package lambdapi
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lambdapi.tool
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package lambdapi
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Evaluation and conversion.
Preliminary remarks. We define the head-structure of a term t as:
- λx:_,h if t=λx:a,u and h is the head-structure of u
- Π if t=Πx:a,u
- h _ if t=uv and h is the head-structure of u
- ? if t=?M
t1,..,tn(and ?M is not instantiated) - t itself otherwise (TYPE, KIND, x, f)
A term t is in head-normal form (hnf) if its head-structure is invariant by reduction.
A term t is in weak head-normal form (whnf) if it is an abstration or if it is in hnf. In particular, a term in head-normal form is in weak head-normal form.
A term t is in strong normal form (snf) if it cannot be reduced further.
val eta_equality : bool Timed.refFlag indicating whether eta-reduction should be used or not.
type stack = Term.term listAbstract machine stack.
val tree_walk :
Term.problem ->
Term.ctxt ->
Term.dtree ->
stack ->
(Term.term * stack) optiontree_walk p tr ctx stk tries to apply a rewrite rule by matching the stack stk against the decision tree tr in context ctx. The resulting state of the abstract machine is returned in case of success. Even if matching fails, the stack stk may be imperatively updated since a reduction step taken in elements of the stack is preserved (this is done using TRef). Fresh metavariables generated by unification rules with extra pattern variables are added in p.
whnf ~rewrite c t computes a whnf of the term t in context c. User-defined rewrite rules are used only if ~rewrite = true.
eq_modulo c a b tests the convertibility of a and b in context c. WARNING: may have side effects in TRef's introduced by whnf.
pure_eq_modulo c a b tests the convertibility of a and b in context c with no side effects.
snf c t computes the strong normal form of the term t in the context c. It unfolds variables defined in the context c.
hnf t computes a head-normal form of the term t wrt beta-reduction, user-defined rewrite rules and variables defined in the context c.
simplify t computes a beta whnf of t belonging to the set S such that:
- terms of S are in beta whnf normal format
- if
tis a product, then both its domain and codomain are in S.
If s is a non-opaque symbol having a definition, unfold_sym s t replaces in t all the occurrences of s by its definition.
type strat = {strategy : strategy;(*Evaluation strategy.
*)steps : int option;(*Max number of steps if given.
*)
}