Group: procedure and typevalued 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 typevalued 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)
