\indexentry{$\normalize$ (normal form question)}{2} \indexentry{$\models$ (semantic entailment relation)}{2} \indexentry{$\Emodels$ (equational semantic entailment relation)}{2} \indexentry{$\answers$ (answer relation)}{2} \indexentry{$\answers_{\formeq}$ (equational answer relation)}{2} \indexentry{$\solve$ (equation solving question)}{3} \indexentry{$\bot$ (undefined value)}{4} \indexentry{$\bot$ (undefined value)}{4} \indexentry{$\cons$ (list constructor)}{5} \indexentry{$\true$}{5} \indexentry{$\false$}{5} \indexentry{$\car$ (first projection)}{5} \indexentry{$\cdr$ (second projection)}{5} \indexentry{$\hypos\:\proves_{\cal R}$ (proof by rule)}{8} \indexentry{$\hypos\:\infproves$ (inferential trinary proof relation)}{10} \indexentry{$\infhyproves$ (inferential binary proof relation)}{10} \indexentry{$\onerewrite{\boldscript{T}}$ (one step rewrite relation)}{10} \indexentry{$\mathbold{T}_{\sor+}$ (positive parallel or)}{21} \indexentry{$\mathbold{T}_{\sor-}$ (negative parallel or)}{22} \indexentry{$\mathbold{T}_{SK}$ (combinatory logic)}{23} \indexentry{$\mathbold{T}_{\mathord{\mbox{\it poly}}}$ (Horner-rule addition)}{24} \indexentry{$\mathbold{T}_{\sor+}$ (positive parallel or)}{34} \indexentry{$\onerewritem{\boldscript{T}}{\omega}$ (one step $\omega$-rewrite relation)}{37} \indexentry{$\onerewritem{\boldscript{T}}{\omega}$ (one step $\omega$-rewrite relation)}{38} \indexentry{$\mathbold{T}_{\sor+}$ (positive parallel or)}{44} \indexentry{$\Sig$ (signatures)}{46} \indexentry{$\bfnil$ (meta-nil for term tables)}{46} \indexentry{$\val$ (parameter valuation)}{46} \indexentry{$\repl$ (parameter replacement)}{46} \indexentry{$\ind$ (signature index)}{46} \indexentry{$\val$ (parameter valuation)|(}{46} \indexentry{$\val^*$ (extended parameter valuation)}{47} \indexentry{$\val$ (parameter valuation)|)}{47} \indexentry{$\val^*_{\repl}$ (extended parameter valuation/replacement)|(}{48} \indexentry{$\val^*_{\repl}$ (extended parameter valuation/replacement)|)}{48} \indexentry{$\val^{\mbox{\it max}}_{\repl}$ (replaced parameter valuation)|(}{48} \indexentry{$\val^{\mbox{\it max}}_{\repl}$ (replaced parameter valuation)|)}{49} \indexentry{$\mathbold{T}^{\Omega}_{P}$ ($\Omega$-terms)}{54} \indexentry{$\Omega$ (unknown subterm)}{54} \indexentry{$\sqsubseteq$ (less defined relation on $\Omega$-terms)}{54} \indexentry{$\sqcap$ (greatest lower bound of $\Omega$-terms)}{54} \indexentry{$\uparrow$ (consistency relation on $\Omega$-terms)}{54} \indexentry{$\patt$ (left-hand side patterns in equations)}{54} \indexentry{$\melt^{\boldscript{T}}_{\omega}$ (melting $\Omega$-terms)|(}{55} \indexentry{$\bullet$ (marker for strongly needed redex)}{55} \indexentry{$\melt^{\boldscript{T}}_{\omega}$ (melting $\Omega$-terms)|)}{55} \indexentry{$\mathbold{U}_{\boldscript{T}}$ (universal subpattern set)}{59} \indexentry{$\eval$ (strict normalization procedure)}{64} \indexentry{$\heval$ (head-normalization procedure)}{65} \indexentry{$\rhs$ (right-hand side construction procedure)}{65} \indexentry{$\rhs$ (right-hand side construction procedure)}{65} \indexentry{$\norm$ (lazy normalization procedure)}{66} \indexentry{$\val^{\mbox{\it max}}_{\repl}$ (replaced parameter valuation)|(}{66} \indexentry{$\val$ (parameter valuation)|(}{66} \indexentry{$\repl$ (parameter replacement)|(}{66} \indexentry{$\ind$ (signature index)|(}{66} \indexentry{$\heval$ (head-normalization procedure)}{66} \indexentry{$\rhs$ (right-hand side construction procedure)}{67} \indexentry{$\heval$ (head-normalization procedure)}{67} \indexentry{$\val^{\mbox{\it max}}_{\repl}$ (replaced parameter valuation)|)}{67} \indexentry{$\val$ (parameter valuation)|)}{67} \indexentry{$\repl$ (parameter replacement)|)}{67} \indexentry{$\rhs$ (right-hand side construction procedure)|(}{67} \indexentry{$\heval$ (head-normalization procedure)|(}{67} \indexentry{$\rhs$ (right-hand side construction procedure)|)}{67} \indexentry{$\ind$ (signature index)|)}{68} \indexentry{$\heval$ (head-normalization procedure)|)}{68} \indexentry{$\eval$ (strict normalization procedure)}{72} \indexentry{$L_{\omega_1,\omega}$ (infinitary con/disjunctions)}{76} \indexentry{$\lim$ (term limit)}{77} \indexentry{$\appr$ (canonical set of approximations)}{77} \indexentry{$\heval$ (head-normalization procedure)}{80} \indexentry{$\solve$ (equation solving question)}{82} \indexentry{$\what$ (`what' question)}{82}