Documentation

Lean.Meta.InferType

Auxiliary function for instantiating the loose bound variables in e with args[start:stop]. This function is similar to instantiateRevRange, but it applies beta-reduction when we instantiate a bound variable with a lambda expression. Example: Given the term #0 a, and start := 0, stop := 1, args := #[fun x => x] the result is a instead of (fun x => x) a. This reduction is useful when we are inferring the type of eliminator-like applications. For example, given (n m : Nat) (f : Nat → Nat) (h : m = n), the type of Eq.subst (motive := fun x => f m = f x) h rfl is motive n which is (fun (x : Nat) => f m = f x) n This function reduces the new application to f m = f n

We use it to implement inferAppType

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          isPropQuick e is an "approximate" predicate which returns LBool.true if e is a proposition.

          isProp e returns true if e is a proposition.

          If e contains metavariables, it may not be possible to decide whether is a proposition or not. We return false in this case. We considered using LBool and retuning LBool.undef, but we have no applications for it.

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            isProofQuick e is an "approximate" predicate which returns LBool.true if e is a proof.

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              isTypeQuick e is an "approximate" predicate which returns LBool.true if e is a type.

              Return true iff the type of e is a Sort _.

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                Return u iff type is Sort u or As → Sort u.

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                  Return true iff type is Sort _ or As → Sort _.

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                    Return true iff type is Prop or As → Prop.

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                      Return true iff e : Sort _ or e : (forall As, Sort _). Remark: it subsumes isType

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                        Given n and a non-dependent function type α₁ → α₂ → ... → αₙ → Sort u, returns the types α₁, α₂, ..., αₙ. Throws an error if there are not at least n argument types or if a later argument type depends on a prior one (i.e., it's a dependent function type).

                        This can be used to infer the expected type of the alternatives when constructing a MatcherApp.

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                          Infers the types of the next n parameters that e expects. See arrowDomainsN.

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