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## Topic: symbolic manipulation of formulas

topics > Group: mathematics

Group:
procedure and type-valued variables

Topic:
abstraction in programming
Topic:
list processing
Topic:
programming as mathematics
Topic:
processing a sequence
Topic:
reduction languages
Topic:
string transformation languages
Topic:
symbolic execution
Topic:
symbolic representation
Topic:
theorem proving systems

#### Summary

Computers can manipulate algebraic formulas as syntax trees. Expressions can be named, derivatives taken, theorems defined, expressions build, expressions analyzed and equations solved. Formula manipulation is performed by tree traversal and transformation. Memory requirements may be high. (cbb 5/80)
Subtopic: symbolic systems

 Quote: computing science may provide symbolic calculation that is better than human reasoning; Leibniz's dream [»dijkEW12_1989]

Subtopic: formula manipulation

 Quote: Boys developed an EDSAC program for symbolic differentiation [»wilkMV_1985] Quote: FEA developed for information storage and retrieval of algebraic theorems, definitions, axioms [»postSW7_1978] QuoteRef: cbb_1973 ;;formac FORMAC formula manipulator : replace, substitute, expand, search equivalent QuoteRef: sammJE_1969 ;;383 list processing generally for symbol manipulation i.e. logical sequential QuoteRef: sammJE_1969 ;;454 AMBIT for math symbol manipulation

Subtopic: symbolic assignment

 QuoteRef: sammJE_1969 ;;479 variables containing algebraic expressions with rational and floating point constants eg let y=a+b*c results in an expression QuoteRef: sammJE_1969 ;;584 symbol variables have stacks associated with them QuoteRef: elcoEW_1971 ;;472 statements (assertion of structure) are expressions with a true value indicated by ";" eg a+b=3 and a=1; sets b=1 QuoteRef: reynJC_1965 ;;42 synthetic assignment eg z/=(term/(factor)*(factor)), x,y. gives z(term/abe*bcd) if x is (factor/abe) and y (factor/bcd) QuoteRef: reynJC_1965 ;;42 analytic assignment eg z=/ (term/(factor)*(factor)), x,y. is inverse splits z eg in (factor/abe) and y (factor/bcd) into x and y

Subtopic: problems with symbolic systems

 QuoteRef: sammJE_1969 ;;476 general problem with formula language is easy to outgrow available memory

Related Topics

Group: procedure and type-valued variables   (4 topics, 95 quotes)

Topic: abstraction in programming (67 items)
Topic: list processing (15 items)
Topic: programming as mathematics (27 items)
Topic: processing a sequence (17 items)
Topic: reduction languages (17 items)
Topic: string transformation languages (17 items)
Topic: symbolic execution (9 items)
Topic: symbolic representation (26 items)
Topic: theorem proving systems
(20 items)

Updated barberCB 2/05