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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorPaoloPerrone
   • CommentTimeOct 7th 2020
   • PermaLink
   Author: PaoloPerrone
   Format: MarkdownItexPage created for now. More content to be added soon. <a href="https://ncatlab.org/nlab/revision/partial+evaluation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/partial+evaluation">current</a>

   Page created for now. More content to be added soon.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorHurkyl
   • CommentTimeOct 8th 2020
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexI've seen the phrase "partial evaluation" refer to morphisms $Z^{X \times Y} \to Z^Y$ induced by the evaluation map $(Z^Y)^X \to Z^Y$ corresponding to a (global) element of $X$, or more generally for higher arity. More plainly the operation of converting a function $f(-,-)$ to a function $f(x, -)$. Wikipedia's page for the same phrase describes a special case of this operation in the context of optimizing computer programs, and prefers "partial application" for the general operation. The newly created page, while discussing related ideas, runs the risk of confusion. There should probably be some sort of disambiguation mechanism.

   I’ve seen the phrase “partial evaluation” refer to morphisms $Z^{X \times Y} \to Z^Y$ induced by the evaluation map $(Z^Y)^X \to Z^Y$ corresponding to a (global) element of $X$, or more generally for higher arity. More plainly the operation of converting a function $f(-,-)$ to a function $f(x, -)$. Wikipedia’s page for the same phrase describes a special case of this operation in the context of optimizing computer programs, and prefers “partial application” for the general operation.

   The newly created page, while discussing related ideas, runs the risk of confusion. There should probably be some sort of disambiguation mechanism.

3. • CommentRowNumber3.
   • CommentAuthoratmacen
   • CommentTimeOct 8th 2020
   • (edited Oct 8th 2020)
   • PermaLink
   Author: atmacen
   Format: MarkdownItexHuryl, in program optimization, the program to partially evaluate doesn't actually have to have type ($I_s \times I_d \to O$). That's just a conceptual way of organizing the situation. Usually, the static input is syntactically substituted into the program, and partial evaluation then simplifies the program without having the dynamic input. This seems closer to Paolo Perrone's usage. In other words, I think you're both getting at the same thing.

   Huryl, in program optimization, the program to partially evaluate doesn’t actually have to have type ($I_s \times I_d \to O$). That’s just a conceptual way of organizing the situation. Usually, the static input is syntactically substituted into the program, and partial evaluation then simplifies the program without having the dynamic input. This seems closer to Paolo Perrone’s usage. In other words, I think you’re both getting at the same thing.

4. • CommentRowNumber4.
   • CommentAuthoratmacen
   • CommentTimeOct 8th 2020
   • PermaLink
   Author: atmacen
   Format: MarkdownItexMaybe after the definition, there should be an explanation of how to get $(3 + 4 + 5) \longrightarrow (7 + 5)$ out of it?

   Maybe after the definition, there should be an explanation of how to get $(3 + 4 + 5) \longrightarrow (7 + 5)$ out of it?