy Reserves. Hopper began her computing career in 1944 when she worked on the Harvard Mark I team led by Howard H. Aiken. In 1949, she joined the Eckert–Mauchly Computer Corporation and was part of the team that developed the UNIVAC I computer. At Eckert–Mauchly she began developing the compiler. She believed that a programming language based on English was possible. Her compiler converted English terms into machine code understood by computers. By 1952, Hopper had finished her program linker (originally called a compiler), which was written for the A-0 System. During her wartime service, she co-authored three papers based on her work on the Harvard Mark 1.

Hopper had tried to enlist in the Navy early in World War II. She was rejected for a few reasons. At age 34, she was too old to enlist, and her weight to height ratio was too low. She was also denied on the basis that her job as a mathematician and mathematics professor at Vassar College was valuable to the war effort. During the war in 1943, Hopper obtained a leave of absence from Vassar and was sworn into the United States Navy Reserve; she was one of many women who volunteered to serve in the WAVES. She had to get an exemption to enlist; she was 15 pounds (6.8 kg) below the Navy minimum weight of 120 pounds (54 kg). She reported in December and trained at the Naval Reserve Midshipmen's School at Smith College in Northampton, Massachusetts. Hopper graduated first in her class in 1944, and was assigned to the Bureau of Ships Computation Project at Harvard University as a lieutenant, junior grade. She served on the Mark I computer programming staff headed by Howard H. Aiken. Hopper and Aiken co-authored three papers on the Mark I, also known as the Automatic Sequence Controlled Calculator. Hopper's request to transfer to the regular Navy at the end of the war was declined due to her advanced age of 38. She continued to serve in the Navy Reserve. Hopper remained at the Harvard Computation Lab until 1949, turning down a full professorship at Vassar in favor of working as a research fellow under a Navy contract at Harvard.

In 1934, she earned a Ph.D. in mathematics from Yale under the direction of Øystein Ore. Her dissertation, "New Types of Irreducibility Criteria", was published that same year. Hopper began teaching mathematics at Vassar in 1931, and was promoted to associate professor in 1941.

Grace was very curious as a child; this was a lifelong trait. At the age of seven, she decided to determine how an alarm clock worked and dismantled seven alarm clocks before her mother realized what she was doing (she was then limited to one clock). For her preparatory school education, she attended the Hartridge School in Plainfield, New Jersey. Hopper was initially rejected for early admission to Vassar College at age 16 (her test scores in Latin were too low), but she was admitted the following year. She graduated Phi Beta Kappa from Vassar in 1928 with a bachelor's degree in mathematics and physics and earned her master's degree at Yale University in 1930.

Grace Brewster Murray Hopper (née  Murray December 9, 1906 – January 1, 1992) was an American computer scientist and United States Navy rear admiral. One of the first programmers of the Harvard Mark I computer, she was a pioneer of computer programming who invented one of the first linkers. She popularized the idea of machine-independent programming languages, which led to the development of COBOL, an early high-level programming language still in use today.

She was married to New York University professor Vincent Foster Hopper (1906–1976) from 1930 until their divorce in 1945. She did not marry again, but chose to retain his surname.