A typing judgment asserts that expression $e$ has type $\tau$ under a typing context $\Gamma$. A rule displays prerequisite typing judgments above a line and their conclusion below it. Repeatedly applying rules gives a derivation; the addition example under type system uses two assumptions and one addition rule.

In the examples here, a simple type is a finite expression built from the base types int and bool using function types:For example, $\mathrm{int}\to \mathrm{bool}$ describes a function accepting an integer and producing a Boolean value. During type inference, the grammar is extended with type variables such as $\alpha$ for types not yet determined. A type scheme additionally binds such type variables; it is distinct from the individual simple type used at one call.

For a deterministic single-tape Turing machine, an instruction reads a state $q$ and scanned tape symbol $a$, writes $b$, changes state to $p$, and moves the head one cell left, one cell right, or not at all according to $D$. The state and tape alphabets are finite; an undefined transition halts. A dedicated terminal state can be introduced by directing undefined transitions to it without changing whether computation halts.

An instantaneous description records the current control state, head position, and tape contents. For a tape blank outside a finite window, a word $huqvh$ records the symbols $u$ to the left of the head and $v$ from the scanned cell rightward, with unrecorded cells blank. If $v$ is empty, the head scans an implicit blank. Extra outer blanks can represent the same infinite tape. The instruction of a Turing machine determines its successor description.

Online text: physics.nist.gov/PhysRefData/MolSpec/Triatomic/Html/sec5.html

Cited passages: NIST, Triatomic Spectral Database, Special Units: debye in coulomb metres.

By Jonny Evans.

Online text: jde27.uk/tg/quot02.html

Cited passages: Jonny Evans, 3.02 Quotient topology: continuous maps, notes at 0.14–1.47 and 4.30–7.33.

By Jonny Evans.

Online text: jde27.uk/tg/quot01.html

Cited passages: Jonny Evans, 3.01 Quotient topology, endpoint identification and circle preimages, notes at 7.39–11.13.

Online text: vlab.amrita.edu/?brch=63&cnt=2&sim=1336&sub=3

Cited passages: Materials Required, items 1–8; Working steps, items 1–9: separate acid and base titrations.