The terms representing equality and disequality, respectively.
The wildcard term, usually used in place of type arguments to explicit polymorphic functions to not explicit types that can be inferred by the type-checker.
The type of types, defined as specific token by the Zipperposition format; in other languages, will be represented as a constant (the "$tType" constant in tptp for instance). Used to define new types, or quantify type variables in languages that support polymorphism.
The type of propositions. Also defined as a lexical token by the Zipperposition format. Will be defined as a constant in most other languages (for instance, "$o" in tptp).
The type of boolean, defined as a specific token by the Alt-ergo format; in other languages, it might be represented as a constant with a specific name.
The type unit, defined as a specific token by the Alt-ergo format; in other languages, it might be represented as a constant with a specific name.
The type of integers, defined as a specific token by the Zipperposition and Alt-ergo formats; in other languages, it might be represented as a constant with a specific name (for isntance, tptp's "$int") .
The type of integers, defined as a specific token by the Alt-ergo format; in other languages, it might be represented as a constant with a specific name (for isntance, tptp's "$int") .
The type of bitvectors of the given constant length, defined as a specifi token by the Alt-ergo format; in other languages, it might be represented as a constant with a specific name (for isntance, smtlib(s "bitv") .
The only value of type unit, defined as a specific token by the Alt-ergo format.
The constants for the true and false propositional constants. Again defined as lexical token in the Zipperposition format, while treated as a constant in other languages ("$true" in tptp).
Standard logical connectives viewed as terms.
implies_t is usual right implication, i.e
apply implies_t [p; q] is "p implies q", while
apply implied_t [p; q ] means "p is implied by q" or "q implies p".
Term without semantic meaning, used for creating "data" terms. Used in tptp's annotations, and with similar meaning as smtlib's s-expressions (as used in the
sexpr function defined later).
Variable and constant constructors. While in some languages they can distinguished at the lexical level (in tptp for instance), in most languages, it is an issue dependant on scoping rules, so terms parsed from an smtlib file will have all variables parsed as constants.
Atoms are used for dimacs cnf parsing. Positive integers denotes variables, and negative integers denote the negation of the variable corresponding to their absolute value.
Used in tptp to specify constants different from other constants, for instance the 'distinct' "Apple" should be syntactically different from the "Apple" constant. Can be safely aliased to the
const function as the
distinct function is always given strings already enclosed with quotes, so in the example above,
const would be called with
"Apple" as string argument, while
distinct would be called with the string
Constructors for words defined as numeric or string formats by the languages specifications. These also can be safely aliased to
const, but then the provenance information is lost, which might complicate the task of a type-checker.
Bitvetor litteral, defined as a specific token in Alt-ergo; Expects a decimal integer in the string to be extended as a bitvector.
Represents juxtaposition of two terms, usually denoted "t : t'" in most languages, and mainly used to annotated terms with their supposed, or defined, type.
Proposition construction functions. The conjunction and disjunction are n-ary instead of binary mostly because they are in smtlib (and that is subsumes the binary case).
Application constructor, seen as higher order application rather than first-order application for the following reasons: being able to parse tptp's THF, having location attached to function symbols.
Conditional constructor, both for first-order terms and propositions. Used in the following schema:
ite condition then_branch else_branch.
Pattern matching. The first term is the term to match, and each tuple in the list is a match case, which is a pair of a pattern and a match branch.
Binders for variables. Takes a list of terms as first argument for simplicity, the lists will almost always be a list of variables, optionally typed using the
colon term constructor.
- Pi is the polymorphic type quantification, for instance the polymorphic identity function has type: "Pi alpha. alpha -> alpha"
- Letin is local binding, takes a list of equality of equivalences whose left hand-side is a variable. Letand is the parrallel version of Letin.
- Forall is universal quantification
- Par is universal quantification over type variables specifically (i.e. the same as forall, but only for a list of type variables, which thus may omit the
colonannotations in the arguments).
- Exists is existential quantification
- Lambda is used for function construction
- Choice is the choice operator, also called indefinite description, or also epsilon terms, i.e "Choice x. p(x)" is one "x" such that "p(x)" is true.
- Description is the definite description, i.e "Description x. p(x)" is the only "x" that satisfies p.
Function type constructor, for curryfied functions. Functions that takes multiple arguments in first-order terms might take a product as only argument (see the following
product function) in some languages (e.g. tptp), or be curryfied using this constructor in other languages (e.g. alt-ergo).
Product type constructor, used for instance in the types of functions that takes multiple arguments in a non-curry way.
Union type constructor, currently used in tptp's THF format.
Check whether some expression matches a given adt constructor (in head position).
Project a field of an adt constructor (usually unsafe except when guarded by an adt_check function).
Create a predicate for whether a term is within the given bounds (each bound is represented by a term which is tis value and a boolean which specifies whether it is strict or not).
Create a multi-trigger (i.e. all terms in the lsit must match to trigger).
triggers ~loc f l annotates formula/term
f with a list of triggers.
filters ~loc f l annotates formula/term
f with a list of filters.
Attach a list of attributes (also called annotations) to a term. Attributes have no logical meaning (they can be safely ignored), but may serve to give hints or meta-information.