object MRealizability
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- m-realizability.scala
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- MRealizability
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- def flat(formula: Formula)(implicit systemT: Context): Ty
computes the type of a potential m-realizer for the formula
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- def mrealize(proof: NDProof, re: Boolean = true)(implicit ctx: Context): (Map[SequentIndex, Var], Expr)
Extracts an mrealizer for a theorem from its proof.
Extracts an mrealizer for a theorem from its proof.
- proof
proof from which the realizer is extracted
- re
boolean whether or not the result should be normalized with respect to the empty program (default) or not
- ctx
system T
- returns
a term M of system T, and a map of sequentindices of the antecedent of the conclusion of the proof, to variables x1,...,xk, such that: if M1,...,Mk are m-realizers for the formulas in the antecedent, then M[M1/x1]...[Mk/xk] m-realizes the succedent of the conclusion
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- def recursor(indType: TBase, resultType: Ty)(implicit ctx: Context): Const
Gives a recursor constant for an inductive type.
Gives a recursor constant for an inductive type.
- indType
the inductive type that the recursor is for
- resultType
type of the result of applying terms to the recursor
- ctx
context that the inductive type is defined in
- returns
recursor constant
- def remEmpProg(term: Expr)(implicit systemT: Context): Expr
removes all occurences of the empty program i : 1 from term, or is i : 1 itself, except for match and inl and inr term: sometimes not possible to remove all occurences.
- def remEmpProgType(typee: Ty)(implicit systemT: Context): Ty
removes all occurences of the empty program type 1 from term, or is 1 itself, except for the sum type.
- def remEmpProgTypes(types: List[Ty])(implicit systemT: Context): List[Ty]
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Transforms a context into system T.
Transforms a context into system T.
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original context
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original context with recursors for inductive types, pair and sum types and terms, and the empty program
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This is the API documentation for GAPT.
The main package is gapt.