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Bibliographic Item (1.0)

  1. David Gries & Fred B Schneider
  2. Teaching Math More Effecively Through Calculational Proofs
  3. Am Math Monthly V102n8(Oct 1995)pp691-697)
  5. Advert for [GriesSchneider93]
    1. 15 axioms and 4 rules
    2. = is transitive, can substitute a free variable,
    3. equanimity:
    4. if P and (P ≡ Q) then Q
    5. and Liebnitz:
      1. E[v:=P]
      2. = <P=Q>
      3. E[v:=Q]

      Where P and Q are expressions and v some variable not found in P or Q and E[v:=P] some expression with every ovccurrence of v replaced by P and E[v:=Q] the same expression with every v replaced by Q.

      Also treats ≡ as an associative (serial) operator, and equals as a parallel operator.

      Unified notation for all quantification, summation, etc:

    6. (op var | condition : expression)

      Formal notation is a repository of facts and a means of clarification. It provides rules for judging the soundness of inference and detecting and eliminating ambiguity.

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